L ASER PROCESSING FOR THIN AND HIGHLY EFFICIENT
LASER PROCESSING FOR THIN AND HIGHLY EFFICIENT SILICON SOLAR CELLS by Jostein Thorstensen Thesis submitted in partial fulfillment for the degree of Philosophiae Doctor Department of Physics Faculty of Mathematics and Natural Sciences University of Oslo March, 2013 ACKNOWLEDGEMENT Although it may seem so from an outside perspective, a Ph. D. thesis is definitely not a solo race. (At least mine haven’t been one.) I can’t even take full credit for the decision to apply for a Ph. D. position at IFE, as this decision was strongly influenced by sensible and good advice from my friend and colleague Trygve Mongstad. Without him, I might not have ended up doing a Ph. D. at all, which would have been a great loss. I have really appreciated the unique possibility given to me to devote myself for three years to play with cool lasers and stuff while at the same time trying to do my share at saving the world. However, the ride wouldn’t have been nearly as rewarding if I hadn’t been working with some of the best people I have yet come to know. You have always been positive and ready for fruitful discussions on all of the solar related topics that I have needed your help for, thereby doing your share at forming the contents of my thesis. At lunch breaks, coffee breaks, late evenings, conferences and cabin trips, you have been there, making sure that every day has had an enjoyable side. You have given me memories for life, I hope that I have given you something back. I’ll remember you always. My work on light-trapping structures would not have been the same without my cooperation with Jo Gjessing. Your competence, patience and collaboration on this topic has been greatly appreciated. My semiconductor and passivation expert, Halvard Haug has been a smile full of knowledge throughout my thesis. I would like to thank my supervisors, Sean Erik Foss, Aasmund Sudbø and Erik Marstein for the valuable input and guidance I have received. Erik, you are always positive and encouraging, emphasizing that cool and important may very well be the same thing. Aasmund, your experience and knowledge has been invaluable, especially in the process of writing articles and the thesis. You are always patient and thorough, and my work has benefited greatly from your effort. Sean Erik, I probably haven’t been the easiest of Ph. D. students, demanding quite a lot of space in your busy schedule. But I hope that you agree with me when I say that working together on finding our way through the maze that is laser processing for silicon solar cells has been a great journey. You have somehow always i found time for me, and our many discussions has lead us to some pretty interesting findings (although different findings than what we expected three years ago). I wish to thank my parents for being there, always interested when I talk about my work (which must be pretty abstract for you by now), and always supportive no matter what. Finally, thank you, Åsa, love of my life. You never doubted that I could do this, even when I sometimes did. You make me stronger than I would be without you. ii ABSTRACT Solar energy is rapidly becoming one of the most promising renewable energy sources available to us. Its abundant availability greatly surpasses any other energy source, and with the immense progress seen in production technology for photovoltaics (PV) over the last decade, the price for converting solar energy into electricity is rapidly decreasing. However, further price reductions are still required for solar energy to be directly cost competitive with conventional energy sources in the majority of the world. This thesis focuses on the use of lasers as a processing tool for silicon based PV. Lasers may perform a range of solar cell processes, such as edge isolation, doping, removal of dielectrics, structuring and contact formation, and have the potential to enable processes required for advanced, high efficiency solar cell concepts. Two objectives were formulated for this thesis. The first objective focuses on acquiring new fundamental knowledge on the interaction between ultrashort pulse lasers and silicon and dielectrics used for solar cells. Such knowledge is valuable in itself, and is important for process understanding and development. The second objective focuses on the development of laser based techniques for the production of light-trapping textures. This as light trapping gets increasingly important as the wafer thickness used in industry is constantly being reduced and as new wafering techniques may render traditional texturing methods obsolete. On the interaction between pulsed lasers and silicon or dielectric layers, emphasis has been put on ultrashort laser pulses. Mechanisms causing ablation and the process result after ablation have been the main focus. The most investigated dielectric has been silicon nitride thin films. Through experiments and simulations it has been found that the dense electron-hole plasma created during the leading edge of an ultrashort laser pulse, either through linear or two-photon absorption, will play a prominent role in the ablation behavior of both silicon and silicon nitride using such ultrashort laser pulses. It has been shown that this plasma formation causes optical confinement of the laser energy which in silicon greatly reduces the optical penetration depth, and as such reduces the depth of the laser induced damage. Using lasers at a wavelength of 532 nm, the depth of the laser induced damage is reduced from approx. 3 µm to around 0.25 µm when going from nanosecond to picosecond pulse duration. Knowledge about the depth of laser damage as function of pulse duration is valuable when seeking the right laser for a given process. In iii silicon nitrides, the plasma formation causes significant energy deposition into normally transparent films and may open for direct ablation of the dielectrics. It has also been shown that the ablation threshold on silicon is dependent on the temperature of the silicon substrate. In production, this would mean that the use of slightly elevated substrate temperatures would reduce the laser power required for a given throughput, or correspondingly increase throughput achievable with a given laser power. On the topic of light-trapping structures fabricated by the use of lasers, two processes have been developed, and the performance of the textures has been measured. The patch texture, a geometric light-trapping texture for <100>-oriented monocrystalline silicon, showed a simulated increase in of 0.5 mA/cm2 when compared with the random pyramids texture, being the current industry standard. New wafering techniques provide thin silicon wafers for which the patch and random pyramids textures may not be applicable, and for which no industry standard texturing process exists. With this in mind, a diffractive honeycomb texture was developed. The use of microspheres on the wafer surface as focusing elements enabled the production of features with sizes well below 1 µm. The diffractive honeycomb texture shows a photogenerated current of 38 mA/cm2 on 21 µm thick silicon wafers. The results summarized above shows that both fundamental understanding of the laser-material interaction and results that are directly applicable have come from the investigation of laser-material interaction. The texturing processes that have been developed show that laser based texturing processes are capable of delivering high quality textures suitable for a range of different substrates. iv TABLE OF CONTENTS ACKNOWLEDGEMENT .................................................................................................................... I ABSTRACT .................................................................................................................................... III TABLE OF CONTENTS ..................................................................................................................... V 1 2 3 4 INTRODUCTION .................................................................................................................... 1 1.1 SILICON SOLAR CELLS ............................................................................................................. 3 1.2 MOTIVATION AND OBJECTIVE OF THE THESIS ................................................................................ 6 1.3 STRUCTURE OF THE THESIS ...................................................................................................... 8 1.4 SUMMARY OF THE ARTICLES ..................................................................................................... 9 EXPERIMENTAL TOOLS AND TECHNIQUES .......................................................................... 14 2.1 LASERS ............................................................................................................................. 14 2.2 EXTRACTION OF LASER PARAMETERS ........................................................................................ 16 2.3 THIN FILM DEPOSITION ......................................................................................................... 19 2.4 MICROSCOPY ..................................................................................................................... 19 2.5 WET CHEMICAL PROCESSING .................................................................................................. 20 2.6 REFLECTANCE AND TRANSMITTANCE MEASUREMENTS .................................................................. 22 2.7 MINORITY CARRIER LIFETIME .................................................................................................. 23 2.8 SILICON SUBSTRATES ............................................................................................................ 24 LASER PROCESSING FOR SILICON SOLAR CELLS................................................................... 26 3.1 STATE OF LASER PROCESSING FOR SILICON SOLAR CELLS ................................................................. 26 3.2 LASER-MATERIAL INTERACTION ............................................................................................... 30 3.3 SIMULATIONS ON LASER-MATERIAL INTERACTION ........................................................................ 33 3.4 LASER INDUCED DAMAGE ...................................................................................................... 42 LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS .................................................... 46 4.1 LIGHT MANAGEMENT IN SILICON SOLAR CELLS ............................................................................ 46 4.2 STATE OF LASER TEXTURING ................................................................................................... 50 4.3 MASKED LASER TEXTURING .................................................................................................... 52 5 CONCLUSION...................................................................................................................... 57 6 DISCUSSION AND OUTLOOK............................................................................................... 60 BIBLIOGRAPHY ............................................................................................................................ 62 A. ANALYTICAL EXPRESSION FOR RECOMBINATION BY LASER DAMAGED REGION ................ 69 v A.1 ELECTRON DISTRIBUTION .................................................................................................. 70 A.2 SURFACE RECOMBINATION VELOCITY.................................................................................... 72 A.3 EFFECTIVE LIFETIME ......................................................................................................... 72 LIST OF ABBREVIATIONS .............................................................................................................. 74 PAPER I ........................................................................................................................................ 75 PAPER II ....................................................................................................................................... 81 PAPER III ...................................................................................................................................... 91 PAPER IV...................................................................................................................................... 99 PAPER V..................................................................................................................................... 109 PAPER VI.................................................................................................................................... 123 PAPER VII................................................................................................................................... 133 PAPER VIII.................................................................................................................................. 141 vi 1 INTRODUCTION Electricity from sunlight. Direct harvesting of the immense and never-ending power brought to us by the sun. Not long ago, this elegant way of generating electricity was associated with satellites and space stations, or remote off-grid locations needing electricity to power a light bulb in a cabin. Today, on the other hand, we can read that Germany generates 50 % of its electric power from photovoltaic (PV) energy during mid-day hours on a sunny day ! In 2011, more than 28 GW of new PV generating capacity was installed globally . This corresponds to about 200 km2 of solar panels, or 1.5 times the size of the city of San Francisco! Obviously, our view on PV as a small niche market needs to be reviewed. In a world where a rapidly increasing demand for energy is ever more strongly conflicting with an urgent need to cut back on greenhouse gas emissions, it seems necessary and inevitable that renewable energy sources will play a major role in our future global energy system. A recent report from the Intergovernmental Panel on Climate Change  predicts that wind and PV will account for up to 30 % of the world’s electricity production by 2050, even in the moderate scenarios. Direct solar energy is a tremendous energy resource, delivering around 4x1024 J of energy to the earth’s surface per year (assuming a solar flux of 1 kW/m2). The world’s total energy consumption was in 2010 around 5.6x1020 J , meaning that the solar energy hitting the earth in about one hour is sufficient to cover the energy needs of the humanity for a whole year! This is by far the biggest source of energy available to us, and a great candidate for a transition to a more sustainable energy system. Furthermore, silicon based PV is based on non-toxic, abundant materials, silicon being the second most abundant element in the earth’s crust after oxygen. PV is currently the fastest growing renewable energy source, with an average growth rate of above 40 % per year since the year 2000 (Figure 1.1). Silicon based solar cells have an 85 % market share , and is thereby the absolutely dominant technology in PV. The growth in PV has been linked to economic incentives, and continued growth in 1 2 CHAPTER 1: INTRODUCTION installed PV cannot rely on politically driven incentives alone. PV learning curves have, since the 1970’s shown a 20 % reduction in module prices per doubling of cumulative production , a quite tremendous price reduction. This trend in price reductions however, has to be continued as incentives are continuously being reduced. This can either happen through reduction of production costs (fewer $ per solar cell), or by an increase in efficiency (more watts per solar cell). A combination of both would of course be ideal. In the current situation, the price for manufacturing of the solar cell and solar module has been dramatically reduced. This leads to a situation where balance of system costs, such as installation costs, the costs of mounting brackets, land usage costs etc. are beginning to dominate the total cost of a PV energy system . Increased efficiency of the solar cell will reduce balance of system costs, e.g. by reducing the number of brackets and land area required for a given output power, meaning that retaining or improving the efficiency of the solar cell is essential for reduction of PV system costs. The strive towards low cost, high efficiency solar cells has led to the introduction of several new processing tools and techniques that have enabled the impressive cost reductions seen in the PV industry. One group of tools that has the potential to change existing production techniques, and enable new processes and even new solar cell designs are lasers. Lasers have the ability to structure, cut or remove materials, alter the chemical composition of materials through the introduction of impurities, and several other processes. As shall be shown later in this thesis, there exists a range of solar cell related processes for which lasers can be applied. This thesis will focus on the use of lasers as a processing tool for improvement of silicon PV, where lasers have the potential to improve the efficiency of the solar cell and to reduce production costs. Figure 1.1: Total installed PV production capacity. Taken from refs , , . Preliminary data from 2012 indicates that the total installed PV production capacity has passed the 100 GW mark . CHAPTER 1: INTRODUCTION 3 1.1 SILICON SOLAR CELLS Solar cells operate by converting sunlight into electricity. In this section a brief review of the solar cell physics will be given. For a more thorough introduction, see e.g. . One of the critical properties that make silicon suitable as a solar cell material is that it is a semiconductor, possessing a band-gap. This band-gap is a range of energies that the electrons in the materials are not allowed to have. The electron can either have an energy placing it in its ground energy state in the valence band, or it can be in an excited state in the conduction band. The electron can transition from valence band to conduction band and back through excitation and recombination processes described below. The energy required for an excitation may come from a photon, being the smallest package of energy one can divide light into. The sunlight consists of photons with a wide range of energies. The energy of the photon corresponds to what we observe as the color of the light, where the blue light consists of photons with a higher energy, and the red light consists of photons with lower energy. The energy of the photon also corresponds to a wavelength of the light, where the blue light has a shorter wavelength, and the red light has a longer wavelength. The spectral energy distribution of the sunlight is shown in Figure 1.3, adding up to 1000 W/m2 at the earth’s surface under given conditions, in what is known as the Air Mass 1.5 spectrum (AM1.5). When a photon hits the silicon, it may be absorbed by an electron in the silicon, providing enough energy for the electron to be excited from its ground energy state in the valence band to an excited state in the conduction band, as indicated in Figure 1.2 a). Such an absorption process may only take place if the photon carries an energy corresponding to at least the band gap energy. The electron being excited will leave behind a hole in the valence band; an electron-hole pair is created. In a solar cell, the electron-hole pair moves by diffusion until it reaches the p-n junction. The p-n junction is a built-in asymmetry in the solar cell, where an electric field ensures that the electron will travel in one direction, while the hole travels in the opposite direction. As such, the electron may reach one of the electrical contacts, while the hole reaches the other contact, as a result of a combination of random diffusion and directional drift in an electric field. This is the principal mechanism for current generation in a solar cell. Only photons with high enough energy may be absorbed by the electrons. A photon with energy lower than the band-gap energy will not carry sufficient energy to lift the electron to the conduction band, and will as such not be absorbed in the semiconductor. Hence, its energy will not be converted into electricity. 4 CHAPTER 1: INTRODUCTION This situation is indicated in Figure 1.2b), and is called sub-bandgap loss. On the other hand, photons with high energy can create an electron-hole pair as indicated in Figure 1.2 c), lifting the electron high above the conduction band edge. However, all the excess energy that is put into the electron will be rapidly lost, as the electron will collide with other electrons or atoms, losing energy until it reaches the conduction band edge. This loss process is called thermalisation. Figure 1.2: Illustration of some absorption and loss mechanisms in a solar cell. a) Absorption, b) photon with insufficient energy for absorption, c) absorption and thermalisation, d) recombination. Figure 1.3 shows the spectral energy distribution from the sun as function of the wavelength of light. The area below the top graph indicates the total incoming solar energy, while the area below the lower graph indicates the energy available to us when taking into account the loss contributions discussed above, with a collective term called spectrum loss. Spectrum loss is a function of the band-gap energy of the semiconductor, and limits the efficiency of a silicon solar cell to below 50 %. In a real solar cell, not all generated electron-hole pairs will contribute to current generation. There is always the chance that an electron finds a hole on its way to the contacts and relaxes back across the band gap, in a process called recombination, indicated in Figure 1.2 d). Recombination may happen slowly in the bulk of a high-quality silicon wafer, but it will always take place even in a perfect material. These unavoidable recombination mechanisms are termed intrinsic recombination mechanisms. In a more realistic material, recombination happens faster. Examples of recombination-active areas are crystal defects or impurities in the silicon, highly doped silicon, silicon crystal boundaries or wafer surfaces and metal-silicon interfaces, such as contacts. By combining intrinsic recombination mechanisms with spectrum losses, we reach a maximum efficiency of a CHAPTER 1: INTRODUCTION 5 solar cell, known as the Shockley-Queisser limit , which for silicon under an irradiance corresponding to the AM1.5 spectrum is around 29 % . Currently, the record efficiency of a silicon solar cell is 25 % , which is actually quite close to the theoretical maximum of 29 % given by the Shockley-Queisser limit. Figure 1.3: Solar irradiance (upper, black curve) and the maximum available energy to a silicon solar cell when considering spectrum losses . The efficiency of the solar cell, is of course of outmost importance. Several factors determine this cell efficiency which can be collected into the expression = = = In this expression, irradiance . 1.1 is the output power density of the cell, is the solar is the current density at short circuit conditions, being the maximum current available from a solar cell. is the voltage at open circuit conditions, being the maximum voltage available from a solar cell. As both open and short circuit conditions would lead to zero power output of the solar cell, the maximum power output of the solar cell is found by operating the solar cell at a voltage somewhat lower than maximum power point. and are current density and voltage at maximum power point, respectively, and the fill factor the expression that , and , in what we call the is the ratio of should be as high as possible. to . We see from 6 CHAPTER 1: INTRODUCTION 1.2 MOTIVATION AND OBJECTIVE OF THE THESIS The record silicon solar cell with an efficiency of 25 % mentioned earlier is a beautiful example of solar cell engineering. The problem, however, is that in order to make such a cell, several processes that cannot be directly transferred into mass production are employed. A common feature of several high-efficiency solar cell concepts is that they require some form of local processing, which on lab-scale cells has been enabled by photolithography. Photolithography is, however, generally considered incompatible with the very high throughput required by the solar cell industry. As lasers provide excellent spatial resolution and translational control, they may provide similar local processing capabilities with much simpler processes, and may as such open for industrial scale local processing and high solar cell efficiencies in industrial production. Indeed, local laser processing is making its way into industrial production lines today. Laser processing may, however, only be successfully implemented if the process does not have a negative impact on the quality of the solar cell materials. In order to develop low damage laser processes, fundamental insight into the physical interaction between the laser and the solar cell materials is absolutely crucial. Using pulsed laser sources, the laser-material interaction will depend on laser pulse duration, laser wavelength and material properties. Fundamental understanding of these dependencies will give understanding of the laser parameters required for successful laser processes. As such, knowledge about the dominating physical mechanisms involved in laser-material interaction will serve as a foundation for development of good laser processes, or even the other way around, serve as a pointer towards yet to be developed laser sources required for a given process. Fundamental knowledge about laser-material interaction would be useful also outside the field of silicon photovoltaics. As such, the first main objective of this thesis is: To gain fundamental understanding of the interaction between pulsed lasers and materials relevant for silicon solar cells. The materials in focus shall be silicon and dielectric layers covering the silicon, functioning as e.g. anti-reflection coatings, passivation layers or diffusion or etch barriers. CHAPTER 1: INTRODUCTION 7 The main focus shall be on parameter ranges giving material removal, called ablation, as ablation is required for a wide range of laser processes. This understanding shall be sought through a combination of experimental techniques and simulations. Laser sources with varying wavelength and pulse duration shall be applied on a selection of materials. Simulation models accounting for the physics encountered with the use of long (nanosecond) and ultrashort (picosecond) pulses shall be developed. The second main topic of the thesis concerns thin silicon wafers. Silicon is an indirect band-gap semiconductor meaning that photons may travel quite a distance in silicon before they are absorbed. Thicker wafers would thus increase light absorption. Unfortunately, silicon is quite expensive, meaning that thick cells would be too costly. Currently, there is a strong drive in the industry to reduce the standard wafer thickness from the thickness used today (around 160 µm) to 120 µm by 2020 . Today, wafers are typically manufactured by wire sawing, and almost half of the silicon is lost as “saw dust”, or kerf loss. Several novel techniques are being developed in order to eliminate kerf loss and enable production of even thinner wafers, between 20 and 50 µm thick [16–19], thus drastically reducing silicon consumption. With this trend in mind, development of highly efficient light-trapping techniques for efficient collection of the sunlight is needed. For these new kerf-less wafers, traditional texturing methods may not be applicable, due to e.g. (i) the crystal orientation of the wafer or (ii) the lack of saw damage on the silicon surface for seeding of the structures or (iii) simply because currently available texturing processes remove too much of the silicon . Several approaches have been suggested, but a solution suitable for mass production is yet to be developed. The use of lasers for texturing of silicon wafers is interesting, due to the laser’s ability to create precisely defined geometrical patterns on the wafer surface. The use of a highly accurate laboratory laser setup would identify the practical limits to the texture quality achievable by laser based texturing. The second main objective for this thesis is To develop laser-based techniques for manufacturing of efficient light-trapping textures. The focus shall be on textures investigated theoretically in the literature, but for which no industry standard method exists. As laser-based texturing is not yet a mature technique, 8 CHAPTER 1: INTRODUCTION emphasis shall be put on investigation of the achievable quality of the developed textures and their practical, rather than theoretical light-trapping potential. 1.3 STRUCTURE OF THE THESIS This thesis is written as a collection of papers with an introductory text. The findings already presented in the papers will not be repeated to any length in the main text. The purpose of the main text is to provide an introduction to the field of solar cell research, motivate the topic of the thesis, and provide additional theory and experimental details that are not presented in the papers. The papers are appended at the end of the thesis. The thesis is divided into 6 chapters. In chapter 1, the thesis is placed in a broader context and an introduction to solar cell technology is provided. At the end of the chapter, a summary of the articles is given. Chapter 2 presents details of the main experimental tools and techniques utilized during the work with this thesis. Chapter 3 is dedicated to laser-material interaction and laser damage. The chapter begins with an overview of the state of the art of laser processing for silicon solar cells. Then, laser-material interaction and the difference between long and ultrashort pulses are presented, followed by details on the simulation models applied within the thesis. Additional simulation results and physical insights that are not included in the papers are also presented in this chapter, and some methods for characterization of laser-induced damage are summarized. Chapter 4 is dedicated to the subject of light trapping in silicon solar cells. The need for light-trapping structures is motivated, and some typical structures are presented. Some previously investigated methods for laser assisted structuring of silicon are reviewed, and the approach to laser assisted structuring chosen in this thesis is motivated. The industrial feasibility and potential of the processes is discussed, comparing the structures to industry standard methods. Chapters 5 and 6 provide conclusions and suggestions on further work related to the investigation of laser-induced damage, investigation of laser-material interaction and further development of the light-trapping structures presented in the thesis and papers. CHAPTER 1: INTRODUCTION 9 1.4 SUMMARY OF THE ARTICLES This section presents an overview of the papers included in this thesis. The papers are appended in their entirety at the end of the thesis. PAPERS I – IV consider textures for light trapping in silicon, while PAPERS V – VIII discuss the fundamentals of laser-material interaction for the silicon and dielectric on silicon systems. PAPER I J. Thorstensen and S. E. Foss, “Laser assisted texturing for thin and highly efficient monocrystalline silicon solar cells,” in Proceedings of the 26th European Photovoltaic Energy Conference, pp. 1628 – 1631, 2011. In this conference contribution, a process was developed for production of inverted pyramids and patch textures on <100> - oriented monocrystalline silicon for light-trapping. These textures have a high potential for light-trapping, but are normally produced by photolithography. The process described in this paper is based on the use of a laser to create openings through an etch barrier, after which KOH etching of the underlying silicon develops a pattern consisting of <111> crystal orientations. The geometrical accuracy of the laser system is good, and the structures develop as intended, resulting in a texture with up to an estimated 94 % area coverage. PAPER II J. Thorstensen, S. E. Foss, and J. Gjessing, “Light-trapping properties of patch textures created using Laser Assisted Texturing,” Progress in Photovoltaics: Research and Applications, available online, DOI: 10.1002/pip.2335, 2013. In this paper, the light-trapping properties of the patch texture developed in PAPER I was investigated. Jo Gjessing (IFE) was of great assistance during the optical measurements. Optical absorption measurements on a patch textured silicon wafer are performed and these measurements are compared with ray-tracing simulations. This enables us to extract information about the quality of the texture. From these simulations, the current-generating potential of the textures is extracted. It is found that the created texture gives an increase in of up to 0.5 mA/cm2 compared to the random pyramids texture, and as such, it is concluded that it is possible to generate high quality textures with laser based methods. The process would be interesting for application on <100>-oriented monocrystalline 10 CHAPTER 1: INTRODUCTION silicon. It is recognized that the process must be simplified in order to justify the added process complexity. PAPER III J. Thorstensen, J. Gjessing, E. Haugan, and S. E. Foss, “2D periodic gratings by laser processing,” Energy Procedia, vol. 27, pp. 343–348, 2012. In this conference contribution a process for producing diffractive structures in silicon is presented. The process is similar to the process described in PAPER I, but a monolayer of polystyrene microspheres is this time applied onto the etch barrier. In the laser processing step, the microspheres act as focusing elements, and serve to increase the spatial resolution of the laser to below 1 µm. An isotropic etch develops a texture consisting of nearly hemispherical dimples in a honeycomb pattern. The process is applicable to monocrystalline silicon with any crystal orientation, or to multicrystalline silicon. With this masked etching process, only the silicon from the dimples is removed, causing a thinning of the silicon wafer of below 350 nm, ideally suited for thin silicon wafers where preservation of wafer thickness is crucial. The paper serves as a proof of concept of the remarkable increase in spatial resolution brought about by the application of the micro-lens array made up by the microspheres. PAPER IV J. Thorstensen, J. Gjessing, E. S. Marstein, and S. E. Foss, “Light-trapping Properties of a Diffractive Honeycomb Structure in Silicon,” IEEE Journal of Photovoltaics, vol.3, no. 2, pp. 709 – 715, 2013. In this paper, the honeycomb structure generated in PAPER III is examined in more detail. Firstly, the texture is applied to large area, by utilizing a top-hat beam shaper, an optical component transforming a Gaussian beam profile to a uniform, square intensity distribution. The structure is applied to silicon wafers with a thickness of 21 – 115 µm. Optical absorption characteristics were measured by Jo Gjessing, who also analyzed the contributions to optical loss. The observed trends are explained and the diffractive honeycomb textures are compared with random pyramids, isotropic etched samples and polished wafers, as these constitute various relevant references. It is found that the diffractive honeycomb structure delivers light trapping that surpasses many of the relevant references showing a photogenerated current of 38 mA/cm2 on 21 µm thick wafers. As such, the texture has the potential to provide a significant increase in on wafers where CHAPTER 1: INTRODUCTION 11 random pyramids cannot be efficiently applied, e.g. for kerf-less wafers with a non-<100> crystal orientation. PAPER V J. Thorstensen and S. E. Foss, “Temperature dependent ablation threshold in silicon using ultrashort laser pulses,” Journal of Applied Physics, vol. 112, no. 10, p. 103514, 2012. In this paper the physics of the interaction between silicon and ultrashort laser pulses is considered. Experiments are performed showing that the ablation threshold fluence varies with silicon substrate temperature. A numerical model is established, considering the dynamics of the absorption of the incoming laser light, i.e. the energy deposition, and the generation dynamics of conduction band electrons. From this model, information about the dominating physical processes is extracted, and the experimentally observed temperature dependence is reproduced in simulations. The paper contributes to new knowledge on the temperature and wavelength dependence of the ablation threshold of silicon using ultrashort laser pulses, in addition to interpretations on the underlying physical mechanisms. PAPER VI Jostein Thorstensen, Ragnhild Sæterli and Sean Erik Foss, “Laser ablation mechanisms in thin silicon nitride films on a silicon substrate,” submitted to IEEE Journal of Photovoltaics, April 2013. In this paper the ablation of silicon nitrides with varying index of refraction from silicon is investigated. Varying laser pulse duration and three laser wavelengths are applied, and the mechanism for ablation is investigated. In this paper, TEM analysis was performed by Ragnhild Sæterli (NTNU). A transition region is observed when using a wavelength of 515 nm, where the ablation goes from indirect to direct. In some cases, both direct and indirect ablation is observed in the same spot. In these cases, it is found that the free-carrier contribution must be significant in the interaction between the laser pulse and the dielectric – silicon stack. The focus in this article on the underlying physical mechanisms of silicon nitride ablation is novel. 12 CHAPTER 1: INTRODUCTION PAPER VII Jostein Thorstensen and Sean Erik Foss, “New approach for the ablation of dielectrics from silicon using long wavelength lasers,” submitted to Energy Procedia, March 2013. This conference contribution shows a different approach to ablation of dielectrics from semiconductors. By investigating the absorption characteristics of silicon and various PVrelevant dielectrics, it is found that in the mid- to far-IR, silicon is transparent, while the dielectrics are absorbing. This behavior is interesting, as it opens for energy deposition in the dielectric rather than in the silicon, potentially resulting in lower substrate damage. For the measurements of absorption in dielectrics, Ørnulf Nordseth (IFE) prepared samples with aluminum oxide (AlOx), and Halvard Haug (IFE) prepared samples with silicon dioxide. Simulations on the temperature dynamics of the process are performed, and it is seen that short laser pulses may be able to remove the dielectric without melting the silicon substrate. In experiments however, signs of melting of the silicon are found, indicating that a pulse duration of 100 ns is still too long. As such, the paper brings the idea of a new process, while it remains to be proven if the process can be successful using shorter laser pulses. PAPER VIII Jostein Thorstensen and Sean Erik Foss, “Investigation of depth of laser damage to silicon as function of wavelength and pulse duration,” accepted for publication in Energy Procedia, May 2013. This conference contribution describes an experiment determining the depth of laser induced damage. Ultrashort laser pulses at three wavelengths are applied to a silicon substrate. Thereafter, a controlled wafer thickness is removed by wet chemical etching, and the wafer is passivated. The minority carrier lifetime is measured as function of etch depth and the depth where bulk lifetime is restored gives a measure of the depth of the laser induced damage. The results are compared with previous investigations by Engelhart et al. , and show that the depth of damage is severely reduced when going to ultrashort laser pulses, as a result of reduced thermal diffusion and increased optical confinement due to non-linear absorption. While thermal and optical confinement is expected when using ultrashort laser pulses, the presented quantitative experimental evidence on silicon is novel. In addition, An estimate on the minority carrier lifetime in the laser damaged volume is presented. These calculations are also novel in the context of laser damage. CHAPTER 1: INTRODUCTION 13 MAIN FINDINGS On the topic of production of light-trapping structures on silicon using lasers, two innovative production techniques are presented, and the produced textures outperform important reference textures. As such, it is shown that it is possible to create high quality textures by the use of lasers. The processes would require significant modifications in order to be industrially relevant, however, for thin, non-<100>-oriented wafers, no industrially mature methods exist. As such, the process presented in PAPERS III and IV is of contemporary interest. On the investigation of the physics of the interaction between pulsed lasers and solar cell materials, several new findings are presented. The temperature dependent ablation thresholds presented in PAPER V are novel, and are particularly interesting as the simulation model provides possible explanations to the underlying physical mechanisms. For practical applications, the use of a slightly elevated substrate temperature can significantly reduce the required laser power, or correspondingly increase the process throughput. This effect is strongest at the fundamental wavelength of the laser, making it more interesting to use this wavelength, thereby reducing the complexity of the laser equipment. In PAPER VIII, concrete evidence of thermal confinement and non-linear optical confinement is presented. Considering the interest in ultrashort-pulse lasers for industrial purposes seen over the last few years, these results should be directly applicable and relevant to the industry, as the depth of laser damage is a critical parameter in laser processing. PAPER VII is an example of how fundamental insight may spawn ideas to novel processes where the necessary tools are yet to be developed 2 EXPERIMENTAL TOOLS AND TECHNIQUES In this thesis, a number of experimental tools and techniques have been applied. Silicon wafers must be cleaned and prepared for processing. Often, a dielectric coating has been deposited onto the wafer surface. The laser has been the primary process tool, often accompanied by wet chemical etching. For characterization of the process result, a range of optical characterization techniques such as spectroscopy and microscopy have been applied. Also the electrical properties of the samples have been characterized. This chapter presents an overview of the main experimental tools and techniques applied during this thesis. 2.1 LASERS The laser is the most important processing tool in this thesis. To two laser systems have been available at the Department for Solar Energy (IFE), and other lasers have been applied at other locations. These will be described below. The laser parameters are summarized in Table 1. Green nanosecond laser The affordable workhorse laser for silicon processing is the green nanosecond laser, more specifically, the frequency doubled diode-pumped solid-state (DPSS) laser. A Rofin PowerLine 20 E – LP SHG2 laser has been available at IFE. It operates at 532 nm, with a pulse duration between approx. 50 and 250 ns. The laser has been used as reference in PAPER VIII and for process development for the patch pattern described in PAPER I and PAPER II. Other solid state lasers At the Laser Zentrum Hannover, experiments have been performed using solid state lasers with nanosecond pulse duration with a wavelength of 266 and 355 nm and 10-40 ns pulse 14 CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES 15 duration (Coherent AVIA) and 1064 nm and 30 ns pulse duration (IPG YLPM-1-A4-2020). Short pulsed CO2-laser For the work with PAPER VII, a short pulsed CO2-laser from a commercial supplier was applied. The laser pulse duration was approx. 100 ns, and the wavelength was 9.3 µm. Ultrashort-pulse laser For the majority of the work in this thesis, an Amplitude Systemes s-Pulse HP laser was applied. This laser has a second harmonic – third harmonic generation (SHG – THG) module. The laser itself delivers pulses that by an adjustable pulse compressor can be freely selected to values between approx. 0.5 ps and 6.5 ps at a fundamental wavelength of 1030 nm. Second and third harmonic wavelengths of 515 and 343 nm are available by adjusting the power through the SHG – THG module. The laser is equipped with both a galvo scanner and fixed lenses, and an xyz-table for sample translation. For the processing in PAPER IV, a top-hat beam shaping element from Eksma Optics was applied. This element transforms a Gaussian beam profile into a uniform, square intensity distribution. Such an intensity distribution allows for uniform processing of larger areas, but the output intensity distribution is sensitive to the exact beam shape and quality of the incoming beam, as observed in PAPER IV. Table 1: Summary of laser parameters. Laser model . Parameter Oxford Laser/ Rofin PowerLine Other nanosecond Amplitude s-pulse LP lasers 532 266,355, 1064 and HP Wavelength [nm] 343, 515 and 1030 9300 Pulse duration [s] 0.5 − 6.5 × 10 50 − 250 10 − 100 × 10 × 10 Repetition rate [kHz] 1-300 10-100 Beam diameter in 9-40 40 <1.3 <1.3 focus [µm] Beam quality (M2) <1.4 16 CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES For the majority of the work within this thesis, non-overlapping laser pulses are utilized, as incubation effects are observed where multiple pulses are applied . Slight surface and volume modifications from previous pulses will increase absorption, thereby reducing the ablation threshold and cause the formation of larger surface structures (ultimately providing black silicon,) that are undesirable when investigating the topics of this thesis. Two types of incubation effects are shown in Figure 2.1, using ultrashort laser pulses. (Top left) SEM image of self-assembling structures similar to those found in socalled black silicon, developed by irradiating one spot with multiple pulses. (Top right) SEM image of laser-induced periodic surface structures (LIPSS). LIPSS are periodic waves or ridges with size on the order of the wavelength of the applied light, developed by applying partially overlapping pulses . (Bottom left) AFM height profile of LIPSS. (Bottom right) Area covered with LIPSS viewed at different angles. Different viewing angles gives different wavelength, characteristic for diffraction. Figure 2.1: Surface modifications caused by ultrashort laser pulses. Top left: SEM image of multiple pulse irradiation in one spot, causing surface structures to appear. Top right: SEM image of Laser-induced periodic surface structures (LIPSS). Bottom left: AFM height map of the same LIPSS structure. Bottom right: Wafer with LIPSS photographed at different angles, showing the typical rainbow-appearance characteristic of diffractive surfaces. 