Master_thesis_Johan_Blanker.

Master_thesis_Johan_Blanker.

TiO

2

nanoparticles as back reflector in thin-film solar cells

Master thesis

Sustainable Energy Technology

Johan Blanker 2012

TU Delft PVMD research group

Date of Master thesis defence:

15-01-2013

Graduation committee: prof. dr. M. Zeman - dr. ir. A.H.M. Smets - dr. ir. T.J. Savenije

Supervisor: dr. ir. R. Santbergen

Abstract

In this work investigation is done on the optical properties of a layer of binderfree TiO

2 nanoparticles for the use of back reflector material in thin-film photovoltaic solar cells. Different deposition methods are researched where dropcasting appears to be the most suitable deposition method, due to its simplicity.

Optical properties are determined when light is scattered at both the interfaces of

TiO

2

nanoparticles/air and TiO

2 nanoparticles/silicon. Refraction affects the angular intensity distribution significantly. When light is scattered into material with a high refractive index this results in a much narrower angular intensity distribution. Experiments with a combination of binder-free TiO

2

nanoparticles and silver nanoparticles show that this combination can be used to keep a broad angular intensity distribution when scattering light in a medium with a higher refractive index.

Different solar cells are fabricated and simulated and the material is compared with silver as back reflector. It is shown that binder-free TiO

2 can be competitive with silver for back reflector material and simulation software can accurately simulate this material in a solar cell. i

Preface

This research is a thesis of the Delft University master study Sustainable Energy

Technology (SET), which is a study that focuses on different facets of the transition from present day energy delivery to the to be believed new standard, where the energy cycle is sustainable. This means that the sources used to extract the energy from are inexhaustible. The basic available sources are geothermal energy, tides, wind energy and solar energy.

This study will not focus on the reason for this need, whether it is the depletion of fossil fuels, the need for less pollution or a logic next step in the industrial evolution from carbon rich fuels to carbonless fuels (coal-petrol-methanehydrogen), but take the fact for granted and assume that all readers can acknowledge that there is a necessity for the use of renewables for some of the above reasons. With this graduation project I hope to contribute to this transition and work towards a, in my opinion, better world.

This research is done in the research group of Photovoltaic Materials and Devices

(PVMD) which focuses on the development of thin-film solar cells. This group has the two general interests to be named “Materials and technologies for low-cost

solar cells” and “Advanced concepts for high-efficiency solar cells”, with the general intention to decrease the costs and quantities of material and number of layers deposited, and increase the energy extracted from the solar cell. This is done by both improving the electrical properties within the cell introducing novel structures and materials and improving the light management by antireflective coating and adding intermediate and back reflectors.

Acknowledgements

I would like to thank the PVMD group for allowing me to work in their group, and especially Rudi Santbergen for the guidance in my research and Hairen Tan for all the lab work he has done for me. Further gratitude goes to Benjamin Lee from the

National Renewable Energy Laboratory (NREL), as his research formed the foundation for this research and he provided the TiO

2

-nanoparticles. ii

Table of content

Abstract ................................................................................................................................................ i

Preface .................................................................................................................................................. ii

Acknowledgements .............................................................................................................................. ii

List of figures ........................................................................................................................................ v

List of Tables ........................................................................................................................................ vi

1. Introduction .................................................................................................................................... 1

1.1 Crystalline silicon solar cells ...................................................................................................... 1

1.2 Thin-film solar cells.................................................................................................................... 2

1.3 External quantum efficiency ..................................................................................................... 4

1.4 Reflection .................................................................................................................................. 4

1.5 Light trapping ............................................................................................................................ 5

1.6 Scattering .................................................................................................................................. 6

1.7 The Yablonovitch limit ............................................................................................................... 8

1.8 White paint ................................................................................................................................ 9

1.9 Objectives ................................................................................................................................ 10

2. Experimental setup and simulation models .................................................................................. 12

2.1 Perkin-Elmer Lambda 950 ....................................................................................................... 12

2.2 The profilometer Dektak 150 .................................................................................................. 15

2.3 Opticalculate ........................................................................................................................... 15

2.4 ASA .......................................................................................................................................... 18

3. Fabrication and optical properties of white paint ......................................................................... 20

3.1 Different deposition techniques ............................................................................................. 20

3.2 Optical properties of white paint at the interface with air ..................................................... 28

3.3 Scattering properties at white paint-silicon interface ............................................................ 31

iii

4 Simulation and fabrication of solar cells ........................................................................................ 39

4.1 Solar cell designs ..................................................................................................................... 39

4.2 Fabricated solar cell results ..................................................................................................... 41

4.3 ASA Simulations ....................................................................................................................... 46

4.4 Discussion ................................................................................................................................ 48

5 Conclusions and recommendations ............................................................................................... 50

Conclusions ................................................................................................................................... 50

Recommendations ........................................................................................................................ 51

Literature ........................................................................................................................................... 52

Appendix 1: ASA input file ................................................................................................................. 55

Appendix 2 Dektak results dropcasted samples ............................................................................... 57

Appendix 3 Scattering WP with different thicknesses ...................................................................... 59

Appendix 4 ASA parameters in simulations ...................................................................................... 60

iv

List of figures

Figure 1 Schematic of a c-Si solar cell [1]. ............................................................................................................... 1

Figure 2 Atomic lattice of c-Si (left) and a-Si (right) [1]. .......................................................................................... 2

Figure 3 Schematic of a a-Si cell [1]......................................................................................................................... 3

Figure 4 Diffuse and specular reflection [31]. ......................................................................................................... 4

Figure 5 Different incident angles and total internal reflection [30]. ..................................................................... 5

Figure 6 Reflection coefficient versus angle of incidence illustrating the Fresnel equations [3]. ........................... 6

Figure 7 Artist impression of diffuse reflection by a back reflector. ....................................................................... 7

Figure 8 Surface and bulk scattering [25]. .............................................................................................................. 8

Figure 9 Annealing effect on TiO

2

: the resistivity as function of annealing time and temperature [16]. ............. 10

Figure 10 Top view schematic of the ARTA. .......................................................................................................... 12

Figure 11 Measured angular intensity distribution of the reflection measured in at wavelengths 350-850nm. . 13

Figure 12 Schematic of the ISRT setup. ................................................................................................................. 14

Figure 13 Dektak 150 measuring........................................................................................................................... 15

Figure 14 AID based on the Phong distribution [3]. .............................................................................................. 17

Figure 15 Illustration of a simulated reflector indicating the dominant parameters at different wavelengths ... 17

Figure 16 Changes in EQE with different thicknesses (left) and AID (right) ........................................................ 18

Figure 17 Height profile of best obtained result dropcasting, (b) photo of samples on Asahi and Corning glass. 21

Figure 18 Spin-coating results with different solutions (Left to right: DI-water, ethanol, methanol, aceton). ... 22

Figure 19 Best obtained result spin-coating, thin(left) and thicker(right) layer. .................................................. 23

Figure 20 Best obtained result spin-coating, thin(left) and thicker(right) layer. .................................................. 23

Figure 21 Proposed snow globe method [15]. ...................................................................................................... 24

Figure 22 Snow globe setup and results ............................................................................................................... 24

Figure 23 Result “snow globe” method with methanol: (a) Dektak result and (b) photo of the sample. ............ 25

Figure 24 Schematic illustration of pressure paste. .............................................................................................. 26

Figure 25 Pressure paste results. Height profile (a) and photo of the sample (b) ................................................ 26

Figure 26 IS results: absorption (a), transmission (b), reflection (c), and haze (d). .............................................. 28 v

Figure 27 Transmittance plotted against thickness and compared to the results of B. Lee [8]. ........................... 29

Figure 28 AID result of white paint measurement with ARTA. ............................................................................. 30

Figure 29 Single wavelengths compared to the Lambertian distribution. ............................................................ 30

Figure 30 Setup of measurements for Opticalculate study. ................................................................................. 31

Figure 31 Simulation and measurement of double side polished c-Si wafer. ....................................................... 32

Figure 32 Absorption of wafer and wafer with white paint. ................................................................................. 33

Figure 33 Simulations and measurement with Tipp-ex. ....................................................................................... 34

Figure 34 Transition simulated for wafer with white paint. ................................................................................. 35

Figure 35 Simulation transition phase of wafer with white paint and nanoparticles. .......................................... 37

Figure 36 The different scattering distributions based on the simulations. ......................................................... 38

Figure 37 Schematics of the different cell configurations, left to right: flat NIP, rough NIP, flat PIN, rough PIN. 40

Figure 38 Measured EQE of flat NIP cell with and without white paint and silver back reflector. ....................... 41

Figure 39 Measured EQE of rough NIP cell with and without white paint and silver back reflector. ................... 42

Figure 40 Measured EQE of rough NIP cell (with adjusted values for the results without back reflector). ......... 42

Figure 41 Measured EQE of a flat PIN solar cell without and with silver and white paint back reflector. ........... 44

Figure 42 EQE of a rough PIN solar cell without and with silver and white paint back reflector. ........................ 45

Figure 43 ASA simulations of flat cells .................................................................................................................. 46

Figure 44 ASA simulations of rough cells .............................................................................................................. 47

Figure 46 Measurements and simulations compared........................................................................................... 49

List of Tables

Table 1 Summarizing table deposition methods ................................................................................................... 27

Table 2 Thicknesses of white paint layers for different samples .......................................................................... 29

Table 3 Parameters of the different cells. ............................................................................................................. 48

vi

1. Introduction

This study focuses on a development within the field of photovoltaic solar cells, hereafter simply named solar cells. These solar cells convert light directly into electricity. This is done by exciting electrons from the valence band into the conduction band and separating the formed electron and electron hole pair. There are many different types of solar cells and related technologies. The crystalline silicon solar cell is the dominant technology used in present day industry and therefore the structure and working principles of this technology will briefly be discussed in section 1.1. This will be followed by a similar introduction of thin-film solar cells (1.2), as that is the field in which this research is done, explaining the fundamental differences with the crystalline silicon cells. This chapter continues by elaborating on some theoretic fundaments related to this research (1.3-1.7) and at the end of this chapter some previous research is discussed (1.8) leading to the objectives of this work (1.9).

1.1 Crystalline silicon solar cells

Crystalline silicon (c-Si) solar cells have a structure based on a p-doped silicon wafer varying in thickness between 200-500 µm with a n-doped top layer and a stronger p-doped bottom layer

(schematically shown in figure 1). Layers are doped to increase the number of charge carriers. In

silicon p-type doping is done by adding a trivalent atom such as boron to the material, creating extra positive charge carriers, also called electron holes. The top layer of the cell consists of a n-doped layer (usually doped with phosphorus), creating extra negative electron carriers. At the junction between the p-layer and n-layer, respectively electrons and electron holes diffuse into these layers and form a depletion region without surplus carriers and free electrons. At this region an internal electrical field is created with a positively charged n-layer and negatively charged p-layer [1].

Figure 1 Schematic of a c-Si solar cell [2].

1

Light can be absorbed by the material when the energy of a photon is higher than the difference between top of the valence band and the bottom of the conduction band, which is defined as the band gap of the absorber material. In c-Si this band gap is 1.11 eV corresponding to a wavelength of

1107 nm. This means that light with larger wavelengths is not absorbed.

When a photon with sufficient energy is absorbed in the bulk material it excites an electron into the conduction band, resulting in an electron and an electron hole that can move freely through the material. For generating electricity the electron must reach the depletion region by diffusion where it will be transferred into the n-layer by the electric field. The electron returns via an external circuit and the extra p-doped layer at the back contact to the bulk material to recombine with an electron hole. Diffusion is limited to the lifetime of the excited electron, because after some time the electron will recombine with electron holes in the p-type layer. This time is related to the diffusion length.

The diffusion length of the electrons in the p-doped material must be larger than the thickness of the layer and is a very important parameter, and it strongly determines the performance of these devices. This parameter can be manipulated by the doping concentrations and the diffusion length is in the range of 250-700 µm. As the dominant transport mechanism of the electrons is diffusion, the c-Si solar cell is called a diffusion device [2] [3].