2.2 EXTRACTION OF LASER PARAMETERS As stated above, non-overlapping pulses were applied during the majority of the work with this thesis. Processing with these conditions normally gives a region on the wafer surface that has in some way been affected, and the extension of the affected area will depend on a CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES 17 range of laser and process parameters. The process most frequently investigated in this thesis is the ablation of dielectrics from a wafer surface, and the ablated diameter is often sought. Examples of spots with a clearly defined ablated diameter are seen in Figure 2.1 (Top left) and Figure 2.2. The laser ablation process is often characterized by the laser fluence required for ablation to take place, known as the ablation threshold fluence (ablation threshold) . This quantity is of outmost importance when describing the ablation process, and is generally dependent on material parameters and laser parameters such as laser wavelength and pulse duration. While the wavelength is set directly by the laser, the pulse duration and laser fluence must be measured or controlled externally. The laser fluence is only available to us indirectly, by measuring several quantities, these being average laser power, pulse repetition rate and spatial fluence distribution. The average laser power was measured using a PS19Q thermopile power sensor from Coherent Inc. This sensor has a rated sensitivity of 10 µW, and a calibration accuracy of 1 %. Practically, however, the measured power tends to fluctuate more than this, especially at low powers, as a result of power sensor inaccuracies or as a result of actual variations in laser output power. Therefore, 5 % has been used as the uncertainty of the laser power meter. The spatial fluence profile of a laser beam may be quantified by its M2 – number, where M2 = 1 describes a Gaussian fluence distribution. This distribution is also the one where the tightest focus is obtainable. All other fluence distributions have an M2 > 1, and as such have larger foci by a factor of M2. The lasers applied in this thesis are nearly Gaussian, showing an M2-value of below 1.3. As such, the fluence profile is assumed to be Gaussian. However, also the width of the Gaussian fluence distribution must be known, which will vary depending on how far from the focal plane the sample to be processed is located. Liu  describes a method for extracting the beam diameter of a Gaussian beam by measuring the diameter of the ablated area as function of pulse energy. The method also gives the ablation threshold fluence, and is as such a valuable tool in characterization of laser ablation, and is described by the expression: = Here, = is the ablated radius, − ( ) 2.1 is the beam radius measured at the point where the intensity has dropped to 1/e2 of the peak fluence level. and are the peak fluence 18 CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES of the laser pulse and the ablation threshold fluence. Using the right hand side expression, requires only the ablated radius and pulse energy , which both can be measured, and the unknown quantities, namely and , that are found by fitting the expression to the measurement data. The ablated diameter has been found using the image processing program ImageJ , by using the color contrast between the ablated spot and the remaining dielectric layer, as shown in Figure 2.2. One challenge using this technique is that the color change seldom is step-like. There will always be a blurry area where the color is in between that of the spot and the surroundings. This error contribution has been analyzed in PAPER V, and was found in combination with uncertainty in the power meter and deviations from the modeled trend to be around +/- 20 %. It is also seen in Figure 2.2 that the spot is not perfectly round. The ablated radius, the relation = , is estimated from the ablated area, through / . Figure 2.2: Typical set of images used as data for the method by Liu . Shown here is the ablated spot obtained when ablating SiNx from Si using a laser wavelength of 1030 nm and a pulse duration of 3 ps. The applied laser pulse energy increases from left to right. The pulse duration was only measured for the ultrashort pulses, at the fundamental wavelength using a PulseCheck 50 autocorrelator from APE (Angewandte Physik & Elektronik GmbH). The pulse duration at second and third harmonic wavelengths were not directly measured, as the autocorrelator was not built for these wavelengths. The pulse duration at harmonic wavelengths may be shorter than at the fundamental wavelength, as a result of the intensity dependence of the efficiency of the wavelength conversion process, or longer, as a result of dispersion effects. The manufacturer has measured the pulse duration at the second harmonic wavelength, finding that this pulse duration approximately equals that of the fundamental wavelength, possibly being marginally shorter. The laser manufacturer expects the same behavior at the third harmonic wavelength. In this work, it is assumed that the second and third harmonic pulse have the same pulse duration as the fundamental wavelength pulse. CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES 19 2.3 THIN FILM DEPOSITION In solar cell processing, thin dielectric films are frequently deposited onto the silicon wafer in order to improve optical or electrical properties. The typical blue color of a solar cell arises from a thin anti-reflection coating, reducing the reflectivity of the solar cell. Other films may primarily be deposited in order to reduce recombination at the wafer surfaces. The dielectrics used in this work (with the exception of one thermal oxide) were all deposited by plasma-enhanced chemical vapor deposition (PECVD), a technique commonly used for dielectric deposition in the PV industry. In the PECVD process, reaction gases are ionized by an electric field, in the PECVD system applied in this thesis an RF field. This ionization helps improving the reaction rate and allows for fast deposition at relatively low temperatures. An Oxford Instruments Plasmalab System 133 PECVD system was used for this deposition. For laser processing, silicon nitride (SiNx) has been most frequently used, but also some silicon oxide (SiOx) and silicon oxynitride (SiOxNy) films. For passivation, amorphous silicon (a-Si) was used in order to obtain very low surface recombination velocity. Generally, all films deposited by PECVD will contain relatively large amounts of hydrogen, and the films deposited in this thesis are amorphous. As such, a more precise description of the films would be e.g. hydrogenated amorphous silicon nitride (a-SiNx:H), but for convenience, the shorter notation given above shall be used. For PAPER VI, several different SiNx films were deposited. The composition of these films was varied by adjusting the flow of silane (SiH4) to the chamber, while keeping all other deposition parameters (gas flows, pressure and temperature) constant. As noted in PAPER VIII, surface-near damage to the silicon is observed after deposition of PECVD SiNx, observed in the form of reduced lifetime on samples where the SiNx was removed in a 5 % hydrofluoric acid solution and the wafer was subsequently passivated with a-Si. As this damage was discovered late in the thesis, there was no time for more thorough investigation of the damage mechanisms, and the damage is tentatively attributed to ion bombardment from the deposition process. 2.4 MICROSCOPY Both in the work with texturing processes and in the work on laser – material interaction, microscopy has been used extensively for measurements on ablated diameters and general 20 CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES quality of process assessments. For this work, a Zeiss Axioskop 2 MAT optical microscope was used. A Hitachi S-480 scanning electron microscope (SEM) has been applied for more detailed analysis. The SEM has very high depth of view and high resolution, and is as such well suited for the investigation of textured surfaces and small features. Bare silicon or silicon with a partial dielectric cover have been investigated in the SEM. The limited electrical conductivity of these samples has in some cases limited the resolution and contrast of the SEM images, but has the advantage that the process result is not covered up, as would be the case if coating the sample with a conductor before performing SEM. For accurate height-profiles on the nano-scale, a PicoStation atomic force microscope (AFM) from Surface Imaging Systems has been applied. This AFM was not equipped with a microscope, and hence, searching across the sample was a tedious task. Furthermore, scanning as large as 47x47 µm requires rather large scan speeds, on the order of 10 µm/s. This results in vulnerability to loss of accuracy, especially when encountering debris on the surface. The open-source program Gwyddion  was used for postprocessing of the images. As most AFM images show bow or tilt, a polynomial background (2nd order) was removed by masking out the laser spot and assuming that the wafer surface outside of the laser spots was flat. However, the leveling may not be completely accurate. As such, the line profiles may still carry some artifacts due to bow or tilt that hasn’t been completely removed. In Paper VI, ablation craters from the ablation of SiNx are analyzed, showing height differences of a couple of tens of nanometers over a couple of tens of micrometers. Such slow height variations will be sensitive to residual bow, and the measured height differences should be treated with caution. These distortions are not expected to be critical to the analysis of the profiles, as e.g. step-like height profiles are still clearly visible. 2.5 WET CHEMICAL PROCESSING Several different wet chemical processes have been applied in this thesis, either for cleaning or for structuring or removal of the silicon. These will be briefly summarized here. CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES 21 Cleaning All samples were dipped in a 5 % hydrofluoric acid (HF) solution for 1 minute before thin film deposition. This removes any oxide layer on the wafer surface. HF was also used after laser processing in the cases where remaining SiNx or SiOx needed to be removed, specifically if the wafer was to be passivated or the whole surface was to be etched. Samples intended for lifetime measurements were in addition etched in a piranha solution (4:1 sulfuric acid:hydrogen peroxide, (4:1 H2SO4:H2O2)) and in concentrated hydrochloric acid (HCl), in order to ensure the best possible surface passivation. Piranha removes organic residues, while HCl removes metallic contaminations. These etches remove no or only very little silicon, and as the surface-near laser damage is sought, this processing will not influence the sought-after results. Silicon etches Three silicon etches have been applied in this thesis. Firstly, for the creation of the patch textures in PAPER I and PAPER II, a 10 % potassium hydroxide (KOH) solution at 88 °C was applied. Low concentration KOH solutions preferentially creates pyramidal structures by exposing <111> crystal planes. Increasing the concentration of KOH from 2 to 10 % ensured a more practical etch time reaching a depth of 10 µm in less than 10 minutes. Figure 2.3 (top left) shows an inverted pyramid structure which is not fully formed, as a result of too short etch time, and complete inverted pyramids by increasing etch time (top right). For the etch-back experiments, flat surfaces are desired, and a homogenous etch is preferred. For this purpose, a 47 % KOH solution at 88 °C was used, as high concentration KOH solutions tend to leave behind a rather flat wafer surface. An example of a wire-sawn wafer etched in high concentration KOH is shown in Figure 2.3 (bottom left). The samples applied in this thesis are polished, and the result of high concentration KOH etching is very flat as shown in Figure 2.3 (bottom right). The high concentration KOH etch showed an etch rate of approx. 1 µm/min, and it was as such easy to achieve relatively shallow etches. Both KOH etches were kept in a water-bath for better temperature control. For the diffractive structures in PAPER III and PAPER IV, an isotropic etch was required. An HNA (Hydrofluoric acid, Nitric acid, Acetic acid) etch was chosen. As described in PAPER III, the processing results were improved when increasing the HF content in the HNA solution from 1:40:15 to 5:40:15, as under-etching was suppressed. It is suspected that under-etching is caused by a mechanism allowing the acid to penetrate more rapidly along the wafer surface, thereby increasing the area of attack of the etch. 22 CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES Such mechanisms could be either an interface oxide layer, as silicon oxide has a high etch rate in this solution, or surface-near crystal damage. Surface-near damage from ion bombardment is noted in PAPER VIII, and would be present also in the samples used in PAPER III and PAPER IV. Damaged crystals may have more attack points for the etch, and may as such have a higher etch rate than an undamaged crystal. Figure 2.3: (Top) Inverted pyramid structure showing incomplete (left) and complete (right) etching. (Bottom) KOH polishing etch on slurry-sawn wafer (left) and on polished wafer (right). No structures are observed on the polished wafer, an image with a piece of debris in the lower right corner is chosen in order to indicate the image resolution and contrast. 2.6 REFLECTANCE AND TRANSMITTANCE MEASUREMENTS For several of the experiments in this thesis, optical quantities must be characterized. For experiments on laser – material interaction, the reflectance gives information about the amount of laser energy entering the silicon. Reflectance for these samples was measured using a spectrometer-based setup from OceanOptics, using an integrating sphere in a oneport setup. Such a setup will introduce a substitution error when the calibration sample has a different reflectance than the sample to be characterized, the substitution error increasing with increasing difference between the reflectance of the calibration sample and that of the measurement sample. For these measurements, polished silicon was used as reference CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES 23 sample, ensuring that the absolute error when measuring a reflectivity around 5 – 15 % is well below 1 %. As the reflectivity in the case of laser-material interaction experiments only influences the intensity entering the silicon by a small amount, this substitution error is acceptable, and much lower than e.g. the uncertainty in the method by Liu, described in section 2.2. For measurements on light-trapping structures, on the other hand, greater accuracy is required. For the geometric light-trapping structures, the same spectrometer-based setup was used, but the integrating sphere was replaced with a two-port sphere. This sphere allows for the calibration sample to be mounted at one port and the sample to be mounted at a second port, allowing the sphere as such to remain unchanged between calibration and measurement. This eliminates the substitution error described above. For the diffractive light-trapping structures (PAPER IV), Jo Gjessing (IFE) performed the optical measurements using a two-port integrating sphere setup as described above, but with a 30 W QTH (Quartz Tungsten Halogen) lamp, using a Digikröm DK240 monochromator from CVI Laser Corporation and a chopper, pre-amplifier and lock-in amplifier for the best signal-to-noise ratio. The laser intensity dependence of the reflectance has also been estimated through rough measurements. As will be discussed in section 3.3.3, the dielectric response of a material containing a dense plasma of excited electrons may deviate from its steady-state value if the plasma contribution to the dielectric permittivity is considerable. In order to monitor this behavior, the reflectance was measured in-situ while laser processing. For these measurements, the sample was processed at 15° angle of incidence, and the reflected laser power was measured as function of incoming laser intensity using the thermopile power meter described above. This ratio gives the average reflectance. These measurements will be rough, as there is substantial uncertainty in the power measured with the power meter. Furthermore, the measured reflectance will be averaged both in time and over the whole area of the spot. Any diffusely reflected light will not be collected by the power meter. Still, there is a measurable trend towards higher reflectivity when increasing the optical intensity. 2.7 MINORITY CARRIER LIFETIME In order to quantify the effect of laser induced damage, the effective minority carrier lifetime has been measured. Quasi-steady state photoconductance decay (QSSPC) 24 CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES measurements have been applied, using a WTC-100 setup from Sinton instruments. This technique registers changes in conductivity of a sample under varying illumination, while at the same time measuring the illumination intensity. This gives information about how quickly the carriers decay in the wafer. Photoluminescence imaging (PL) has also been applied, using a LIS-R1 instrument from BTimaging. PL is a quick method for obtaining a spatially resolved lifetime map of a sample. This technique measures the photoluminescence signal from a wafer, and uses a QSSPC measurement to calibrate the relation between the photoluminescence signal and the minority carrier lifetime. The calibration measurement must be performed on a wafer or part of a wafer with relatively homogenous lifetime for good calibration accuracy. Both of these measurement techniques measure the effective minority carrier lifetime. When measuring the lifetime of a laser processed sample, the inverse effective minority carrier lifetime can be expressed as the inverse sum of lifetime from various recombination mechanisms. Contributions may be divided into surface recombination, bulk recombination, recombination in the laser-damaged areas and any other relevant recombination mechanisms: = + + +⋯. In order to isolate the effect of the laser processing, A large 2.2 and is ensured by using a high-quality substrate while a large should be large. achieved by applying an efficient surface passivation. As described above, amorphous silicon was used for surface passivation as it gives excellent surface recombination properties. is discussed further in Appendix A, Section 3.4 and PAPER VIII. 2.8 SILICON SUBSTRATES Throughout this thesis, polished silicon wafers have been applied. Hermann et al.  have shown that laser processing of textured substrates may induce more damage than if processing on polished substrates, and as such, the transition to textured surfaces is not expected to be trivial. For the diffractive texture described in section 4.3.2, it may be difficult to spin the microspheres onto non-polished wafers. Also the passivation of rough surfaces may be more difficult than passivating polished surfaces. Still, the use of polished substrates is relevant, firstly, as trends and results may be clearer and easier to interpret, CHAPTER 2: EXPERIMENTAL TOOLS AND TECHNIQUES 25 and secondly, as several of the emerging kerf-less wafering technologies deliver substrates with surfaces that are close to polished in appearance. 3 LASER PROCESSING FOR SILICON SOLAR CELLS This chapter provides a review of the state of laser processing for silicon solar cells. Thereafter, the theory behind laser-material interaction is discussed, and the simulation models are presented. Some of the results from these simulations are presented, along with some thoughts on laser interaction with a free-electron gas. Thereafter, the characterization and quantification of laser damage is discussed. 3.1 STATE OF LASER PROCESSING FOR SILICON SOLAR CELLS In many cases, a laser being directed at a material is nothing but a source of energy or heat. The laser carries energy which may be absorbed by the material, thereby depositing energy into the material. Depending on how much energy is deposited, the material may be heated, melted or vaporized / ablated. This mechanism is the primary mechanism by which lasers may process a material or device. Laser processing of silicon is not a new idea. In the late 1970’s scientists were applying lasers to anneal damage from ion implantation . When annealing, the material, in this case silicon, is heated, normally by an infrared lamp, in order to increase the thermal energy of the atoms in the lattice. Thereby, defects, e.g. atoms that have been moved out of their regular place in the lattice, may diffuse back, restoring the regularity of the crystal. In laser annealing, the energy from the laser causes a controlled, localized heating of the wafer, and it was intended as an alternative to conventional thermal annealing. For silicon solar cells, one of the primary motivations for applying lasers is the need for local processing, i.e. the need to process only a small part of a solar cell. Lasers show outstanding focusing, translational and temporal properties, making them potent tools 26 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS 27 for local processing. A range of laser-related processes for silicon solar cells have been developed, some of which will be briefly summarized below. Some of these processes and their influence on solar cell performance are indicated in Figure 3.1. Laser edge isolation In a solar cell process, one often obtains a cell where the diffused emitter is wrapped all the way from the front side of the cell to the rear side of the cell, thereby shunting the cell. This shunt must be removed, and lasers may be applied for the process. By removing the emitter by laser ablation around the edge of the solar cell, the shunt is effectively eliminated, and the fill factor, , is increased , . This is shown in Figure 3.1 as a grove through the emitter at the edge of the solar cell. Laser edge isolation is currently implemented in industry. Local contact openings The metal-semiconductor interface shows a very high rate of electron-hole recombination, and is as such a significant source of efficiency loss in a solar cell. By applying local rear contacts instead of contacting the entire rear surface of a solar cell, recombination losses may be strongly reduced. Reduced recombination increases , and also , by increasing the fraction of the generated electron-hole pairs that reach the contacts. Local contacts may be created using lasers, simply by applying a laser to locally remove a passivating dielectric layer from the wafer surface, and metallize through these holes, shown in Figure 3.1. The main obstacle for successful implementation of this process is the laser induced damage to the silicon substrate [31–34]. Locally contacted solar cell designs are on their way into industrial production, applying laser opening of the contacts. Laser fired contacts Laser fired contacts (LFC) is another method for creating local contact openings. In the LFC process, the silicon wafer is covered with a passivating dielectric layer, and the rear contact aluminum is deposited onto this dielectric. Contact with the silicon is created by irradiating this stack with a laser, whereby the aluminum, dielectric, silicon stack melts and the aluminum is forged into contact with the silicon , . In this process, the silicon and aluminum are mixed, and aluminum diffuses into the silicon bulk. This creates a socalled back surface field, an electric field that will repel the electron from the recombinative metal-semiconductor surface, thereby strongly reducing recombination also in the metallized areas themselves. Industrial production equipment for LFCs is available . 28 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS Laser transferred contacts One further way of creating metal contacts using lasers is the Laser transferred contacts or Laser induced forward transfer. In this method, a thin metal foil on a transparent carrier is kept close to the solar cell surface. A laser is irradiated through the transparent carrier, and the metal is ablated from its carrier, being deposited onto the solar cell . Laser doping Laser doping normally occurs through laser heating and melting of a silicon surface covered with a dopant-containing substance, whereby dopant atoms may be rapidly introduced into the silicon material, causing the silicon to become doped. Laser doping of silicon has been performed since the 1980’s , . Currently, laser doping is most relevant for the application of selective emitters, where doping is only performed on parts of the substrate, in order to form low resistance contacts, while allowing for a lighter emitter doping on the rest of the cell. Selective emitters thereby reduce series resistance, increasing , while reducing emitter recombination, thereby increasing . Several fabrication methods have been proposed. Firstly, doping from a solid state dopant source on the wafer surface may be applied. A spin-on dopant or the phosphorus glass from the emitter doping process may be used as dopant sources , . Alternatively, laser chemical processing (LCP) has been proposed, in a method where the laser light is guided to the wafer in a jet of phosphoric acid, the acid serving both as a dopant source, light guide and cooling medium . Also laser transfer doping has been suggested. This is a process similar to laser transferred contacts, where doped amorphous silicon is transferred to the wafer . Selective emitters is shown in Figure 3.1 as a dark grey area under the front contacts. Selective emitters will allow for lower emitter doping on the rest of the wafer surface, thereby reducing recombination losses in the emitter, increasing the collection probability of the short-wavelength part of the sunlight, whereby increasing and . Industrial production equipment for selective emitters by laser processing is available . Laser surface texturing Surface texturing increases light-trapping, thereby increasing . Several approaches to surface texturing by the use of lasers have been reported. Ultrashort-pulse lasers may be applied for laser texturing. When a silicon substrate is irradiated by multiple ultrashort laser pulses, self-organizing structures begin to emerge. These often cone-like structures reduce the front surface reflectance of the solar cell, in what is often called black silicon CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS 29 . Alternatively, a macroscopic pattern may be drilled into the wafer, in a process where the laser does the material removal . A third option would be to use an etch mask that is opened locally using a laser, followed by etching through these holes. In this process, the etching does the material removal . Laser surface texturing shall be considered in more detail in chapter 4. Figure 3.1: Schematic cross-section of a solar cell, highlighting potential areas for laser processing, and their influence on solar cell performance. The silicon wafer is shown in white, the emitter in light grey, local overdoping under the contacts in dark grey, anti-reflection coating in dark blue, rear surface passivation layer in light blue, contacts in black. Residual laser damage may be present in all laser processes. Alternatives to laser processing For the processes mentioned above, alternatives that do not apply lasers exist. Edge isolation may be performed by etching of the edges of the cell . Selective emitters may be formed e.g. by creating a thick emitter over the whole wafer surface followed by a masked etch, whereby the thick selective emitter is left under the contacts, while the emitter is thinned over the rest of the wafer , or by applying doping from locally printed dopant sources . Local contacts may be formed e.g. by dispensing the metallization paste in a pattern ensuring that the silicon-metal contact is formed only locally . Surface texturing is currently performed by wet-chemical etching, but also reactive ion etching (RIE) and microwave plasma etching may be applied , . Laser processing is not automatically beneficial for the solar cell, as it may damage the quality of the solar cell materials, e.g. by introducing defects into the silicon, thereby increasing recombination, and decreasing Voc. As such, laser processing is only relevant in cases where the laser process outperforms the alternative in terms of overall increase in cell efficiency, process simplicity, or cost. From the overview given in this section, it is seen that the interaction between laser and material can give rise to a wide variety of processes. It is also seen that the damage to 30 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS the material resulting from the laser process must be under control for successful process implementation. As such, knowledge about the laser-material interaction is crucial, as is knowledge about the laser induced damage. The next sections are devoted to these topics. 3.2 LASER-MATERIAL INTERACTION One of the main topics of this thesis is the laser-material interaction. The silicon, or a silicon–dielectric stack, is irradiated with laser pulses, and the laser light is absorbed. How and where this absorption takes place, combined with the properties of the irradiated materials and the laser parameters, such as pulse duration, laser wavelength and laser intensity distribution determines the outcome of the laser processing. In order to predict experimental trends or understand experimental results, it is relevant for us to understand the laser–material interaction in detail. For the case of silicon, there is an observable change in processing results when reducing the laser pulse duration. A transition happens somewhere between nanosecond (“long”) and picosecond (“ultrashort”) pulse duration. Some typical process results when removing silicon nitride from silicon is seen in Figure 3.2, showing SEM images of processing with long and ultrashort laser pulses in the UV (343 / 355 nm), visible (515 / 532 nm) and infra-red (IR) (1030 / 1064 nm). The ultrashort pulse laser operates at the shorter wavelengths. Starting with long pulses in the visible wavelength range, the result is a molten area in the silicon, however, with relatively homogenous size. Long pulses have time to melt a significant amount of silicon, and re-distribution, i.e. pits and silicon expulsion is frequently observed. Looking at long pulses in the IR, the situation is somewhat similar, the melting is clearly visible. However, the pulse to pulse variation in processing result is much larger. This as a result of the inherent instability of the process. When cold, silicon is nearly transparent to this wavelength, with the laser light penetrating several hundred micrometers. However, some of the laser light is still absorbed. The silicon is slowly heated to the point where it absorbs strongly, whereby the deposited energy density strongly increases and enough energy is deposited to melt and vaporize the material. This feedback mechanism makes processing near the process threshold unstable, as the onset of absorption may depend on local material parameters. At shorter wavelengths, the picture changes. In the UV, the laser energy is absorbed by the SiNx, decomposing this. However, the image shows an inhomogenous process result. This is an indication that some of the laser light penetrates to the silicon, with the possibility that the CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS 31 silicon is vaporized and expels some of the SiNx. Experiments have also been performed at 266 nm, where the SiNx absorbs even stronger. Here, the instabilities observed when processing at 355 nm are not observed, as very little laser light will penetrate to the silicon. With ultrashort laser pulses, the picture changes somewhat. In the UV, the SiNx still absorbs, but no instabilities are observed. Also in the visible and IR, the process results are, in general, much more homogenous. Furthermore, the obvious signs of melting and expulsion are gone, leaving a seemingly flat wafer surface. Whether using a pulse duration of 0.5 ps or 10 ps, the process results look similar when observed by SEM. Processing in the far-IR using long pulses gives process results resembling those observed with pulses in the IR, as similar heat-dependent feedback-mechanisms are dominant also here, and as the pulses are long enough for material expulsion and redistribution. Figure 3.2: Typical process results when irradiating a silicon nitride on silicon stack with long and ultrashort laser pulses at 355 (UV), 532 (Visible) and 1064 nm (IR). Above, it is stated that the laser light may be deposited into the SiNx if the wavelength is short enough. Using ultrashort laser pulses, it can sometimes be rather straightforward to see where the energy has been deposited. Figure 3.2 shows that when processing in the UV using ultrashort laser pulses, the surface is covered in fine debris. In this case, the energy is deposited into the SiNx, and the SiNx is blown apart upon removal. This is in contrast to what is the case e.g. in the visible wavelength range, where the laser energy is deposited into the silicon. Here, it is frequently observed that the SiNx which is blown off remains in one single piece that can be found elsewhere on the wafer upon inspection. This is shown in Figure 3.3. 32 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS Figure 3.3: SEM images of complete pieces of SiNx removed from the wafer surface using ultrashort pulses in the visible wavelength range. (Left: Overview, Right: closeup) As the mechanism for ablation is different in these two situations, a distinction shall be made. The process where the laser energy is deposited in the substrate, and the film is lifted off by the vapor pressure substrate shall be referred to as indirect ablation. On the other hand, if the energy is deposited into the film, we shall refer to the process as direct ablation. Not only the appearance of the processing result changes when reducing the duration of the laser pulses. Also the physics of the interaction will change. Generally, the laser energy is absorbed by the electrons in the material, moving these to an excited state. When applying long laser pulses, this energy has time to dissipate to the lattice through collisions, whereby the electrons relax into less excited states. As such, there is equilibrium between the electron and lattice systems, the number density of excited electrons will remain moderate. There is also enough time for the heat to be transported a significant distance from where it is deposited. This picture changes when going to ultrashort laser pulses. Now, the electrons will not have time to transfer their energy to the lattice before the pulse is through, and as such, the electrons may have significantly higher energy than the lattice during the pulse. Nonlinear absorption may be encountered, meaning that the absorption is changing with the intensity of the applied light. The excited electrons in the conduction band may absorb light through free-electron absorption, and they may promote further electrons to the conduction band through impact ionization. Furthermore, the electrons may not have time to relax into less excited states, and very high densities of highly excited electrons may be obtained. If dense enough, this electron cloud may start to behave as a plasma, significantly altering the physical properties of the material. Furthermore, thermal diffusion is strongly limited when applying ultrashort laser pulses. Clearly, very different models are required when treating laser-material interaction with long or with ultrashort laser pulses. CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS 33 3.3 SIMULATIONS ON LASER-MATERIAL INTERACTION Simulation of laser-material interaction is a rather complex task. The process is threedimensional, and if considering material transport, such as convection in a molten material or even ablation, i.e. material removal, the simulations get extremely large and timeconsuming. For ultrashort laser pulses, many optical, electrical and thermal properties of the materials to be simulated are uncertain and must be applied far from equilibrium, in a material that is under influence of tremendous stress. It was chosen to apply somewhat simplified models in this thesis, in order to gain physical insight while keeping model complexity to a minimum. For the simulations, one important parameter is the ablation threshold fluence, as this is the fluence required for the process to take place. Criteria for ablation are required in order to determine this ablation threshold. For long laser pulses, it is assumed that material is removed only if some material reaches vaporization temperature. Vaporization will remove material in itself, but it will also create recoil pressure that will expel more material. At fluencies close to the ablation threshold, the majority of the material will be removed through expulsion . This ablation threshold will be valid both for long and ultrashort pulses. With ultrashort laser pulses, there may also exist other ablation mechanisms, as discussed in PAPER V. These mechanisms are connected to the point where a high number density of excited electrons creates a strongly absorbing plasma in the material. As such, in the case of ultrashort pulses, the second criterion for ablation is when the critical electron density is reached. Two significant physical mechanisms are left out of the simulations, namely material removal and convection. When material is expelled from the melt pool or in other ways removed from the substrate, it will carry with it some of the laser energy. Furthermore, convection and stirring within the melt pool will alter the dynamics of the process. While it would be interesting to investigate these mechanisms as well, it would be outside the scope of this thesis. Still, some considerations can be made. Convection and stirring only has time to take place for long pulses. Generally, convection and stirring within the melt pool will decrease the vertical temperature gradient within the melt pool. The bottom of the melt pool will be hotter, potentially increasing the melting rate for the solid material surrounding the melt pool. As such, convection and stirring may increase the 34 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS obtained depth of the melt pool. At the same time, the surface temperature will be reduced, increasing the threshold for ablation. On the other hand, material removal will carry with it some of the laser energy, reducing the energy stored in the wafer, hence reducing the thermal impact to the wafer. Quantification of these effects would be difficult, however, Mangersnes et al.  have performed simulations omitting these effects, still obtaining good correspondence between simulations and experiments. This seems to indicate that the effect of convection and stirring may be minor when seeking to determine the ablation threshold fluence. For the simulation of both long and ultrashort laser pulses, the partial differential equation solver pdepe  was applied. This is included as a standard routine in Matlab . One approximation performed in all simulations is that the physical situation is onedimensional. This implies that the laser irradiation is homogenous and the laser spot is infinitely large. This is of course not the case, however, the approximation is reasonable. The laser spot is normally on the order of 40 µm in diameter, while the laser energy is deposited within 1 µm from the wafer surface, sometimes within the first 0.1 µm from the surface. As such, the lateral length scale is much larger than the length scale into the substrate. The pulses were assumed to have a Gaussian temporal distribution, with the pulse duration being the full-width half-maximum (FWHM) duration. The surface reflectivity was set to zero, looking at the optical intensity entering the material. This as the reflectivity can be changed rather arbitrarily by the application of suitable (anti-)reflection coatings. 3.3.1 LONG PULSES Using long laser pulses, the absorption in the material is given by the linear absorption coefficient of the material. The temperature rise of the material is given by laser energy input, heat capacity and heat conductivity. The heat equation is given by : = where = + is the thermal energy of the material, is the temperature, is the thermal conductivity and 3.1 is the heat capacity of the lattice, and are the optical attenuation coefficient and intensity respectively. This equation describes how the thermal energy of the system changes as a result of thermal conduction and as a result of energy input from optical absorption. The optical intensity distribution follows the Beer-Lambert law: CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS ( ) = − ( ) ( , ) → ( , ) = with a constant However, 35 ( ) −∫ ( ( )) ′ 3.2 , this expression gives an exponentially decaying intensity. is generally temperature dependent. With temperature dependent , there is a feedback mechanism. Optical absorption causes a temperature rise, which again causes a change (normally an increase) in absorption by changing . Phase changes are taken into account by modifying into containing the enthalpy of phase change. The model developed by Mangersnes et al. ,  was applied for simulations on long laser pulses in the visible wavelength range. 126.96.36.199 Long laser pulses at long wavelengths Semiconductors are generally considered to be transparent, for all practical purposes, for photon energies below the band-gap of the material, as the photon does not carry enough energy to bridge the band-gap. However, in some cases, free-carrier absorption may become relevant. Free carrier absorption is absorption by carriers in the conduction band, and has an absorption coefficient described by = 3.3 Normally, this effect is very weak, as the number density of conduction band electrons is fairly small. However, if the temperature of the semiconductor is high enough, a significant number of thermally excited electrons will exist. In addition, the free-carrier absorption coefficient generally increases with , meaning that this effect will be very pronounced at long wavelengths. With high temperature substrates and long wavelengths, free-carrier absorption may be strong, as is discussed in PAPER VII. The model developed by Mangersnes et al. ,  was adapted to be suitable for the absorption encountered at a wavelength of 9.3 µm, as discussed in PAPER VII. No experimental investigation was found describing the temperature dependence of the absorption in silicon at 9.3 µm. As such, a theoretical expression was used. In PAPER VII the temperature dependence of the free carrier absorption is described as ( , )= Here, (10 , 300) × ( ) × , ( , ) . 3.4 ( , ) is the free-carrier absorption (FCA), the only contribution to absorption that is taken to be temperature dependent. Starting with FCA at room 36 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS temperature, the temperature dependence comes from the temperature dependence of the number density of conduction band electrons, ( ) and from the temperature dependence of the mobility, ( , ). These two quantities have not been investigated close to the melting point of silicon, where the simulations are most sensitive to the value of . This constitutes a serious source of uncertainty in the simulations. Another source of error is the thermal interface resistance between the dielectric and silicon. This quantity is taken to be temperature independent, however, at least when the dielectric melts, the interface thermal resistance must be expected to change. The paper also clearly shows that correspondence between simulations and experiments is rather poor, the only result that should be valid is that shorter pulses will allow for less heat transfer to the silicon substrate. As for the experimental investigations of laser ablation by CO2-lasers, the lack of lasers with shorter pulse durations has excluded the exploration of potentially very interesting parameter ranges. 3.3.2 ULTRASHORT PULSES The term ultrashort pulses has probably arisen from the need of a counterpart to the rather short pulses in the nanosecond range, which are in this context regarded as “long”. Normally, the term “ultrashort pulses” is applied to pulses with a duration in the pico- and femtosecond range. Here, “ultrashort pulses” is taken to mean pulses where non-linear interaction is expected to be a significant part of the physics, but where the assumption that the extension of the pulse is large compared to e.g. optical absorption lengths etc. is still valid. This will hold well for pulse durations down to 0.5 ps, the shortest pulses applied within this thesis, having an extension in silicon of about 35 µm. As described in section 3.2, ultrashort laser pulses call for a different physical model than long pulses. As a result of the potentially different temperature in the electron and lattice systems, two coupled heat equations are required in order to describe the system, one for the electrons and one for the lattice, following the work by Sim et al.  and van Driel : = − ( − )+ 3.5 = + ( − ) 3.6 In equations 3.5 and 3.6, / , / and / are the thermal energy, temperature and heat conductivity of the electron/lattice system, respectively. is the electron-lattice CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS coupling time, 37 is the total energy input from the laser, conduction band electrons and is the number density of is the Boltzmann constant. As the number density of electrons is not constant, but is changing through generation and recombination mechanisms, the number density of electrons must be accounted for, adding a third coupled equation: = Here, − is the electron diffusivity, coefficient, +∑ + 3.7 ℏ is the Auger coefficient, is the n-th order absorption coefficient and ℏ is the impact ionization is the photon energy. The total energy input from the laser is: = = (∑ + ) ≃( + + ) 3.8 where the summation indicates all relevant multi-photon absorption processes, and the last term is the free-carrier absorption. is the two-photon absorption coefficient. When working on silicon, linear absorption, two-photon absorption and free-carrier absorption will be the dominant processes. Two-photon absorption is the simultaneous absorption of two photons, and is a mechanism which has an absorption coefficient that is proportional to the optical intensity. Two photon absorption may induce absorption in materials where the photon energy is not high enough to bridge the band-gap, but where two photons combined have sufficient energy, or it may increase absorption significantly in cases where linear absorption is weak, e.g. for photon energies close to the band-gap energy in silicon. Looking at the equations, it is clear that the laser energy is deposited into the electron system, while the electron-lattice coupling term causes an energy flow between the hotter electron system and the colder lattice system until the two reach equilibrium. Impact ionization and band-to-band absorption cause an increase in the number density of conduction band electrons, while Auger recombination removes electrons. Free-carrier absorption does not contribute to the number density of conduction band electrons, but causes an increase in the temperature of the electron system. The absorption in the medium becomes dependent both on the optical intensity and on the number density of conduction band electrons. In the model described above, the expressions for optical absorption and assumptions on constant optical reflectivity break down when approaching the critical electron density, as a result of the free-electron contribution to the dielectric constant of the 38 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS material. This implies that anything happening to the substrate after this point, such as phase transformations and material removal is not accurately described in the simulations. In fact, the physics behind melting or disordering mechanisms resulting from ultrashortpulse irradiation of semiconductors is quite complex. Several authors have pointed towards melting of the semiconductor (as opposed to e.g. Coulomb explosion) , and that the melting turns non-thermal by ultrafast disordering mechanisms if the laser fluence is sufficiently above the melting threshold , . Also breaking of the material resulting from internal stress caused by the strong temperature gradients obtained by ultrashort laser pulses has been suggested as material removal mechanism . Other mechanisms that are not considered within the two-temperature model are the incomplete thermalisation between optical and acoustic phonons, the electric field arising within the material due to electron emission and modification of material properties due to deformation of the material itself , . While these mechanisms have an influence on the interaction dynamics, this thesis focused on obtaining meaningful results while keeping the complexity of the model and the number of uncertain material parameters to a minimum. Results in PAPER V indicate that the main physical mechanisms are included also in the two-temperature model, and that the choice of model as such is a sensible one. The pdepe solver is able to solve sets of coupled partial differential equations. However, the expression for optical intensity cannot be explicitly obtained, and needs to be found from the integral expression in equation 3.2. In order to make the solution converge, a set of iterations are implemented. Firstly, a temperature distribution and distribution of number density of electrons are set as functions of time and space coordinates, assuming quite limited heating and excitation. From these distributions, the optical intensity is calculated as function of time and space, starting with quite low incoming optical fluence. Then, this optical intensity distribution is used as the source term in the equations. When a solution is found, the temperature and electron distributions are used to re-calculate the intensity distribution, and repeat until the solution converges. Thereafter, the incoming optical fluence is increased by a certain ΔF, and the previously found temperature and electron distributions are again used to calculate the optical intensity distribution, and the procedure is repeated. These iterations are repeated until one of the criteria for ablation is reached. These criteria are discussed in section 3.3, and are that the lattice reaches vaporization temperature, or that the number density of electrons in the conduction band reaches the CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS critical electron density, 39 . Then, the Δ is reduced, until two pulse fluencies are found, one being above the ablation threshold and one below, and the difference between them is lower than 3 %. 188.8.131.52 Some results from the simulations Figure 3.4 shows the optical intensity normalized to the intensity at the wafer surface as a function of depth into the silicon wafer, in order to illustrate the optical attenuation. The figure shows data for a laser wavelength of 1030 nm, 0.575 J/cm2 and a substrate temperature of 300 K. The pulse duration is 3 ps (FWHM). Three curves are shown, at 3 ps before the peak of the pulse, at the peak of the pulse, and at 3 ps after the pulse. At 3 ps before the pulse, both the optical intensity and the number density of excited electrons are low, and hence the relatively weak linear absorption dominates. This gives only very moderate absorption. At the peak of the pulse, the optical intensity is very high, and the absorption is dominated by two-photon absorption. At 3 ps after the pulse, the optical intensity is equal to the intensity at 3 ps before the pulse, and linear and two-photon absorption are in principle equal in these two cases. The fact that highest absorption is observed at the trailing end of the pulse indicates that free-carrier absorption is dominant late in the pulse. (Heating of the silicon will increase the linear absorption coefficient late in the pulse, but this effect is less dominant than the effects described above.) It is clear that, at least for the case of IR-irradiation of silicon using ultrashort pulses, the laser energy is confined close to the silicon surface when the laser intensity and number density of electrons rise. Also shown in Figure 3.4 is the same data for a pulse with a laser wavelength of 515 nm. Although the absorption increases with time during the pulse, probably as a result of free-carrier absorption, the difference is less prominent than for 1030 nm laser wavelength. 40 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS Figure 3.4: Normalized intensity distribution through a silicon slab at various times during a laser pulse of 3 ps duration. The laser wavelength is 1030 nm (left) and 515 nm (right). Non-linear absorption mechanisms are far more prominent for the case of irradiation at 1030 nm, as the linear absorption is quite strong at 515 nm. Note the differences in x-scale. 3.3.3 FREE ELECTRON THEORY In a dielectric or semiconductor, a high number density of electrons in the conduction band can be generated e.g. by optical excitation. These electrons (and their corresponding holes in the valence band) are quasi-free, and may be described as a plasma. The dielectric response of the material will be affected by the presence of such a plasma, and freeelectron theory may be applied in order to describe this response. Free-electron theory is treated in PAPER V, however, this field shall be reviewed here in some more detail. The dielectric response of a material can, in free-electron theory be described by , : = where + = 1− + ( ) 3.9 is the background relative permittivity of the silicon material without free carriers. Here, is defined as = , 3.10 being the plasma frequency with a dielectric background. γ is the reciprocal collision time, is the effective electron mass and ω is the frequency of the applied electric field. With + =√ , the Fresnel reflection can be calculated as 3.11 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS ( =( 41 ) 3.12 ) for normally incident light on a substrate with index of refraction coefficient . Depending on the ratio between , and extinction and , the reflectance as function of number density of electrons can show different shapes. This has effects for laser processing with ultrashort pulses. Figure 3.5 shows the theoretical reflectance curves as functions of electron density in silicon and silicon nitride for the case of irradiation at a wavelength of 515 nm. Silicon has a high index of refraction, giving high reflectivity for the case of low electron densities, while silicon nitride has a lower index of refraction. Now, is related to the mobility of the material. Using a mobility of 100 cm2/Vs in silicon (high carrier density ), and 1 cm2/Vs in silicon nitride , it is evident that the reflectance behavior at high electron densities is very different in the two cases. Figure 3.5: Theoretical reflectance as function of free electron density in silicon and silicon nitride. The shape of the curves is very different in the two cases, as a result of the different ratio between , and . Silicon has a fairly high electron mobility (resulting in ≪ ), while silicon nitride has a fairly low electron mobility (resulting in ≫ ). As such, the plasma response in silicon is dominated by the rapidly alternating electrical field, while the response in silicon nitride is dominated by collisions within the material. This difference results in a well-defined plasma frequency in silicon, while the increase in reflectance is much slower for silicon nitride. The fairly high electron mobility in silicon results in mobility in silicon nitride results in ≫ ≪ , while the fairly low electron . As such, the plasma response in silicon is dominated by the rapidly alternating electrical field, while the response in silicon nitride is dominated by collisions within the material. This difference results in a well-defined plasma frequency in silicon. The reflectance drops when approaching the critical electron density, increasing rapidly to unity thereafter. In this situation, it will be very difficult to introduce more laser energy into the material once the critical electron density has been 42 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS reached, as the laser light will be completely reflected. For the case of silicon nitride, on the other hand, the reflectivity varies more slowly. Here, it will always be possible to continue laser energy input. 3.4 LASER INDUCED DAMAGE When laser processing silicon, the material is normally heated and molten, or in some other way structurally altered. The process result will be a silicon wafer with some degree of crystal damage, as re-crystallization or re-structuring seldom is damage-free. It can be expected that the area influenced by the laser process will be degraded in some way, and this degradation will have a negative influence on the solar cell performance. In order to get a view on the quality and applicability of the laser process, the laser damage must be quantified in some way. This section considers methods for characterization of laser induced damage, and the influence on effective minority carrier lifetime from a laser damaged area is analyzed. 3.4.1 CHARACTERIZATION OF LASER-INDUCED DAMAGE IN SILICON The quality of a solar cell is closely linked to its efficiency, where the highest possible efficiency is desirable. Any process reducing the efficiency of the cell must therefore outweigh this efficiency decrease by some other benefit, often lower production costs. Laser processing of silicon solar cells is one such process with the potential to reduce the efficiency of the cell, and ideally, the efficiency of a cell with laser processing should be compared to a damage-free reference process in order to quantify laser-induced damage. However, it is not always desirable, practical or even beneficial to create complete solar cells and monitor the resulting efficiency, and often more indirect ways of quantifying laser-induced damage are applied. In this section, some methods for characterization of laser damage are discussed. When looking at a silicon wafer, one important material parameter influencing the potential efficiency of a solar cell made from that wafer is the minority carrier lifetime. Laser damage may reduce this lifetime, decreasing the maximum potential efficiency of the finished solar cell. This reduction in lifetime comes from the introduction of recombination sites, such as various crystallographic defects. Whether using long laser CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS 43 pulses resulting in melting and recrystallization of silicon or ultrashort pulses where the material processing may take place by ultrafast disordering mechanisms, the resulting crystal quality must always be considered. Especially in the case of ultrashort pulses, one is often lead to believe that the ablation may be completely damage-free, as redistribution of silicon may be suppressed, and the process result may look very smooth and clean. Transmission Electron Microscopy (TEM) is rather frequently used for investigation of laser damage, and may reveal seemingly perfect silicon crystals under such ablation spots. However, TEM is not necessarily the best suited characterization tool for finding defects which may be small and low-concentration. A good example is shown in Figure 3.6. This figure shows TEM images of cross-sections of ablation spots from irradiation by a nanosecond laser at 1064 nm wavelength on an atomic scale. As shown by Engelhart et al. , such a laser produces electrically active defects down to around 25 µm below the wafer surface, while the TEM images show amorphous silicon at the surface of the wafer, and very good crystal quality below a couple of tens of nanometers. TEM is unable to reveal the damage leading to reduced lifetime, which may not be very surprising. As shown by Davis et al. , electrically active defects may affect silicon solar cell performance even at defect levels between 1011 and 1016 1/cm3, corresponding to a defect level of less than one ppm (and potentially much lower). Although the density of defects in a laser treated area is unknown, it is not impossible that one is looking for one defect among a million silicon atoms, a task that is impossible for TEM analysis. As such, it seems obvious that electrical characterization is imperative in order to quantify laser damage. One way of quantifying laser damage is to measure the effective lifetime of a laserirradiated wafer as described in section 2.7. The laser damage will result in a lowering of the lifetime, potentially revealing information about the extent of the laser damage. During this thesis, several experiments have been performed ablating SiNx from silicon wafers using lasers with pulse duration from ~100 ns to 500 fs and from UV to IR, and the effective lifetime of these samples has been measured. However, it was observed in all of these experiments that the effective lifetime was the same, and corresponded to the lifetime of a single sided diffusion limited surface recombination. This behavior shall be discussed in further detail. 44 CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS Figure 3.6: TEM images of silicon wafer irradiated by nanosecond pulses with a wavelength of 1064 nm. The images show cross-sections of the laser spot, where an amorphous silicon layer can be observed in the lower-left corners (near the wafer surface), and an ordered silicon crystal in the upper-right part of the images. (TEM performed by Annett Thøgersen, UiO.) Consider a wafer with a bulk lifetime and , and surface recombination velocities . Now, introduce a laser damaged region close to one wafer surface, as shown in Figure 3.7. To a first approximation, it is assumed that the wafer has been degraded to a certain depth below the wafer surface, and that in this region, the lifetime has been lowered to the value . In this situation, a recombination current will flow into the laser damaged area. Inserting a virtual boundary between the laser damaged area and the undamaged bulk, it is possible to assign an effective surface recombination velocity to the recombination caused by the laser damage, derived, assuming that is small compared to the recombination taking place in the laser damaged bulk. In this case, = where . In Appendix A, such an expression is is given by: ℎ . is the electron diffusion coefficient and ≫ region. With 3.13 is the width of the laser damaged , i.e. if the laser damaged region is much thinner than the diffusion length, this expression goes to zero. If, on the other hand, ≪ , i.e. if the laser damaged region is much wider than the electron diffusion length, this goes to / , . According to Sproul , the surface lifetime reaches a limiting value of = when > 10 cm/s. CHAPTER 3: LASER PROCESSING FOR SILICON SOLAR CELLS 45 Figure 3.7: Schematic representation of a wafer with a laser damaged region. The laser damaged region has a width w and a lifetime . However, the depth of the laser induced damage is still unknown. PAPER VIII describes measurements on lifetime in laser-irradiated silicon wafers as function of etch depth. By removing a controlled thickness of the laser damaged region, the effective lifetime of the wafer will increase, until the point where the complete laser damage has been removed, and the bulk lifetime is restored. Equation 3.13 can be used to extract from the behavior of the experimentally determined as described in section A.3. In PAPER VIII, it is found that, using a laser wavelength and pulse duration of 515 nm and 3 ps, the lifetime is completely restored when removing 230 nm from the wafer surface, and that the lifetime in the laser damaged region must be on the order of 1 ns. For long pulses, geometric factors are taken into account, and is estimated to around 100 ns. In PAPER VIII, it is also found that, while nanosecond lasers show damage several micrometers from the surface, ultrashort laser pulses show damage confined to a much more shallow depth. These findings can be implemented in simulation models predicting the efficiency decrease that can be expected from the laser process. In samples with emitters, the measured effective lifetime is strongly reduced, due to recombination in the emitter. As a result, the laser-induced lifetime degradation is not necessarily as pronounced as with lowly doped silicon. In this case, one should rather use the dark saturation current density, as this can be related directly to the achievable open circuit voltage, , . Also analysis of the diode ideality factor can give information about the damage . Such analysis has not been performed within this thesis. 4 LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS This chapter motivates the use of light-trapping structures in silicon solar cells and presents the benefits of light trapping. Then, some typical light-trapping structures are shown, followed by a description of some of the alternative routes to fabrication of light-trapping structures using lasers. Thereafter, the approach taken in this thesis to the fabrication of light-trapping structures using lasers is presented. Finally, the results and the applicability of the textures are discussed. 4.1 LIGHT MANAGEMENT IN SILICON SOLAR CELLS In a solar cell, one major task is to make sure that as much as possible of the incoming sunlight is converted into electricity. In order to achieve this, optical losses must be reduced as much as possible. The effort of reducing these losses is termed light management. Figure 4.1 shows a sketch of possible optical losses in a silicon solar cell. denotes the front surface reflection, which consists of the light being reflected off the front surface without entering the solar cell. denotes the escape light, light which has entered the solar cell, but is able to escape before being absorbed. Three parasitic absorption mechanisms, absorption that does not generate current in the solar cell, are also indicated. absorption, denotes optical absorption in an imperfect rear mirror, free-carrier , is the absorption by conduction band electrons, an optical absorption mechanism which does not generate electron-hole pairs. This mechanism is intrinsic to silicon, and is strongest in highly doped silicon, such as in the emitter. Also the antireflection coating may absorb some of the incident light, here denoted as 46 . CHAPTER 4: LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS 47 With a quite high index of refraction, bare silicon reflects on the order of 30 % of the incoming sunlight due to Fresnel reflection. In order to reduce , two tricks are normally applied. Firstly, an anti-reflection coating can be applied to the surface, consisting of a transparent layer with a thickness of /4 and an index of refraction ideally equal to , thus minimizing or eliminating reflection at the target wavelength, and significantly reducing overall reflection. (For an introduction to Fresnel and thin-film optics, see e.g. .) Typically, when weighting the reflectance spectrum with the AM1.5 spectrum, integrating over a 300 – 1200 nm wavelength range, an integrated reflectance of around 10 % can be achieved by application of an anti-reflection coating. Secondly, texturing of the surface may further increase the optical coupling into the silicon. If the light experiences multiple bounces off the silicon surface, each bounce will reduce the total reflectance. Figure 4.1: Sketch of a wafer showing various contributions to optical absorption and loss in a solar cell. The rear reflector is shown in black, while the anti-reflection coating is shown in blue. ASi denotes the silicon absorption, the only absorption mechanism generating electron-hole pairs. The optical loss is divided into front side reflectance, Rf , escape light, Resc, absorption in the rear reflector, AReflector, absorption in the AR-coating, AARC, and absorption by free carriers, AFCA Silicon is an indirect band-gap semiconductor, meaning that the optical absorption process must be assisted by absorption or emission of a phonon for momentum conservation. This characteristic makes silicon a rather poor optical absorber. While other solar cell materials may show acceptable absorption in a 1 µm thick absorber, silicon requires quite long absorption lengths. This trend is especially clear for photon energies near the band-gap energy of silicon. In Figure 4.2 (left), the attenuation coefficient and optical penetration depth in silicon is shown. The optical penetration depth is defined as the distance the light has to 48 CHAPTER 4: LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS travel through silicon in order to be attenuated to 1/e intensity level. The hatched range is a range of penetration depths ranging from 160 µm to 20 µm. 160 µm is around the current industry standard wafer thickness, while 20 µm corresponds to a realistic long-term target thickness. It is seen that wavelengths above approx. 800 nm will have the possibility to penetrate the thinnest of these wafers, the penetration depth easily reaches several millimeters at wavelengths above 1100 nm, meaning that the light can travel much further than the thickness of the wafer before being absorbed. It is at wavelengths showing a penetration length on the order of, or longer than the thickness of the wafer that contributions to Resc are expected. In order to reduce loss contributions from Resc, the path length of the light through silicon must be increased. The act of increasing the path length is often called light trapping. Figure 4.2 (right) shows the photogenerated current, generated from band-to-band absorption by sunlight (AM1.5) passing through a given path length in silicon. Optical losses occur even to optical path lengths exceeding 1000 µm. Figure 4.2: Left: The optical attenuation coefficient and corresponding optical penetration depth in silicon as function of wavelength. Also indicated is a relevant range of wafer thicknesses for solar cell applications. The need for light-trapping for wavelengths above 800 – 1000 nm depending on wafer thickness is obvious. Right: The photogenerated current from sunlight (AM1.5) absorbed by a given path length in silicon (solid line). Also indicated is the maximum current available (dashed line). Data taken from ref. . Figure 4.3 shows a collection of light-trapping strategies. A shows a planar silicon slab with no rear reflector, where the light gets only one straight pass through the wafer. This must be considered as an absolute worst case scenario. B shows a planar structure with a rear reflector, ensuring two straight passes through the wafer. In a solar cell, the rear metal contact often acts as a mirror (although not a perfect one). C shows a front side textured structure, where the path length in the silicon is increased as a result of the oblique angle taken by the light passing through the wafer. A high probability of escape after two passes is indicated. In silicon, any light hitting the silicon / air interface will be totally CHAPTER 4: LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS internally reflected if the incidence angle is larger than = sin ( 49 / ) , which for silicon in air, at wavelengths near the band-gap equals approx. 16.5°, a fairly shallow angle. Angles below 16.5° are referred to as the escape cone, as light within this cone will have a high probability of escaping the silicon wafer. Figure 4.3: Sketch of various light-trapping schemes. A - no light trapping, B - rear reflector, C – front surface texture, D – symmetry-breaking front side texture, E – diffractive rear reflector, F – Lambertian rear reflector. D and E are examples of more advanced light-trapping structures. In D, a textured surface is shown, but unlike C, the symmetry of the texture is broken. Created correctly, such symmetry-breaking structures can cause most of the light to hit the wafer surfaces at angles outside the escape cone, thereby causing total internal reflection to be dominant, and multiple passes are ensured for the majority of the light. E is meant to indicate a diffractive rear reflector, where the incoming light is diffracted into several diffraction orders. The angle of the diffraction orders can be tuned by varying the grating period so that total internal reflection is ensured for all but the specular diffraction order. If, in addition, the specular order is suppressed, the light trapping can be very efficient. F is meant to indicate the case of Lambertian light trapping. Lambertian light trapping is an idealized theoretical light-trapping scheme, where a perfect rear reflector reflects the light homogenously in all directions, independent of the angle of the incoming light. It can be shown that the Lambertian light trapping is the maximum achievable light trapping for a sample uniformly illuminated from all directions. The path length of light in a Lambertian light-trapping scheme can be calculated to 4 , where is the refractive index of the material and w is the wafer thickness. In silicon, this path length enhancement 4 is about a factor 50. While light-trapping is not critical in thick wafers, Figure 4.2,(right) shows that thinner wafers benefit strongly from light-trapping. Increasing the path length 50 CHAPTER 4: LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS in a wafer from 20 µm by the Lambertian factor to 1000 µm would increase the photogenerated current from around 70 % of the available photocurrent to above 90 %. The industry standard for mono-crystalline silicon texturing is today the doublesided random pyramid structure. This is created by etching a <100>-oriented silicon wafer in a diluted KOH solution, often adding an alcohol for improved quality of the texture. Such an etch preferentially exposes the <111> crystal planes, leaving a random pattern of upright pyramids. This texture shows a low front surface reflectance, due to the steep angles of the pyramids, and also shows very decent light trapping, as there will be a strong randomization of the direction of the light when refracted or reflected off the various pyramid facets. For multi-crystalline silicon, the random pyramid texture is less efficient, as the direction of the pyramids is dependent of the crystal orientation of the wafer. Therefore, for multi-crystalline wafers or mono-crystalline wafers with e.g. a <111> orientation, isotropic acidic etching is normally applied. This texture will form random dimple-like structures. As the dimples are generally flatter than the pyramids, the chance of experiencing multiple bounces off the front surface is limited, and the front surface reflectance is significantly higher than for the random pyramids. The light-trapping properties, however, are rather good, as is discussed in PAPER IV. Common for both of these textures, is that they require some form of seeding or attack points in order to form uniformly. Such seed points are readily available today, as most wafers are cut by wire sawing, where the saw damage generates seed points. However, several new wafering technologies are emerging, where no saw damage is present. This poses a challenge for the traditional texturing methods. Furthermore, wafer thickness is expected to decrease, caused by a need to reduce silicon consumption and silicon costs. The traditional texturing methods will remove significant wafer thickness, being less suitable for thin wafers. To overcome these hurdles, new texturing methods must be developed. This thesis presents two ways of creating light management structures on silicon by laser assisted methods. 4.2 STATE OF LASER TEXTURING Already, several approaches to laser texturing of silicon exist. These will be briefly reviewed in this section, and a motivation is given for the approach to laser texturing taken in this thesis. CHAPTER 4: LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS 51 Black silicon So-called black silicon can be created by irradiation of a silicon surface using ultrashort laser pulses. If a single spot is irradiated by multiple pulses, self-assembling structures tend to emerge, shown in Figure 4.4 (left) . Such structures are often created in a sulfur hexafluoride (SF6) – atmosphere, but they may also be created in air . Black silicon, as the name suggests, displays an extremely low reflectivity over the whole relevant wavelength range, and is as such very close to the ideal anti-reflection coating. On the more practical side, one obstacle seems difficult to bridge. In articles describing black silicon formation, typical parameters may be: Pulse energy density 0.9 J/cm2, repetitions 300 . Using these numbers and multiplying by the size of a 5 inch wafer, a total laser energy of around 44 kJ is required. In current production, 1 wafer/second (or more) is the benchmark for a relevant process. In order to deliver 44 kJ of energy to a wafer in such a short period of time, one would need a 44 kW laser. Not only are such lasers far away from state of the art, but even if one could find such a laser, it would be very interesting to see how a silicon wafer would react to such a violent energy input. With very little material removal, the majority of the laser energy must remain in the silicon wafer. Using the heat capacity and melting enthalpy of silicon, 44 kJ is the energy required to heat and melt a 5 inch wafer with a thickness of around 350 µm. Another issue when working with black silicon in general is the very large surface area that is created. The passivation of such a surface must be of very high quality in order for surface recombination not to be a serious problem. Passivation of black silicon surfaces by the use of atomic-layer deposited Al2O3 is showing promising results . Laser Drilling A second option for laser texturing is simply to drill a suitable geometric structure, such as the honeycomb structure in mc-silicon shown in Figure 4.4 (middle) . Holes are drilled, and thereafter, the structure is etched in order to remove the laser damaged areas and debris from the process. While this process significantly reduces front surface reflectance for mc-silicon, material removal by laser ablation is an energy intensive process. In this case, 10 J/cm2 and 3 repetitions were applied. Assuming an effective area coverage of 25 % (the 10 J/cm2 would not be applied to the whole surface), the required energy for texturing of a 5 inch wafer is around 1 kJ. While this is much better than what was the case for black silicon, and in a range where industrial lasers do exist, this is still quite a lot of energy to put into a wafer within one second. 52 CHAPTER 4: LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS Masked laser processing A third option for laser processing is masked laser processing, shown in Figure 4.4 (right) . Here, a SiNx etch barrier has been applied to the wafer, and the laser is applied only for creating openings through the barrier. A wet-chemical etch (in this case an isotropic etch) is applied for material removal and structure development. By this approach, the laser does virtually no material removal, and much lower laser energy can be applied. Typical pulse energies required for silicon nitride removal is around 0.7 J/cm2. With an area coverage of around 10 % (the image shown has an area coverage of around 5 %), the energy required for opening the etch barrier on a 5 inch wafer is around 10 J, corresponding to a 10 W laser for 1 wafer / second. This is indeed feasible laser power, and easily available today. This masked approach also uses a diffractive optical element (DOE) in order to create several openings through the etch barrier per laser pulse. This relaxes the demand for accurate, high speed scanning and high repetition rate lasers. The requirements on pulse energy rise with the number of spots per pulse, but lasers tend to have pulse energies easily allowing for a high number of simultaneously processed holes. Figure 4.4: Images of black silicon structure  (left), laser drilled texture  (middle) and masked texture with etching  (right). 4.3 MASKED LASER TEXTURING Masked laser texturing followed by wet chemical etching seems to be the most promising approach to laser texturing of silicon. Firstly, as the estimations above show, it is the process requiring the absolutely lowest laser power for relevant process speeds. Of course, also the time needed for etching must be taken into account, however, wet chemical etching can be performed as a batch process, significantly reducing processing time per wafer. Secondly, if done properly, the etch process may remove any laser damage, ensuring that the texturing process is free of laser damage. Thirdly, wet-chemical etching is extensively used in solar cell processing, and is as such a well-known process. Therefore, masked texturing followed by wet-chemical etching is the approach chosen in this thesis. Two structures have been created, with strongly differing characteristics. The structures are CHAPTER 4: LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS 53 discussed in PAPER I-IV, and be referred to as the patch texture and the diffractive structure. SEM micrographs of these textures are shown in Figure 4.5. Figure 4.5: Patch texture (left, center). Diffractive dimple structure (right). In order to predict the performance of geometric light-trapping structures, the raytracing program TracePro  was used. TracePro was used for PAPER II, where the performance of the patch texture was investigated. Diffractive structures receive their properties from interference effects, and raytracing is no longer an adequate method. Predictions on the light-trapping properties of diffractive structures rely on the work by Jo Gjessing. Both the work presented in his Ph.D. thesis  and more recent work have been applied. 4.3.1 PATCH TEXTURE In a series of articles, Campbell et al. [79–81] investigated several light-trapping schemes for monocrystalline silicon. One of these schemes has the potential to outperform the random pyramid texture, and at the same time be quite insensitive to the angle of the incoming sunlight, namely the patch texture. This texture would be an interesting alternative to today’s industry standards. The patch texture is schematically shown in Figure 4.6 (left). It consists of patches of trenches oriented alternatingly along orthogonal directions. The size of the patch is adjusted to the thickness of the wafer in such a way that the light which is reflected off the rear reflector hits the neighboring patch (as indicated by the white arrow), where the direction of the trench ensures total internal reflection. In this way, the light is trapped very efficiently. As the angle traveled by the light inside of the silicon wafer is only weakly dependent on the angle of the incident light, the light-trapping properties will be largely preserved also at other angles of incidence. The drawback with the patch texture is of course that it requires some kind of masked etching in order to develop the desired pattern. 54 CHAPTER 4: LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS Figure 4.6: Sketch of the patch texture (left). Indicated by the white arrow is the function of the texture, namely that light hitting a point on one patch will hit the front surface at the corresponding point in the neighboring patch, whereby total internal reflection is ensured. Also shown is the pattern which must be opened through the etch barrier for development of the texture (right). The patch texture is scalable, making it possible to start with relatively large structures as a proof-of-concept, developing the process gradually, reducing feature sizes. SiNx was chosen as the etch barrier, as SiNx shows high stability in KOH solutions. Patch textures were created opening the etch barrier locally by laser irradiation. An anisotropic KOH etch then developed the pattern. The process and performance of the textures are described in PAPER I and PAPER II. It was found that the patch texture, under some circumstances, can deliver higher than the random pyramid texture taken as reference. The improvement, however, is fairly modest as a result of the fact that the random pyramid texture is a very good lighttrapping structure. It has a low front surface reflectance and decent path-length enhancement. This, combined with the simplicity of the random pyramid texturing process makes it a hard reference to beat. Furthermore, the performance of the patch texture improves when reducing the feature sizes. This, in turn, puts great demands on the performance of the laser system. Single laser pulses were applied, and the pattern was drawn using an xy-table for translation. This is a very slow process, not at all industrially suitable. A galvo scanner would increase scanning speed, but only to a certain degree. A patch pattern with 5 µm wide trenches would require a line somewhat longer than 3 km to be written on a 5 inch wafer, a formidable task even if disregarding accuracy and the fact that it is not simply a straight, continuous line that has to be written. The use of a diffractive optical element (DOE) or other beam-shaping element would have to be applied for industrially relevant implementation of the process. Figure 4.6 (right) shows an image of the laser pattern required for the creation of a patch pattern. If an area on the wafer of 400x400 µm could be processed with one pulse, a laser with 100 kHz repetition rate and a CHAPTER 4: LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS 55 scan speed of 40 m/s would be required. These are still rather strict requirements for a laser system, but more feasible than the one spot per pulse alternative. The second challenge related to the small feature sizes is the positioning accuracy and accuracy of the laser intensity. The positioning accuracy ultimately determines the area coverage as discussed in PAPER II, and demands on positioning accuracy rises with decreasing feature size. A further benefit of using a DOE is that the requirement for relative positioning accuracy between spots would also be greatly reduced, as one spot would cover a larger area. Furthermore, small features require tight laser foci. Tight foci have small focal depth, meaning that the distance to the wafer must be very well controlled in order for the laser fluence to remain within process tolerances. The process would be simplified if using an etch barrier that can be deposited without the need for vacuum processing, such as e.g. spin-coating. 4.3.2 DIFFRACTIVE STRUCTURE Diffractive structures have feature sizes on the order of the wavelength of light. As a result of interference effects, the light will be scattered into certain angles or diffraction orders. For the simplest case of a one-dimensional grating, light incident on the grating at an angle will be diffracted at angles ( where + described by the grating equation )= , is the grating period, 4.1 is the wavelength of the light and = 0,1,2, …is the diffraction order . Varying , the diffraction angles with a given angle of incidence and wavelength may be tuned. By creating the structure in a suitable manner, e.g. by applying a blazed grating, the specular component (0th order diffraction) may be strongly suppressed. If, in addition, the higher diffraction orders are diffracted outside of the escape cone of silicon, which, as described earlier is approx. 16.5°, one may be able to create highly efficient light-trapping structures. Such structures have been explored theoretically by Jo Gjessing [83–85]. Diffractive structures are generally to be applied where geometric light-trapping textures for some reason are not suitable. For thin wafers, geometric structures may simply be too large, removing too much of the silicon material. Another aspect is the fact that the textures currently being applied require seed points for proper formation. Such seed points are currently in rich supply, originating from the wafer sawing process. For thin wafers, on 56 CHAPTER 4: LIGHT-TRAPPING STRUCTURES IN SILICON SOLAR CELLS the other hand, new production methods are emerging. These kerf-less technologies do not apply sawing, and as such, seeding for etching of the textures may become an issue. Considering these points, the need for suitable light-trapping textures is higher for thin wafers. Unfortunately, diffractive structures are a bit challenging to manufacture, due to the small sizes and periodicity required. Common techniques, besides photolithography, include hot embossing and nanoimprint- or interference lithography , [86–88] using reactive ion-etching and plasma-etching. Still, these techniques are not yet implemented in industrial processes, and more attractive alternatives should be investigated. In this thesis, a technique for creating diffractive structures in silicon is presented. According to the work by Jo Gjessing  and Einar Haugan , hexagonally ordered dimples was a realistically achievable structure showing good light-trapping potential. An etch barrier was deposited onto a silicon substrate, and self-ordering microspheres were deposited onto the etch barrier. Then, laser pulses were applied to this structure, whereby the laser light was focused by the microspheres, as investigated by Piglmayer et al. , creating openings through the etch barrier underneath each microsphere. Isotropic wetetching created hexagonally ordered dimple structures. In this process, the spheres are the focusing elements. This has the benefit that very tight foci are obtainable without the focal depth becoming an issue. Furthermore, by applying a laser spot of 170x170 µm, close to 30 000 holes are created through the etch barrier with each laser pulse. However, spincoating of each individual wafer does not seem like an industrially viable solution, especially considering the cost of consumables. An alternative could be to use micro-lens arrays as the focusing elements, potentially being re-usable. A process using microspheres on carriers as micro-lens arrays is described by Piglmayer et al. . As the diffractive dimple structure is suitable for wafers where traditional surface textures do not yield good results, it has a higher potential for improving solar cell performance than the patch texture, which delivers only modest improvement over existing textures. 