1.2 Thin-film solar cells

A thin-film silicon solar cell consists of amorphous silicon (a-Si) rather than c-Si, schematics of the

difference in atomic structure is shown in figure 2. Crystalline material has an atomic unit cell with

defined coordination numbers, which is repeated throughout the entire lattice, where amorphous silicon is a material with an undefined long range order of atoms, and the microstructure is still a topic of investigation [4] [5].

Figure 2 Atomic lattice of c-Si (left) and a-Si (right) [2].

In textbooks it is often represented as a continuous random network, with some longer and some shorter bond lengths and some of the bonds in the material are broken resulting in dangling bonds.

2

For solar cells these dangling bonds have a strong negative effect as dangling bonds strongly promote recombination. When hydrogen is incorporated during the deposition of the material, hydrogen atoms attach to most of the dangling bonds counteracting their negative effect. This is called passivation.

Thin-film silicon solar cells are considered a low-cost alternative to the currently dominant c-Si solar cells as thin-film silicon solar cell consists of a typically 300 nm thin intrinsic amorphous silicon film with on the one side p-doped and on the other side n-doped layer both with a limited thickness of about 20 nm. This p-i-n structure is sandwiched between a transparent front and reflective back

contact layer (figure 3).

Figure 3 Schematic of a a-Si cell [2].

The working principles of the thin-film solar cells are somewhat different from the c-Si cells. In the amorphous material the created electron and electron hole pairs have a much shorter lifetime and charge transport cannot be based on diffusion. Instead a two order of magnitude stronger doped p- and n-layer are placed on either side of intrinsic amorphous layer. These doped layers set up an electric field across the entire intrinsic layer resulting in a drifting force to separate the formed electron and the electron hole. As drift is the dominant transport mechanism in this type of solar cells this is also called a drift device. Both the tendency of recombination and the electric field limit the ideal thickness of these cells.

Another fundamental difference between amorphous and crystalline material is the band gap.

Amorphous silicon has a relatively high band gap of roughly 1.7 eV corresponding to a wavelength of

730 nm. However, due to the inhomogeneity of the material and unequal band strengths the band gap is not as well defined as for c-Si. Locally photons with lower energies can be absorbed in socalled band tails. However, the mobility of these electrons and therefore generating electricity is fairly limited. Wavelengths up to slightly over 800 nm can be absorbed and generate electricity.

3

The high band gap means that much of the high energy photons are absorbed and much more of this energy is converted to electricity. This results in a relative high open circuit density voltage (V

oc

) of approximately 0.9 V (compared to about 0.7 V for c-Si cells), but reduces the short circuit current density (J

sc

) to about 14.5 mA/cm

2

where c-Si provides J

sc

of about 42 mA/cm

2

[2].

1.3 External quantum efficiency

The external quantum efficiency (EQE) is often used to express the efficiency of a solar cell and is defined as the ratio of charge carriers collected by the solar cell to the number of photons of a given energy incident on the solar cell. Ideally every photon created a charge carrier that is collected by the solar cell leading to a ratio of 1.0, but there are a number of losses. Due to recombination not all created charge carriers will be collected, some light is absorbed in another layer than the absorber layer, some of the incident light does not carry enough energy to overcome the band gap, and there are some optical losses due to reflection and transmission [1]. Also, the short circuit current density can be found with the EQE. The J

SC

is calculated from the EQE by the convolution with the AM 1.5g solar spectrum and by integrating over the wavelength range. This method avoids uncertainties in the determination of the solar cell surface area. [6]

1.4 Reflection

Because of the limited thickness of the a-Si film the lower energetic photons, (wavelengths above

730 nm) cannot easily be absorbed in a single pass. For obtaining high photocurrent it is therefore of great importance that light can pass through the silicon film several times without escaping. In today’s thin-film solar cells this is mostly based on the introduction of surface-texture (i.e. rough surfaces) to scatter the light at the front or back, and a reflector, often a metal film layer, at the back of the silicon film [7]. Without a textured surface the light is reflected back under the same angle as the incident angle relative to the surface normal, and the light passes the absorber layer twice. This mirror-like reflection is called specular reflection. When one of the interfaces that the light crosses is textured, the back reflector scatters the light in a broad range of directions, called diffuse reflection,

as shown in figure 4.

Figure 4 Diffuse and specular reflection [34].

4

When non-ideal scattering occurs there is both a specular and diffuse component of reflected light that can be separated to analyse the scattering properties of a material, with ideal scattering there is no specular peak left. The manipulation of the direction of the light is called ‘light management’.

1.5 Light trapping

One of the phenomena used in light management is light trapping. This is based total internal reflection. Total internal reflection means that all of the light is reflected when a light beam that approaches the interface of two media under an angle larger than the so-called critical angle , as

shown in figure 5.

θ

θ

2

2

1

Figure 5 Different incident angles and total internal reflection [33].

With the Fresnel equations it can be determined what fraction of the light is transmitted and what fraction of light is reflected at the interface and thus be trapped in the medium. This is dependent on the incident angle , measured from the interface normal, and the refractive indices of the media on either side of the interface. The reflection coefficient for a flat interface is given by:

| | { } { } (1)

Where is the modified refractive index adjusted for polarization of the light, is the refractive index of the material, and corresponds to the angle of incidence and refraction. Sunlight is equally p-and s-polarized and considered unpolarized.

In figure 6 these equations are illustrated showing that when light travels from a medium with a

higher to a lower refractive index there is a critical angle for which accounts that at angles total internal reflection is reached. The interface of glass and air serves well as demonstrator with the critical angle at 41.8

o

clearly showing behaviour of the equation for incident angles smaller and larger than this angle [3].

5

Figure 6 Reflection coefficient versus angle of incidence illustrating the Fresnel equations [3].

A simpler equation is Snell’s law, (equation 2) that correlates the refraction angles to the differences in refractive indices when light passes an interface and neglects the reflection. When

2

(external medium) gets closer to 90 o

this indicates that the directional propagation of the transmitted lights is closer towards the interface.

(2)

For angles

2

of 90 o

and larger angles no transmission occurs, and total internal reflection occurs.

When

2

is 90 o

, becomes the critical angle . This results in equation 3 below. The arcsine is not defined for values larger than 1, which also shows that total internal reflection can only occur with the internal index of refraction being larger than the external index.

( ) (3)

1.6 Scattering

Light scattering indicates that incident light is reflected or transmitted diffusely and in different angles resulting in a distribution of intensity under different angles. This is called the angular intensity distribution (AID). This research focuses on the AID of the light reflected by the back reflector. This is dependent on the scattering properties of the back reflector material.

6

Figure 7 shows a simplified picture of the reflection with the back reflector and the absorber layer

indicated. Most light reflected in an angle smaller than relative to the normal is lost (the red area), light reflected under a larger angle is fully internally reflected and trapped in the absorber layer.

Figure 7 Artist impression of diffuse reflection by a back reflector.

The intensity of scattered light at a certain angle increases under larger angles as the area of the sphere increases and it is calculated by:

(4)

This is also graphically shown in figure 7 where an equal angle θ from the surface upwards shows a

much larger distribution area (the light green area). Except the increased intensity also the path length L = d/cos increases with larger reflection angles. This explains the relevance of diffuse scattered light scattered under a large angle. The Lambertian distribution, which is defined as a perfect diffuse angular intensity distribution, provides light distributed evenly over the whole hemisphere resulting in that the AID will look like . This is a limit that can be approximately reached by intensely roughening the reflector surface and use materials with good scattering properties.

7

Back reflectors can work under two different mechanisms namely surface scattering and bulk scattering. There are some fundamental differences between these mechanisms. Surface scattering works like a mirror, the light does not enter the back reflector material, but is completely reflected at

the interface as denoted A to B in figure 8.

Figure 8 Surface and bulk scattering [30].

Bulk reflection is caused by the Tyndall effect that can be approached by Mie scattering material.

Small pigments, in the order of magnitude of the wavelength scatter the light in random directions.

And is partially reflected (A to C). When a layer is thick enough this results in total reflection (A to D).

Consequences of bulk scattering are that the optical properties of a bulk material reflector are of importance as the light passes the interface and the light will be refracted towards the normal when returning into the interface. On the other hand the reflection is diffuse, as the continuous reflection and refraction within that material will return the light in all directions. As long as the particles are not orders of magnitude smaller than the wavelengths, the influence of the size of the particles is negligible [8] [9].

1.7 The Yablonovitch limit

The Yablonovitch limit has defined the maximum absorption enhancement due to perfect scattering.

It is defined as 4

2

with n being the refractive index of the active layer. This limit is constructed by the chance of the photon to be internally reflected and the enhanced path length of the light. The chance that light is reflected in a smaller angle than the critical angle is leading to a maximum of

2

internal reflections. The reflection on itself increases the path length by a factor 2, as it passes the absorber layer at least twice. The average path length enhancement due to internal reflection

(D/cos(θ)) is also a factor 2. This leads to a total increase of 2x2

2

= 4

2

[10].

It has been proved that the Yablonovitch limit can be surpassed. However, up to now only at specific wavelengths using interference and smart nanostructuring have led to beating of this limit [11]. The limit still holds for overall absorption enhancements.

8

1.8 White paint

TiO

2 is the white pigment that combined with a binder is better known as white paint. With sufficient thickness it can function as a bulk scattering material. This white paint is used as back reflector in some industrial thin-film solar cells [12]. There is still research done to improve the optical properties of these reflectors. In this section the optical properties of white paint as found in literature will be discussed (1.8.1). This is followed by reviewing some novel researches done that are relevant to this thesis (1.8.2).

1.8.1 Optical properties of white paint

The band gap of rutile TiO

2

is 3.06 eV, (λ=405 nm) [13], which means that the material does not absorb light for wavelengths larger than 405 nm. The refractive index of TiO

2

is n=2.74 (at λ=550 nm) which can be considered reasonably high. As explained before, the difference of refractive index at the interface determines critical angle and refraction towards the normal is less with smaller difference in refractive index. However, with conventional used white paint the TiO

2

is mixed with a binder material with a much lower refractive index, typically in the order of n=1.4-1.7, decreasing the effective refractive index (n eff

) of the paint, which is determined by volume fraction of either material. It can be assumed that the effective refractive index of white paint with binder with good optical properties is about n eff

≈1.8 [14].

White paint seems to have excellent scattering properties with values close to the Lambertian distribution [15] [14]. These observations were made measuring the angular distribution at λ =633 nm at the interface of the white paint and air.

There have been different studies comparing white paint to other back reflectors, considering white paint as a competitive alternative for silver back reflectors. It offers several advantages.

First of all, it is capable of high optical reflectance over a broad wavelength band, which is a primary goal for a reflector [12] [14]. Secondly, it scatters light diffusely, maximising the fraction of photons that are trapped due to total internal reflection at both cell surfaces, which is now managed by surface texturing [16] [17]. Finally, it has the potential for low cost production, it is a material that is widely available on earth, making its intrinsic value low in comparison to silver. If it can eliminate texturing the solar cells, it eliminates both a process step as well as cell damage occurring due to depositions on textured substrates. [16] [17]

9

1.8.2 Novel research

Recently novel research has been done on the effect of using binder-free 270 nm rutile TiO

2 nanoparticles to improve scattering. A high concentration of densely packed nanoparticles with air in between them results in an n eff

≈2. Due to this higher n eff

an improvement over the conventional white paint is a more diffuse scattering of the light. These nanoparticles were deposited by dropcasting and this back reflector tested and compared with alternatives on absorption enhancements in a c-Si wafer and improvements on EQE in solar cells. It revealed that binder-free

TiO

2

can boost the performance with at least twice as much as a flat BR with over 50 % improvement of overall cell performance. It must be noted that this improvement was found on a 2.5 µm thick c-Si film which had a fairly poor EQE of a maximum under 30 % efficiency without a back reflector. [9]

There has also been done novel research on different deposition methods called snow globemethod, for creating a white paint coating. By deposition through a liquid medium the material will whirl down on the substrate creating a very homogenous layer. [18]

Other previous research focused on influencing the conductivity of TiO

2 as the material is initially an

insulator. Figure 9 below shows the conductivity of a rutile TiO

2.2

film as a function of annealing time.