5 CONCLUSION This thesis had two main objectives. The first objective was to gain fundamental understanding of the interaction between pulsed lasers and materials relevant for silicon solar cells, with an emphasis on parameter ranges leading to ablation. The understanding of laser-material interaction is important from a fundamental point of view, as it forms the basis for the successful development of laser processes. The second objective was to develop laser-based techniques for manufacturing of efficient light-trapping textures. Emphasis was to be on the investigation of the practically achievable quality of textures already explored theoretically in literature. Light-trapping structures are highly relevant for silicon solar cells, considering the decrease industry standard of wafer thickness and the new emerging wafering technologies. On the topic of light trapping, two processes were developed for the production of two light-trapping structures, namely the patch texture and the diffractive honeycomb texture. The performance of these textures was investigated by optical absorption and transmission measurements, and compared with reference textures. It was found through simulations that the patch texture gives an increase in of up to 0.5 mA/cm2 compared to the random pyramids texture. The diffractive honeycomb structure delivered a photogenerated current of 38 mA/cm2 on 21 µm thick silicon wafers. The lack of industry standard methods makes comparison somewhat arbitrary, but at a wafer thickness of 100 µm, the diffractive honeycomb structure gives an increase in of 2 and 4 mA/cm2 when compared to isotropically etched and polished samples, respectively. As such, it was clearly shown that laser based texturing may provide highly efficient light-trapping structures suitable for thin substrates, including substrates with a crystal orientation different than the <100> orientation. On the topic of laser-material interaction, several investigations have been undertaken. The investigations, while focusing on different topics, all revolve around the topic of ablation mechanisms. The four papers on laser-material interaction focus on: 57 58 CHAPTER 5: CONCLUSION Temperature dependent ablation of silicon, ablation of silicon nitrides, laser damage resulting from ablation and ablation of dielectrics using long wavelength lasers. In order to understand the interaction between ultrashort pulse lasers and the silicon substrate, a simulation model known as the two-temperature model was implemented. In experiments, it was found that the ablation threshold of silicon is dependent on the temperature of the silicon substrate. At a laser wavelength of 1030 nm, the ablation threshold is reduced from 0.43 J/cm2 at room temperature to 0.24 J/cm2 when the substrate temperature is 320 °C. The simulation model reproduced the experimental trends. Combining results from experiments and simulations, it was found that a high number density of electrons in the silicon substrate causes the ablation, rather than substrate melting and vaporization as would be the case for pulses in the nanosecond range. For practical applications, the use of a slightly elevated substrate temperature can significantly reduce the required laser power, or correspondingly increase the process throughput. The largest reduction in ablation threshold is observed with a laser wavelength of 1030 nm making this wavelength comparably more interesting. As the use of this wavelength eliminates the need for wavelength conversion stages, the complexity of the laser equipment may be reduced. The differences in interaction between silicon and long (ns) and ultrashort (ps) laser pulses were investigated through the characterization of the depth of the laser induced damage. It was found that the depth of the laser-induced damage is considerably smaller when applying ultrashort laser pulses than when applying long pulses, being reduced from around 3 µm when using long pulses to around 0.25 µm when using ultrashort pulses at a laser wavelength of 532 nm. This is a result of stronger thermal and optical confinement of the laser energy. An estimate on the minority carrier lifetime in the laser irradiated areas is also presented. Knowledge about the depth of laser damage as function of pulse duration and wavelength is a valuable tool when seeking the right laser for a given process. When investigating the interaction between various silicon nitrides and ultrashort laser pulses, it was found that, using a laser wavelength of 532 nm, the laser energy was deposited either in the silicon or in the dielectric, depending on the laser pulse duration and the composition of the silicon nitride. Low refractive index nitrides or long laser pulses gave indirect ablation, while high refractive index nitrides or short pulses gave direct ablation. The possible absorption mechanisms were investigated, pointing towards significant interaction between the laser pulse and a dense electron-hole plasma in the silicon nitride. As direct and indirect ablation give differing process results, detailed CHAPTER 5: CONCLUSION 59 knowledge on the ablation behavior of silicon nitrides with varying composition as function of laser pulse duration and laser wavelength is valuable for process development. The use of long wavelength lasers for the ablation of dielectrics from silicon was investigated theoretically and experimentally, as long wavelength lasers may be absorbed directly in the dielectric, without being absorbed in the silicon. Simulations predict that short laser pulses would provide ablation with minimal heating of the silicon. Experiments using a CO2-laser operating at a wavelength of 9.3 µm with a pulse duration of 100 ns, however, shows silicon melting, and hence too strong silicon heating. As such, the concept remains to be proven. This thesis brings contributions to the understanding of the interaction between laser pulses, in particular ultrashort laser pulses, and silicon and dielectrics. This fundamental knowledge adds to the previous literature on the topic, and may serve as basis both for further fundamental studies and for process development. On the topic of lighttrapping, two laser based methods are developed for the production of geometric and diffractive light-trapping structures on silicon. It is shown that high-quality light-trapping textures may be produced by laser based processes. 6 DISCUSSION AND OUTLOOK In this chapter, a discussion of the work in this thesis is given, along with suggestions on the possible continuation of this thesis. On the topic of light trapping, the high quality of laser-based texturing processes has been demonstrated. The main weakness of this work does not lie in the performance of the textures, but in the complexity of the production processes. In order to achieve the required process speeds, the patch texture requires the use of a diffractive optical element in order to process larger areas with each laser pulse, as discussed in PAPER I. For the diffractive honeycomb structure, large laser spots can be utilized, and much lower positioning accuracy is required. As such, the laser processing stage is not the critical part of this process. Here the deposition and use of microspheres for the focusing of the laser light is the major obstacle for industrial application. If the microspheres were to be replaced by a re-usable microlens array, the process would be simplified significantly. Both texturing processes would benefit from the implementation of an etch barrier deposition technique that is simpler than the PECVD deposition used within this work. The implementation of the two textures in solar cells would constitute final evidence that the textures have a positive overall influence on a complete solar cell. On the topic of laser-material interaction, a series of investigations have been undertaken within this thesis, and several interesting and directly applicable findings have been made. The continuation of this work could follow several paths, either towards further fundamental studies and simulations, or towards more application oriented studies. As a direct continuation of the work presented in PAPER VII, short pulse, long wavelength laser ablation should be investigated further. E.g. optical parametric oscillators (OPOs) could be able to produce pulses significantly shorter than the 100 ns tested herein, with a tunable laser wavelength. Such lasers would be a powerful tool for investigation of long wavelength laser ablation, provided that they deliver sufficient pulse energy. Alternatively, or in parallel, improvement of the simulation models would lead to better prediction of the parameter ranges required for ablation of dielectrics without silicon substrate melting. As 60 CHAPTER 6: DISCUSSION AND OUTLOOK 61 simulation results are no more accurate than the physical parameters used in the simulations, it would be beneficial to acquire more detailed knowledge on the temperature dependence of several critical parameters used in the simulations. E.g. thermal properties of the dielectrics and free-carrier absorption coefficients have not been explored at temperatures close to the melting temperature of silicon. As a continuation of the work on ablation of silicon nitrides, the practical differences between direct and indirect ablation of silicon nitrides should also be investigated further. Both the minority carrier lifetime of the substrate and the specific contact resistance of metallizations applied through the contact openings should be investigated for both direct and indirect ablation It has been demonstrated within this thesis that several important laser processes yield some degree of laser damage. 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Figure A.1 shows the assumed geometry. A wafer with thickness recombination velocities has a width and + has a bulk lifetime , and surface . A laser damaged region is located near surface 2, and and a degraded lifetime , where is assumed to be constant throughout the damaged region. We wish to investigate the influence of the parameters and on effective lifetime in this structure. In order to do so, we seek to quantify the recombination taking place in the laser damaged region. The local recombination is quantified as = where A.1 is the recombination rate per unit volume, carriers and is the local number density of excess is the lifetime of these carriers. Integrating over the recombining region ∈ [ , + ], we obtain the recombination rate per unit area, =∫ where A.2 is the total recombination per unit area from the laser damaged region. As the laser damage is a surface-near defect, we wish to express the recombination taking place in the laser damaged region as a surface recombination rate. Inserting a virtual surface at the boundary between bulk and damaged region, we use the definition of surface recombination velocity: 69 70 APPENDIX A: ANALYTICAL EXPRESSION FOR RECOMBINATION BY LASER DAMAGED REGION ≡ where ∗ A.3 is the number density of electrons at the boundary ( = ), and is the effective laser surface recombination velocity. In order to solve these expressions, we need to find the electron distribution, ( ). Figure A.1: Assumed geometry of a laser damaged wafer. Indicated are the surfaces with surface recombination velocities, and , being located at = and = + . A laser damaged region extending from = to = + is shown in hatched red. Also indicated as a dotted line is the shape of the electron distribution resulting from such a geometry (with = = and = ∞), being linear in the bulk, and exponentially decaying in the laser damaged region. A.1 ELECTRON DISTRIBUTION = As a first approximation, we assume that = 0, while = ∞, meaning that the only recombination takes place in the laser damaged region. We also assume that the photogeneration is taking place close to surface 1 ( = 0). We use the continuity equation: = where − − is the number density of electrons, is time, is the bulk generation rate, A.4 is the distance through the wafer, is the bulk recombination rate and is the electron current. As we seek a stationary solution, we require the time derivative to be zero. With only surface photogeneration, = 0. We relate recombination to lifetime = =− and consider only diffusion current (in electrons /cm2 s) A.5 APPENDIX A: ANALYTICAL EXPRESSION FOR 71 RECOMBINATION BY LASER DAMAGED REGION =− Here, . A.6 is the electronic diffusivity. For a stationary solution with no photogeneration in the bulk, we then have = . A.7 The boundary conditions are: ( = 0) = where , A.8 is the surface photogeneration rate, and ( = + )=0 A.9 as there is no surface recombination at surface . Furthermore, there is continuity in number density of carriers and in current at the boundary between bulk and laser damaged area: ( = )= ( = ) ( = )= A.10 ( = ) A.11 This yields solutions of the form: ( )= + A.12 /√ ( ) = /√ + A.13 Applying boundary conditions yields ( )=− ( ) = ( − )+ 2 cosh A.14 ( √ ) A.15 where = and tanh √ A.16 72 APPENDIX A: ANALYTICAL EXPRESSION FOR RECOMBINATION BY LASER DAMAGED REGION =− . A.17 √ The electron distribution following from equations A.14 – A.17 is shown in Figure A.1. A.2 SURFACE RECOMBINATION VELOCITY Now that we have obtained expressions for the electron distribution in the laser damaged region and the undamaged bulk, we can solve equation A.2. using the electron density obtained in equation A.15. = ( cosh ∫ √ √ = ) ℎ = √ √ A.18 To no surprise. The laser damaged region is the only recombination source, and must balance out the photogeneration. Solving equation A.3 for by using the findings in equations A.14 and A.16 gives ≡ = = √ ( ) = = ℎ If √ ≪ √ . A.19 , i.e. if the laser damaged region is much wider than the electron diffusion length, this goes to / . (holds to within 4% if /√ > 2). The width of the laser damaged region does not make any difference anymore. The recombination is diffusion limited. In the other extreme, with a very narrow laser damaged region, S goes to zero. The expression for can also be obtained without any assumptions on the bulk of the wafer, simply using equation A.13 for . A.3 EFFECTIVE LIFETIME Using the expression by Sproul  for the surface lifetime, = A.20 APPENDIX A: ANALYTICAL EXPRESSION FOR 73 RECOMBINATION BY LASER DAMAGED REGION where is the smallest eigenvalue solution of the equation ( )=( + )/( − ) A.21 and using that the effective lifetime is given as = + A.22 we can calculate the effective lifetime as function of the width and lifetime of the laser damaged area. Assuming a bulk lifetime of = 1800µ and a thickness of the wafer of 300 µm, we obtain the result shown graphically in Figure A.2. With high lifetime in the laser damaged region or a very shallow laser damaged region, the effective lifetime is limited by the bulk lifetime, while for very low lifetime in the laser damaged region or very thick laser damaged region, the effective lifetime is that of diffusion limited recombination at one surface. Figure A.2: Effective lifetime as function of the lifetime in the laser damage region and the width of the laser damaged region. LIST OF ABBREVIATIONS Abbreviation AM1.5 ARC AFM DLTS DOE FTIR FCA FWHM IR IFE LCP LFC LIPSS HNA MFD OPO PL PV PECVD QSSPC RIE SEM SHG SRV THG TEM UV Meaning Air Mass 1.5. Standard solar spectrum for solar cell efficiency measurements Anti-reflection coating Atomic Force Microscopy Deep-level transient spectroscopy Diffractive Optical Element Fourier-Transform Infrared Spectroscopy Free-carrier absorption Full Width Half Maximum Infra-red Institute for Energy Technology Laser Chemical Processing Laser fired contacts Laser Induced Periodic Surface Structures Mix containing Hydrofluoric acid, Nitric Acid, Acetic Acid Mode Field Diameter Optical parametric oscillator Photoluminescence imaging Photovoltaic energy Plasma-Enhanced Chemical Vapor Deposition Quasi-steady state photoconductance decay Reactive Ion Etching Scanning Electron Microscopy Second Harmonic Generation Surface recombination Velocity Third Harmonic Generation Transmission Electron Microscopy Ultra-violet 74 PAPER I J. Thorstensen and S. E. Foss, “Laser assisted texturing for thin and highly efficient monocrystalline silicon solar cells,” in Proceedings of the 26th European Photovoltaic Energy Conference, pp. 1628 – 1631, 2011. 75 LASER ASSISTED TEXTURING FOR THIN AND HIGHLY EFFICIENT MONOCRYSTALLINE SILICON SOLAR CELLS Jostein Thorstensen and Sean Erik Foss Department for Solar Energy, Institute for Energy Technology (IFE) P.O. Box 40, NO-2027 Kjeller, Norway [email protected] ABSTRACT: A method for creating surface textures based on <111> planes on monocrystalline silicon has been developed, using laser openings in a SiNx etch mask followed by a KOH etch. Both inverted pyramids and patch textures with good area coverage have been successfully demonstrated, with feature sizes of 15 – 50 µm, and an area coverage of 94 % and 76 % for patch structures and inverted pyramid structures respectively, as estimated by reflectance measurements and ray-tracing simulations. Keywords: Etching, Laser Processing, Light Trapping, Texturisation 1 INTRODUCTION Thin and highly efficient monocrystalline silicon solar cells will require surface textures offering light trapping superior to that of the random pyramid texture. Structures promising this have been explored by Campbell et al [1 – 3] and include inverted bi-pyramids, perpendicular slats and patch textures. Of these, the patch texture promises a good combination of good light trapping and low sensitivity to angle of incidence of the incoming light. The patch texture is a single-sided texture shown schematically in Figure 1. The principle of operation is that a ray hitting one of the main facets of the trench will bounce by total internal reflection at the back side of the wafer, hitting the corresponding spot of a neighboring patch, as indicated by the red arrow. This patch will have its trenches in the orthogonal direction, once again ensuring total internal reflection. To achieve this, the size of each patch must be adjusted to fit the thickness of the wafer. Figure 1: Schematic representation of the patch texture. Flat areas between the trenches will be present in realistic textures, and are included in the figure. When it comes to manufacturing these textures, the inverted textures have traditionally been created using photolithographic methods, commonly accepted as too expensive for mass production of solar cells. This work describes a method for creating structures based on inverted pyramidal or other structures consisting of <111> planes on monocrystalline silicon wafers, using a laser assisted method. This as a means for achieving good light trapping textures using industrially feasible methods. To our knowledge, laser assisted methods for creating such inverted texturing schemes have not yet been published. A somewhat similar procedure for producing honeycomb structures on multicrystalline silicon has, however, been reported by Morikawa et al . The honeycomb texture is mainly aimed at decreasing surface reflectance, while our texture is aimed at improving light trapping properties. 2 EXPERIMENTAL 2.1 Texturing process Figure 2 shows the schematic steps of the texturing process. A monocrystalline <100> Si wafer is covered with PECVD-deposited a-SiNx, which acts as an etch barrier. Then a laser is used to create local openings in the a-SiNx in a pattern aligned to the crystal axis of the wafer. An anisotropic KOH etch is performed, and the aSiNx is removed in an HF dip. Figure 2: Schematic representation of the process flow for creation of inverted textures A figure of merit for these textures is the area coverage. When looking at the processed wafers from above, the area will consist of the area covered by inverted pyramids or trenches (processed area), and flat areas between each pyramid or trench (unprocessed area). This is indicated in Figure 1. We define the area coverage as processed area divided by total area. Furthermore, we define the base size as the distance between the center of two neighboring pyramids or between the bottom of two neighboring trenches. This as opposed to the actual pyramid size or trench width which, in general, will be smaller than the base size. For high area coverage, the actual pyramid size or trench width should be as close to the base size as possible. Two different lasers were used to fabricate these structures. The first laser is a Rofin PowerLine 20E – LP SHG 532 nm Q-switched laser, delivering pulses of about 100 ns. (Will in the following be referred to as the nslaser.) This laser has a spot size (1/e2 diameter) of 40 µm and no beam alignment system. This limits both resolution and accuracy of the created textures. The textures created with this laser have a base size of 40 – 50 µm. As an attempt of overcoming these problems, a second laser was used for further processing. This is an Amplitude Systèmes s-Pulse HP fs – ps laser set to deliver pulses of around 3 ps. The fundamental wavelength of this laser is 1030 nm, and second and third harmonics of this wavelength are available. (Will in the following be referred to as the ps-laser.) In order to achieve maximum resolution, the third harmonic wavelength (343 nm) was chosen for processing, giving a spot size of 9 µm. The textures created with this laser have a base size of 15 µm. This laser has an imaging system and options for rotation, meaning that alignment to crystal axis is easily implementable. In practice, the wafers were cleaved along a <100> plane, in order to expose a known crystal direction, and this direction was used as alignment. In practice, accuracy down to 0,1 degrees was possible to achieve. The size of the opening through the SiNx etch barrier influences the actual size of the pyramid or trench, and thereby the area coverage of the texture. The size of the opening through the SiNx is adjustable by adjusting the laser power, by the relation described by Liu , which holds for gaussian beam profiles: It is also possible to increase the size of the pyramids by increasing etch time. Once a complete inverted pyramid has been created, increasing the etch time will only slowly increase the pyramid size, as the etch rate in the <111> direction is very slow. If, on the other hand, there are imperfections in the pattern or etch barrier, increased etch time may lead to complete under-etch of the etch barrier and collapse of the pyramidal structures, which will reduce texture performance. Therefore, adjusting the laser pulse energy is a more appealing alternative for controlling the pyramid size or trench width. Figure 4: Inverted pyramid textures with 15µm base size. Applied laser power increases towards the right. Increasing the laser power increases the size of the inverted pyramid textures. Figure 5 shows the practical process steps for forming inverted pyramids using the ns-laser. Frame 1 shows a microscope image of the laser ablated openings in the a-SiNx, the bright areas being exposed silicon. Frame 2 shows a microscope image of the etched sample. The blue areas are silicon covered with a-SiNx, the black areas are the holes left from the laser ablated spots, and the white areas are under-etched a-SiNx. Frame 3 shows a scanning electron microscope – image (SEM-image) of the sample, after the a-SiNx has been removed in an HFdip. The patch texture is created in the same way, by decreasing spot-to-spot distance in one direction by a factor of two, leading to the formation of trenches rather than inverted pyramids. Here, rabl is the ablated radius, c is the 1/e2 radius of the laser beam, I0 is the center laser intensity and Iabl is the ablation threshold intensity. c and Iabl are fitting parameters, in practice determining the inclination of the curve and the intercept with the x-axis. Figure 3 shows an example of our measurements on ablated radius vs pulse energy (red squares), showing a good fit between predicted values and measurements. Figure 4 shows an example of increasing pyramid size resulting only from increasing the applied laser power. Figure 5: Images of samples showing three process steps used for forming inverted pyramids: (top left) laser opening of the a-SiNx layer, (top right) anisotropic KOH etch and (bottom) removal of a-SiNx in HF, revealing the final structure. The two upper images are optical microscope images, while the bottom image is a SEM image. Figure 3: Measured and fitted values for square of ablated radius as function of applied pulse energy. The main challenges of the procedure are visible in these three frames. The first frame shows that the spots are of uneven size, creating an uneven starting point leading to uneven inverted pyramid sizes. This was improved using the ps-laser, which gives more uniform process results. The second frame shows that the spots and pyramids are not completely evenly distributed, as a result of an imperfect laser scanning system. This was improved using the more accurate xy-table of the pslaser. The third frame shows the challenge of achieving good area coverage. Flat, unwanted areas are visible between the inverted pyramids, while at the same time one of the walls between two pyramids has collapsed (top right) as a result of the complete under-etch of the a-SiNx etch barrier. It is also possible to see in the second and third frames that the laser spots are not perfectly aligned to the crystal axis, as it is clear that the inverted pyramids are slightly tilted compared to the grid. This was more or less eliminated using the possibility for rotation using the ps-laser. Images of complete patch textures designed for 100 µm wafer thickness created with the ps-laser are shown in Figure 6. A base size of 15 µm was chosen. The images are ordered from low area coverage, through an optimum, to severe collapse of the structure. The degree of collapse must be balanced by the highest possible area coverage. the patch textures and the inverted pyramid structures respectively. The deviation in Figure 8 between measurements and simulations at long wavelengths are due to the fact that the simulations are done only for front surface reflection, not taking reflections from the back side of the silicon wafer into account. The light trapping performance of the textures, including reflections from the back side of the wafer and transmission through the back surface is to be determined in an upcoming article. Figure 7: Enlarged image of the upper right frame from Figure 6. Patch texture for 100 µm wafer thickness with a base size of 15 µm. Figure 6: Patch textures for 100 µm wafer thickness showing varying degrees of area coverage and structure collapse. The base size is set to 15 µm. 2.2 Characterization The textures were characterized using optical microscopy and SEM imaging for visual verification of the quality of the textures. Reflectance was measured using an integrating sphere from OceanOptics, using a Mg film as reflectance calibration. Furthermore, estimation of area coverage from SEM images was very difficult, as the width of the flats between pyramids and trenches was varying, and a representative selection was difficult to make. Front surface reflection from partially covered surfaces was therefore simulated in TracePro, a ray tracing program, in order to estimate the area coverage of the samples. 3 RESULTS Figure 7 shows a patch texture with good area coverage and relatively low degree of collapse. Figure 8 shows reflection measurements performed on 15 µm base size samples with inverted pyramids and patch textures. Simulations on partially covered textures are also shown, fitted to estimate area coverage fraction. The measured and simulated values for polished silicon are also shown. Fitting to measured reflection gives an area coverage of 94% for the patch texture and 76% for the inverted pyramids. This corresponds to 0.8 µm and 2 µm between Figure 8: Measured and simulated short wavelength reflectance from polished silicon wafer and processed wafers. Deviations between simulations and measurements at long wavelengths are due to back surface reflection, which is not taken into account in simulations. 4 DISCUSSION It has been shown that good area coverage is possible to obtain by laser assisted surface texturing for monocrystalline <100> silicon. However, it should be noted that high precision is required for the laser system. Firstly, the power of the laser must be controlled accurately. In our setup, one of the major challenges was to obtain repeatable low power, as we were operating the laser at a very low fraction of its nominal power. Secondly, the positioning of the laser spots must be very accurate, and an error in any direction of only a fraction of a micron will be detrimental to the texture, as shown in section 3. In these experiments, high positioning accuracy was obtained by using a precision xy-table, positioning the wafer before each opening in the a-SiNx. For relevant processing speeds, on the fly-processing would be required, setting high demands for a suitable scanning system. A 5 inch wafer would require 72 million spots for an inverted pyramid structure with 15 µm base size, and twice that for a patch structure. As seen in Table I, even very high repetition rate systems would require too long processing times for one hole per pulse processing except if using repetition rates above 100 MHz. A more realistic approach might then be to use a diffractive optical element (DOE) for splitting the beam in order to obtain many holes per pulse. Table I: Examples of processing times in seconds for patch texture on 5 inch wafers with 15 µm features, on the fly processing. Repetition rate Single spot per pulse DOE with 100 spots per pulse DOE with 100 x 100 spots per pulse 5 1 MHz 100 kHz 10 kHz 144 1,44 1440 14,4 14400 144 0,014 0,14 1,44 CONCLUSION Light trapping structures in monocrystalline <100> silicon have been created using laser assisted texturing. Polished wafers are covered with PECVD-deposited aSiNx, which acts as an etch barrier. Then a laser is used to create local openings in the a-SiNx. An anisotropic KOH etch is performed, creating inverted pyramid or patch textures. Reflection measurements combined with raytracing simulations show an estimated area coverage of up to 94%. REFERENCES  P. Campbell and M. A. Green, Solar Energy Materials and Solar Cells 65 (2001), pp. 369 - 375  P. Campbell,S.R. Wenham and M. A. Green, Photovoltaic Specialists Conference (1988), pp. 713 – 716 vol.1  P. Campbell and M. A. Green, J.Appl. Phys. 62, 1987, pp. 243 – 249.  H. Morikawa et al, Current Applied Physics 10 (2010) S210 – S214.  J.M. Liu, Opt. Let., vol. 7(5), 196, 1982. PAPER II J. Thorstensen, S. E. Foss, and J. Gjessing, “Light-trapping properties of patch textures created using Laser Assisted Texturing,” Progress in Photovoltaics: Research and Applications, available online, DOI: 10.1002/pip.2335, 2013. 81 PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS Prog. Photovolt: Res. Appl. (2013) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/pip.2335 APPLICATION Light-trapping properties of patch textures created using laser assisted texturing Jostein Thorstensen1,2 *, Sean Erik Foss1 and Jo Gjessing1,2 1 Department for Solar Energy, Institute for Energy Technology (IFE), Kjeller, Norway 2 Department of Physics, University of Oslo, Oslo, Norway ABSTRACT For crystalline silicon solar cells, the efficient collection of light at wavelengths in the infrared is a challenge because of long absorption lengths. Especially for thinner wafers, an efficient light-trapping scheme, such as the patch texture, is required for high short-circuit current densities. We have measured the light-trapping properties of patch textures produced by laser assisted texturing (LAST) on polished h100i silicon wafers, and compared them with ray-tracing simulations. Singlesided random pyramid textures are created for comparison. Excellent agreement between simulations and measurements is achieved by employing diffuse scattering with a narrow angular distribution in the simulations, confirming the successful implementation of the process. We use our optical measurements of the textures for simulations of textures with rear reflectors, where we also investigate the influence on light-trapping properties when varying geometry and reflectance properties. The results from the optical simulations are imported into the solar cell simulation program PC1D. For a 50 m-thick solar cell, we simulate an improvement in Jsc of up to 0.4 mA/cm2 when going from single-sided random pyramid textures to patch textures, even when the performance of the texture is limited by process inaccuracies. Removing the physical inaccuracies of the laser system, the potential gain in Jsc on a 50 m-thick cell with a patch texture covering the complete wafer surface is 0.8 mA/cm2 . We therefore conclude that the LAST method for creating patch textures is suitable to achieve an improved Jsc in thin monocrystalline silicon solar cells. Copyright © 2013 John Wiley & Sons, Ltd. KEYWORDS light trapping; laser processing; texturing; silicon solar cells *Correspondence Jostein Thorstensen, Department for Solar Energy, Institute for Energy Technology (IFE), Kjeller, Norway. E-mail: [email protected] Received 23 November 2011; Revised 21 June 2012; Accepted 27 October 2012 1. INTRODUCTION For thin and highly efficient silicon solar cells, the use of light trapping for efficient collection of the long wavelength (long absorption length), part of the incoming sunlight is required. Geometric or ray-optical light-trapping textures have typical sizes, which are larger than the wavelength of light. Such textures for monocrystalline silicon have been explored theoretically by Campbell et al. in several articles [1–3]. The texture showing the most promising performance, both with respect to light-trapping properties and insensitivity to the incoming angle of the solar irradiation, is the patch texture shown in Figure 1. We see a single-sided texture consisting of patches of trenches oriented alternatingly along orthogonal directions. The texture is made up of h111i crystallographic planes, easily revealed by, for example, potassium hydroxide (KOH) etches, and is as such only Copyright © 2013 John Wiley & Sons, Ltd. applicable to h100i monocrystalline silicon substrates. For related processes suitable for multicrystalline silicon, see, for example,  using masking and  using masking with laser openings. The function of the patch texture is well-described in an article by Campbell et al. , and is based on the fact that this texture ensures a high probability that incoming rays will experience multiple total internal reflections, provided that the size of the patch is fitted to the thickness of the wafer. Additionally, light hitting the end facets of the trenches will not be efficiently trapped, meaning that the trenches should be as narrow as possible. We have previously reported a method for producing the patch textures by means of laser assisted texturing (LAST) . The purpose of this article is to examine the light-trapping properties of the actual processed texture, as opposed to the properties of an idealized theoretical texture, and investigate the optical properties of the Light-trapping properties of patch textures created using LAST J. Thorstensen, S. E. Foss and J. Gjessing Figure 2. Schematic representation of the texturing process. Figure 1. Figure of the patch texture as seen from above. The light path of an incoming light beam is indicated by the white arrow. surfaces. In the work described herein, we have produced single-sided patch textures with no rear reflector on polished h100i wafers. Single-sided random pyramid textures are created for comparison, being easier to fabricate, yet they yield good light trapping. We have measured light-trapping performance on these textures and created an optical ray-tracing model, which corresponds excellently to the measured properties. We keep the inaccuracies of the laser scanning system and the optical properties of the surfaces found from measurements and simulations, and perform simulations on the same structures with two different rear reflectors in order to estimate the lighttrapping properties in a solar cell relevant structure. As a final figure of merit, we have investigated through simulations how the textures affect the Jsc of a solar cell. On h100i monocrystalline silicon, the random pyramid etch is currently a well-established and efficient texture. As such, the extra effort presented by LAST is most likely to be justified in thin cells, where the random pyramid etch would remove too much silicon, or in thin highefficiency cells, such as passivated emitter and rear cell (PERC)-type cells. It is with these thin and highly efficient monocrystalline cell designs in mind that we conduct the investigations herein. 2. EXPERIMENTAL 2.1. Texturing process We have developed a method for creation of good lighttrapping textures based on h111i crystal planes on h100i silicon wafers. The process steps are shown in Figure 2 as follows: 1. Polished h100i wafers with thickness 120 and 300 m are covered with an 80 nm-thick plasmaenhanced chemical vapor deposition (PECVD)deposited SiNx , front and back, to act as an etch barrier. 2. A pulsed laser is used to make circular openings in the SiNx in a square pattern. Because of limitations in the laser processing equipment, the spot to spot distance was chosen at 15 m for an inverted pyramid structure. To create the trenches required for patch textures, the spot to spot distance is reduced in x or y direction, ensuring that the openings in the SiNx are overlapping along one direction. 3. The wafers are etched in an 88ı C 10% KOH solution for 5–10 min, whereby the local laser openings serve as attack areas for the etch, forming inverted pyramidal structures or trenches beneath the openings in the SiNx etch mask. In this process, 10 m of Si below the laser spot is removed. Any laser damage is reported to be completely removed after 2–3 m of etching using a laser at 532 nm wavelength and ns-pulse duration . Shorter pulse durations and wavelengths further reduce the extent of the laser damaged region. 4. The SiNx etch barrier is removed in a 5% HF-dip. The processed wafer surface will consist of the area covered by inverted pyramids or trenches (processed area) and flat areas in between (unprocessed area). We define area coverage as processed area divided by total area. We also define the distance between neighboring pyramid apexes, or the distance between the bottoms of two neighboring trenches as the base size of the pattern. For these experiments, we used a laser with 3 ps pulse duration and a wavelength of 343 nm, as this was the available laser setup with the smallest spot diameter (approx. 9 m diameter at 1/e2 ). In a more industrially feasible setting, a 532 nm Q-switched solid state laser might be a more suitable choice of laser source. Single-sided KOH-etched reference samples were created on the same thickness wafers, by applying a SiNx etch barrier on one side, etching in 1% KOH, 4% IPA at 78ı C for 40 min. We chose not to include application of rear surface reflectors for our textures, as such reflectors would introduce uncertainties in the form of unknown wavelength dependent absorption and degree of scattering reflections. With a single-sided texture, the light will generally hit the rear surface at angles larger than the angle of total internal reflection. Thereby, the main function of the texture is maintained, even without a rear reflector. Prog. Photovolt: Res. Appl. (2013) © 2013 John Wiley & Sons, Ltd. DOI: 10.1002/pip J. Thorstensen, S. E. Foss and J. Gjessing 2.2. Characterization After completing the texturing process, the wafers were characterized optically, measuring transmittance and reflectance of the samples. Absorption was calculated as 1 - (transmittance + reflectance). The measurements were performed using a 4-inch Labsphere integrating sphere (Labsphere, Inc., North Sutton, NH, USA) with measurement ports with a diameter of 25.4 mm, and spectrometers from OceanOptics (Ocean Optics, Inc., Dunedin, FL, USA) a two-port measurement setup with the calibration sample at one port, and the sample to be measured at the other port. Using such a setup, the response of the integrating sphere will not vary between calibration and measurement, minimizing the substitution error, which will occur in one-port measurements. During characterization, the light must be absorbed or escape through a wafer surface within the area covered by the texture or the area of the measurement port, whichever is smaller. Otherwise, the light would have a high probability of being lost from the measurements, a behavior observed as measured absorption > 0 for wavelengths where the silicon is transparent. When measuring absorption at 1200 nm, we observed loss of light when using a smaller integrating sphere with a measurement port of only 6 mm diameter. The measured absorption at 1200 nm varied from 0, as expected, using thin wafers with poor light-trapping properties, to around 40% for 300 m wafers with patch textures, indicating significant loss of light. These errors were eliminated using an integrating sphere with larger measurement ports and a size of the textured areas of 13 13 mm2 . A sputtered magnesium film showing specular reflectance was chosen as reflectivity reference sample for the measurements, and scanning electron microscopy (SEM) was performed for inspection of quality and area coverage of the textures. 3. SIMULATIONS 3.1. Optical simulations The ray-tracing software TracePro  was used to simulate the light-trapping performance of the textures. The absorption in silicon was modeled using the data by Green , together with free-carrier absorption (FCA) coefficients by Clugston , and a p-type carrier concentration of 2E16 cm–3 . Simulations were either performed with a bare silicon wafer, or with a silicon wafer covered with a double-layer anti-reflection coating (DLARC). The coating consisted of two non-absorbing layers, with thickness and refractive index of d1 = 107 nm n1 = 1.4 and d2 = 56 nm n2 = 2.3, where the higher index material is closest to the silicon. A DLARC is chosen for two reasons. Firstly, a DLARC will potentially have a larger wavelength range with low reflectivity, giving a better response in the infrared, where our analysis is most important. Secondly, we assume that a DLARC would be a reasonable choice Prog. Photovolt: Res. Appl. (2013) © 2013 John Wiley & Sons, Ltd. DOI: 10.1002/pip Light-trapping properties of patch textures created using LAST of anti-reflection coating for a high efficiency cell, which would be most suitable for the textures described herein. It should be noted that a solar cell under air would have a larger benefit from applying a DLARC than a cell in a module, and that the optimum DLARC in a module would have different d and n compared with that found for a cell in air. As one of the main goals of these experiments was to investigate the optical behavior of the textured surface after etching, we simulated non-specular reflection from the front surface. There are several ways of modeling partially diffuse scattering. With the Lambert factor, a specified fraction of the light is Lambert-scattered, whereas the rest is specularly reflected. The Phong model  assumes a diffuse reflection / cosw (˛), where a high value of w corresponds to specular reflection. In TracePro, the ABgmodel is implemented . Here, the reflection R(˛) = A/(B + sing (˛)). A/B gives the small angle roll-off value, g influences the scattering width, and A calibrates the diffuse scattered part. Scattering transmission is described in an identical manner. In both the Phong and ABg models, ˛ is the angle between specular and scattered light. It is possible to assign A in a way that ensures a value for R lower than unity, and it is possible to define one part specular reflection and one part described by the ABg model. Similarly, it is possible to define scattering or partially scattering transmitting surfaces. In the simulation program, scattering can not be introduced at the boundary between two materials without altering the fresnel reflection and transmission taking place at this boundary. Therefore, the scattering character of the surface was introduced by applying a scattering sheet near the surface. We used either completely specular transmission, or diffuse transmission with no specular part described by the ABg model, setting A to a value ensuring a total transmission of 1. 3.2. Simulations of Jsc To estimate the influence on Jsc from the textures, the simulated absorption in silicon was used as input in a PC1D model . The front reflectance in the PC1D simulations was set to 1-absorption, and 100% internal reflectance front and back was used, to ensure complete absorption Table I. Simulation parameters used for the PC1D model. Parameter Surface recombination velocity Bulk lifetime Emitter profile Emitter depth Emitter peak doping concentration Base doping Shunt resistance Series resistance Front and rear surface Value 0 1 ms erfc 0.3 m 2E19 cm–3 1.5E16 cm–3 1 0 Optically rough Light-trapping properties of patch textures created using LAST of the rest of the incident light. The rest of the simulation parameters employed are summarized in Table I. These are rather ideal parameters not normally encountered in industrial solar cells, but chosen to let the results be independent of design limitations of specific solar cell designs and to reflect the intended use in high-efficiency cell concepts. From the ray-tracing results, we obtain total absorption, meaning photons absorbed by both band-toband absorption and by FCA. The fraction absorbed by FCA will not generate current, and must, as such, be removed again in the PC1D-simulations. Therefore, FCA was included in the PC1D model, using the same formula for FCA absorption as in the ray-tracing simulations. In doing so, the same fraction of the incoming light would be absorbed by FCA in both simulations, and the same fraction would be absorbed by band-to-band absorption generating current. J. Thorstensen, S. E. Foss and J. Gjessing 4. RESULTS 4.1. Patterning The area coverage is an important figure of merit for these textures. Light hitting unprocessed areas will experience higher front surface reflectance and no light trapping, and as such will decrease the performance of the texture. Therefore, the highest possible area coverage is desirable. The size of the pyramids (and correspondingly the width of the trench in the patch pattern) is determined by the size of the laser opening through the etch barrier, which can be controlled by varying the applied laser pulse energy. The square of the ablated radius is proportional to the logarithm of the pulse energy, as described by Liu . Figure 3 shows how the inverted pyramid size increases when increasing the pulse energy. Figure 3. Inverted pyramid textures with 15 m base size with increasing laser power towards the right. Increasing the laser power increases the size of the inverted pyramid textures, thereby increasing area coverage. Figure 4. Scanning electron microscopy images of the textures, starting from the top left: inverted pyramid, patch for 100 m wafer, random pyramids and patch for 300 m wafer. Note the difference in scale of the images. Prog. Photovolt: Res. Appl. (2013) © 2013 John Wiley & Sons, Ltd. DOI: 10.1002/pip 4.2. Optical reflectance and transmittance measurements and simulations Figure 5 shows optical measurements on the reflectance, transmittance and absorption of the patch texture on a 120 m wafer. A ray-tracing model was created with a certain flat area between each of the trenches in the patch. By fitting simulation results to measured reflectance for short wavelengths, the width of this flat area was estimated to be 0.8 m, giving an area coverage of 94%. From SEM images (Figure 4), we estimate area coverage of 90–95%, which correlates well with the reflectance results. The limitation on area coverage is determined by the accuracy of the laser scanning system. In our case, it seems realistic to achieve flat areas down to 0.8 m. This number should be independent on the base size of the pattern. As such, it would be easier to achieve high area coverage for patterns with larger base size. Starting with perfect specular surfaces, correspondence between measurements and simulations at long wavelengths was improved by using diffuse reflection, as shown for the patch texture in Figure 5, indicating that the wafer Prog. Photovolt: Res. Appl. (2013) © 2013 John Wiley & Sons, Ltd. DOI: 10.1002/pip surfaces are slightly scattering. For the scattering sheet, A, B and g values of 0.0139, 0.0001 and 2.5, respectively, were chosen, giving an angular width of the scattering of around 3ı full width at half maximum. However, as the scattering was modeled with a sheet detached from the surface, all rays passed the scattering surface twice, increasing the degree of scattering. As a comparison, Kray  has performed fitting of measured reflectance spectra on front side textured wafers with polished rear and a SiO2 + silver back reflector, obtaining a scattering width of 9ı using the Phong model. This diffuse reflection also yields good correlation with measurements on the random pyramid texture shown in Figure 6, indicating that the optical quality of the surface is similar for the patch and random pyramid process. 