This result is found on a continuous layer in contrast to the TiO

2

nanoparticles to be researched in this work, but it is an intrinsic material characteristic while the transparency is determined by the bulk structure. This figure shows that with annealing the conductivity of the material could be influenced [19]. However, even if the optimal result could be achieved in our work, the resistivity would be brought back to about 1 Ωm. This reduction is insufficient for conduction towards a back contact or for use as back contact itself, as that would require a resistivity in the order of 10

-6

Ωm and in the orders of 10

-8

Ωm respectively.

Figure 9 Annealing effect on TiO

2

: the resistivity as function of annealing time and temperature [19].

10

1.9 Objectives

This thesis builds on expanding the previous research done by Lee [9] and in the continuation of this report reference to white paint will indicate binder-free white paint material. When conventional white paint is meant (i.e. with binder), this will be mentioned explicitly.

The objective is to analyse binder-free white paint, by determining the best deposition methods, find the scattering properties of the material and the effect on the different solar cells. Furthermore the goal is to create input variables that can represent the white paint for the simulation tools.

In this research the optical properties of the white paint are determined, both as single layer material and as back reflector within different solar cells. The optical properties of binder-free white paint are investigated in relation to thickness and scattering properties in different media are investigated.

Different deposition procedures to apply white paint back reflectors are investigated, such as dropcasting, spin-coating and the snow globe method.

Several solar cell configurations are fabricated and simulated. The white paint is tested on different a-Si solar cells fabricated in the PVMD laboratory and are compared to both a silver back reflector as the reference cell, as no performance improvement of high quality a-Si solar cells have been found in literature. The next step then is to optimize the performance of a-Si solar cells with white paint back reflectors and optimize scattering.

This research is subdivided in multiple sections. In chapter 2 the different tools and models used are introduced. In the next chapter, the white paint is analysed as a single layer sample. The samples are tested on overall reflectance/ transmittance, and the angular intensity distribution. The 4th chapter will include the fabrication and simulation of solar cells of different kinds, comparing the results of white paint back reflector with other back reflector and without any back reflector. The report will finish with a section including conclusions and recommendations based on the results discussed in the report.

11

2. Experimental setup and simulation models

This chapter considers all different experimental setups including explanation of the models used for simulating different layers and cells.

2.1 Perkin-Elmer Lambda 950

The Perkin-Elmer Lambda 950 allows to measure reflection and transmission of samples correlating to specific wavelengths. Technical specifications can be found at the manufacturer’s site [20] [21].

This chapter will discuss used settings and practical information relevant to this research.

The machine has different extensions with different possibilities for measuring samples. First discussed in 2.1.1 is the extension called the Automated Reflectance / Transmittance Analyser (or in short ARTA). Afterwards in 2.1.2 the integrating sphere is discussed, which is the other used extension.

2.1.1 ARTA

The ARTA allows to measure the reflection and transmission of a sample under different angles. For

this research only reflection is measured with the ARTA. The tool has a detector (C in figure 10) that

measures a horizontal plane of 360 degrees circle around the sample and determines the intensity of light reflected or transmitted to each angle. The light beam enters the measurement area via mirror

A (as indicated in figure 10) which blocks the area behind it (area D) restricting the detector to

measure reflection there. The incident angle of illumination of the sample can be adjusted by adjusting the orientation of the sample holder (B). This allows to measure distribution of different incident angles.

Figure 10 Top view schematic of the ARTA.

12

The sample is placed under a slightly tilted angle of 10

O

to overcome the problem of the specular reflection otherwise cannot be measured. The distribution of the reflected light can be measured from -90

O

to 90

O

degrees but a homogenous scattering distribution is assumed and therefore measurements are restricted from 0

O

to 90 o

relative to the specular peak. The output of the ARTA is given in absorbance ‘A’ and the relative intensity of the scattered light of the horizontal plane over the hemisphere can be calculated by .

Figure 11 Measured AID of the reflection measured in at wavelengths 350-850nm.

The reflection and transmission is scattered in all directions, but only the small part scattered in the horizontal plane is measured. This results in that typical intensities found are in the order of magnitude of 10

-4

. The output is set in arbitrary units as the measurement is also dependent on the detector slit used and the exact values are not relevant. This measurement gives a scattering distribution with different angles and wavelengths. This distribution is comparable and gives a good indication on the scattering properties of different materials. Demonstration of the outcome of a

typical ARTA measurement is given in figure 11. This shows the intensity of the scattered light

ranging from 10

O

to 90

O

and the wavelength range from 300 to 850 nm.

13

2.1.2 the integrating sphere

The integrating sphere (IS) measures the reflectance and transmittance of a sample through an integrating sphere. This is a sphere coated with spectralon (a white diffusely reflecting coating scattering the light uniformly throughout the sphere) so that all the reflected or transmitted light is detected.

The only opening of the sphere is a hole in the front side of the sphere (A in figure 12) to allow the

light beam in the sphere. When transmission is measured the sample is placed outside the sphere covering this entrance, by which all transmitted light is detected inside the sphere.

For reflection measurements the sample is placed at the back outside the sphere (B), which is otherwise covered with a disk that is also coated with spectralon. The sample is placed slightly tilted so that the specularly reflected light is not reflected back into the entrance hole of the sphere, but towards another part in the sphere indicated in the schematic with C.

Light beam

Figure 12 Schematic of the ISRT setup.

It is possible to measure only the diffusely scattered light by allowing the specularly reflected light to escape. For transmittance measurements the spectralon coated disk is left off, resulting in a hole at the backside. The cap around the spectralon (B) is coated black so that all the light leaving that hole is absorbed. This means that all specular light is absorbed and the diffuse light is detected. For reflection measurements a little hole can be opened releasing the specular light only (C). All the light is to be reflected via the integrating sphere and light should not be measured directly transmitted or reflected from the sample. For this reason a baffle is placed around the detector (D), covering it from any possible direct transmitted or reflected light.

14

Complete measurements with the integrating sphere include diffuse and total reflection and transmission measurements, which means that every sample undergoes four different measurements. From this data also the absorption can be calculated by subtracting the total reflection and transmission from 100 %.

2.2 The profilometer Dektak 150

This tool uses a needle with a tip of 12.5 µm that moves across the surface of a sample. This leads to a straightforward analysis of the roughness and thickness of samples. The measurement scale [1 µm-

524 µm] is adjustable and as for the samples within this research the thickness varies approximately between 50-100 µm, this is a good tool to get a reasonable approximation of the thicknesses.

Also the speed with which the needle moves over the sample can be set freely, by which the accuracy of the measurement is adjusted. In this research there is not so much need for high resolution measurement as the tool is mainly used to determinate whether the samples are sufficiently thick.

The output is levelled based on a manual input reference value of a flat surface. This measurement gives the height of the sample as a function of horizontal displacement.

Figure 13 The Dektak 150 measuring a sample.

15

2.3 Opticalculate

Opticalculate is a Matlab-based optical simulation tool. It simulates the propagation of rays when passing different interfaces. It only needs thicknesses and names of the different material layers as it has a small database with all necessary properties of these materials. In this database there is also an option to introduce a reflector for which reflectance of the reflector and AID in the wafer can freely be chosen. Output is given in terms of absorption and total reflectance and transmittance per layer.

Due to the band gap a c-Si wafer becomes transparent for light with larger wavelengths. As the band gap corresponds to 1107 nm for perfect crystalline material this transition occurs between wavelengths of 1000 and 1250 nm. This transition can be very useful to determine the angular intensity distribution of reflected light in the case of an introduced back reflector. This is because the slope of this transition changes with different scattering and can thus function as a signature of the scattering properties of different back reflectors [22] [23].

In Opticalculate Phong’s reflection model [24] is used for determining the approximate distribution as given by equation 5 below. It models both specular and diffuse reflection in a single cosine and has been used in different previous solar cell related researches [3] [23]. Equation 5 below describes the function used in this model, where the intensity is expressed as a function of different scatter angles:

(5)

In this research results are discussed based on the diffuse angle. The diffuse angle (equation 6) below is the angle under which the intensity is half of the specular intensity (the half-width-halfmaximum value):

(

( )

)

(6)

The effect of increasing the diffuse angle is illustrated in figure 15. A diffuse angle of 60 degrees

correlates to a Phong exponent of 1 resulting in the Lambertian distribution. The lower the diffuse angle the higher the Phong exponent becomes and the narrower the distribution. With very high

Phong exponents the model returns a fairly narrow peak, corresponding to a high degree of specular reflection.

16

Figure 15 AID based on the Phong distribution [3].

Figure 14 shows the simulated 1-reflectance of a 300 µm thick c-Si wafer for different hypothetical back reflectors. Figure 14a shows the effect of the diffuse angle (difa) of a back reflector. This shows

that this parameter is dominant between 1000 and 1200 nm and that the slope of reflection in the

transition phase is strongly dependent on the diffuse angle. Figure 14b shows the effect of

reflectance of the back reflector material. This shows that the overall reflectance is strongly affected by the reflectance of the back reflector. This parameter dominates the simulation of wavelengths larger than 1200 nm. Varying both parameters can accurately determine properties of back reflector material.

Figure 14 Illustration of a simulated reflector indicating the dominant parameters at different wavelengths

(a)Different scattering distributions (specular - Lambertian) (left) and (b) reflectance properties (right).

17

2.4 ASA

ASA is short for Advanced Semiconductor Analysis and is a simulation tool developed by the PVMD group that can simulate complete solar cells combining both optical and electrical simulations. An input file (see Appendix 1) is required to describe different layers of a cell, differentiated by front layers, electrical layers, and back layers. For all layers input is needed for thicknesses and refractive indices. The refractive indices need aside of the n-value also the k-value, which is the complex index of refraction. This k-value is also called the extinction coefficient and determines the absorption losses when light travels through a material. Optional extra input parameters for different scattering properties can be assigned such as AID and haze. Without these extra input parameters it runs under the default setting which assumes no diffuse scattering.

For the electrical layers additional information is required. Different doping levels, mobility, dangling bonds, band gaps, and band tails all need to be set before the file can run. In the PVMD group many simulations have run to optimize these settings in such a way that it has proven to be able to accurately simulate solar cells [25].

Figure 16 Changes in EQE with different thicknesses (left) and AID (right).

ASA is used to illustrate the effect of a changing the thickness of the i-Iayer and the scattering distributions. These are two ways of increasing the path length light travels through the absorbing

layer, which increases chance of absorbance and obtaining a higher EQE. In figure 16 these effects

are shown. The left figure illustrates that increasing the thickness of the i-layer enhances absorption at all wavelengths larger than 550 nm. The i-layer absorbs light of smaller wavelengths very well and with a thickness of 100 nm light up to 500 nm is absorbed, and for thicknesses above 200 nm no effect is seen up to wavelengths of 550 nm.

18

The right figure illustrates the effect of different back reflectors and different assigned scattering distributions. It can be seen that aluminium (black line) is outperformed by silver (red line) when the same scattering (cos

2

(θ)) is assigned. When looking at the simulations with silver as back reflector it can be noted that the distribution is of significant importance for the EQE. From specular reflection

(pink line), to a broader distribution approached by cos

2

(θ) (red line) towards the Lambertian distribution (green line) a clear increase in the EQE is observed.

19

3. Fabrication and optical properties of white paint

This chapter includes all the different research done on the white paint as a single layer. Different fabrication methods are analyzed, including dropcasting, spin-coating, the snow globe method and a novel method named the pressure paste method (3.1). Different aspects of the optical properties are measured such as transmittance, reflectance, and scattering at the white paint-air interface (3.2) and at the interface of white paint and the c-Si wafer (3.3). Also the effect on scattering of the novel combination of TiO

2

with Ag-nanoparticles is tested.

TiO

2

used in this research consists of particles around 270 nm in diameter, and is supplied in powder form. When combined with demiwater this forms a suspension that can be used for depositions. The suspension can be distributed on the samples, the water evaporates, leaving the TiO

2 nanoparticles on the surface.