1.0 Reflectance, Transmittance, Absorption Adjusting the size of the openings, we are able to obtain very high area coverage. Figure 4 shows results of the patterning process with high area coverage and a quite striking homogeneity in the processing results. However, when looking into the details of the etching process, a couple of interesting points should be mentioned. We observe that typically, ablated diameters of around 9 m are required for the creation of inverted pyramids of around 14 m, meaning that the size of the pyramid is substantially larger than the size of the opening, and much larger than what could be expected based on under-etching taking place in the h111i direction where the KOH etch has a low etch rate. We suspect this to be the result of primarily two mechanisms. Firstly, the removal of the SiNx is an indirect ablation process, meaning that the SiNx is blown off by the vapor pressure from the heated silicon. It is often observed after indirect ablation, that the dielectric surrounding the ablated area will be delaminated from the silicon, as shown for SiO2 in , a mechanism which will increase the area of attack of the etch. Secondly, the flanks of the Gaussian laser beam may have left a defect-rich area around the ablation area, where the etch rate will be substantially higher than in the h111i direction. The homogeneity of the processing results indicates that both the variation in the size of the openings through the etch barrier is low, and that the etch process is also very reproducible, despite the previously mentioned aspects of the pyramids being larger than the opening in the SiNx . We observe some irregularities where the pattern has collapsed in small areas. The limit to obtainable area coverage of the texture is a compromise between having wide trenches on one hand, and limiting pattern collapse as a result of underetching, on the other hand. For the random pyramid etch, we estimate close to 100% area coverage. Light-trapping properties of patch textures created using LAST 0.8 Reflectance Transmittance Absorption 0.6 0.4 0.2 0.0 400 500 600 700 800 900 1000 1100 1200 Wavelength [nm] Figure 5. Measured optical properties of 120 m-thick patch structure (solid lines) shown together with simulations using specular (dashed lines) and partially scattering (dotted lines) back surface. 1.0 Reflectance, Transmittance, Absorption J. Thorstensen, S. E. Foss and J. Gjessing 0.8 Reflectance Transmittance Absorption 0.6 0.4 0.2 0.0 400 500 600 700 800 900 1000 1100 1200 Wavelength [nm] Figure 6. Measured optical properties of 120 m-thick singlesided random pyramid structure (solid lines) shown together with simulations using partially scattering (dotted lines) back surface. Light-trapping properties of patch textures created using LAST 4.3. Simulations on textures with rear reflectors After establishing an optical model for ray-tracing, which corresponds excellently to our created textures, further optical simulations were performed, with rear reflectors applied to our textures. The results were analyzed in PC1D as described in Section 3.2. For all of these simulations, the DLARC described in Section 3.1 was applied to the ray-tracing model. Firstly, we performed simulations on patch textures with 100% area coverage, 15 m trench width, 120 m wafer thickness and a 100% rear mirror, both with specular reflections and with the degree of diffuse scattering obtained in Section 4.2. This is to see how the surface imperfections would affect a perfect pattern. The results are shown in Table II, and shows that the textures with diffuse reflection actually performed better than the ones with specular reflection, giving an increase in Jsc of 0.2 mA/cm2 . With diffuse reflections, the angular distribution of the light is increased with every reflection, which in turn may break some of the symmetries that normally lead to out-coupling of the light. Interestingly, this means that non-perfect surfaces may actually be beneficial to the light-trapping properties of these textures. We also simulated on 50 and 120 m-thick wafers the influence of going from 15 m wide trenches to 5 m wide trenches on ideal patch textures. This change will reduce the area fraction covered by the end facet of the trenches, this area fraction being 1/2m where m is the number of trenches in the patch. The change in area fraction is largest for the J. Thorstensen, S. E. Foss and J. Gjessing 50 m-thick wafers, going from 8.3% to 2.8%. Here, we observe an increase in Jsc of 0.2 mA/cm2 when going to 5 m trenches, whereas for the 120 m-thick wafers, the increase in Jsc was negligible. Furthermore, we simulated realistic structures with width of flat areas and degree of diffuse scattering as deduced from the 120 m patch textured wafers in Section 4.2, where we applied rear side mirrors with either 90% or 100% reflectance. Kray  estimates rear reflectances of between 94% and 99% on reflecting stacks of 104 nm-thick SiO2 and Al or Ag. Reflecting stacks of dielectrics and metals will be relevant, for example, for PERC  or other high efficiency solar cell designs. As such, a 90% reflecting mirror would be a low estimate for rear reflectance for relevant solar cell structures, whereas 100% reflectance would be a high estimate. For 50 m wafer thickness, both a base size of 15 m and a reduced base size of 7.5 m were simulated, both textures having flats between trenches of 0.8 m. The results of the simulations are shown in Table III. We see that for all wafer thicknesses, realistic patch textures provide an increase in Jsc as compared with that obtained using single-sided random pyramids of around 0.4 mA/cm2 using 100% reflective mirrors. This increase is reduced to around 0.3 mA/cm2 using 90% reflective mirrors, due to parasitic absorption in the rear mirror. In the case of a screen-printed Al-Back Surface Field, often encountered in current industrial solar cells, the rear reflectance is reported to be around 65%. Using parameters similar to those found by Kray , we obtain no gain in Jsc at all when applying patch textures. Table II. Short circuit densities simulated in PC1D, for textures with 100% area coverage, for investigation of diffuse versus specular scattering, and the influence of trench width. Double-layer anti-reflection coating applied. Texture 100% rear mirror [mA/cm2 ] 120 m patch, 15 m, specular, full area coverage 120 m patch, 15 m, diffuse, full area coverage 50 m patch, 5 m, diffuse, full area coverage 50 m patch, 15 m, diffuse, full area coverage 42,57 42,74 41,88 41,68 Table III. Short-circuit densities simulated in PC1D, based on simulated light-trapping performance on textures with area coverage equal to the textures created with laser-assisted texturing, and diffuse scattering as extracted in Section 4.2. Double-layer anti-reflection coating applied. Texture 300 m single sided random pyramid 300 m patch, 15 m 120 m single sided random pyramid 120 m patch, 15 m 50 m single sided random pyramid 50 m patch, 7.5 m 50 m patch, 15 m 100% rear mirror [mA/cm2 ] 90% rear mirror [mA/cm2 ] 42.99 43.42 42.20 42.62 41.13 41.58 41.50 42.43 42.72 41.42 41.68 40.12 40.37 40.31 Prog. Photovolt: Res. Appl. (2013) © 2013 John Wiley & Sons, Ltd. DOI: 10.1002/pip J. Thorstensen, S. E. Foss and J. Gjessing The slightly higher front reflectance found in the patch textures actually make the random pyramid etch better by 0.2 mA/cm2 . We see clearly that the patch texture requires a good rear reflector in order to be beneficial. 5. DISCUSSION 5.1. Comments on optical simulations We have chosen to calculate the generation profile using PC1D, rather than by the ray-tracing program. This choice is made as a result of program limitations in the raytracing program. In this article, we are concerned with light trapping at long wavelengths, where the generation profile can be assumed to be homogenous throughout the wafer. Therefore, in combination with the material properties applied in the PC1D simulations, we do not expect the exact generation profile to have any influence on the simulated differences in Jsc . It should also be noted that in the ray-tracing simulations, a base doping of 2E16 cm–3 and no emitter was used, whereas in the PC1D model, we would have contributions both from the emitter and from a base doping of 1.5E16 cm–3 . As FCA is linear in carrier concentration, and as optical absorption is weak at the wavelengths where FCA is considerable, it is possible to use the average doping concentration of the wafer as an estimate of the overall influence of FCA. This average concentration will depend on the thickness of the wafer when the emitter is kept constant. With our parameters and a 300 m-thick wafer, the average concentration is 2.8E16 cm–3 , fairly close to the parameters used for the ray-tracing simulations. The average doping concentration for a 120 m-thick wafer is 4.7E16 cm–3 . Therefore, we conducted a series of raytracing simulations for the 120 m-thick wafer using a carrier concentration of 5E16 cm–3 . The results of these simulations show slightly different values for Jsc ; however, the difference between the patch and random pyramid textures remain unchanged. 5.2. Uncertainty in optical measurements Although we obtain very good correspondence between optical measurements and simulations at long wavelengths for the random pyramid etch in Figure 6, the simulated reflectance at short wavelengths is around 0.5% lower than the measured reflectance. The observed difference could be due to calibration inaccuracies of the optical measurement system, for example, as a result of using a specular reflectance standard, instead of a diffuse one. From measurements, we estimate the absolute uncertainty of our optical measurements to be around ˙5% rel. However, these should be systematic errors, and should not be critical to our estimates on difference in simulated Jsc . The repeatability of the measurements is much higher. Prog. Photovolt: Res. Appl. (2013) © 2013 John Wiley & Sons, Ltd. DOI: 10.1002/pip Light-trapping properties of patch textures created using LAST 5.3. Simulated angular scattering width In Section 4.2, we find a width of the scattering function of around 3ı ; however, it should be noted that simulations showed that varying the diffuse scattering angular width over a quite large range had relatively small effect on the resulting reflectance and transmittance properties of the texture. This could mean that the texture is indeed quite insensitive to the quality of the optical properties of the front and back side of the wafer, which would be beneficial for similar textures created on non-polished wafers (etched wafers). 5.4. Importance of number of trenches and process considerations We observe from Table III that the potential increase in Jsc for the realistic patch textures compared with single sided random pyramid textures is rather constant with varying wafer thickness, being around 0.4 mA/cm2 with a perfect rear mirror, and around 0.3 mA/cm2 with a 90% mirror. However, for patch textures with 100% area coverage, we see that the potential for light trapping is increasing with decreasing wafer thickness, being as large as 0.8 mA/cm2 for a 100% coverage patch pattern with 5 m trench width and a perfect rear mirror on 50 m wafers. The reason why good patch textures are more difficult to produce on thinner wafers, is that such textures will require narrower trenches for lower area fraction covered by end facets, and also narrower flats between the trenches, in order to keep the area coverage high. We chose to use a constant flat area of 0.8 m between each trench, as a realistic limitation to the accuracy of a laser system similar to ours. To fully exploit the potential of the patch texture on wafers as thin as 50 m, a more accurate laser system with a smaller spot size would have to be applied. The patch texture is a texture requiring some kind of masking before the etching step, and as such is more complicated than the random pyramid etch. However, the process described herein is not the only possible manufacturing process. Two simplifications to the LAST process would be to replace the PECVD etch barrier with a sprayon barrier, saving one vacuum-step, and as discussed in , a diffractive optical element could be used to increase laser processing speed. Also, smaller spot-sizes than what was available in our setup would improve efficiency when the texture is applied to very thin ( 50 m) wafers. Alternatively, other texturing methods such as large area nano-imprint lithography  could be applied. 6. CONCLUSION Patch textures for light trapping in monocrystalline silicon solar cells have been created using LAST. Excellent correspondence between the measured light-trapping properties of these textures and ray-tracing simulations have been shown, serving as a good starting point for simulations on Light-trapping properties of patch textures created using LAST similar textures. Simulations on Jsc of these textures have been performed in the solar cell device simulator PC1D, showing an increase in Jsc when comparing the patch texture to the single sided random pyramid texture of around 0.4 mA/cm2 on 120 m thick cells with a DLARC and a 100% reflecting rear mirror. On 50 m cells with 7.5 m trenches, the increase is around 0.5 mA/cm2 in the same situation. This shows that these textures have the ability to improve Jsc in monocrystalline silicon solar cells by around 1%. Furthermore, we have seen that a small degree of scattering at the wafer surface or rear reflector may increase light-trapping performance. We have also seen that the width of the trenches used for the patch texture is critical to the performance of the textures, where smaller trench width is desirable. The area coverage of the texture should be as high as possible to minimize the front side reflectance. When removing the limitations on area coverage posed by the inaccuracies of the laser scanning system, we simulate a potential improvement in Jsc on a 50 m cell of 0.8 mA/cm2 compared with a single sided random pyramid texture. J. Thorstensen, S. E. Foss and J. Gjessing 6. 7. 8. 9. 10. ACKNOWLEDGEMENTS Thanks to Terje Finstad for discussions on etching of silicon using KOH. This work has been funded by the Research Council of Norway through the project “Thin and highly efficient silicon-based solar cells incorporating nanostructures”, NFR Project No. 181884/S10. 11. 12. REFERENCES 1. Campbell P, Green MA. Light trapping properties of pyramidally textured surfaces. Journal of Applied Physics 1987; 62: 243–249. DOI:10.1063/1. 339189 2. Campbell P, Wenham SR, Green MA. Light trapping and reflection control with tilted pyramids and grooves, In Conference Record of the Twentieth IEEE Photovoltaic Specialists Conference, Las Vegas, NV, 1988; 713–716. DOI:10.1109/PVSC.1988.105795 3. 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Nanoimprint lithography for honeycomb texturing of multicrystalline silicon, In Proceedings of SiliconPV, 2011; 648–653. Prog. Photovolt: Res. Appl. (2013) © 2013 John Wiley & Sons, Ltd. DOI: 10.1002/pip PAPER III J. Thorstensen, J. Gjessing, E. Haugan, and S. E. Foss, “2D periodic gratings by laser processing,” Energy Procedia, vol. 27, pp. 343–348, 2012. 91 Available online at www.sciencedirect.com Energy Procedia 27 (2012) 343 – 348 SiliconPV 2012, 03-05 April 2012, Leuven, Belgium 2D periodic gratings by laser processing J. Thorstensena, J. Gjessing, E. Haugan, S.E. Foss Institute for Energy Technology, Pb. 40, 2027 Kjeller, Norway Abstract As the thickness of crystalline silicon wafers for use in solar cells is reduced, transmission-related losses become increasingly important. Very thin silicon solar cells will benefit from surface structures exhibiting efficient light trapping, such as 2D periodic structures with diffractive properties. Furthermore, multicrystalline silicon solar cells will benefit from a front surface texture which exhibits lower reflectance than the standard iso-etch. In this paper, we investigate three new methods for creating such structures based on the formation of a 2D periodic template from a colloidal suspension of microspheres and subsequent laser processing and etching. Polystyrene spheres with 1 μm diameter are spin-coated onto a silicon wafer, and forms a hexagonal pattern through self-ordering. The wafer is irradiated with an ultrashort-pulse laser with sufficient power to form pits in the wafer surface below the individual polystyrene spheres, thus transferring the hexagonal pattern to the silicon wafer. The maximum obtained diameter and depth of the pits are 600 nm and 100 nm respectively. To increase the depth of the pits we deposit the self-ordering microspheres on a silicon nitride etch barrier, followed by laser irradiation for local opening of the barrier and an isotropic etch through these holes. With this approach we are able to create structures with a base diameter of 800 nm and a depth of 350 nm. These structures are found in simulations to have good light-trapping properties and the method may therefore be suitable for the fabrication of 2D photonic crystals for light-trapping in silicon solar cells. © Ltd.Selection and/or review under responsibility of the Centro de Micro ©2012 2012Published PublishedbybyElsevier Elsevier Ltd. Selection andpeer peer-review under responsibility of the scientific Análisis de Materiales, Universidad committee of the SiliconPV 2012 Autónoma conferencede Madrid. Keywords: Light trapping; photonic crystals; etching; laser processing 1. Introduction Light management in very thin silicon solar cells (<50 μm) is an important topic for several reasons. Firstly, these cells will be so thin that efficient absorption of long wavelength light will be difficult, due to a Corresponding author. Tel.: +47 63806445 fax: +47 63812905 E-mail address: [email protected] 1876-6102 © 2012 Published by Elsevier Ltd.Selection and/or peer review under responsibility of the Centro de Micro Análisis de Materiales, Universidad Autónoma de Madrid. doi:10.1016/j.egypro.2012.07.074 344 J. Thorstensen et al. / Energy Procedia 27 (2012) 343 – 348 the long absorption length at these wavelengths. To further complicate matters, the traditional approach of wet chemical etching may be unsuitable due to the relatively large structures created by these methods, and the large amount of wafer material removed in the texturing process. Furthermore, some methods for creating thin silicon wafers will produce <111> oriented wafers , which are not suitable for anisotropic KOH texturing at all. Diffractive structures for light trapping in thin silicon solar cells has received a lot of attention, due to their potential to increase the light absorption in thin solar cells. Various structures have been shown theoretically in simulations to provide good light trapping, but the production of cost effective large scale diffractive structures remains a challenge for commercial realization. Fabrication methods that have been suggested include nano-imprint lithography or hot embossing  and interference lithography . Also, methods using self-ordered spheres have been reported . Gjessing et al. [5,6] has theoretically investigated the light trapping potential of cylinders, cones, inverted pyramids and dimples in a square pattern, all of which show good light trapping potential with lattice periods in the range of 0.7 – 1 μm and a fill factor from 0.6 to max fill factor (pi/4 for non-overlapping circular structures). The optimum depth of the features is reported to be in the range of 200 - 500 nm. Structures in a triangular / hexagonal pattern were also reported to achieve similar performance as the square patterns. In this work, we seek to produce a diffractive dimple structure similar to that reported in , based on a honeycomb / hexagonal pattern of pits. Our production method is based on the deposition of self-ordering colloidal spheres on a silicon wafer. These spheres will, under correct deposition-parameters, preferentially grow hexagonal / honeycomb 2D-crystals, and they will act as microlenses when irradiated by a laser . Previous work has shown the potential for creating surface structures using such microlenses . We propose three different processes for creating the desired structures, summarized in Table 1. In the simplest form of the process, the spheres are deposited directly on the silicon wafer, followed by laser irradiation. Here, the laser irradiation itself should remove a substantial material volume, and create structures suitable for light trapping. This would be the process requiring the least number of processing steps. Another possibility is to deposit the spheres on an etch barrier, e.g. a silicon nitride (SiN x) layer, let the laser create small openings in the SiNx, and perform an isotropic etch through these openings. In this process, the etching, rather than the laser irradiation ensures material removal and the creation of the pattern. The third process which we investigate is a process where we cover a Si wafer with spheres and subsequently deposit PECVD SiNx on top of this structure. Thereafter, the spheres are removed by sonication. This process will leave openings in the SiNx etch barrier where the spheres have been in direct contact with the silicon wafer. Table 1: Summary of the process steps involved in the three processes for creating 2D periodic structures Process 1 Microsphere deposition Laser irradiation Process 2 SiNx deposition Microsphere deposition Laser irradiation Etching Process 3 Microsphere deposition SiNx deposition Microsphere removal Etching J. Thorstensen et al. / Energy Procedia 27 (2012) 343 – 348 2. Experimental The method for depositing self-organizing colloidal spheres follows the work in . A 30 % (vol) solution of 1 μm polystyrene (PS) or 800 nm silica beads was applied to a hydrophilic polished silicon wafer surface, or a silicon wafer covered in a 150 nm thick PECVD-deposited SiNx-layer. Self-assembly was achieved by spin-coating the sample at 4000 – 7000 RPM. The result was a mono-layer of polycrystalline hexagonally ordered beads covering most of the wafer. Irradiation of the samples was performed using an ultrashort-pulse laser with 3 ps pulse duration and a wavelength of 515 nm. The beam had a Gaussian spatial distribution. Single (non-overlapping) pulses were employed. For experiments with the SiNx etch barrier, isotropic etching through the openings in the barrier was performed using a hydrofluoric acid, nitric acid, acetic acid (HNA) solution. The HF concentration was varied from 1HF:40HNO3:15CH3COOH (HNA 1:40:15) to 5HF:40HNO3:15CH3COOH (HNA 5:40:15), whereby the etch rate in this range at 21 °C increased with HF content from around 300 nm/min to around 2500 nm/min. For characterization of the processing results, Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM) were used. 3. Results 3.1. Process 1: Microspheres on silicon wafer In this process the microspheres were deposited directly on silicon wafers and irradiated by laser. In the irradiation process, the microspheres are blown off the wafer along with the silicon ablated from the wafer. Any remaining microspheres were rinsed off in DI water before further characterization. SEM images revealed a hexagonal pattern of pits, corresponding to the pattern of the microspheres. The size of the pits varied with the distance from the center of the Gaussian beam as illustrated in Fig. 1a. In the center of the spot, it is clearly seen that the substrate has melted completely, destroying the hexagonal pattern, while far from the center of the spot, the pits created are rather small. In fact, at the edges of the Gaussian distribution, we routinely obtain structures with sizes below 250 nm, which is far smaller than the wavelength of the applied light, and a nice proof of the resolution obtainable using microspheres for the focusing of the light. Fig. 1b shows a close-up of an area with a laser intensity giving relatively large pits. Here, the pits have a diameter of around 600 nm, giving a lower fill factor than the optimum calculated in , but in the range where an increase in light trapping efficiency is simulated. Higher intensities lead to melting of the substrate, instead of creating ordered structures with larger pits. In the right image we observe a rim of debris around the pits. This rim has also been observed in Ref. , where an HF dip was suggested to remove the rim. We performed a 5 min, 20 % HF dip, which removed the rim, but which also degraded some of the smoothness of the processing result. The depth of the pits was investigated in an AFM, before removal of the rim. We found the depth of the pits to be around 100 nm. This is a considerable depth, but shallower than the depth suggested in . 345 346 J. Thorstensen et al. / Energy Procedia 27 (2012) 343 – 348 Fig. 1. Wafer surface after laser irradiation through microspheres.(a) The Gaussian intensity distribution, leading to melting near the center of the beam. (b) A close-up of the pits created 3.2. Process 2: Local opening of etch barrier by laser irradiation Our second approach (see Table 1) is based on depositing the PS-spheres on top of a SiNx etch barrier, using the laser to create local openings in the SiNx. Microspheres were deposited on a 150 nm thick SiNx etch barrier on a silicon wafer, and this structure was irradiated by laser, forming openings in the etch barrier and pits into the silicon. Remaining spheres were removed with sonication. Thereafter, a 15 - 30 second etch in the 1:40:15 HNA solution was performed. It was observed that, while this etch enhanced the depth of the pits in the silicon, considerable under-etching of the etch barrier was also observed, thereby limiting the available etch time before etch barrier collapse. Therefore, rather limited pit depths were obtained using this solution. A possible reason for the under-etch, could be an interface oxide layer between the silicon and the SiNx. To overcome the problem of under-etching, we increased the HFconcentration gradually to HNA 5:40:15. If the under-etch rate is limited by transport in the layer between the silicon and the SiNx, a more rapid etch would allow for deeper pits while limiting the under-etch. This is indeed what was observed, shown in Fig. 2. Shorter etches in a more HF-rich HNA solution provided deeper pits without etch barrier collapse. Fig. 2. Wafer surface after laser irradiation through etch barrier and subsequent etching, using (a) 1:40:15 HNA (b) 3:40:15 HNA J. Thorstensen et al. / Energy Procedia 27 (2012) 343 – 348 Structures similar to those shown in Fig. 2, but etched with a 5:40:15 HNA solution were also investigated using AFM for depth profiling. The results are shown in Fig 3. A depth of around 350 nm and a base diameter of around 800 nm were observed, giving nearly hemispherical pits. Fig. 3. Depth profile of wafer surface after laser irradiation through etch barrier and subsequent etching, using 5:40:15 HNA. The depth of the structures is around 350 nm and the base diameter around 800 nm 3.3. Process 3 : SiNx deposition on microspheres The third processing possibility investigated, was to deposit silica mircospheres on the silicon wafer, followed by PECVD-deposition of SiNx on top of this structure. After this deposition, the silica spheres were removed by sonication. In , this method was shown to give a shallow SiNx coverage over the majority of the wafer, while small openings remained where the spheres had been in contact with the wafer. In , a KOH etch was performed through these openings, showing that the SiN x acted as an etch barrier, and that the attack points were on the order of 100 nm. We reproduced this result using a KOH etch, however, we did not succeed in creating hemispherical structures using the HNA etch. We observed a rapid collapse of the etch barrier, and the structures created were very shallow. In  the thickness of the SiNx layer was suggested to be below 5 nm, a thickness which would rather rapidly be dissolved in our HF-containing HNA-solution. 4. Discussion We have investigated three different processes to create hemispherical dimples in silicon wafers. These processes are summarized in Table 1. Process 3 proved to have an insufficient etch barrier for the HNA etch, failing to give depth to the structures. Process 1 gave dimples in the silicon, but the dimples were too shallow for our simulated target depth. Process 2 gave close to hemispherical shapes with a depth of around 350 nm. These shapes are of a size which is simulated to give good light trapping properties. For large-area processing, Fig. 1a shows the industrial potential of this method. A high energy laser pulse would have the possibility to create thousands or even millions of pits using a single laser pulse. However, a top-hat laser beam profile would be required, in order to avoid the inhomogeneous processing resulting from the gaussian beam. A square, top-hat laser beam could be scanned over the surface of the wafer, rapidly being able to cover the whole wafer surface. A laser with a spot size of 400x400 μm and a repetition rate of 100 kHz would be able to cover a 5 inch wafer in one second. In , a method is 347 348 J. Thorstensen et al. / Energy Procedia 27 (2012) 343 – 348 presented where the microspheres, instead of being deposited on the wafer, is deposited on a transparent carrier placed above the wafer. This method could allow for re-use of the 2D template, potentially simplifying the process. 5. Conclusion We have created hexagonally ordered pits in a silicon wafer with 1 μm lattice period based on selfordered PS-spheres. When depositing the spheres directly on a silicon wafer followed by irradiation by laser, pits with a diameter and depth of 600 nm and 100 nm respectively were created. When depositing the spheres on a SiNx etch barrier, followed by laser irradiation and a subsequent isotropic etch, close to hemispherical dimples were created in the silicon, with a depth of around 350 nm and a base diameter of 800 nm. These dimensions are in a range where light trapping properties are expected. As we employ an isotropic etch, this process will be suitable for <100> and <111> monocrystalline silicon as well as for multi-crystalline silicon. Acknowledgements This work has been funded by the Research Council of Norway through the project “Thin and highly efficient silicon-based solar cells incorporating nanostructures”, NFR Project No. 181884/S10. References  F. Henley, S. Kang, Z. Liu, L. Tian, J. Wang and Y.-L. Chow, “Beam-induced wafering technology for kerf-free thin PV manufacturing”, Proceedings of the 34th IEEE Photovoltaic Specialists Conference, Philadelphia, Pennsylvania, USA, 2009, pp. 001718-001723  A. Gombert, K. Rose, A. Heinzel, W. Horbelt, C. Zanke, B. Bläsi and V. Wittwer, “Antireflective submicrometer surfacerelief gratings for solar applications”, Sol. Energy Mater. Sol. Cells 54, 333 (1998)  S. H. Zaidi, J. M. Gee and D. Ruby, Proceedings of the 28th IEEE Photovoltaic Specialists Conference, Anchorage, AK, 2000, pp. 395–398.  P. C. Tseng, M. A. Tsai, P. Yu and H. C. Kuo, “Antireflection and light trapping of subwavelength surface structures formed by colloidal lithography on thin film solar cells”, Progress in Photovoltaics: Research and Applications, 2011.  J. Gjessing, A. S. Sudbø and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” Journal of Applied Physics 110 (3), 033104, (2011)  J. Gjessing, E. S. Marstein and A. Sudbø, “2D back-side diffraction grating for improved light trapping in thin silicon solar cells.,” Optics express 18 (6), pp. 5481-95, 2010.  S. M. Huang et al., “Pulsed laser-assisted surface structuring with optical near-field enhanced effects,” Journal of Applied Physics 92 (5), p. 2495-2500, 2002.  D. Brodoceanu, L. Landström and D. Bäuerle, “Laser-induced nanopatterning of silicon with colloidal monolayers,” Applied Physics A 86 (3), pp. 313-314, 2006.  E. Haugan, H. Granlund, J. Gjessing and E. S. Marstein, “Colloidal Crystals as Templates for Light Harvesting Structures in Solar Cells,” Proceedings of the European Materials Research Society Conference, 2011, pp. 1-5.  K. Piglmayer, R. Denk and D. Baሷuerle, “Laser-induced surface patterning by means of microspheres,” Applied Physics Letters, vol. 80, no. 25, p. 4693, 2002. PAPER IV J. Thorstensen, J. Gjessing, E. S. Marstein, and S. E. Foss, “Light-trapping Properties of a Diffractive Honeycomb Structure in Silicon,” IEEE Journal of Photovoltaics, vol.3, no. 2, pp. 709 – 715, 2013. 99 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 2, APRIL 2013 709 Light-Trapping Properties of a Diffractive Honeycomb Structure in Silicon Jostein Thorstensen, Jo Gjessing, Erik Stensrud Marstein, and Sean Erik Foss Abstract—Thinner solar cells will reduce material costs, but require light trapping for efficient optical absorption. We have already reported development of a method for fabrication of diffractive structures on solar cells. In this paper, we create these structures on wafers with a thickness between 21 and 115 μm, and present measurements on the light-trapping properties of these structures. These properties are compared with those of random pyramid textures, isotropic textures, and a polished sample. We divide optical loss contributions into front-surface reflectance, escape light, and parasitic absorption in the rear reflector. We find that the light-trapping performance of our diffractive structure lies between that of the planar and the random pyramid-textured reference samples. Our processing method, however, causes virtually no thinning of the wafer, is independent of crystal orientation, and does not require seeding from, e.g., saw damage, making it well suited for application to thin silicon wafers. Index Terms—Laser processing, light trapping, optical characterization, silicon solar cells. I. BACKGROUND HOTOVOLTAIC energy is rapidly moving toward direct competitiveness with conventional energy sources, and grid parity is already reached in some locations . One way to continue this trend is to reduce silicon consumption. This can be achieved by using thinner wafers, and/or by moving to kerfless wafering technologies that are capable of delivering cells with a thickness of 20 μm or below. Such methods have been presented by several authors, being based on proton implantation , etching and layer transfer , exfoliation , or epitaxial growth . Some of these methods are currently commercially available. Thin cells also reduce the requirements on material bulk quality and allow higher open-circuit voltage Vo c . However, in such thin cells, a significant part of the sunlight P Manuscript received November 12, 2012; revised December 20, 2012 and January 7, 2013; accepted January 10, 2013. Date of publication February 1, 2013; date of current version March 18, 2013. This work was supported by the Research Council of Norway through the Project “Thin and highly efficient silicon-based solar cells incorporating nanostructures,” under Project 181884/S10, and by the Norwegian Research Centre for Solar Cell Technology under Project 193829, a Centre for Environment-friendly Energy Research cosponsored by the Norwegian Research Council and research and industry partners in Norway. J. Thorstensen and J. Gjessing are with the Department of Solar Energy, Institute for Energy Technology, Kjeller 2027, Norway, and also with the Department of Physics, University of Oslo, Blindern, Oslo 0316, Norway (e-mail: [email protected]; [email protected]). E. S. Marstein and S. E. Foss are with the Department of Solar Energy, Institute for Energy Technology, Kjeller 2027, Norway (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JPHOTOV.2013.2240563 may be lost due to insufficient absorption in the near infrared. In order to overcome this problem and avoid excessive efficiency loss, an efficient light-trapping scheme must be applied. For monocrystalline silicon with a 1 0 0 orientation, the industry standard for light-trapping structures today is the random pyramid texture, which is an excellent light-trapping texture created by anisotropic alkaline etching. However, neither for the multicrystalline silicon (mc-silicon) nor for the 1 1 1-oriented wafers typically created by proton implantation , can the random pyramid texture be applied, and one is left with the far less efficient isotropic acidic etch for surface texturing. Furthermore, both of the aforementioned texturing processes cause significant thinning of the wafer, and seeding for the textures may prove a challenge for wafers with no saw damage . These textures may as such be unsuitable for thin cells altogether. Diffractive structures are periodic structures with periodicity in the range of the wavelength of light. These structures can be optimized to trap light by tuning their dimensions such as periodicity and structure height . However, fabrication of such structures remains an obstacle for commercial use. Only a few fabrication methods for creation of diffractive structures that are suitable for thin silicon solar cells have been shown, among which are nanoimprint or interference lithography – using reactive ion etching and plasma etching. In this paper, we investigate a different route for fabrication of submircometer sized diffractive structures in thin Si wafers based on wet etching. In previous work , we present a method for fabrication of a hexagonal dimple structure suitable for a diffractive rear reflector. Using isotropic wet etching, the process is suitable both for mc-silicon and for 1 1 1 silicon. In this paper, we investigate the optical properties of these structures, deposited on silicon wafers with a thickness of 21–115 μm. For reference, we use Si wafers with random pyramids, with isotropic texture resulting from acidic etching, and a planar wafer. We quantify the optical absorption as a function of wavelength, and examine sources of loss. As schematically shown in Fig. 1, we divide the sources of loss into primary reflectance Rf , escape light Resc , and absorption in the rear mirror AAg . Free-carrier absorption (FCA) is neglected in this analysis due to the thin lowly doped substrates (1–10 Ω·cm, p-type). Absorption in the antireflection coating (ARC) is also neglected; both of these approximations are justified later. The primary reflectance consists of the light that is reflected off the front surface and, hence, does not enter the wafer. For a textured surface, some of the light may experience a second bounce off the surface, provided that the surface angles are steep enough. This will reduce front-surface reflection. Double bounces will not occur on a planar surface, and Rf 2156-3381/$31.00 © 2013 IEEE 710 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 2, APRIL 2013 Incoming Rf Resc ASi AAg A Fig. 1. Schematic figure showing the various absorption and loss mechanisms. (Not to scale.) The silicon wafer is shown in gray and the rear reflector in black. The ARC is shown in light blue at the front surface, while the dielectric spacing layer is shown in dark blue at the rear, between the wafer and the reflector. To the left, an evaporated rear reflector is shown, being conformal to the rear-side structure, while to the right, a planar, detached rear reflector is shown. Indicated absorption mechanisms are the front reflectance R f , the silicon absorption A S i , the parasitic absorption in the rear mirror A A g , and the escape light R e sc . SiNx etch barrier deposition Microsphere Micros phere deposition p Laser irradiation Openings through etch barrier Etching Finished structure (front / rear) Fig. 2. Schematic representation of the texturing process. will be higher for planar than for textured front surfaces. Escape light refers to the part of the light that has entered the wafer, but is not absorbed and escapes through the front surface. This contribution is an indication of the light-trapping properties of the texture. Finally, the rear reflector may absorb a fraction of the light that reaches the rear surface. This contribution will depend on the type of metal used, and on the geometry of the reflector. A textured metal surface will have a larger absorption than a planar rear reflector, as a result of enhanced absorption by surface plasmons . In order to investigate the optical properties closer, we shall use our texture either as a front-side texture or as a rear-side texture. II. EXPERIMENTAL DETAILS A. Texturing Process Our method to create honeycomb structures on silicon is schematically represented in Fig. 2. Details on the process may be found elsewhere , . The spheres have a diameter of 0.96 μm, close to the predicted optimum for a rear-side diffractive grating on 20-μm-thick Si wafers , . In order to be able to process the entire surface uniformly, we have applied a square top-hat intensity profile, by the insertion of a beamshaping element before the focusing lens. The size of the laser spot is approximately 150 μm × 150 μm. The texture is characterized using scanning electron microscopy (SEM). After creation of the textures, a SiNx ARC is deposited on the front surface of the wafer by plasma-enhanced chemical vapor deposition (PECVD). Our SiNx has a refractive index of 2.0 at 600 nm. We have detectable absorption in SiNx in the wavelength range below 450 nm, constituting an equivalent current loss of 0.06 mA/cm2 on a planar surface. As this is an insignificant loss, this contribution is neglected in the calculations. A 200-nm-thick PECVD-SiOx spacing layer is deposited on the rear surface. For the rear-side reflector, we apply two different silver (Ag) reflectors. The first Ag reflector is a detached planar reflector, which is evaporated onto a microscope slide and placed at the rear of the wafer. The second Ag reflector is a reflector, which is evaporated onto the rear of the wafer (onto SiOx ). This reflector will follow the shape of the wafer and spacing layer as shown in Fig. 1. For the comparison of the properties of the textures, we also prepare reference textures; random pyramid textures and isotropic-textured wafers are prepared from diamond-sawed wafers. For the reference textures, both sides are textured, whereas the diffractive honeycomb structures are single-side textured. The random pyramids are etched in a 1% (wt) KOH, 4% (wt) isopropanol solution at 78 ◦ C for 40 min. The isotropic etched samples are etched in a CP5-solution (10:5:2, HNO3: CH3COOH:HF) at 20 ◦ C for 70 and 180 s. A double-side polished wafer is also used as reference. Each of the reference structures exhibits the same SiNx ARC and SiOx spacing layer as the dimple structures. B. Optical Characterization and Calculation of Optical Losses We measure the reflectance of the samples with an integrating sphere in a center-mount configuration, i.e., with the samples inside the integrating sphere (Labsphere RTC-060-SF). Reflectance is first measured with detached rear reflectors, and then measured again after we evaporate Ag onto the rear side of the samples. Using a center-mount configuration implies that reflectance and transmittance are measured simultaneously and cannot be separated; however, we also measure the transmittance above the bandgap of Si to be in the range between 0.1% for Ag deposited on planar surfaces and between 0.3 and 0.7% for Ag deposited on dimples. As such, we ignore transmission as it is close to zero and define the spectral absorption, Am eas (λ), as unity minus the measured reflectance, i.e., 1 − Rm eas (λ). From absorption measurements, we extract the various contributions to optical losses. The method for estimation of the loss contributions is described later. For wavelengths, above the bandgap of Si (1200–1400 nm) the absorption stabilizes at plateau levels which are typically between a few percent and up toward 20%, as shown in Fig. 4. We use this plateau value to separate Ag absorption from Si absorption. Hence, we assume a constant rear reflectivity in the spectral range, where Si is sufficiently transparent for light to be transmitted to and absorbed by the Ag rear reflector, i.e., about 800–1400 nm. The measured reflectivity of evaporated Ag varies with less than 1% in this spectral range. Nevertheless, for the case of textured surfaces and thin dielectric layers where THORSTENSEN et al.: LIGHT-TRAPPING PROPERTIES OF A DIFFRACTIVE HONEYCOMB STRUCTURE IN SILICON 711 now found by AAg (λ) = Aplat Fig. 3. Absorption in a 90-μm-thick wafer with a Lambertian rear reflector with 99% reflectivity. Absorption found by ray-tracing simulations are compared with estimated absorption extracted using the method described in Section II-B. Also, the correspondence between the simulated front-side reflectance and the linearly extrapolated front-surface reflectance is shown. interference can occur, the rear-side reflectivity may vary even though the reflectivity of the rear-side material is constant, making the assumption invalid. In our case, the 200-nm SiOx buffer layer does not support any Fabry–Pérot modes above 600 nm, and we observe a flat reflectance curve above the bandgap of Si. These observations do not indicate any resonance effects in the relevant wavelength range, hence supporting our assumption. We estimate the front-side reflectance Rf (λ) by linear extrapolation of the measured reflectance at shorter wavelengths, where the contribution from rear-side reflectance is negligible. Typically, this method of extrapolation results in an overestimation of Rf (λ) and corresponding underestimation of escape light. We quantified this error to be in the range 0.1–0.2 mA/cm2 for planar surfaces by comparison with ray-tracing simulations using the software package TracePro , shown in Fig. 3 as the difference between the blue-dotted line and the red-dashed line. The discrepancy is highest for thin samples and for samples with a planar front side. We now normalize the absorption spectra by (1 − Rf (λ)) to correct for the effect of varying Rf (λ) on absorption. These normalized spectra are here marked with prime ( ) symbols, e.g., Am eas (λ). The normalized Ag plateau value Aplat is equal to the measured absorption above the bandgap wavelength of Si, λE g , i.e., Aplat = Am eas (λ > λE g ). (1) In practice, we used the mean value in the range 1250– 1300 nm to determine the plateau value, although the precise choice of this interval did not have any significant influence on our results. The escape light is the reflected light minus the front-side reflectance, i.e., (λ) = Rm Resc eas (λ) − Rf (λ). (2) To separate Ag and Si absorption, we used the escape light as a weighting function, by normalizing it with (1 − Aplat ); therefore, it ranges between 0 and 1. The Ag absorption AAg is Resc . 