The fabrication of the different mixtures later mentioned are all done with a balance with an accuracy of 0.1 mg and the dissolvent is added with a pipette with 1 µL accuracy and all weighing is done with 1 mg accuracy. In all cases mixtures of at least 10 mL were made to make the inaccuracy insignificant.

3.1

Different deposition techniques

Deposition of paint with binder can be done with brush and simply painting the surface of a substrate. For deposition of white paint without a binder a different technique is required. In this research the particles are mixed with a material that completely evaporates leaving only the layer of the particles on the surface. For depositions of the TiO

2

nanoparticles there are a few variables: the concentration of TiO

2

, the suspension dissolvent, and the method of deposition.

Literature suggests that a layer thickness of more than 50 µm is needed for sufficiently reducing transmittance. So that is taken as reference thickness when trying different deposition techniques.

The optical measurement tools have a maximum spot size of 2 cm, so the second requirement for the depositions is that it has sufficient thickness to cover that area. The area of solar cells made in our laboratory have a surface of 4x4 mm

2

, so when depositions satisfy this requirement, depositions on solar cells are also possible. For some configurations of solar cell designs there is an additional requirement. If the roughness can be reduced to the order of 50 nm, the rest of the solar cell films could possibly be deposited on top of this white paint layer, so homogeneity will also be considered.

And a final requirement is that the result must be reproducible. The different deposition techniques will be reviewed on these 4 requirements.

20

3.1.1 Dropcasting

In all cases deposition was done by dropcasting with a measuring pipette dropping 10 drops of the mixture. The samples are dried for 12 hours before measurements were done. Different mixtures were made with concentrations varying between 0.1 g/L and 1.0 g/L. The highest concentrations were measured first, and it was determined that this concentration was needed to come near the required thickness.

Different substrates were used in testing the method. Corning glass, the rough side of Asahi glass and wafers have been used and all materials have also been etched in for different times (1-60 s) in a solution of 1 % HF. Conclusions were that all of these variations had no effect. Dropcasting the samples and not moving them until they were sufficiently dried turned out to be a good deposition method for all substrates.

Figure 17(a) Height profile of best result dropcasting, and (b) photo of samples on Asahi and Corning glass.

For different white paint samples the thickness differed quite much. As seen from the Dektak results the drop sizes were large enough for optical measurements. The height profile of the flattest sample

is presented in Figure 17a and the height profile of multiple other samples can be found in appendix

2. The samples were not very flat, but by increasing the amount of drops and the locations of where the drops are dropcasted the covered area and the thickness can very easily be adjusted.

In many samples there was also a high peak is found in the height with two times higher thickness.

This was caused by uneven drying, and was visually already noticeable.

21

3.1.2 Spin-coating

Spin-coating is often used to create thin flat layers, which can be made thicker by repetition of the process. Its working principle is that the substrate, for which Corning glass is used, is spinning at a certain speed, while dropping the deposition material on it. By centrifugal force, the material is spread to the side of the substrate while the solution evaporates. It therefore requires a volatile solution. Different solutions liquids were tried all with a 10 % concentration TiO

2

, but all turned out to become suspensions rather than solutions. The suspensions were shaken moments before the deposition to get a high concentration of particles suspended in the liquid. The solution liquids used were ethanol, methanol and acetone and DI-water. All are common volatile chemicals often used in spin-coating except for DI-water, which was added for completeness.

Spinning speeds were varied between 300 and 6000 rpm. These variations were optimized per solution as volatility determined the layer homogeneity for the different solutions. The more volatile the dissolvent, the higher speeds were needed as for lower speeds the solution liquid was evaporated before reaching the edge of the substrate.

Figure 18 Spin-coating results with different solutions (L to R: DI-water, ethanol, methanol, aceton).

It was hard to obtain homogenous layers with increasing thickness. As figure 18 shows, the volatile

materials evaporated before reaching the edge of the sample with the result that all layers turned out to be inhomogeneous even while the layer was still so thin that it was still visually transparent, so significantly below the required thickness.

22

Spin-coating with DI-water at 3000 rpm gave the best result. The middle of the sample was reasonably flat when the layer was still insufficiently thick. Although these results are relatively good compared to the other solutions, homogeneity was already lost in the thin sample, and result got

worse by thickening the layer, as can be seen in figure 19 and figure 20.

Figure 19 Best obtained result spin-coating, thin(left) and thicker(right) layer.

Figure 20 Best obtained result spin-coating, thin(left) and thicker(right) layer.

Overall obtained insight is that no thick flat layers of binder-free white paint can be made by spincoating as can be seen from the photos above. Additional problem was that this result was not easily reproducible. This problem occurs as the concentration might differ slightly per sample, the highly concentrated suspension was shaken, but leaves an undefined concentration of TiO

2

in the drops.

The concentration can be assumed to be 10 % but could vary slightly. Furthermore it is a process based on personal handling rather than machinery. For obtaining this thickness 20 drops were deposited by a pipette and a squeeze balloon, and to drop numerous drops of equal size and at exact the same position is a difficult process.

23

3.1.3 Snow globe method

The snow globe method is a novel method found in literature [18] for forming a uniform coating layer by dispersing the particles on the substrate through a liquid medium. The substrate is placed at the bottom of a liquid medium and the particles are dispersed at the top of this liquid bath as shown

in Figure 21. The swirling down the liquid provides a uniform coating layer.

Figure 21 Proposed snow globe method [18].

In this research it is tried to reproduce the method, and different parameters were adjusted. As

shown in figure 22 three different setups were tested. One with the traditional snow globe method

with the glass substrate at the bottom of a bath of demiwater and two alternative setups that were left to dry, as it was anticipated it could be difficult to get the uniform layer out of the solution.

Figure 22 Snow globe setup and results (left): three setups: low concentration, high concentration, traditional setup (right): from top to bottom: Traditional setup, high concentration, low concentration.

The alternatives considered were one with a high and one with a low concentration TiO

2 nanoparticles mixed with ethanol. The high concentration mixture was a 10 % TiO

2

suspension in ethanol that was shaken and dispersed over the entire sample and surrounding setup, resulting in a highly concentrated bath. When a suspension was at an equilibrium state, it seemed to have a very light concentration of TiO

2

that was dissolved in the solution. This was used for the low concentration

setup. Results obtained are shown in figure 22.