1 − Aplat (3) This weighting function is unity above the Si bandgap and yields an Ag absorption which is equal to the plateau value. On the other hand, when no light escapes, the sample the weighting function will be zero, and thus, Ag absorption will be zero. This assumption will underestimate the Ag absorption if the rear-side reflectivity is low, as we discuss later. In our case, the rear-side reflectivity is well above 95% for all samples, and the error is not significant. Our samples are lowly doped (1–10 Ω·cm, p-type). In a worst case scenario with a 1 Ω·cm, 100-μm-thick substrate the FCA is calculated using the model by Green  to be less than 1.5% for an optical thickness of 25 times the thickness of the substrate. FCA being small, we ignore the loss contribution from FCA. The light that is not absorbed in Ag is assumed to be Si absorption, ASi (λ): ASi (λ) = Am eas (λ) − AAg (λ). (4) To get the nonprimed absorption values, we simply multiply the primed values with (1 − Rf (λ)). The optical losses that are related to front-side reflectance, parasitic absorption, and escape light can be calculated from Rf (λ), AAg (λ), and Resc (λ). To test the procedure that is described in this section, we apply it to ray-tracing simulations. The simulations allow the extraction of wavelength-dependent Si absorption, Ag absorption, and front-side reflection. We simulate a planar structure, a structure with a Lambertian reflector with 99% reflectivity, and a double-side pyramidal structure . From reflectance curves, the Ag absorption plateau is extracted. Ag and Si absorption that is determined by the method described previously agrees well with Ag and Si absorption registered by the raytracing program for all test structures. An example is shown in Fig. 3, where the estimated and simulated Si and Ag absorption is shown, for a Lambertian rear reflector with 99% reflectivity. However, if we reduce the rear-side reflectivity the aforementioned method tends to underestimate the rear absorption. To quantify this effect, we perform the simulation with different Lambertian reflectors. For a rear-side reflectivity of 70, 90, and 99%, we see that the rear absorption is underestimated by an equivalent current of 0.75, 0.25, and 0.02 mA/cm2 , respectively. The Si absorption is overestimated with the same amount. The samples that we measure have a reflectivity closer to 99% than to 90%; therefore, the error from this approximation is small. We integrate the optical losses from 0.35 to 1.2 μm, this being a reasonable upper wavelength representing useful light for a silicon solar cell. Fig. 4 shows measured absorption, Si absorption, and the various optical losses in a 28-μm-thick sample with rear-side dimples, as extracted using the method that is described previously. We see that Rf contributes both at short and long wavelengths, whereas Resc and AAg only contribute at long wavelengths, where long optical absorption lengths allow the light to reach the rear surface and potentially to escape through the front of the wafer. 712 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 2, APRIL 2013 B. Optical Properties of the Samples Fig. 4. Optical losses for a 28-μm-thick cell with a planar front side and dimples on the rear side as found using the model described in Section II-B. The optical properties of the samples are analyzed, and the results are summarized in Fig. 6. The photogenerated current Jph is shown in Fig. 6(a). We observe that the samples with front-side structures generate more current than the rear-side structures, a difference of about 2 mA/cm2 . The samples with detached reflectors generate slightly more current than the ones with evaporated reflectors. Furthermore, we observe that the dimple structures generate more current than the planar reference, but less than the pyramidal structures. We shall analyze the contributions to this behavior in more detail. Thicker wafers absorb more light than thinner wafers, as a result of the longer absorption lengths available. This is observed in the figure as increasing Jph with increasing wafer thickness. C. Primary Reflectance In order to quantify the optical properties in terms of current density or current density loss, the spectral properties are weighted against the AM1.5 solar spectrum. From the silicon absorption ASi , we extract the photogenerated current density Jph . Correspondingly, we extract the equivalent current losses from the various loss mechanisms. From Rf , we extract the primary reflectance loss Jreﬂ , from Resc , the escape light loss Jesc , and from AAg , the loss from parasitic absorption Jparasitic . III. RESULTS A. Texturing Process Fig. 5(d) shows an SEM image of the dimple structure within a part of one laser spot. We see a fairly homogenous processing result, with defects at imperfections in the microsphere crystal. The crystal is polycrystalline, i.e., there is periodicity on a short range, but the long-range order is lacking due to relatively small crystal grain sizes. We also see the edge between two adjacent laser spots as a line to the right. Here, the intensity is high enough for removal of the microspheres, but not high enough to penetrate the SiNx etch barrier. Hence, the pattern will not form here. Some larger unprocessed areas are also observed (not shown here), where the microspheres have formed multilayer structures rather than monolayer structures. When the dimple texture is illuminated by a white-light source, a circular diffraction pattern is observed [see Fig. 5(e)]. The circular pattern is an indication that we do not have any prevailing crystal orientation, as is also obvious from the SEM image. The rainbow colors imply a wavelength dependence of the scattering angle, indicating that the structure is indeed diffractive, and not simply diffuse. This means that although the crystal grains are randomly oriented, the average neighbor to neighbor distances are well defined and are dominating the scattering properties. Fig. 5 also shows SEM images of our reference textures: (a) random pyramids; (b) 70 s isotropic etch; and (c) 180 s isotropic etch. The lines from the sawing process are clearly visible for the isotropic etches, and barely visible for the random pyramid etch. Note also how the appearance of the isotropic etch changes from the 70-s etch to the 180-s etch. Fig. 6(b) shows the primary reflectance loss Jreﬂ . It is around 2 mA/cm2 higher for the rear-side textures, i.e., the textures with a planar front surface, compared with the front-side textures, explaining the majority of the observed differences in photogenerated current. Textured front surfaces will allow for the light to experience multiple bounces at the wafer surface, increasing the transmission into the wafer. We observe that the random pyramids have a lower Jreﬂ than the dimples. The random pyramids texture has steep angles (54.7◦ ). This ensures multiple bounces for all the incident light and, hence, low primary reflectance. The dimples, on the other hand, have a lower Jreﬂ than the isotropic textures. It is important to note that the differences in Jreﬂ will be lower when the cell is encapsulated under module glass and laminate, making this contribution less dominant. Simulations that are performed by Baker–Finch et al.  show that a simulated difference in Jreﬂ of around 1.8 mA/cm2 in air is reduced to around 0.6 mA/cm2 after encapsulation. D. Escape Light The escape light increases with decreasing wafer thickness as a result of the shorter optical path lengths that are encountered in this case, as described in Section III-B. This constitutes one of the primary problems with going to thinner wafers for silicon solar cell production, and must be counterbalanced with the application of very efficient light-trapping structures. The escape light loss Jesc [see Fig. 6(c)] for the planar reference is very high, indicating the lack of light trapping in this sample. All other structures behave similarly, indicating that escape light is fairly independent of the texture applied. The scatter in the measurements on the dimples may be indicative of a slight inhomogeneity in the texture. We see that the use of front- and rear-side dimples result in the same Jesc , indicating that the light-trapping properties of the texture are similar whether the texture is on the front or rear surface. Surprisingly, the 70-s isotropic etched sample shows the lowest Jesc , while showing fairly high primary reflectance loss. This behavior is indicative of the fact that multiple front-surface bounces require quite steep front surface angles, which are not dominant for the isotropic etch, while fairly shallow rear surface angles will ensure that THORSTENSEN et al.: LIGHT-TRAPPING PROPERTIES OF A DIFFRACTIVE HONEYCOMB STRUCTURE IN SILICON 713 Fig. 5. (a) Random pyramid etch. (The pyramids are fully formed; however, the image is taken at an angle, giving the impression of somewhat truncated pyramids.) (b) 70-s isotropic and (c) 180-s isotropic etches. (d) Honeycomb dimple pattern in silicon, showing part of one laser spot. A homogenous processing result is seen, with minor defects caused by irregularities in the microsphere layer and at the edge of the laser spot. (e) Diffraction pattern from the diffractive honeycomb texture when illuminated by a white-light source. Fig. 6. Extracted optical performance of the textures. Filled symbols indicate detached rear reflector, whereas open symbols indicate evaporated rear reflector. Gray areas indicate the dominating behavior of a group of textures. Several trends are clear: rear-side textures have lower photogenerated current, mainly caused by higher primary reflectance. Evaporated reflectors cause higher parasitic absorption, especially for rear-side textures. Pyramidal structures show higher photogenerated current than the dimple structures, mainly as a result of very low primary reflectance. the light reflected from the rear surface will hit the front surface at angles outside of the escape cone of silicon. E. Parasitic Absorption We observe that all structures with detached rear reflectors show very low Jparasitic [see Fig. 6(d)]. The evaporated re- flectors, on the other hand, have higher Jparasitic , indicating a stronger coupling to the rear reflector in this case. For the case of rear dimples with evaporated reflector, we see a significant increase in Jparasitic . This trend is not as strong for nondiffractive samples, indicating that microscopic periodicity is required for increased parasitic absorption, as investigated by Springer et al. . 714 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 2, APRIL 2013 Silver is a material with high reflectivity, minimizing the impact of parasitic absorption. Using, e.g., screen-printed aluminum, which has a much lower reflectivity, would increase Jparasitic for all the structures. A screen-printed aluminum would be most detrimental to the rear-structured samples, where the interaction with the rear reflector is strongest. On the other hand, the process that was proposed by Hauser et al.  may yield a planar dielectric on microtextured surfaces, reducing Jparasitic for rear-structured samples. IV. DISCUSSION Other authors have fabricated macroscopic honeycomb structures, using laser processing or masked wet or dry etching. Such structures would also constitute a relevant reference. While direct comparison with the reported results is difficult, it is seen in the literature that deep (deeper than hemispherical) honeycombs as produced by laser drilling  or anisotropic etching  can perform comparably with random and inverted pyramidal structures on a cell level. However, hemispherical honeycombs that are based on isotropic etching ,  show much higher front-surface reflectance as a result of the relatively flat bottoms in the dimples, the reflectivity being around 18% on bare silicon at 900-nm wavelength. Our dimple structures show slightly higher reflectivity than these structures, around 21% at the same wavelength. The light-trapping properties are not possible to compare; however, our investigations show that Jesc is fairly similar for all the investigated structures with the exception of the polished sample. In a situation where random pyramid textures are unsuitable due to crystal orientation, where the wafers have no saw damage for seeding of isotropic etches, or where material removal has to be limited, other texturing methods must be found. The use of diffractive structures such as the honeycomb structure may be a good option in this situation. Microscope images (not shown here) have shown that samples with dimple structures have areas that are not textured. Such areas will naturally not contribute to light trapping or lower reflection. It is, therefore, viable that even better light trapping might be achieved by improving the monolayer fill factor. Improvement of the crystallinity of the diffractive structure may also alter the light-trapping properties. Laser damage to the wafer has been measured on other samples using similar laser parameters, where etching of 0.27 μm from the surface completely restored bulk lifetime. As such, we do not expect laser damage to be detrimental to this texture when applying ultrashort laser pulses. Furthermore, the fact that our texture is a single-sided texture may be beneficial, potentially simplifying subsequent laser processing (e.g., for local contact openings) on the planar side of the wafer  and reducing surface recombination. V. CONCLUSION We have fabricated thin silicon wafers with a diffractive structure that is based on a hexagonally ordered dimple pattern, and experimentally compared the light-trapping properties of our structures with a random pyramid texture, isotropic textures, and planar references. We see that applying the texture to the front surface is far more efficient than applying it to the rear surface, as a result of lower front reflectance combined with lower parasitic absorption. The performance of our dimple structures lies between that of the planar and random pyramid textures, being roughly similar to the 70-s isotropic etched structures. The main sources of loss compared with the random pyramid texture are front-surface reflectance, a contribution which will be significantly lower when the cell is incorporated in a module, and parasitic absorption, especially in the cases where a microstructured rear reflector is used. The main benefit of our structure is that it is suitable for very thin wafers and wafers without saw damage, and that the etching process does not cause significant thinning of the wafer. Further improvement of the performance of the texture may be obtained through higher area coverage and better crystal quality of the texture, and by improving the hemispherical shape of the dimples. ACKNOWLEDGMENT The authors gratefully acknowledge the input received from Prof. A. Sudbø (University of Oslo) in forming the contents of this paper. REFERENCES  K. Branker, M. J. M. Pathak, and J. M. Pearce, “A review of solar photovoltaic levelized cost of electricity,” Renew. Sust. Energ. Rev., vol. 15, no. 9, pp. 4470–4482, Dec. 2011.  F. Henley, S. Kang, Z. Liu, L. Tian, J. Wang, and Y.-L. Chow, “Beaminduced wafering technology for kerf-free thin PV manufacturing,” in Proc. IEEE 34th Photovolt. Spec. Conf., Philadelphia, PA, USA, 2009, pp. 001718–001723.  M. Ernst and R. Brendel, “Layer transfer of large area macroporous silicon for monocrystalline thin-film solar cells,” in Proc. IEEE 35th Photovolt. Spec. Conf., Honolulu, HI, USA, 2010, pp. 003122–003124.  R. A. Rao, L. Mathew, S. 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Stroj, “Impact of surface topography and laser pulse duration for laser ablation of solar cell front side passivating SiNx layers,” J. Appl. Phys., vol. 108, no. 11, pp. 114514-1–114514-8, 2010. Authors photographs and biographies not available at the time of publication. PAPER V J. Thorstensen and S. E. Foss, “Temperature dependent ablation threshold in silicon using ultrashort laser pulses,” Journal of Applied Physics, vol. 112, no. 10, p. 103514, 2012. 109 JOURNAL OF APPLIED PHYSICS 112, 103514 (2012) Temperature dependent ablation threshold in silicon using ultrashort laser pulses Jostein Thorstensen1,2,a) and Sean Erik Foss1 1 Institute for Energy Technology, P.O. Box 40, 2027 Kjeller, Norway University of Oslo, Department of Physics, P.O. Box 1048 Blindern, 0316 Oslo, Norway 2 (Received 26 April 2012; accepted 20 October 2012; published online 21 November 2012) We have experimentally investigated the ablation threshold in silicon as a function of temperature when applying ultrashort laser pulses at three wavelengths. By varying the temperature of a silicon substrate from room temperature to 320 C, we observe that the ablation threshold for a 3 ps pulse using a wavelength of 1030 nm drops from 0.43 J/cm2 to 0.24 J/cm2, a reduction of 43%. For a wavelength of 515 nm, the ablation threshold drops from 0.22 J/cm2 to 0.15 J/cm2, a reduction of 35%. The observed ablation threshold for pulses at 343 nm remains constant with temperature, at 0.10 J/cm2. These results indicate that substrate heating is a useful technique for lowering the ablation threshold in industrial silicon processing using ultrashort laser pulses in the IR or visible wavelength range. In order to investigate and explain the observed trends, we apply the two-temperature model, a thermodynamic model for investigation of the interaction between silicon and ultrashort laser pulses. Applying the two-temperature model implies thermal equilibrium between optical and acoustic phonons. On the time scales encountered herein, this need not be the case. However, as discussed in the article, the two-temperature model provides valuable insight into the physical processes governing the interaction between the laser light and the silicon. The simulations indicate that ablation occurs when the number density of excited electrons reaches the critical electron density, while the lattice remains well below vaporization temperature. The simulated laser fluence required to reach critical electron density is also found to be temperature dependent. The dominant contributor to increased electron density is, in the majority of the investigated cases, the linear absorption coefficient. Two-photon absorption and impact ionization also generate carriers, but to a lesser extent. As the linear absorption coefficient is temperature dependent, we find that the simulated reduction in ablation threshold with increased substrate temperature is linked to the temperature dependence of the linear absorption coefficient. Another factor influencing the ablation threshold is the wavelength dependence of the interaction with the excited electron plasma. This wavelength dependence can explain that we observe experimentally similar ablation thresholds for a wavelength of 1030 nm at 320 C and for 515 nm at room temperature, even though the linear absorption coefficient in the latter case is much higher. C 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4766380] V I. INTRODUCTION Ultrashort pulse lasers are finding their way into industrial applications as a result of their minimal thermal influence on the workpiece, and their ability to process more or less any material, including materials which are transparent at moderate optical intensities.1–3 In solar cell research and industry, ultrashort pulse lasers are of growing interest, due to the lower thermal influence and potentially higher quality process results and lower degradation of the electronic quality of the solar cell material.4–6 In this article, we experimentally and theoretically investigate the interaction between ultrashort laser pulses and silicon. When processing with laser pulses in the nanosecond range and moderate laser intensities, the laser can essentially be described as a heat source, providing a distributed energy input to the material. The material experiences a temperaa) Author to whom correspondence should be addressed. Electronic mail: [email protected] 0021-8979/2012/112(10)/103514/11/$30.00 ture rise described by the (linear) laser absorption coefficient and pulse duration, and by material parameters such as heat capacity and heat conductivity. The heat equation can be applied in order to solve for the temperature evolution in the substrate. Observable changes to the material normally occur when melting or vaporization temperatures are reached.1 With ultrashort pulses in the pico- and femtosecond range, the interaction between light and matter starts to deviate from this behavior. In semiconductors, we have to describe the laser as an energy source to the conduction band electron system (from here: electron system), raising both the temperature and the number density of this system. The laser penetration depth (or the corresponding effective absorption coefficient) becomes dependent on laser intensity through non-linear absorption and on the number density of conduction band electrons (from here: electron density) through free-carrier absorption. The electron system dissipates energy to the lattice system through collisions on a time-scale which can be comparable to, or longer than the 112, 103514-1 C 2012 American Institute of Physics V Downloaded 22 Nov 2012 to 184.108.40.206. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 103514-2 J. Thorstensen and S. E. Foss pulse duration. As a result of this, the temperature of the electron system may, during the pulse, be significantly higher than the temperature of the lattice system. In order to model the evolution of such a system, we need separate coupled heat equations for the electron and lattice systems. Bulgakova et al.7 provide an excellent review of several different approaches to the modeling of interactions between ultrashort laser pulses and dielectrics, semiconductors and metals. The more elaborate models take electron emission from the surface and electric fields within the material into account. In this work, we perform ablation from a silicon substrate using 3 ps laser pulses at wavelengths of 343, 515, and 1030 nm. The temperature of the silicon substrate is varied between 25 and 320 C, and the ablation threshold fluence is measured as a function of temperature. The ablation threshold fluence (ablation threshold) is defined as the minimum laser pulse fluence required for material removal. In order to explain the experimental results and trends, we wish to model the interaction between the laser pulse and the silicon substrate. A model often chosen for its relative simplicity is referred to as the two-temperature model, where we have separate heat equations for the electron and lattice systems. Significant work on the two temperature model has been performed, some main findings summarized by B€auerle.1 When choosing to use the two-temperature model, we are aware that this is a simplified model, leaving out a number of effects which are described in the threetemperature model or in full kinetic models. The threetemperature model divides the lattice system into optical and acoustic phonons, and energy transfer from the electrons is primarily to optical phonons, which in turn transfer the energy to the acoustic phonons. As such, the twotemperature model will give a stronger and more rapid lattice heating than if using the three-temperature model. Effects which can be described in full kinetic models, such as incomplete thermalization of electrons and drift in electric fields and phenomena related to the elastic stress of the silicon crystal are also left out of our model. Nevertheless, we believe that we can extract much information about the physics of our experiments with the comparatively less elaborate two-temperature model. Sim et al.8 present a theoretical study on the two- and three-temperature models in silicon, while Mao et al.9 apply a two-temperature model with electron emission. Christensen et al.10 apply a twotemperature model for metals. We vary the simulated substrate temperature, and extract information about the dynamics of the ablation process. J. Appl. Phys. 112, 103514 (2012) II. EXPERIMENTS We have performed experiments investigating the temperature dependence of the ablation threshold of an 80 nm thick layer of amorphous silicon nitride (SiNx) with an index of refraction of n ¼ 2.1, deposited by plasma-enhanced chemical vapor deposition (PECVD) at 400 C, on a silicon wafer. In these experiments, the SiNx, a dielectric commonly investigated for thin film ablation, plays a passive role, and is only included in order to make the ablation more easily visible. The SiNx will be lifted off in the areas where the Si experiences ablation. We apply pulses with pulse duration of 3 ps, a repetition rate of 1 kHz and three wavelengths, namely 343, 515, and 1030 nm to the silicon wafer. An xy-table translates the wafer, ensuring a spatial separation of the pulses of 100 lm. The 1/e2 diameters of the Gaussian intensity profile of the pulses are approximately 10, 30, and 44 lm at 343, 515, and 1030 nm, respectively. A to-scale illustration of the irradiation geometry is shown in Fig. 1. We see that the SiNx film thickness and the laser penetration depth are both much smaller than the spot radius. We apply several different intensities per wavelength and temperature, and apply the method of Liu,11 where the relation between ablated radius and pulse energy is used in order to accurately determine the ablation threshold fluence and beam diameter, 2 rabl c2 F0 c2 2E ln ¼ ln ¼ lnðFth Þ : pc2 2 Fth 2 (1) Here, rabl is the ablated radius, c is the beam diameter at 1/e2 fluence level, F0 and Fth are the peak fluence of the laser pulse and the ablation threshold fluence, respectively. The right hand side expression contains only the ablated radius and pulse energy E, which both can be measured, and the unknown quantities, namely ablation threshold and beam diameter. We have measured the wavelength-dependent reflectance of our samples, and subtract the reflected light from our reported ablation thresholds so that we are only looking at the light entering the silicon. The temperature of the silicon wafer was varied by placing the wafer on a heating plate in ambient air. The temperature was recorded both at the heating plate and at the surface of the silicon wafer, both measured using a thermocouple. The discrepancy between these measurements indicates imperfect thermal contact in our setup. The temperature recorded at the silicon surface is taken as the sample temperature, while the temperature of the heating plate is taken as an upper boundary. FIG. 1. Left: The irradiation geometry. The silicon wafer (grey) is covered with a thin silicon nitride (SiNx) layer (blue) which is removed by a laser pulse (green). SiNx film thickness and laser penetration depth are both small compared to the laser spot radius. Right: Microscope image of an ablated spot, showing the contrast between silicon (light blue) and surrounding SiNx (dark blue). Downloaded 22 Nov 2012 to 220.127.116.11. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 103514-3 J. Thorstensen and S. E. Foss J. Appl. Phys. 112, 103514 (2012) FIG. 2. Experimental data for determination of ablation threshold (left) (before subtracting reflectance). Ablation threshold for silicon at 343, 515, and 1030 nm, 3 ps pulse duration (right). III. EXPERIMENTAL RESULTS The reflectance is measured at low light intensity using a broadband light source consisting of a deuterium and a tungsten halogen lamp, at an incidence angle of 8 in a spectrometer-based integrating sphere setup. The reflection coefficients measured are 0.60, 0.17, and 0.16 at 343, 515, and 1030 nm, respectively. At high optical intensities, however, the reflection coefficient will change from its low intensity value, due to the influence on dielectric constants from the large number density of excited electrons as will be discussed in Sec. IV B. In an experiment, we have monitored reflected power as function of incident power as we irradiate our samples using our laser at wavelengths 515 nm and 1030 nm using the laser parameters described in Sec. II, at 15 incidence angle, thereby measuring the time-averaged reflectance from our sample. The wafer was moved using the xy-table, ensuring non-overlapping laser spots, as described in Sec. II. At intensities below the observed ablation threshold, we observe a decrease in reflectance by 2% absolute (12% relative). The observed variation, however, is on the order of the inaccuracy of our reflectance measurements. Increasing the incident power beyond the ablation threshold, the reflectance rises steadily by up to 70% relative at laser intensities much higher than the ablation threshold. A decrease in reflectance can be expected at electron densities approaching the critical electron density,12 followed by a sharp increase in reflectance when the critical electron density is reached (Fig. 3). The observed increase in average reflectivity indicates that the critical electron density is encountered earlier in the pulse with increasing laser fluence. However, near the ablation threshold, critical electron density is encountered late in the pulse. For the fluence range discussed herein, the reflectance remains at the low intensity value, or is in fact lowered somewhat, and we therefore approximate the reflectance to be constant at the low intensity value. An example of the data for extraction of the ablation threshold is shown in Fig. 2 (left), along with the measured ablation thresholds at 343, 515, and 1030 nm at temperatures from room temperature to 320 C (right). Well-defined ablation spots are observed, and we estimate an uncertainty in the measured ablation threshold of 620%, based on uncertainty in measured ablated diameter and deviation from the trend in Eq. (1) and the uncertainty of the power meter. The ablation threshold at 515 and 1030 nm decreases with increasing substrate temperature, while it remains constant at 343 nm. IV. SIMULATION MODEL In order to investigate the physics behind the experimental results, simulations are performed, using the before mentioned two-temperature model. The two-temperature model is a tool for modeling a situation with different temperature in the electron and lattice systems. One assumption of the model is that the electrons reach a thermal distribution on a time-scale which is short compared to the pulse duration. The electron thermalization time is reported to be around 10 fs,8 meaning that this criterion is well fulfilled in our case. The two-temperature model can mathematically be written as a set of coupled differential equations. In order to reduce the required equations to containing only one spatial variable, we shall make the approximation that the incoming laser power is uniformly distributed over the silicon surface, i.e., the laser spot is homogeneous and infinitely large. As FIG. 3. Theoretical free carrier absorption coefficient (left) and reflection coefficient (right) as functions of carrier density, for three wavelengths. Downloaded 22 Nov 2012 to 18.104.22.168. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 103514-4 J. Thorstensen and S. E. Foss J. Appl. Phys. 112, 103514 (2012) shown in Fig. 1, the laser penetration depth is smaller than the spot radius by at least an order of magnitude, making the approximation reasonable. Following Sim et al.,8 adding diffusion of carriers,13 we write the equations @Ue @ @Te @ @N 3Nkb ¼ þ ke Eg D0 ðTe Tl Þ @t @x sel @x @x @x þ qtot ; @Ul @Tl @ @Tl ¼ Cl ¼ kl @t @t @x @x (2) 3Nkb þ ðTe Tl Þ; sel X an I n @N @ @N ¼ D0 c0 N 3 þ dN þ : @t @x @x nhx qtot ¼ atot I ¼ dI X n ¼ an I þ hNI ’ aI þ bI2 þ hNI; dx (5) where I is the optical intensity. As the intensity at a depth x is depending on the absorption between the surface and the position x, we need to express the intensity as an integral equation. We integrate Eq. (5) to obtain ð x X 0 n1 0 þ hNðt; x Þ dx0 : an Iðt; x Þ Iðt; xÞ ¼ I0 ðtÞ exp 0 (6) (3) (4) The meaning and value of all parameters are tabulated in Tables I and II. Equations (2) and (3) are heat/diffusion equations with the temporal change in energy being balanced by diffusion terms and source terms. Equation (2) describes the energy in the conduction band electron system and Eq. (3) the energy in the lattice system. Equation (4) is a continuity equation for the number density of conduction band electrons. qtot is a collective source term covering all laser absorption mechanisms. For the case of silicon and wavelengths between 343 and 1030 nm, we only consider linear and two-photon band-to-band absorption, along with free carrier absorption (FCA), and we can write qtot as1 In this equation, we have ignored the time delay experienced by the pulse as it travels through the workpiece. Note that I0(t) ¼ I(t,x ¼ 0) is the intensity of the laser pulse entering the silicon surface, equal to the incoming intensity minus the reflected intensity. Going a bit more into the details of Eqs. (2)–(6), we see that linear and non-linear band-to-band absorption mechanisms, along with free-carrier absorption, increase the energy stored in the electron system. Linear and non-linear band-toband absorption introduces energy as both potential energy (increase of number density of electrons) and kinetic energy (electron system temperature). Free-carrier absorption only introduces kinetic energy. Auger and impact ionization processes do not contribute to the overall energy of the electron system, but transfer energy to kinetic energy and potential energy (number density of electrons), respectively. Kinetic TABLE I. Explanation of symbols encountered in the equations for the two-temperature model. Symbol Parameter Ue N kb Te ke se-l Electron system thermal energy Number density of electrons Boltzmann constant Electron temperature Electron heat conductivity Electron-lattice coupling time Ncr_sh an h Shielding electron density n-th order absorption coefficient Free-carrier absorption coefficient Ul Tl Cl kl Lattice system thermal energy Lattice temperature Lattice heat capacity Lattice heat conductivity D0 c0 N3 Electron diffusivity Screened Auger recombination c tmin d Auger coefficient Minimum Auger lifetime Impact ionization coefficient Eg Ncr Band gap in silicon Critical electron density Value Unit Reference 3Nkb Te J/m3 1/m3 J/K K W/(K m) s 25 15 6 1026 see Table II see Table II 1/m3 15 Cl T l J/m3 K J/(m3 K) W/(K m) 26 26 1:38 1023 0:556 þ 7:13 103 Te 2 240 1015 1 þ NcrN sh 2:2368 106 ð300 K < Tl < 1683 KÞ 1:521 105 Tl1:226 ð300 K < Tl < 1200 KÞ 896 Tl0:502 ð1200 K < Tl < 1683 KÞ 2:98 107 Te N= cN1 2 þ tmin m2/s 7 7, 20 3:8 1043 6 1012 m6/s s 1/s 13 7, 20 23 J 1/m3 1, 14 1:0 1011 ðUe Eg Þ4:6 (energies in eV) 1:86 1019 6:2 1027 (343 nm) 2:7 1027 (515 nm) 6:9 1026 (1030 nm) Downloaded 22 Nov 2012 to 22.214.171.124. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 103514-5 J. Thorstensen and S. E. Foss J. Appl. Phys. 112, 103514 (2012) TABLE II. Optical constants in silicon for three different wavelengths. Symbol 1030 nm (measured at 1064 nm) a1 ¼ a 5895 þ 62:26Tl 0:2309Tl2 þ3:186 104 Tl3 þ 9:967 108 Tl4 1:409 1011 Tl5 a2 ¼ b h 1:5 1011 Tl 5 1022 300 515 nm 343 nm Unit Reference Tl 5:02 105 exp 430 1:09 108 1/m 26, 27 0 m/W m2 28 and 29 28 1:8 1012 Tl 1:2 1022 300 energy loss from the electron system also occurs through the electron-lattice coupling term. Radiative and ShockleyRead-Hall recombination mechanisms take place over much longer time scales than our pulses and are therefore neglected in our simulations. We use a partial differential equation solver with one spatial dimension in order to solve the three coupled equations (2)–(4) and the equation for optical intensity (6). We simulate Gaussian laser pulses centred at t ¼ 0 and a pulse duration of 3 ps (FWHM), for irradiation wavelengths of 343, 515, and 1030 nm. We take the intrinsic doping level (carrier density) to be 1016 1/cm3. The pulse fluence is increased in steps of 3% until one of the criteria for ablation is reached. A. Ablation threshold in simulations There are two possible mechanisms causing ablation when a sample is irradiated by a laser pulse. The first mechanism is the “thermal ablation,” which occurs if the lattice reaches vaporization temperature. This mechanism is typical when applying long laser pulses. The second, “non-thermal ablation” is typical for short pulses, and occurs if the number density of conduction band electrons reaches a critical density, suggested to be 2:7 1021 1/cm3 for irradiation at 532 nm.14 Details on the physics in such a dense plasma are described by a free-electron gas, summarized in Sec. IV C. The mechanism signifying ablation in our simulations is the mechanism which reaches ablation threshold first. B. Comments on the parameters In Tables I and II, we have stated values for several material properties of silicon. For many of these parameters, several groups report values which differ significantly. We have used an electron-lattice coupling time of 240 ð1 þ ðN=Ncr Þ2 Þ fs,15 based on experiments on silicon. However, several articles16,17 make use of much longer coupling times of around 1–10 ps, based on work by van Driel13 and measurements on GaAs,18 which we expect to be less representative for our case. The three-temperature model described by Sim et al.8 uses values from a general statement in the book by Tien et al.19 that electron–optical phonon coupling is on the order of 100 fs, while the optical phononacoustic phonon coupling time is on the order of 10 ps for “most semiconductors.” Auger recombination at high electron densities is also subject to uncertainty. Yoffa20 predicts theoretically a minimum value for the Auger lifetime of 6 ps as a result of 5:4 1023 Tl 300 Coulomb-screening. On the other hand, experimental work21 indicates Auger lifetimes down to and below 1 ps without deviation from the N2 trend for Auger lifetime. Here, polycrystalline silicon was used, however, with properties close to those of crystalline silicon. For the electron diffusivity, we have used 2:98 107 Te (m2/s),7 while van Driel13 uses 18 103 ð300=Tl Þ (m2/s). The impact ionization coefficient has generally only been simulated, and the values reported vary strongly. Examples are 3:61010 expð1:5Eg =ðkB Te ÞÞ(1/s),13 1011 ððUe 1:2Þ=1:2Þ2 (1/s),22 and 1011 ðUe Eg Þ4:6 (1/s) (with Ue and Eg in eV).23 For the 1030 nm wavelength, we have used values for the linear absorption coefficient based on measurements at 1064 nm. The temperatures encountered in our simulations are higher than those reported in the measurements (up to 200 C); however, other work24 indicates that the extrapolation is valid also to temperatures up to around 850 C. At 515 and 343 nm, the temperature dependence is based on measurements up to 700 C. Generally, where we have found several different values for parameters, we have used the newest values available, or the ones where the simulations or experiments most closely resemble our experimental conditions. It is important to be aware of the large discrepancies in reported experimental values for some of the parameters used in these simulations. This represents a significant source of uncertainty in our simulation results. C. Free-electron gas Many excellent books review the Drude free-electron theory. Briefly summarized, a free-electron gas will have a dielectric response according to30,31 ! ~ 2p ~ 2p c x bg x 0 00 ; (7) þ i ¼ þ i ¼ bg 1 2 xðx2 þ c2 Þ x þ c2 n þ ik ¼ pﬃﬃ ; (8) where bg is the background relative permittivity of the 2 ~ 2p ¼ bgNe silicon material without free carriers. We define x 0 mef f as the plasma frequency with a dielectric background, c is the reciprocal collision time, mef f is the effective electron mass, and x is the frequency of the applied electric field. With c x, the real part of the dielectric coefficient equals ~ p ¼ x. k is an expression for the attenuation zero when x Downloaded 22 Nov 2012 to 126.96.36.199. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 103514-6 J. Thorstensen and S. E. Foss J. Appl. Phys. 112, 103514 (2012) caused by free carriers, that is the free carrier absorption. Dividing this expression by N gives the free-carrier absorption coefficient. In some limiting cases, the expression can be simplified, some results are given here. For the case ~ p ; cÞ x, the expression (7) simplifies to ðx ! ~ 2p c x 0 00 (9) ¼ þ i ¼ bg 1 þ i 3 ; x ! ~ 2p c x pﬃﬃﬃﬃﬃﬃ n þ ik ¼ bg 1 þ i 3 ; 2x (10) V. ANALYSIS OF SIMULATIONS which yields af ca pﬃﬃﬃﬃﬃﬃ 2 pﬃﬃﬃﬃﬃﬃ 2 ~ pc ~ pc 2 bg x bg x 2xk ¼ ¼ ¼ hN ¼ k 2 2 c x c 4p c3 e2 c 2 ¼ 2 pﬃﬃﬃﬃﬃﬃ Nk : 4p 0 mef f bg (11) For our case, this corresponds to the situation with low electron densities and small values of k, and this is the wellknown k2 behavior of the FCA. We also see that FCA is proportional to N, meaning that h is constant with N. However, ~ p to the point an increase in N will eventually increase x where it is approaching x, and the absorption will deviate from the low electron density limit, meaning that the approximations in Eqs. (9)–(11) will no longer hold. Fig. 3 (left) shows the FCA coefficient in silicon, based on the expressions (7) and (8) and values in Tables I and II, plotted as a function of N, for wavelengths of 343, 515, and 1030 nm. It ~ p approaches x, will see a dramatic is clear that we, when x increase in FCA, as a result of the sharply increasing FCAcoefficient, leading to the formation of a highly absorbing electron gas near the surface of the substrate. This gas will reach very high electron temperatures and temperature gradients. These gradients are suggested17 to be the driving force for lattice expansion, resulting in lattice stress to the point of material fracture. We take this as the physical mechanism behind the “non-thermal ablation,” and we therefore ~ p ¼ xÞ. This gives define Ncr as Ncr ¼ Nðx Ncr ¼ x2 bg 0 mef f / 1=k2 : e2 ~ p approaches x, n and k will devitered herein. Also, when x ate significantly from the low electron density value, as the contributions from the free electron gas grow. As the reflection is dependent on , the reflectance of the sample will change during the pulse. Fig. 3 shows the reflectance as function of carrier density. However, as explained in Sec. III, the reflectance will start changing late in the pulse at fluencies close to the ablation threshold, giving only a minor change in the average reflectance. Hence, the reflectance change is omitted in the simulations. (12) Based on the findings in Eqs. (11) and (12), we extrapolate reported values for Ncr14 and h28 to the wavelengths encoun- From our simulations, we extract the electron generating dynamics and the temperature evolution of our sample. Fig. 4 (left) shows contributions to the electron density from the individual carrier generating mechanisms, and we see that the critical electron density of 6:9 1020 1/cm3 is reached towards the end of the pulse. The right figure shows the temperature in the lattice and electron systems at the surface of the sample. We clearly see that the electron system is much hotter than the lattice system during the pulse, and that equilibrium is reached shortly after the pulse. The lattice temperature stays below 1000 K, well below melting temperature. Hence, ablation is non-thermal, and follows from reaching Ncr. This behavior is seen for all of our simulations. As the electron density clearly plays a crucial role, we investigate the electron density created by the various mechanisms. In silicon, carriers are generated through linear and two-photon absorption and from impact ionization, while carriers are removed through Auger recombination. A. Substrate at 27 C The simulations show that, at 343 and 515 nm, linear absorption is the dominant electron generating mechanism. At 1030 nm, however, two-photon absorption accounts for over half of the generated electrons, closely followed by linear absorption. The modeled electron density for 1030 nm, 27 C, 3 ps pulse duration, and a pulse fluence of 0.58 J/cm2 is shown in Fig. 4 (left). It is interesting to observe that the two-photon absorption is centered on the peak of the pulse, while the linear absorption is clearly shifted towards the end of the pulse as a result of the temperature dependence of the linear absorption coefficient. This is more clearly seen in Fig. 5. Significant electron densities are created even during the very weak leading flanks of the Gaussian pulse. Impact FIG. 4. Simulated contributions to the cumulative generated electron number density (1/cm3) from the various electron generating mechanisms (left) and lattice and electron temperatures (right) at the surface (z ¼ 0) for 1030 nm excitation wavelength, pulse fluence 0.58 J/cm2, 3 ps pulse duration (centered at t ¼ 0) and 27 C. Linear absorption and twophoton absorption are the main electron generating mechanisms. Downloaded 22 Nov 2012 to 188.8.131.52. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 103514-7 J. Thorstensen and S. E. Foss J. Appl. Phys. 112, 103514 (2012) B. Varying substrate temperature, absorption mechanisms FIG. 5. Simulated power density deposition (W/cm3) at the surface (z ¼ 0); 1030 nm excitation wavelength, pulse fluence 0.58 J/cm2, 3 ps pulse duration (centered at t ¼ 0), 27 C. Free-carrier absorption is the dominating absorption mechanism. For Auger and impact ionization, the power corresponds to the energy shifted between potential and kinetic electron energy. ionization contributes with around 5% of the total number density of generated electrons. As Auger recombination is a strong function of electron density, its influence is strongest late in the pulse and after the pulse. (Auger recombination is of course not a source of electrons, but rather a sink for electrons, and should therefore be interpreted as having a negative sign.) Also shown in Fig. 4 (right) is the temperature evolution in the electron and lattice systems at the surface of the wafer, shown for the same pulse. The electron system is much hotter than the lattice system during the pulse, and that equilibrium is reached shortly after the pulse. The lattice temperature stays below melting temperature during the simulations. We now increase the substrate temperature, by varying the initial and boundary conditions in our differential equations, and observe how the simulated ablation threshold changes. The simulated ablation threshold and absorption coefficient in silicon are shown in Fig. 6. We see that the linear absorption coefficient at 515 nm and 1030 nm increases with increasing temperature. As absorption in indirect band-gap semiconductors is dependent on phonon assistance, the absorption coefficient increases with increasing temperature and phonon abundance. Simulations have shown32 that the acoustic phonons are responsible for the temperature dependence of the linear absorption coefficient. At 343 nm, however, direct transitions are allowed in silicon, and no temperature dependence is observed,27 as no phonon assistance is required for direct transitions. At 343 nm, linear absorption is very strong, rendering all other contributions to absorption negligible. As a result of this combined with the temperature independence of the linear absorption at this wavelength, the simulated ablation threshold remains constant with varying temperature. At 515 nm, linear absorption is the dominating absorption mechanism at room temperature, and due to its exponential increase with temperature, linear absorption is even more dominant at higher temperatures. This is shown in Fig. 7. The simulated reduction in ablation threshold is attributed to the stronger linear absorption. At 1030 nm and 27 C, two-photon absorption is the dominant carrier generating mechanism as shown in Fig. 4. FIG. 6. (Left) Simulated ablation threshold for 3 ps pulses. (Right) The linear absorption coefficient for the three wavelengths as a function of temperature. FIG. 7. Simulated cumulative generated electron number density (1/cm3) at the surface (z ¼ 0) for 3 ps pulse at 515 nm. Temperature and pulse fluence are 27 C and 0.14 J/cm2 (left) and 827 C and 0.026 J/cm2 (right), respectively. Linear absorption is dominant in both cases. Two-photon absorption and impact ionization are more suppressed at higher substrate temperatures. Downloaded 22 Nov 2012 to 184.108.40.206. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 103514-8 J. Thorstensen and S. E. Foss J. Appl. Phys. 112, 103514 (2012) However, this changes already at the next simulated temperature, 127 C (400 K). From this temperature and upwards, linear absorption is the dominant mechanism, and the reduction in ablation threshold can be attributed to the increasing linear absorption coefficient. C. Impact ionization and free-carrier absorption When working with ultrashort pulses, non-linear interactions are expected, as a result of the high optical intensities and high electron densities encountered. During a 3 ps pulse in silicon, however, our simulations show that the main contributor to the increased electron density is linear absorption. We would like to examine impact ionization and free-carrier absorption closer. IR-pulses at room temperature experience the weakest linear absorption of our pulses. Under these conditions, the main energy absorption mechanism is actually free-carrier absorption, which at the surface of the wafer absorbs around 10 times as much energy as linear and two-photon absorption combined (Fig. 5). According to our simulations, the vast majority of the excess electron energy caused by FCA is transferred to the lattice through the electron-lattice coupling, which operates with a time constant of 240 fs in silicon.15 As such, FCA contributes only indirectly to the ablation, by raising the lattice temperature and thereby raising the temperature dependent linear absorption. The only mechanism which could potentially transform electron kinetic energy into electron-hole pairs directly, namely impact ionization, is a too weak process to have any significant contribution. D. Varying electron-lattice coupling The time constant of electron-lattice coupling is of great importance to the simulation results. As stated earlier, this constant is somewhat uncertain, and we have also chosen not to include the additional thermal delay between optical and acoustic phonons presented in the three-temperature model. We therefore wish to investigate the influence of an increased electron-lattice coupling time, as this could give results more similar to those obtained with the threetemperature model. In the three-temperature model, the temperature in the acoustic phonon system will remain lower, as the coupling time between optical and acoustic phonons is long.19 The acoustic phonon temperature is the driving mechanism for the temperature dependent linear absorption coefficient in silicon,32 and as such, longer time for the energy to reach the acoustic phonon modes would decrease the linear absorption experienced in the pulses. In our simulations, we increase the coupling time to 1 ð1 þ ðN=Ncr Þ2 Þ ps. This will increase the temperature in the electron system, which in turn will promote stronger impact ionization. On the other hand, the lattice will remain cooler, decreasing the linear absorption. These two mechanisms result in a lower ablation threshold at 1030 nm, as the increased impact ionization outweighs the reduced linear absorption. At room temperature, the ablation threshold decreases from 0.58 J/cm2 to 0.46 J/cm2. As shown in Fig. 8, we observe that linear absorption dominates the electron generation in the beginning of the pulse, two-photon absorp- FIG. 8. Simulated cumulative generated electron number density (1/cm3) at the surface (z ¼ 0) for 1030 nm excitation wavelength, pulse fluence 0.46 J/cm2, 3 ps pulse duration (centred at t ¼ 0). Electron-lattice coupling time is 1 ð1 þ ðN=Ncr Þ2 Þ ps. Linear absorption, two-photon absorption, and impact ionization all dominate at different times during the pulse. Impact ionization is the most important electron generating mechanism. tion dominates towards the peak of the pulse, while impact ionization dominates towards the end of the pulse, generating twice the number density of electrons compared with twophoton absorption. Contrary to this, the ablation threshold increases somewhat at 515 nm, because the reduced linear absorption is more important compared to contributions from impact ionization in this case. At 343 nm, linear absorption is dominant and not temperature dependent, and the ablation threshold therefore remains unchanged with varying electron-lattice coupling time. E. Auger recombination As stated above, also the Auger recombination rate is subject to discussion. Experimental results21 suggest that there is no screening of the Auger recombination down to 1 ps. Therefore, we remove the lower bound on the Auger lifetime and repeat the simulations. As seen in Fig. 9, the simulated ablation threshold remains essentially unchanged at 1030 nm, while a substantial increase is observed for 343 and 515 nm. This is as expected due to the higher electron densities encountered using shorter wavelengths giving a FIG. 9. Simulated ablation threshold with Auger lifetime limited to 6 ps (line þ symbol), and with the limit removed (line). A substantial increase in simulated ablation threshold is observed for 343 and 515 nm. Downloaded 22 Nov 2012 to 220.127.116.11. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 103514-9 J. Thorstensen and S. E. Foss J. Appl. Phys. 112, 103514 (2012) We take the experimental results as an indication that FCA and Ncr are indeed wavelength-dependent quantities, and that the ablation mechanism is indeed linked to the high electron densities encountered during the pulses. VII. DISCUSSION FIG. 10. Ablation threshold fluence for silicon at 343, 515, and 1030 nm (3 ps pulse duration). Symbols: Experimental values. Lines: Simulated ablation threshold using un-screened Auger recombination. larger discrepancy between the screened and the un-screened Auger recombination rates. We also observe, however, that the temperature dependencies remain essentially unchanged. VI. COMPARING EXPERIMENTAL RESULTS AND SIMULATIONS The measured ablation threshold at 343, 515, and 1030 nm at temperatures from room temperature to 320 C is shown in Fig. 10, along with the simulation results using unscreened Auger recombination. Although there are discrepancies between simulations and experiments, the temperature dependencies of the ablation threshold are reproduced in simulations. An interesting point to note is that the experimentally observed ablation threshold at 1030 nm and 320 C substrate temperature is similar to the experimentally observed ablation threshold at 515 nm at room temperature. We will discuss this in more detail. In simulations, we have identified the linear absorption as the most important absorption mechanism for all wavelengths at elevated temperatures. However, looking at the linear absorption coefficients, these are 104 1/cm and 3 102 1/cm for 515 nm at room temperature and 1030 nm at 320 C, respectively. This means that despite the fact that the laser pulse at 515 nm experiences a 35 times stronger absorption, the ablation thresholds are similar. In a linearly absorbing material where the ablation mechanism is vaporization, e.g., using pulses in the ns-range, pulses with such strong differences in absorption coefficient would certainly not see a similar ablation threshold. This effect must be related to the fact that we are applying ultrashort laser pulses. From our simulations, we can explain this result by two factors. First, the k2-dependence of the freecarrier absorption leads to stronger lattice heating at 1030 nm, resulting in a stronger temperature driven increase in absorption coefficient at 1030 nm. Second, and most importantly, the 1/k2-dependence of Ncr reduces the critical electron density at 1030 nm by a factor of 4 compared to that at 515 nm and hence reduces the required electron generation. To further verify this, simulations were performed where 515 and 1030 nm had the same Ncr. In these simulations, the ablation threshold at 515 nm was always lower than for 1030 nm as expected from the argumentation above. The temperature dependence of the linear absorption coefficient plays a crucial role for the dynamics of absorption. With pulses at 1030 nm, linear absorption is dominant except at room temperature, and two-photon absorption and impact ionization are of minor importance. However, if the electronlattice coupling is slower than assumed in this article, as would be the case if implementing the three-temperature model, impact ionization would be a significant contributor to electron density for the case of irradiation at 1030 nm. When choosing the two-temperature model, we are aware of the implied simplifications; however, more elaborate models would require an even larger number of uncertain material parameters. Already by applying the twotemperature model, many of the parameters used in our simulations are not easily accessible experimentally. The impact ionization coefficient, free-carrier absorption cross section, electron-lattice coupling, and several other parameters which need to be applied far from equilibrium situations have a significant influence on the simulation results. A shift in some of these material parameters may yield different electron generating dynamics and different ablation thresholds. We have presented in tables the values for these parameters that we have chosen to use in our simulations. We have motivated our choices in the main text. And in the main text, we have discussed how sensitive our main conclusions are to deviations in the parameters from the chosen values. There are several other quantifiable factors contributing to uncertainty in the comparison between experiments and simulations. The pulse duration can be measured with 10% accuracy. Simulating the ablation threshold using pulse duration of 3 ps 6 10% gives a variation in ablation threshold of up to 5%. The ablation threshold is determined to within 3% in the simulations, also contributing to discrepancy. The heat capacity in the simulations is taken as constant. Simulations with temperature varying heat capacity showed a discrepancy of 3%. In the simulations, we used the low intensity value for the reflectance. Measurements showed that the reflectance may vary by around 2% from the low intensity value for the fluencies encountered herein. Most of these error contributions can be assumed to be systematic (pulse duration, heat capacity, and reflectance), while the determination of ablation threshold poses a random error. As such, linear summation should be representative, giving a total error contribution of about 10%. The simulated ablation thresholds deviate from the experimentally observed ablation thresholds by 60%, 43%, and þ37% for 343, 515, and 1030 nm, respectively, when using screened Auger recombination. As we see, the underestimation grows with decreasing wavelength. Two mechanisms could contribute towards this behavior. As already shown, by applying un-screened Auger recombination, most of the under-estimation is removed, and simulation results are Downloaded 22 Nov 2012 to 18.104.22.168. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 103514-10 J. Thorstensen and S. E. Foss within 15% to þ37% of the experimental values. Another mechanism which may contribute to the same trend is diffusion of carriers. Diffusion which is stronger than the simulated values would manifest itself as an increased ablation threshold compared to simulated values, and this effect would be most pronounced for the wavelengths with strong energy confinement, namely 515 and especially 343 nm. Process temperatures well in excess of the temperatures investigated in this work are commonly used, for example, in the solar cell industry. These processes introduce little or only acceptable material degradation. As such, it is a realistic scenario to apply moderate substrate heating in order to better utilize expensive laser power and increase process throughput. J. Appl. Phys. 112, 103514 (2012) We observe experimentally that ablation with 1030 nm pulses at 320 C requires similar fluence as ablation by 515 nm pulses at 25 C. This experimental result can only be explained by treating both the free-carrier absorption and the critical electron density as wavelength dependent quantities, as predicted by Drude free-electron theory, and in doing so accepting that the ablation is related to the high number densities of conduction band electrons encountered during the pulses. As only moderate substrate heating is required for significant lowering of the ablation threshold, these experimental results open the possibility of using substrate temperature in order to obtain efficient utilization of laser power when processing silicon with ultrashort laser pulses in the IR or visible wavelength range. ACKNOWLEDGMENTS VIII. CONCLUSION Our experiments on ablation from silicon wafers at elevated temperatures, when applying ultrashort laser pulses with 3 ps pulse duration, show a temperature dependent behavior. We observe that the ablation thresholds at 515 and 1030 nm decrease by 35% and 43%, respectively, when substrate temperatures are increased from room temperature to 320 C, while the ablation threshold at 343 nm remains constant with temperature. In order to explain the observed trends, we have implemented a simulation model for solving the time-dependent two-temperature model for the interaction between silicon and ultrashort laser pulses. From these simulations, we see that the ablation is related to the critical electron density rather than to vaporization of the lattice. We have extracted the dynamic excess carrier generation from different mechanisms, such as linear and two-photon absorption, impact ionization, and Auger recombination. We have seen that the strongest carrier generating mechanism is linear absorption for all investigated cases, with the exception of irradiation at 1030 nm at 27 C where two-photon absorption creates the majority of the carriers. Free-carrier absorption is the strongest energy absorption mechanism for irradiation at 1030 nm; however, this energy is lost through electron-lattice coupling, and does not directly contribute to the number density of conduction band electrons. We have discussed the consequences of choosing to apply the two-temperature model, rather than to apply the more elaborate three-temperature model. The two-temperature model assumes thermal equilibrium between optical and acoustic phonons, which certainly is a simplification for pulses as short as the ones encountered herein. Nevertheless, we are able to reproduce the observed temperature dependence in our simulations, and we are able to extract information about the dominating absorption mechanisms. When applying elevated substrate temperatures in our simulations, we observe that the increase in linear absorption coefficient with temperature causes a lowering of the ablation threshold for irradiation at 515 and 1030 nm. With irradiation at 343 nm, no temperature dependence is observed, as a result of the temperature independence of the linear absorption coefficient at this wavelength. Best agreement between simulations and experiments is obtained when applying unscreened Auger recombination in our simulations. The authors gratefully acknowledge the valuable input received from Professor Aasmund Sudbï (University of Oslo) and Dr. Erik Marstein (Institute for Energy Technology) in forming the contents of this article. This work has been funded by the Research Council of Norway through the project “Thin and highly efficient silicon-based solar cells incorporating nanostructures,” NFR Project No. 181884/S10. 1 D. B€auerle, Laser Processing and Chemistry, 3rd ed. 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Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions PAPER VI Jostein Thorstensen, Ragnhild Sæterli and Sean Erik Foss, “Laser ablation mechanisms in thin silicon nitride films on a silicon substrate,” submitted to IEEE Journal of Photovoltaics, April 2013. 123 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Laser ablation mechanisms in thin silicon nitride films on a silicon substrate Jostein Thorstensen, Ragnhild Sæterli and Sean Erik Foss Abstract— Laser ablation of thin films of silicon nitride (aSiNx:H) from silicon substrates is an important technique for the development of advanced silicon solar cell designs. Depending on parameters such as laser wavelength, laser pulse duration and aSiNx:H composition, the laser energy may be deposited either in the a-SiNx:H film, leading to direct ablation of the film, or in the silicon substrate, giving indirect ablation. We perform laser ablation of a-SiNx:H films with varying composition using laser pulses with a duration of 0.5 to 6.5 ps and wavelengths of 1030, 515 and 343 nm. We find that ablation is indirect, respectively direct when applying laser pulses at 1030 and 343 nm. Using a wavelength of 515 nm, we observe a transition from indirect to direct ablation when increasing the silicon content of the films and when applying shorter laser pulses, observing both indirect and direct ablation within one laser spot. In order to explain this behavior, we find that the interaction between the laser pulse and a high number density of electron-hole pairs in the a-SiNx:H must be significant. These findings allow for tailoring of the ablation behavior by choosing a proper combination of laser wavelength, pulse duration and a-SiNx:H composition. Index Terms—Laser processing, Silicon Nitride, Silicon solar cells. I. INTRODUCTION L ASER ablation of hydrogenated amorphous silicon nitride (a-SiNx:H) from silicon (Si) substrates is an interesting process for the production of advanced silicon solar cells, as it can allow for the fabrication of local electrical contacts , or the patterning of the a-SiNx:H may provide a patterned etchor diffusion barrier . Laser ablation of a-SiNx:H has been studied by several authors [3–6], using long and ultrashort laser pulses at first, second and third harmonics of solid state lasers (wavelength around 1064, 532 and 355 nm). When Manuscript received April 24, 2013. This work has been funded by the Research Council of Norway through the project “Thin and highly efficient silicon-based solar cells incorporating nanostructures”, project number 181884/S10, and by ”The Norwegian Research Centre for Solar Cell Technology” project number 193829, a Centre for Environment-friendly Energy Research co-sponsored by the Norwegian Research Council and research and industry partners in Norway. J. Thorstensen and S.E. Foss are with the Institute for Energy Technology, Department of Solar Energy, P. O. Box 40, 2027 Kjeller, Norway. R. Sæterli is with the Norwegian University of Science and Technology, Department of Physics, 7491 Trondheim, Norway. J. Thorstensen is also with the University of Oslo, Department of Physics, P. O. Box 1048 Blindern, 0316 Oslo, Norway. J. Thorstensen is the corresponding author (phone: +47 63806445; fax: +47 63812905; e-mail: [email protected]). characterizing this process, authors have often tried to determine where the laser energy has been absorbed, i.e. whether the energy has been absorbed in the a-SiNx:H or in the Si, as this will strongly affect the process results. At photon energies significantly below the a-SiNx:H band-gap energy and at long laser pulses, the laser energy will primarily be deposited in the Si, as the a-SiN x:H is transparent in this situation. The Si will be heated to vaporization temperatures, and the vapor pressure will lift off the a-SiNx:H. This is known as indirect ablation. At higher photon energies where a-SiN x:H shows sufficient absorption of the laser energy, the energy may primarily be deposited in the a-SiNx:H, heating this to the point of vaporization, while at the same time shielding the Si from excessive laser energy input. This is known as direct ablation, and may also be obtained with ultrashort laser pulses where non-linear effects will increase the absorption in the a-SiNx:H also for wavelengths where the a-SiN x:H is normally transparent. While direct ablation may be desirable due to its potential to shield the silicon substrate from laser damage, any residual a-SiNx:H may prove to be an obstacle for post-processing. Knorz et al.  report direct absorption in the a-SiNx:H layer using pulses with 30 ns duration at 355 nm. The group of Heinrich et al.,  and Wüterlich et al.  uses ps- and fslasers at 1064, 532 and 355 nm wavelengths, observing signs of direct ablation at 532 and 355 nm. Heinrich et al.  perform investigations on two nitrides with different composition and resulting different refractive indices (n=1.9 and n=2.1), and observe different ablation behavior using 10 ps pulses at 532 nm in the two nitrides. In this work, we perform a study on the ablation of a-SiNx:H with several different refractive indices from n=2.05 to 2.38, laser wavelengths of 1030, 515 and 343 nm, and pulse duration from 0.5 to 6.5 ps (full-width half maximum, FWHM). Possible physical mechanisms explaining the observed behavior are presented. II. METHOD In this work, we ablate silicon nitrides from silicon and glass substrates, and characterize the mechanism of ablation as function of wavelength, pulse duration and a-SiNx:H composition, in order to find out for what parameters direct and indirect ablation can be expected. We investigate the ablation thresholds and morphology of the ablated spots, in order to provide insight in the energy deposition mechanisms. Optical microscopy, scanning electron microscopy (SEM), > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < atomic force microscopy (AFM) and transmission electron microscopy (TEM) have been used in combination with reflectance and absorption measurements and laser power measurements in order to obtain as much information about the process as possible. TEM measurements were performed on a JEOL 2010F microscope. The TEM microscope is also equipped with an INCA Oxford energy dispersive x-ray spectroscopy (EDS) system which was used for compositional analysis. a-SiNx:H has a band-gap energy which may be around 3.5 eV, but also higher or lower, depending on the Si/N-ratio . Depending on the material structure and composition, the aSiNx:H may show significant absorption tails well into the band-gap. Three frequently used laser wavelengths for ablation of dielectrics for solar cell applications, are around 1064, 532 and 355 nm, corresponding to 1.2, 2.3 and 3.5 eV. Considering the band-gap energy of a-SiN x:H, we see that photons with photon energy of 3.5 eV (wavelength of 355 nm) have enough energy to excite an electron-hole pair (promoting the electron from the valence band to the conduction band), and consequently experience significant absorption. Photons with photon energy of 2.3 eV (wavelength of 532 nm) may experience linear absorption only if absorption tails in the band-gap are present. Otherwise, two-photon absorption (TPA) would be required for the generation of electron-hole pairs, whereby the combined energy of two photons may generate an electron-hole pair . Depending on the laser pulse parameters such as pulse duration and laser wavelength and material properties, the dominant band-to-band absorption mechanisms may be linear absorption, TPA or even threephoton absorption for the case of photon energies of 1.2 eV (wavelength of 1064 nm). Multi-photon absorption will only occur at high laser intensities, i.e. short laser pulses. Optical attenuation through linear absorption is described by the expression: ( , ) =− ( , ), (1) where is the linear absorption coefficient, is the distance into the wafer and is the optical intensity. As the laser is pulsed, is also a function of time, , varying over the duration of the pulse. Integration of eq. (1) gives an exponentially decreasing intensity profile if is constant: ( , )= ( ) (2) where ( ) is the intensity at the surface of the absorbing material. When calculating energy deposition by TPA, we use the relation ( , ) =− ( , ) (3) where is the TPA coefficient and the other symbols have the same meaning as in eq. (1). Integrating equation (3) gives the following intensity profile through an absorbing medium experiencing only two-photon absorption: ( , )= ( ) 2 (4) ( ) Furthermore, the energy density deposited in the absorbing ( , ) medium equals − ∫ , and the number density of photogenerated electron-hole pairs, = −∫ ( , ) /( equals ) (5) where is the number of photons participating in the transition, being 1 and 2 for linear and two-photon absorption, respectively, and is the photon energy. Carriers excited to the conduction band may absorb light through FCA, and may promote more carriers to the conduction band through impact ionization processes. It has previously been shown that FCA can be a dominant absorption process in the ablation of dielectrics . From free-electron theory, one can expect a change in dielectric constant in a material with a high number density of excited electrons, given by the expression ,  = + = 1− + ( ) (6) where is the background relative permittivity of the dielectric material without free carriers. We define = /( ) as the plasma frequency with a dielectric background, is the reciprocal collision time, is the effective electron mass, is the angular frequency of the applied electric field and is the number density of electrons. will be varying with and , and so will the resulting . Depending on the ratio between and , the behavior of reflectance vs. will vary, but the resulting surface reflection from the interface between air and dielectric will generally increase as approaches (i.e. as the number density of electron-hole pairs increases). III. EXPERIMENTAL Thin films of hydrogenated amorphous silicon nitride, aSiNx:H with varying composition were deposited by plasmaenhanced chemical vapor deposition (PECVD), in an RF direct plasma (Oxford Instruments PlasmaLab 133). Silane (SiH4), ammonia (NH3) and nitrogen (N2) were used as process gases. All process parameters are given in table 1 and were kept constant, with the exception of the SiH4 flow, which was varied between 20 and 38 sccm in order to vary the Si/N ratio. The thickness of the films was 75 nm. The a-SiNx:H was deposited on Si substrates and on microscope glass slides. By varying the flow of SiH4 during deposition, we will get a change in the Si/N ratio. We can observe the varying Si/N ratio in the films by observing a change in refractive index and band-gap energy of the films, the refractive index increasing with increasing Si content and the band-gap energy decreasing. We choose to characterize the films by their > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < TABLE I PROCESS PARAMETERS FOR PLASMA-ENHANCED CHEMICAL VAPOR DEPOSITION OF A-S IN X:H FILMS. Parameter SiH4 flow NH3 flow N2 flow Pressure RF Power RF frequency Deposition temperature Value 20-38 sccm 20 sccm 980 sccm 800 mTorr 46.8 mW/cm2 (40 W) 13.56 MHz 400 °C refractive index, which we measure by spectroscopic ellipsometry. From these measurements, we also obtain the thickness of the films. We find that the refractive index varies from n=2.05 to 2.38 by varying the flow of SiH4. We cannot rule out the possibility that we may also get different Hcontent or different structural properties of the films, however, these effects are not characterized within this work. We irradiate the samples with non-overlapping pulses at 1 kHz repetition rate and 100x100 µm spot-to-spot distance at several laser pulse energies per wavelength and pulse duration. We apply wavelengths of 1030, 515 and 343 nm, and fullwidth half maximum (FWHM) pulse duration of 0.5, 3.0 and 6.5 ps. The laser ablation threshold fluence (ablation threshold) is calculated by the method of Liu , where the ablated radius as function of pulse energy is used in order to extract beam diameter and ablation threshold. = ln = ln − ln( ) (7) Here, is the ablated radius, c is the beam radius at 1/e2 fluence level, and are the central fluence of the laser spot and the ablation threshold fluence. This method requires the laser spot to display a Gaussian fluence distribution, which holds for our pulses. Measuring the laser pulse energy and ablated radius for several different , we can extract and by curve fitting. Although we have slightly oval laser spots, the ablated radius is approximated from the ablated area, , through the relation = / . The reflectance of the samples is subtracted before calculating the threshold fluence. As such, we use the fluence entering the substrate when fitting the experimental results to eq. (7). Two different reflection measurements are performed. Firstly, reflection measurements at low optical intensities are performed using a spectrometer-based integrating sphere setup with a deuterium and a tungsten/halogen lamp. Secondly, intensity-dependent reflection is measured in-situ while laserprocessing, using the same parameters as those used for determination of the ablation threshold. The reflection is measured on samples made from silicon substrates, at an incidence angle of 15°, using a thermopile laser power meter to measure the ratio between reflected power and incident power, at a range of incident powers. These measurements represent reflectance data averaged over time and radius of the spot. We also perform transmission measurements on samples on glass slides using the same spectrometer-based setup as 3 when measuring low-intensity reflectance. IV. RESULTS Using a laser wavelength of 1030 nm, the process results are independent of pulse duration and a-SiNx:H composition, and resemble that of the 515 nm wavelength on low refractive index nitrides. With a wavelength of 343 nm, the process results are also independent of pulse duration and a-SiNx:H composition, but resemble that of the 515 nm wavelength on high refractive index nitrides. We shall see that these two situations correspond to indirect, respectively direct ablation. We therefore focus on the findings using the 515 nm wavelength. A. Optical microscopy Ablating a-SiNx:H from Si using a wavelength of 515 nm, we obtain the optical microscope images shown in Figure 1. The dark blue areas is as-deposited a-SiNx:H, the light blue / grey areas is the exposed bare silicon substrate, and the dark / black areas is the transformed laser-irradiated a-SiNx:H. Using a low refractive index a-SiNx:H, we observe bare silicon within the complete laser spot, a sign that the ablation has been indirect, whereby the vapor pressure from the silicon lifts off the complete a-SiNx:H -layer in the ablated region. On the other side of the scale, using a high refractive index a-SiNx:H, we observe that the laser spot has turned black, and we observe no bare Si. Refractive indices higher than the ones shown in Figure 1 exhibit similar appearances as the one with n = 2.22. Between these extremes, we find a gradual transition showing varying fractions of bare Si and transformed aSiNx:H in a ring pattern. We shall discuss this finding in more detail in the following sections. B. Atomic force microscopy (AFM) In order to further investigate our results, some representative samples were analyzed by AFM. False-color height maps of samples irradiated by the 515 nm wavelength are shown in Figure 2, along with line profiles extracted from Fig. 1. Color microscope images of ablated spots of a-SiNx:H from Si using a wavelength of 515 nm and varying pulse duration, τp, and a-SiN x:H composition, characterized by the refractive index n. The transition from indirect (top left) to direct (bottom right) ablation is shown. The black scale bar is 10 µm. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 Fig. 2. Lower row: False-color AFM height maps of three samples showing indirect (left), partially direct (center) and direct (right) ablation. (Scale bar to the left.) Upper row: Line profiles extracted from the images below, following the lines marked “1”. The samples are irradiated by a laser wavelength of 515 nm. The applied pulse duration and a-SiNx:H refractive indices are 3 ps, n=2.05 (left), 6.5 ps, n=2.10 (center) and 6.5ps n=2.22 (right). We observe more debris on the partially directly and directly ablated samples, a sign that the a-SiNx:H film undergoes disintegration in this case, while for the indirectly ablated samples, the entire a-SiNx:H sheet is lifted off the substrate and can often be found intact. the height maps. The pulse duration and a-SiNx:H refractive index are τp=3 ps and n=2.05 (left), τp=6.5 ps and n=2.10 (middle) and τp=6.5 ps and n= 2.22 (right). Qualitatively, the AFM-analysis shows the same behavior as observed by optical microscopy. The τp=3 ps, n=2.05 sample shows a sharp edge corresponding to the thickness of the a-SiNx:H, meaning that the complete a-SiNx:H has been removed in the spot, while the surrounding a-SiNx:H is unaffected. This is in line with the findings using optical microscopy. The τp=6.5 ps n=2.22 sample shows a gradual thinning of the a-SiNx:H as we approach the center of the spot. This is consistent with direct ablation, where higher laser intensity will heat and remove more a-SiN x:H. Other samples showing direct ablation show a step at the edge of the ablated area, around 20 – 30 nm high. Towards the center of the spot, the ablated depth increases as shown in Figure 2 (right). Fig. 3. SEM micrograph of sample irradiated with 515 nm laser wavelength, 6.5 ps pulse duration and an a-SiNx:H refractive index of n=2.10. A part of the direct ablated ring is seen, with unaltered a-SiNx:H outside (lower right), and transformed a-SiNx:H inside the ring (upper left). The transformed aSiNx:H shows micro-blisters with sizes on the order of 100 nm. Analyzing the sample with n=2.10, irradiated with τp=6.5 ps pulses, we observe the same ring structure as in the optical microscope images. In the ring, the complete a-SiNx:H thickness has been removed, while in the center of the spot, most of the a-SiNx:H remains. This corresponds to the observations of Heinrich et al. , on a-SiNx:H films with n=2.1, laser wavelength of 532 nm and τp=10 ps. This behavior is observed for the samples with n=2.10 for all pulse durations, and for n=2.16 at the longest pulse durations, resulting in varying extension of the ring. As such, these samples are indeed showing signs of both indirect and direct ablation within the same spot. C. Scanning electron microscopy Figure 3 shows a SEM micrograph of the n=2.10 sample irradiated by 6.5 ps laser pulses. The a-SiNx:H in the middle region is covered with micro-blisters. This characteristic feature was observed for all of the directly ablated samples. The size of these micro-blisters is on the order of 100 nm and below. We suggest that these blisters are a result of outgassing of H 2 or N2. The release of H2 from PECVD a-SiN x:H films has been observed by other authors  upon heating. To further test the nature of the remaining porous structure, the structure was etched in a 5% HF solution for 10 minutes. The a-SiNx:H surrounding the laser spots was completely removed after about 5 minutes (by observation of a hydrophobic Si surface), however, the porous structure was thinned only negligibly after 10 minutes of etching. This indicates that the remaining structure has undergone a chemical or structural transformation, and is now much more resistant towards HF. Williams et al.  show that different silicon nitrides may show strongly differing etch rates in HF. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < D. Transmission Electron Microscopy (TEM) We perform TEM on samples with a refractive index of n=2.22, irradiated with τp=3 ps pulses at 515 nm wavelength, in order to obtain detailed information about the structure remaining after direct ablation. Figure 4 (right) is a bright-field TEM image showing two samples glued together. The lower sample shows the middle of the ablated spot, showing that a thinned a-SiNx:H layer of approximately 40 nm remains. Figure 4 (left) is a dark-field Scanning-TEM image showing the edge of an ablated spot. Here, a darker layer is seen in the middle of the film, where energy dispersive x-ray spectroscopy (EDS) reveals that the Si content is lower than in the rest of the film, indicating a porous layer in the a-SiNx:H. This may be a trace of a process wherein the a-SiNx:H develops a weakness at this depth, whereafter the top layer of the a-SiN x:H is ablated. EDS results are shown in Figure 5, where the spectra have been normalized to the silicon peak. Measurements were performed on two different samples. For both samples, measurements were performed within and outside of the ablated area. We see that the nitrogen content in the ablated area is somewhat lower than that of the complete film. This Fig. 4. Transmission Electron Microscope (TEM) images of a-SiN x:H – films on Si samples. Silicon substrate, a-SiN x:H layer and glue are indicated in the images. (Left) Dark-field Scanning-TEM (STEM) image of edge of spot. A darker layer is seen in the middle of the a-SiNx:H layer. EDS shows a reduced Si content in this region, indicating a porous layer. (Right) Brightfield TEM image of two silicon samples with a-SiNx:H -layer and glue in between. The glue has delaminated, giving the bright white line. The lower silicon sample shows the middle of a spot. Approx. half of the a-SiN x:H layer has been removed, and a rough surface is observed. On the upper sample, an unprocessed area is seen, the complete a-SiN x:H remains on the sample surface. Fig.5. Energy dispersive x-ray spectroscopy (EDS) spectra taken from the complete a-SiNx:H film, and the remaining a-SiNx:H in the ablated spot. Laser pulse duration and wavelength are 3 ps and 515 nm, the refractive index of the film is n=2.22. Two different samples have been investigated. We observe somewhat lower nitrogen content within the ablated area, pointing towards some out-gassing of N2 in the ablated spots. 5 indicates that there may be some out-gassing of N from the ablated area. A more silicon-rich a-SiNx:H in the spot might, according to Williams et al. , be more resistant towards etching in HF, supporting our observations on etch stability in section IV.C. E. Optical absorptance and reflectance in the films We measure the low intensity transmittance and reflectance of a-SiNx:H on microscope slides. From these measurements, we can estimate the linear absorption coefficient in the aSiNx:H films as function of wavelength, using the relations =1− − =1− (8) where is the absorptance, is the transmittance, is the reflectance and is the thickness of the film. is the linear optical attenuation coefficient. Solving eq. (8) for , we get = − ln(1 − ). (9) The absorption in the microscope slide is subtracted from the measurements of . The calculated attenuation coefficients are shown in Figure 6. We observe steadily increasing attenuation with increasing index of refraction, and we observe significant attenuation coefficients for most of the nitrides even at a wavelength of 515 nm. From in-situ, high intensity reflection measurements using a laser wavelength of 515 nm, τp=3 ps and an a-SiNx:H refractive index of n=2.10, we observe a low intensity reflectance of 8 % at the 515 nm wavelength, while at 2.4 µJ pulse energy (0.68 J/cm2 pulse peak fluence), the measured average reflectance is 14 %. Following eq. (6), increased reflectance can be a sign of a high number density of excited electron-hole pairs in the a-SiNx:H. The electron-hole pair density will be highest in the central regions of the spot, where the optical intensity is highest. F. Ablation threshold fluencies on silicon and glass substrates As described in section III, and based on optical microscope images, we extract the laser ablation threshold fluencies (ablation thresholds) encountered in our experiments. We define three different ablation thresholds. Firstly, we extract the ablation threshold on Si substrates based on the outermost diameter where the a-SiNx:H has been altered or removed. We define this as the process threshold, as it is the lowest laser fluence required for visible change to the sample. Secondly, we extract the ablation threshold based on the diameter of the dark/black area. We define this as the direct ablation threshold, as we suspect the dark areas to have undergone direct ablation. The third threshold which we extract is based on the outermost diameter of visible change to the samples deposited on microscope slides. Glass is an even higher bandgap dielectric than SiNx, and has a much higher damage threshold . As such, the energy deposition is primarily taking place in the a-SiNx:H when deposited on microscope slides, and we can be certain that the process threshold > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < Fig. 6. Attenuation coefficients as function of wavelength for five a-SiNx:H films with different composition, as measured by optical transmission and reflection measurements. The films are identified by their refractive indices. Also indicated is the attenuation coefficient of the glass substrate, magnified by a factor 1000 for visibility. measured from these samples constitute a direct ablation threshold. As such, the two latter ablation thresholds should both constitute the threshold for direct ablation of the aSiNx:H and their values should be similar. Figure 7 (right) shows the direct ablation threshold as measured by extracting the diameter of the dark areas from the Si substrate samples, and by extracting the diameter of the spots observed on glass substrate samples. Although we observe a seemingly consistently higher ablation threshold from glass, the thresholds are equal to within measurement error. As such our two methods for determining the direct ablation threshold are in agreement, a further indication that the dark areas on Si substrates have indeed undergone direct ablation. The small systematic discrepancy could be due to a slightly different optical intensity in the films as a result of the different refractive index of the substrates. The electromagnetic field within the a-SiNx:H film will be the sum of the electromagnetic wave transmitted from the air and the reflected wave from the film-substrate interface. The reflected wave will have an amplitude given by the Fresnel coefficient = ( − )/( + ), where and are the refractive indices of the film and the substrate, respectively. At a wavelength of 515 nm, the refractive indices are 2.1, 1.5 and 6 4.2 for a-SiNx:H, glass and silicon, respectively, giving a reflection coefficient of 0.17 and -0.33 for the case of glass and silicon substrates, respectively. As our films are thick enough to contain a field maximum at the 515 nm wavelength, the maximum optical intensity in the film will be higher when the substrate is silicon. If direct ablation is caused by high local optical intensity in the film, the ablation threshold from silicon should be slightly lower than that from glass, which is indeed consistent with our findings. With 6.5 ps pulses, we also observe that the difference between the two ablation thresholds shrinks with increasing refractive index of the aSiNx:H, consistent with the fact that the reflection coefficients will get similar for glass and silicon substrates when the refractive index of the a-SiN x:H approaches 2.4. Figure 7 (left) shows the measured process threshold and direct ablation threshold extracted from samples on silicon substrates. For low refractive index a-SiNx:H, the process threshold is much lower than the direct ablation threshold, indicating an indirect ablation process. We observe a steadily increasing process threshold with increasing refractive index, which we interpret as being caused by increasing absorption in, and reflectance from the a-SiNx:H. At a refractive index of 2.16 for 0.5 ps pulses and 2.22 for 3.0 ps and 6.5 ps, the process threshold equals the direct ablation threshold, and we have no indirect ablation. From this point, the process threshold decreases again, as a result of stronger absorption in the higher index nitrides. G. Energy deposition in the a-SiNx:H films In the samples showing both indirect and direct ablation in the same spot, we wish to extract further information. Obviously, at low optical intensities, the a-SiNx:H film transmits sufficient laser energy to vaporize the Si, giving indirect ablation, meaning that at least a fluence corresponding to the indirect ablation threshold has reached the Si surface. However, as the intensity increases, the a-SiNx:H must absorb and reflect a considerable fraction of the incoming radiation, reducing the optical intensity at the Si surface to below the indirect ablation threshold. This claim is evidenced by the fact Fig. 7. (Left) Measured ablation thresholds from Si, using a wavelength of 515 nm. Dotted lines (open symbols) show the process threshold, while the solid lines (closed symbols) show the threshold for direct ablation. (Right) Measured direct ablation threshold from Si substrate (dotted lines, open symbols) and glass substrate (solid lines, closed symbols). > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < that the ablation becomes direct as intensity increases. We wish to examine the physical mechanisms involved in this process. In the situation described above, the laser fluence reaching the silicon substrate must be lower than the indirect ablation threshold outside and inside the ablated ring, while it is higher within the ring itself, as indicated by the black line in Figure 8. Looking again at eq. (4) describing two-photon absorption (TPA), we see that, while the transmitted fraction decreases with increasing intensity, ( ), the absolute transmitted fluence will be steadily increasing with ( ). As such, TPA alone cannot cause the intensity profile required at the silicon surface. The same holds for linear absorption, but an electronhole plasma will change the picture. A dense electron-hole plasma may be excited during the leading end of the laser pulse, by e.g. linear absorption or TPA. This plasma will absorb strongly through free-carrier absorption (FCA), and will also increase reflectance off the surface as described in eq. (6). These effects combined can cause optical shielding in the central regions of the spot in such a way that the intensity profile at the silicon surface may behave as required from the discussion above. As such, FCA must be an important absorption mechanism in order to explain the observed behavior. However, as indicated by Stuart et al.  dielectric breakdown by FCA and impact ionization require seed electrons to be excited at the beginning of the pulse in order for FCA and impact ionization to be efficient later in the pulse. We wish to investigate by which mechanism the seed electrons are generated. Low-intensity transmission measurements show a measurable linear absorption coefficient for the 515 nm laser wavelength for a-SiNx:H with a refractive index of 2.10 and above, due to relatively strong Urbach absorption tails in the band-gap, as shown in Figure 6. The measured absorption coefficient ranges from 3∙10 2 to 3∙103 cm-1, increasing with increasing refractive index. We apply eq. (5) in order to estimate the number density of electron-hole pairs generated by linear and two-photon absorption. Using = 3 × 10 cm-1 at a wavelength of 515 nm and a pulse energy of 0.43 J/cm2 (the threshold for direct ablation of the a-SiNx:H with a refractive index of 2.10) we get a photo-generated density of electron-hole pairs of about 3.5∙1020 cm-3. This means that linear absorption excites a significant free electron density, and may supply the required free electrons necessary for dielectric breakdown due to FCA and impact ionization. For TPA to generate the same number density of electron-hole pairs, we would need = 3.2cm/GW, given a 3 ps pulse duration. A semi-empirical model for the TPA giving good Fig. 8. Indication of intensity profile reaching the silicon substrate in the case of partially direct ablation. Blue: Schematic cross-section of the a-SiNx:H surface through the center of a partially direct ablated sample, dotted red: the ablation threshold fluence in silicon, black: schematic drawing of the intensity profile at the silicon surface required for the observed behavior; higher than the threshold in the ablated region, and lower than the ablation threshold in the center and peripheral regions. 7 correspondence for several dielectrics can be used to estimate the TPA for a-SiNx:H with a band-gap and refractive index corresponding to our material . ≃ where ( ) = 5.67 × 10 (10) 3 J m/W, / = . 2 2 / − 1 /( / ) and and are the refractive index and band gap of the material, respectively, and is the photon energy. Using a photon energy of 2.3 eV, corresponding to a wavelength of 515 nm, a refractive index of 2.1 and a band-gap energy of 3.5 eV, this model yields a TPA coefficient of 3.5 cm/GW. The value obtained is fairly close to what would be required for TPA to be as strong as linear absorption. As such, it would seem likely that linear absorption and TPA generate about the same number density of electron-hole pairs in the case investigated above. For the higher refractive index films, the stronger linear absorption would suggest that linear absorption might generate the majority of the electron-hole pairs, while for shorter pulses, TPA might dominate. V. CONCLUSION We have investigated the behavior of thin films of a-SiNx:H with varying composition and refractive index deposited on silicon and glass substrates when ablated by ultrashort laser pulses at wavelengths 1030, 515 and 343 nm and pulse duration between 0.5 and 6.5 ps. We have determined ablation thresholds and examined the ablation spots by the use of optical microscopy, atomic force microscopy (AFM), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). In addition, the chemical composition of one of the films was examined by the use of energy dispersive x-ray spectroscopy (EDS). Using a laser wavelength of 1030 nm, the ablation is found to be indirect for all pulse durations and a-SiNx:H compositions, an indication of the fact that the a-SiNx:H is transparent at this wavelength, and that the intensity of our pulses is not high enough for three-photon absorption to be efficient. At 343 nm the a-SiNx:H films absorb fairly strongly, and the ablation is found to be direct for all pulse durations and a-SiNx:H compositions, consistent with the findings of Knorz et al.  using long laser pulses. After direct ablation, the remaining a-SiNx:H structure shows a somewhat increased Si/N-ratio, pointing toward out-gassing of N2. SEM images of the direct ablated spots show a micro-porous layer, potentially formed by out-gassing of H2 or N2 during the ablation process. Using a wavelength of 515 nm, we observe a transition from indirect to direct ablation when applying shorter pulses and higher index a-SiN x:H. For several combinations of pulse duration and a-SiNx:H composition, both direct and indirect ablation can be observed in the same ablation spot, showing direct ablation inside of an indirectly ablated ring. Combining the ring shape of the directly ablated region, the observation of increased reflectance with increasing optical intensity and examination of the expressions governing the optical intensity distribution at the silicon surface following from linear and > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < two-photon absorption, there is reason to believe that electronhole pairs excited by linear and two-photon absorption in the leading end of the pulse is causing free-carrier absorption (FCA) to be the dominant absorption mechanism in the direct ablation process, in line with the calculations by Stuart et al. , and that the same dense electron-hole plasma causes an increased reflectance from the films, further reducing the optical intensity reaching the silicon substrate. The behavior of a-SiNx:H when ablated by ultrashort laser pulses can be tailored by varying a-SiNx:H composition, laser wavelength or laser pulse duration. We have thoroughly investigated a set of parameters constituting a transition region, and we have identified the main physical mechanisms in the interaction between the laser pulses and the a-SiNx:H films and substrates. ACKNOWLEDGMENT The authors gratefully acknowledge the valuable input received from Prof. Aasmund Sudbø (University of Oslo) and Dr. Erik Marstein (Institute for Energy Technology) in forming the contents of this article. The authors also acknowledge Eivind Bruun Thorstensen for valuable discussions on the behavior of heated a-SiNx:H. REFERENCES             A. Knorz, M. Peters, A. Grohe, C. Harmel, and R. Preu, “Selective Laser Ablation of SiNx Layers on Textured Surfaces for Low Temperature Front Side Metallizations,” Prog. Photovolt. Res. Appl., vol. 17, pp. 127–136, 2009. P. Engelhart, R. Grischke, S. Eidelloth, R. Meyer, A. Schoonderbeek, U. Stute, A. Ostendorf, and R. Brendel, “Laser Processing for Backcontacted Silicon Solar Cells,” in ICALEO Cong. 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Hasselbeck, “Third-order optical nonlinearities,” in Handbook of Optics, Volume IV - Optical Properties of Materials, Nonlinear Optics, Quantum Optics, M. Bass, G. Li, and E. Van Stryland, Eds. New York: McGraw-Hill, 2010. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B, vol. 13, no. 2, p. 459, Feb. 1996. N. Ashcroft and N. Mermin, Solid state physics, 1st ed. New York : Holt, Rinehart and Winston, 1976. J. Reitz, F. Milford, and R. Christy, Foundations of electromagnetic theory, 4th ed. Reading, Mass. : Addison-Wesley, 1993. J. M. Liu, “Simple Technique for measurements of pulsed Gaussianbeam spot sizes,” Opt. Lett., vol. 7, no. 5, pp. 196 – 198, 1982. D. N. Wright, E. S. Marstein, A. Rognmo, and A. Holt, “Plasmaenhanced chemical vapour-deposited silicon nitride films; The effect of annealing on optical properties and etch rates,” Sol. Energ. Mat. Sol. Cells,, vol. 92, no. 9, pp. 1091–1098, Sep. 2008.  8 K. R. Williams, K. Gupta, and M. Wasilik, “Etch Rates for Micromachining Processing — Part II,” J. Microelectromechanical systems, vol. 12, no. June, pp. 761–778, 2003. PAPER VII Jostein Thorstensen and Sean Erik Foss, “New approach for the ablation of dielectrics from silicon using long wavelength lasers,” submitted to Energy Procedia, March 2013. 133 Available online at www.sciencedirect.com Energy Procedia 00 (2013) 000–000 www.elsevier.com/locate/procedia SiliconPV: March 25-27, 2013, Hamelin, Germany New approach for the ablation of dielectrics from silicon using long wavelength lasers Jostein Thorstensen*,a,b and Sean Erik Fossa b a Institute for Energy Technology, P.O. Box 40, 2027 Kjeller, Norway University of Oslo, Department of Physics, P.O. Box 1048 Blindern, 0316 Oslo, Norway Abstract Laser ablation of dielectrics from silicon substrates represents a useful technique for e.g. the creation of local contacts. However, these dielectrics are transparent at the laser wavelengths normally employed for silicon solar cell processing, i.e. the first, second and third harmonics of solid state lasers (1064, 532 and 355 nm). As a result of this, the ablation is indirect, and follows from energy deposition in the silicon rather than in the dielectric. This mechanism introduces defects in the silicon substrate, an effect which is detrimental to solar cell performance. Attempts have been made to limit the extent of the laser damage, by going to shorter wavelengths and shorter pulse durations. In this work, we suggest an alternative route to low-damage ablation of dielectrics by application of long wavelength laser pulses from e.g. CO2-lasers. At wavelengths above approx. 8 µm, we find absorption bands in many of the dielectrics applied in solar cells. Simulations show that it may be possible to keep the silicon temperature below melting temperature, while reaching vaporization temperature in the dielectric. Experiments using laser pulses at 9.3 µm with a duration of approx. 100 ns show, however, that the silicon substrate experiences melting. We conclude that even shorter pulses must be applied for the method to be successful. © 2013 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the scientific committee of the SiliconPV 2013 conference Keywords: Laser ablation; long laser wavelengths 1. Introduction In processing of silicon solar cells, the local removal of dielectric layers is beneficial for several processes [1–3]. Lasers have been suggested as a possible tool for this local removal, as lithography and masking processes may be incompatible with industrial scale processing. However, laser damage is often * Corresponding author. Tel.: +47 63806445; fax: +47 63812905. E-mail address: [email protected] J. Thorstensen et al. / Energy Procedia 00 (2013) 000–000 observed as a reduction of lifetime in lowly doped silicon, or it can be observed as an increase in the dark saturation current density if processing in emitters [1,4]. This laser damage is a result of laser energy deposition in the silicon. The approach up until now has been to go to shorter pulse durations and wavelengths, in order to either confine the laser energy and damage to a shallow layer in the silicon, or to obtain (non-linear) absorption in the dielectric layers, which normally are transparent at visible and nearinfra-red wavelengths due to their high band-gap energy. The problem with going to short laser wavelengths and ultrashort laser pulses is that the silicon will also be highly absorbing in this situation, meaning that there will always be an inherent mechanism present for energy deposition into the silicon. In this article, we propose a new approach for obtaining low damage ablation of dielectric layers from silicon. We seek a situation where we not only get energy deposition in the dielectric, as will be the case in the situation described above, but where the silicon in addition is transparent to the laser light. In such a situation, once the dielectric is removed, we will get no more laser energy deposition, and one could potentially obtain a much more stable process. Our approach is based on the application of short-pulsed, long wavelength lasers, operating at wavelengths above 8 µm. At these wavelengths, intrinsic silicon is nearly transparent at room temperature, while many dielectrics have absorption bands at these wavelengths. This behaviour opens for the possibility of directly depositing the laser energy into the dielectric, while keeping the silicon at a much lower temperature. We simulate the temperature evolution during such a laser pulse, and compare the results with experiments performed using a CO2-laser at 9.3 µm and a pulse duration of 100 ns. 2. Simulations We apply a partial differential equation solver with one spatial dimension in order to solve the heat equation for our system. The system consists of a stack structure with a dielectric on top of a silicon slab. The silicon substrate is 100 µm thick, and the dielectric is 100 nm thick. We assume that ablation of the dielectric is obtained when the dielectric reaches vaporization temperature, and we shall abort the simulations if the silicon reaches melting temperature, as the recrystallization is assumed to introduce defects in the silicon, being an undesired situation. The heat equation is given by : = + (1 − ) . (1) Here, is the heat capacity, modified to include the enthalpy of phase change, κ is the heat conductivity, α is the optical absorption coefficient. I is the optical fluence, is the reflectivity and (1 − ) is the energy input from the laser. At the boundary between dielectric and silicon, we apply extra thermal interface resistance, , as reported by Huang et al.  and Kuo et al. . This resistance is related to the mismatch between phonon modes in different materials, and will delay heat transfer. Material parameters are taken from the literature and are shown in table 1 and table 2. indicates the vaporization temperature. Table 1. Material parameters for SiO x and SiN x. Parameter SiOx 2.4 × 10 3223 3 0.0123 SiNx 3.7 × 10 2100 1.80 0.0107 Unit cm2K/W K J/cm3 K W / cm K Ref  [8,9] [10,11]  J. Thorstensen et al./ Energy Procedia 00 (2013) 000–000 Table 2. Material parameters for Si. Parameter , , 1.521 × 10 8.96 × , , . Value 2.24 2.33 . (300 < < 1200) (1200 < < 1683) 0.62 Unit J/cm3 K J/cm3 K W / cm K Ref    W / cm K  The optical absorption coefficient is of course of outmost importance for the outcome of the simulations, however, this term is not straightforward in these simulations. For energy deposition in the dielectrics, absorption coefficients from FTIR measurements are used, however, we need an expression for in silicon. As we are applying long wavelength irradiation, band-to-band absorption is prohibited, and we are left with free-carrier absorption (FCA) and absorption by defect states = + . is obtained from FTIR measurements. , on the other hand, is more difficult to quantify. at room temperature is given by the expression = 2 × 10 , where is the background doping level. More fundamentally, FCA is expected to have an absorption coefficient following the trend : ∝ , (2) meaning that is dependent on the mobility , number density of free electrons , and wavelength of the laser irradiation, . As and are temperature dependent, so is . The temperature dependence of is given by : ( ) ( )= + (300) × ( ) ( ) = + (300) × ( ) , (3) × where (300) is the intrinsic carrier concentration in silicon at 300 K, ( ) is the temperature dependent band-gap energy and is the Boltzmann constant. ( ) is given by : ( )= (0) − in units of eV, where (0) = 1.155eV, The electron mobility is given by : ( , ) = 88 where . + , (4) = 4.73 × 10 . . × ⁄ . . × × . is T/300. Combining these expressions, we can write ( , )= (10 , 300) × ( ) = 635 K are fitting parameters. eV/K and × , ( , ) (5) . as (6) When the silicon is cold, is fairly small, and the substrate is fairly transparent. When the temperature rises, however, increases significantly, meaning that we have a mechanism for thermal runaway in silicon, where heated silicon will absorb stronger, confine the laser energy to a smaller volume and hence grow even hotter. It should be noted that and have not been measured at J. Thorstensen et al. / Energy Procedia 00 (2013) 000–000 temperatures close to the melting temperature of silicon, where the FCA is strongest. As such, the values for are uncertain, and introduces a significant source of error in the simulations. Fig. 1. (Left) Ablation threshold for dielectric from silicon using literature values (Solid lines). Also shown is the maximum temperature reached in the silicon substrate (dashed lines). (Right) The same values, but with higher thermal conductivity in the dielectric, and thermal interface resistance removed. Also shown is the melting temperature of silicon (dotted blue lines). Fig. 1 (left) shows the simulated ablation threshold (solid lines) and the maximum temperature of the silicon substrate (dashed lines) using literature values. We see that the substrate temperature decreases with decreasing pulse duration, a sign of reduced heat transfer from the dielectric. Reducing the pulse duration is therefore a way to reach ablation with substrate temperatures well below melting temperature. Fig. 1 (right) shows the same simulations, but with the thermal conductivity, , in the dielectric increased by a factor 10 and the thermal interface resistance removed, constituting a pessimistic scenario. Here, significantly shorter pulses must be applied in order to keep the silicon from melting. 3. Experimental We measure the infrared absorption coefficient of several dielectrics commonly used in solar cell processing, by means of Fourier-transform infrared spectroscopy (FTIR). The dielectrics are deposited by plasma-enhanced chemical vapor deposition (PECVD). The results are shown in Fig 2. We see that SiOx, SiNx and SiOxNy have significant absorption at around 9.3 µm, suitable for the CO2-laser, while AlOx shows absorption only at longer wavelengths. Fig. 2. Absorption coefficient in various dielectrics as measured by FTIR. All are deposited by PECVD, with the exception of the thermal SiO2. Also shown is the absorption in the silicon substrate (x2000). The absorption bands are seen from around 8 µm. J. Thorstensen et al./ Energy Procedia 00 (2013) 000–000 We perform experiments on ablation of thermal SiO2, PECVD - SiOx, SiNx and SiOxNy using a CO2laser at 9.3 µm and pulse duration of 100 ns. The experiments, however, show expulsion of the silicon, shown in fig. 3, and we conclude that the substrate has melted, indicating that the applied pulses are too long for the desired behavior. This also means that the heat conduction from the dielectric or the absorption in the silicon substrate is significantly higher than what we have simulated. We also perform ablation experiments on bare silicon (without dielectric cover), and we find that in this situation, the ablation threshold is very much higher than that obtained with a dielectric covering the silicon. This is taken as an indication that laser energy deposition in cold silicon is indeed very slow, and that the silicon is heated by heat conduction from the dielectric. The heated silicon will thereafter absorb more strongly, leading to melting of the silicon. Fig. 3. Process result from the laser ablation of SiOx using a laser wavelength of 9.3 µm and 100 ns pulse duration. Expulsion of silicon is clearly seen, indicating that the silicon has reached the melting temperature. 4. Discussion We have found that the simulations fail to predict the ablation behavior of dielectrics from silicon when applying 100 ns pulses at 9.3 µm wavelength. We have already noted that this means that either the heat transfer from the dielectric is higher than expected, or the absorption in silicon is stronger. It could, however, also mean that some of our assumptions are incorrect. Firstly, we assume that ablation of the dielectric occurs when the surface of the dielectric reaches vaporization temperature. With some of the dielectric at vaporization temperature, the vapor pressure would expel the remaining dielectric. This description may not necessarily be correct. Secondly, and more importantly, we assume that is temperature independent. This need not be the case, as represents thermal resistance caused by mismatch of phonon modes. With temperature increase and the following melting of the dielectric, this resistance must be expected to change. 5. Conclusion We suggest using long wavelength laser irradiation for removal of dielectric layers from silicon wafers, as many dielectrics have absorption bands at wavelengths above 8 µm, and as silicon is transparent at these wavelengths. Simulations show that there is a possibility of reaching vaporization temperatures in the dielectric while keeping the substrate below melting temperatures if using short enough pulses. Experiments, however, show that substrate melting is observed for pulses as short as 100 ns, indicating that the heat transfer from the dielectric or absorption in the substrate is significantly higher J. Thorstensen et al. / Energy Procedia 00 (2013) 000–000 than what we have simulated. As such, even shorter pulses must be applied for the method to be successful. Acknowledgements This work has been funded by the Research Council of Norway through the project “Thin and highly efficient silicon-based solar cells incorporating nanostructures”, NFR Project No. 181884/S10. References  P. Engelhart, S. Hermann, T. Neubert, H. Plagwitz, R. Grischke, R. Meyer, et al., Laser Ablation of SiO2 for Locally Contacted Si Solar Cells With Ultra-short Pulses, Progress in Photovoltaics: Research and Applications. 15 (2007) 521– 527.  K. Mangersnes, Back-contact back-junction silicon solar cells, University of Oslo, 2010.  A. Knorz, M. Peters, A. Grohe, C. Harmel, R. Preu, Selective Laser Ablation of SiNx Layers on Textured Surfaces for Low Temperature Front Side Metallizations, Progress in Photovoltaics: Research and Applications. 17 (2009) 127–136.  M. Ametowobla, Characterization of a Laser Doping Process for Crystalline Silicon Solar Cells, Universität Stuttgart, 2010.  D. Bäuerle, Laser Processing and Chemistry, 3rd ed., Springer, Berlin Heidelberg, 2000.  S. Huang, X. Ruan, X. Fu, H. Yang, Measurement of the thermal transport properties of dielectric thin films using the micro-Raman method, Journal of Zhejiang University SCIENCE A. 10 (2009) 7–16.  B. Kuo, J. Li, A. Schmid, Thermal conductivity and interface thermal resistance of Si film on Si substrate determined by photothermal displacement interferometry, Applied Physics A. 55 (1992) 289–296.  W.M. Haynes, ed., Physical Constants of Inorganic Compounds, in: CRC Handbook of Chemistry and Physics, 92nd ed., CRC Press/Taylor and Francis, Boca Raton, FL, 2012.  Y. Cerenius, Melting-Temperature Measurements on, Journal of the American Ceramic Society. 82 (1999) 380–386.  C.L. Yaws, Yaws’ Handbook of Thermodynamic Properties for Hydrocarbons and Chemicals, Knovel, 2009.  A. Jain, K.E. Goodson, Measurement of the Thermal Conductivity and Heat Capacity of Freestanding Shape Memory Thin Films Using the 3ω Method, Journal of Heat Transfer. 130 (2008) 102402.  C.K. Ong, H.S. Tan, E.H. Sin, Calculations of Melting Threshold energies of crystalline and amorphous materials due to pulsed-laser irradiation, Materials Science and Engineering. 76 (1986) 79 – 85.  H. Kobatake, H. Fukuyama, I. Minato, T. Tsukada, S. Awaji, Noncontact measurement of thermal conductivity of liquid silicon in a static magnetic field, Applied Physics Letters. 90 (2007) 094102.  D.K. Schroder, R.N. Thomas, J.C. Swartz, Free Carrier Absorption in Silicon, IEEE Transactions on Electron Devices. 25 (1978) 254–261.  J. Nelson, The Physics of Solar Cells, Imperial College Press, UK, 2003.  E.H. Sin, C.K. Ong, H.S. Tan, Temperature Dependence of Interband Optical Absorption of Silicon at 1152, 1064, 750 and 694 nm, Physica Status Solidi (a). 199 (1984) 199–204.  N.D. Arora, J.R. Hauser, D.J. Roulston, Electron and Hole Mobilities in Silicon as a Function of Concentration and Temperature, IEEE Transactions on Electron Devices. ED-29 (1982) 292–295. PAPER VIII Jostein Thorstensen and Sean Erik Foss, “Investigation of depth of laser damage to silicon as function of wavelength and pulse duration,” accepted for publication in Energy Procedia, March 2013. 141 Available online at www.sciencedirect.com Energy Procedia 00 (2013) 000–000 www.elsevier.com/locate/procedia SiliconPV: March 25-27, 2013, Hamelin, Germany Investigation of depth of laser damage to silicon as function of wavelength and pulse duration Jostein Thorstensen*,a,b and Sean Erik Fossa b a Institute for Energy Technology, P.O. Box 40, 2027 Kjeller, Norway University of Oslo, Department of Physics, P.O. Box 1048 Blindern, 0316 Oslo, Norway Abstract When quantifying laser damage in silicon, two key parameters are of importance, namely the depth of the laser damaged region and the minority carrier lifetime in the laser processed region. In this paper, we investigate the depth of the electrically active laser damage as function of laser wavelength and laser pulse duration. By etch-back experiments, we find that the laser damage from picosecond laser pulses is confined to a considerably shallower region than what is the case for nanosecond pulses. This is as expected due to the longer available times for heat conduction experienced in the latter case. However, the depth of damage is also much shallower than what the linear optical absorption coefficient would suggest, pointing towards non-linear optical confinement. We also develop an analytical expression for the effective minority carrier lifetime measured on a wafer with a laser damaged region, and from this expression, we are able to give an estimate on the lifetime in the laser damaged region. Based on these findings, we develop an optimized laser process. Using a wavelength of 515 nm and a pulse duration of 3 ps, an effective lifetime of 1.8 ms is completely recovered after removal of just 240 nm of silicon from the wafer surface. The lifetime in the laser damaged region is in this case estimated to be on the order of 1 ns. © 2013 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the scientific committee of the SiliconPV 2013 conference Keywords: Laser ablation; laser damage; lifetime 1. Introduction In laser processing for silicon solar cells, the laser induced damage is a crucial factor. Both the electrical activity of the damage, in the form of reduction in minority carrier lifetime (from here: * Corresponding author. Tel.: +47 63806445; fax: +47 63812905. E-mail address: [email protected] J. Thorstensen et al. / Energy Procedia 00 (2013) 000–000 lifetime), and the distribution of the damage are of importance. While it is often stated that the depth of the laser induced damage or heat affected zone is reduced when using ultrashort lasers, this depth is rarely measured. In this paper, we present a comparison of the depth of laser induced damage encountered when using nanosecond and picosecond pulses. We ablate silicon nitride (SiNx) from a silicon substrate, etch away a controlled silicon thickness, and measure the effective lifetime of the wafer as function of removed silicon thickness. Furthermore, we develop an analytical model for the effective lifetime measured on a wafer with a laser damaged region at one surface. From the model and the measured depth of the laser damage, an estimate on the lifetime in the laser damaged area is given. 2. Theory 2.1. Depth of laser damage The penetration depth of the laser energy, ≈ + = 1/ + , is often assumed to be  , (1) where = 1/ is the optical penetration depth, is the optical absorption coefficient, τ is the pulse duration and Dth is the thermal diffusion coefficient. describes the depth at which the laser energy is actually deposited, while is the diffusion term, describing how far the energy may diffuse during the pulse. Some comments must be made to this model. Firstly, α is very often temperature dependent, and the temperature of the substrate increases during laser processing. As such, an effective optical penetration depth, should be applied. In order to correspond with the definition of , should be , , defined as the depth after which 1/e of the incoming laser energy remains. As normally increases with increasing temperature, is normally smaller than . Furthermore, the expression = , assumes that the heated material is removed within the duration of the pulse. While this may hold true for laser processing with long pulses, where much of the heated (molten) material is expelled during the laser pulse, it may not be true when applying ultrashort pulses. In this case, the material may be removed some time after the pulse , giving a larger diffusion depth than expected from the expression above. Furthermore, the value for Dth may deviate from its steady-state value, as the electron gas is strongly heated when applying ultrashort laser pulses. As such, the value for the penetration depth, should be treated with caution, and the link between and the depth of laser induced damage likewise. Engelhart et al.  have performed an experiment similar to ours, and report laser damage at 2, 3 and 25 µm, for 30 nanosecond pulses at 355, 532 and 1064 nm, respectively. With of 10 nm, 0.7 µm and ~300 µm for the three wavelengths, and of about 1.5 µm, this result shows that the laser damage in this case is situated deeper than , but may be situated shallower or deeper than both and , depending on which of the above mentioned processes are most dominant. At 355 nm, the depth of damage must be dominated by diffusion, as the optical penetration depth is very small. Hence, ≃2 µm for this pulse duration (eq. (1) gives = 1.5 µm using Dth from ). At 1064 nm, the depth of damage must be dominated by the optical penetration depth . With ~300 µm at this , wavelength, we see that is much smaller than at this wavelength as discussed above. , Some general trends can be expected when going to shorter pulses. With very short laser pulses, heat transport is strongly reduced. In addition, α increases with increasing optical intensity, as a result of nonlinear processes. These two factors both contribute to stronger confinement of the laser energy when applying ultrashort laser pulses. J. Thorstensen et al. / Energy Procedia 00 (2013) 000–000 2.2. Lifetime in laser damaged region We are also interested in estimating the lifetime encountered in the laser damaged region, and need an expression for the effective lifetime measured in a wafer with laser damage near one surface. Applying the geometry shown in Fig. 1, we investigate the minority carrier distribution in the laser damaged region. We assume that photogeneration occurs only in the undamaged bulk of the wafer, and assume that S2 is small compared to the recombination taking place in the laser damaged region. We use the continuity equation =− − = − . (2) where U is the recombination, J is the electron current, Dn is the electron diffusion coefficient, electron density and is the electron lifetime. The stationary solution gives = . is the (3) We apply the boundary condition of zero recombination current across S2. The carrier density in the laser damaged region becomes ( ( ) = cosh ) , (4) with S2 at = + where + is the total wafer thickness, and is the width of the laser damaged region, assumed to be constant over the wafer. The total recombination in the laser damaged region can be found by integrating over the laser damaged region, ∈ [ , + ]: ( ) =∫ = sinh . (5) Fig. 1. Wafer with laser damaged region. Thicknesses, lifetimes and surface recombination velocities are indicated. Inserting a virtual boundary between bulk and laser damaged region ( = ), a surface recombination velocity (SRV) can be defined as ≡ ( ) = tanh (6) where ( = ) is the electron concentration at = . We see that the effective SRV from the laser damage depends on both w and . For ≫ , i.e. laser damage much deeper than the diffusion length, the recombination saturates, and ≈ / is independent of w. For a powerful analysis tool, the expression in eq. (6) can be combined with expressions by Sproul  for the effective lifetime and the surface lifetime: J. Thorstensen et al. / Energy Procedia 00 (2013) 000–000 = where + = + , (7) is the smallest eigenvalue solution of the equation tan( Here, we apply eq. (6) for )=( + )/( − ). (8) , in order to obtain the effective lifetime of the laser damaged structure. 3. Experimental We deposit a 75 nm thick a-SiNx:H (SiNx) film by plasma-enhanced chemical vapor deposition (PECVD) on polished silicon wafers. The SiNx has a refractive index of around 2.05 at a wavelength of 633 nm. We ablate the SiNx by applying non-overlapping laser pulses at 1030, 515 and 343 nm and a pulse duration of 3 ps using a peak fluence of 0.86, 1.2 and 2.1 J/cm2 at 1030, 515 and 343 nm, respectively, and at 532 nm and 100 ns pulse duration using a peak fluence of around 20 J/cm2. The remaining SiNx is removed in an HF dip, and the samples are etched in a concentrated (47 %) KOH solution at 85 °C, showing an etch rate of approx. 1 µm/min. The etch depth is measured by gravimetry, assuming uniform material removal over the wafer. The accuracy of the measurement is +/- 0.2 mg, corresponding to approx. 20 nm etch depth. The samples are then passivated by amorphous silicon (a-Si), ensuring very low SRV, and the effective lifetime of the samples is measured by photoluminescence imaging (PL) using a LIS-R1 setup from BTimaging. The lifetime measured in the laser processed areas is normalized to the effective lifetime measured in damage-free areas. As defects or surface roughness may act as seeds for etching, thereby increasing the local etch rate, we analyze the shape of the laser spots before and after etching by atomic force microscopy (AFM). If the laser spot gets deeper by etching, there would be a preference for etching in the spots, and hence, the depth of damage must be corrected correspondingly. 4. Results 4.1. Depth of laser damage When etching the wafers, the lifetime in the laser treated areas is gradually restored, at some point reaching the 1.8 ms seen outside of the laser treated areas. AFM analysis shows that the shape of the laser spot remains constant with etching, ruling out the possibility of preferential etching in the spots. The results of the etch-back experiments are shown in Fig. 2 (left), showing that the depth of the laser damage using ultrashort pulses is in the range of 70 – 130 nm for 343 nm (between the last measurement point showing lifetime degradation and the first measurement point showing complete recovery of the lifetime), 120 – 240 nm using 515 nm and below 210 nm using 1030 nm laser wavelength (we unfortunately don’t have any measurements showing lifetime degradation for this laser wavelength and pulse duration). Using long laser pulses at 532 nm, the damage is situated much deeper, in the range of 1.8 – 2.7 µm. This depth corresponds approximately to . It should be noted that also on non-laser treated reference samples, surface-near damage was observed as reductions in effective lifetime down to a depth of approx. 70 nm. This is attributed to ion bombardment damage from the PECVD-process. However, this ion bombardment damage is less pronounced than the laser damage, making it easy to extract the contributions from laser induced damage. It is interesting to note the difference between long and short pulses at wavelengths at 515 nm laser wavelength. The 3 ps, 515 nm pulse results in a much more shallow damage than at the same wavelength J. Thorstensen et al. / Energy Procedia 00 (2013) 000–000 using long pulses, confined to within 240 nm of the wafer surface. This is a result of the elimination of thermal diffusion (which at a pulse duration of 3 ps would correspond to around 20 nm). Comparing with measurements by Engelhart et al., the same reduction is also seen in the UV, where the depth of damage using long pulses was dominated by thermal diffusion. Using 3 ps, 343 nm pulses, thermal diffusion is eliminated, and the depth of damage is much smaller. At 1064 nm, the depth of damage using nanosecond-pulses  was around 25 µm, and dominated by the optical penetration depth. Using 3 ps, 1030 nm pulses, we see no reduction in lifetime even at 210 nm from the surface, indicating that the optical penetration depth must have been dramatically reduced (by two orders of magnitude!), as a result of non-linear absorption mechanisms using ultrashort pulses. In combination, the comparison between depth of damage using nanosecond and picosecond lasers at three wavelengths shows that both the optical penetration depth and the thermal diffusion depth are decreased using ultrashort laser pulses. Fig. 2. (Left) Relative lifetime measured as function of etch depth using four different lasers. (Right) Modeled effective lifetime (solid lines) assuming three different values for and measured effective lifetime (symbols) as function of depth of laser damage. Also shown is a calculation of effective lifetime taking into account the finite area coverage and geometry of the laser damage (dotted line). 4.2. Lifetime in laser damaged region We plot the modeled effective lifetime as extracted using eqs. (6-8) as function of the remaining laser damage, shown in Fig. 2 (right) as solid lines. The measured effective lifetime is shifted along the x-axis for best fit, shown as symbols. We see that for the 515 nm, 3 ps sample, a fairly good fit is found if inserting a lifetime in the laser damaged region of 1 ns. However, as we only have a limited number of experimental values, a smaller lifetime in the laser damaged region would give an equally good fit. For the 532 nm, 100 ns sample, however, the fit is not as good, indicating that other effects are taking place. One effect could be the geometry of the laser damage. We have applied spots in a square pattern, with 30 µm pitch. Using long laser pulses, it is not unreasonable to assume that the molten volume will be deepest in the middle of the laser spot. Assuming that the laser damaged volume has the shape of a paraboloid with depth 1.8 µm (estimated from the etch depth showing recovery of the effective lifetime), the area fraction of laser damage will decrease as we etch into the wafer, decreasing the effective SRV. With a width of the paraboloid at the wafer surface of 30 µm, we can calculate the fill factor of the laser damage as function of etch depth. We can then apply Fischer’s formula for effective SRV  = arctan − exp − + + . (9) J. Thorstensen et al. / Energy Procedia 00 (2013) 000–000 Here W is the wafer thickness, p is the laser spot pitch, f is the fill factor of laser damage and Spass is the passivated SRV. Using this value for Slaser, and using a modeled lifetime in the laser damaged region of 100 ns, the red dashed line in Fig. 2 is obtained. Although still not a perfect fit to experimental data, the fit is now much better. Arguably, the assumption that the laser damaged depth takes on a parabolic shape is somewhat arbitrary. In addition, the shape of the lifetime curve using long pulses may also be a result of other mechanisms, such as varying lifetime throughout the laser damaged region. As such, the dashed line in Fig. 2 is only meant as an indication that the shape of the lifetime curve will vary with assumptions on damage geometry and variations in lifetime throughout the laser damaged region. 5. Conclusion We have measured the depth of laser-induced damage in silicon using ultrashort and long laser pulses, by etch back experiments. The laser-induced damage in silicon is found to be confined within 70 nm, 240 nm and 210 nm for 3 ps laser pulses at 343, 515 and 1030 nm, respectively. This is a strong reduction in depth of damage compared to what was observed by Engelhart et al.  using nanosecond pulses at corresponding wavelengths. We conclude that strong reduction in thermal diffusion and non-linear confinement of the optical energy cause this trend. With knowledge of the depth of laser damage, the laser source can be more efficiently targeted to a specific process. As an example, in our process for creation of diffractive structures in silicon , 300 – 350 nm of silicon is removed by etching after laser processing. As such, laser damage is expected to be removed when applying any of the three picosecond lasers investigated herein, yielding a process where the laser-induced damage is eliminated. Acknowledgements This work has been funded by the Research Council of Norway through the project “Thin and highly efficient silicon-based solar cells incorporating nanostructures”, NFR Project No. 181884/S10. References        D. Bäuerle, Laser Processing and Chemistry, 3rd ed., Springer, Berlin Heidelberg, 2000. R. Holenstein, S.E. Kirkwood, R. Fedosejevs and Y.Y. Tsui, Simulation of femtosecond laser ablation of silicon, in: Proc. SPIE 5579, Photonics North 2004: Photonic Applications in Telecommunications, Sensors, Software, and Lasers, Spie, Ottawa, Canada, 2004: pp. 688–695. P. Engelhart, R. Grischke, S. Eidelloth, R. Meyer, A. Schoonderbeek, U. Stute, et al., Laser Processing for Back-contacted Silicon Solar Cells, in: ICALEO Congress Proceedings, Scottsdale, AZ, 2006: pp. 218–226. H.R. Shanks, P.D. Maycock, P.H. Sidles and G.C. Danielson, Thermal conductivity of Silicon from 300 to 1400 K, Physical Review. 130 (1963) 1743–148. A.B. Sproul, Dimensionless solution of the equation describing the effect of surface recombination on carrier decay in semiconductors, Journal of Applied Physics. 76 (1994) 2851–2854. J. Schmidt, A. Merkle, R. Brendel, B. Hoex, M.C.M. Van De Sanden and W.M.M. 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