24

The low concentration sample was still transparent, with a few small flocks of white paint. The traditional setup resulted in a structure with high hills and valleys of somewhat crumbly attached particles. The highly concentrated dried sample showed a reasonable good result on first sight. It was no longer visually transparent and at some parts of the sample it appeared to be a uniform

homogenous layer(figure 23b). The other two samples were discarded and the highly concentrated was further examined. The Dektak result is shown in figure 23a.

Figure 23 Result “snow globe” method with methanol: (a) Dektak result and (b) photo of the sample.

The minimum required thickness of 50 µm was met in part of the sample. The requirement sufficient coverage for spot size for the optical measurement was met. The homogeneity was insufficient though and the sample had incurred several cracks in the drying process. The cracks obviously make it difficult for the purpose of back reflector.

25

3.1.4 Pressure paste

A novel method was tried as well. By mixing TiO

2 nanopartice in powder form on top of a substrate

(Corning glass) and sprinkling it with drops of water a paste can be created. With some pressure the substrate with this paste is pushed together to another substrate and then pulled away from

eachother to leave a flat pressured layer as schematically illustrated below in figure 24. This method

is named pressure paste in this research.

Figure 24 Schematic illustration of pressure paste.

This deposition method seemed to result in a reasonably flat layer (photo figure 25b) and was tested with the Dektak as well. As shown in figure 25a this resulted in the flattest layer obtained so far.

Figure 25 Pressure paste results: (a) height profile and (b) photo of the sample.

As clearly seen in the Dektak result the thickness was strongly depending on the horizontal displacement, but at the layer was sufficiently thick at most locations. As shown in the photo in

figure 25b there were air bubbles created in this process and these air bubbles are a problem as the

as reflection is not guaranteed in this layer.

26

3.1.5 Discussion on the different deposition techniques

Looking at summarizing table 1

below it must be noted that none of the methods meet all the requirements as none of the samples could produce sufficient homogenous layers. The consequence that the homogeneity was insufficient restricts the possible solar cell configurations, as will be discussed later in this report.

With the spin-coating method it is very hard to obtain thick layers of white paint, and additionally it is difficult to reproduce its results. The snow globe method and pressure paste result can be reproduced, but have cracks and air bubbles, respectively. This means that those methods are not only coming short in the homogenous requirement, but the reflectance is not guaranteed at all locations.

Even if this problem could be overcome and only the interesting parts of these samples are considered, these alternative methods require more intensive handling than dropcasting and the obtained results were no significant improvements in relation to dropcasting.

Thickness Size Homogenous Reproducible

Dropcasting

Spin-coating

yes

No

Yes

Yes

No

No

Snow globe method

Yes

Pressure paste

Yes No yes Yes No

Table 1 Summarizing table of deposition methods.

Yes

No

Yes

Yes

It was decided that dropcasting was the best deposition method for this research due to its simplicity and purpose-serving results. All further discussed depositions in this research were done by dropcasting.

27

3.2 Optical properties of white paint at the interface with air

The optical properties are analysed by both the integrating sphere (IS) and the ARTA. The integrating sphere is used to measure total and diffuse reflection and transmission. From these parameters the haze and the absorption are calculated. The haze is defined as the fraction of diffuse reflection divided by the total reflection. The absorption is found by subtracting the total reflection and transmission from 100 %. The IS measurements are discussed in 3.2.1. In 3.2.2 the required thickness of the material will be determined and compared to literature values, and in 3.2.3 the distribution of the diffusely scattered light is analysed.

3.2.1 Results integrating sphere

The dropcasted samples were analysed measuring from the film side. Figure 26 shows the results of

the integrating sphere of selected samples. These samples have been selected on the difference in thickness resulting in different transmissions. At the low wavelength the light is absorbed by the white paint. Light of wavelengths larger than 450 nm is no longer absorbed.

Figure 26 IS results: absorption (a), transmission (b), reflection (c), and haze (d) of different white paint samples on glass substrate, plotted against wavelength.

From this wavelength onwards a reflectance is measured of more than 95 % for wavelengths up to

1000 nm, which is all completely diffuse. This can be seen in the haze parameter being unity. There is a low transmission measured that increases linearly with increasing wavelength. There is some distortion seen around 850 nm and larger wavelengths, this is an artefact caused by the switch of detector. The trends for all the different samples were comparable. As there is no noticeable difference between the samples figures of the trends and overall distributions of the other samples are shown in appendix 3.

28

3.2.2 Required thickness

Literature suggests a linear relation between the thickness and the inverse transmittance of the material [9]. This was used to determine the minimum required thickness for the use of back reflectors. The thickness of the measured dropcasted samples were used and plotted against the transmittance. In the IS measurements the calibrations were such that areas of uniform thickness are measured.

1 2 3 4 5 6

Thickness [µm]

13±5 17±5 18±3 30±8 33±3 45±5

Table 2 Thicknesses of white paint layers for different samples.

7

50±10

The found results are compared to results from literature, and it reveals the same trend. Averaged transmittance values of the wavelengths 600-1200 nm were used. As the transmittance of the

material has a linear relation to the wavelength, as demonstrated in figure 26, this averages to a

required thickness at a wavelength of 900 nm.

Figure 27 Transmittance plotted against thickness and compared to the results of B. Lee [9].

There is a slight difference in the measurement at 800 nm. This result is added to figure 27 because a-Si absorbs light up to this wavelength. Figure 27 shows that transmittance drops below 5 % with

thickness over 50 to 70 µm for averaged wavelengths of 800 and 900 nm respectively. From this we learn that a thickness of >50 µm is required to suffice that less than 5 % of the light is transmitted.

29

3.2.3 AID measurements

With the ARTA different AID measurements were performed. Figure 28 shows the angular intensity

distribution with scattering angles between 0

O

and 90

O

are relative to the specular angle over wavelengths 300-850 nm. Different samples (varying in thickness and substrates) all showed excellent scattering with significant intensity measured under large reflection angles.

Figure 28 AID result of white paint measurement with ARTA.

Distributions at selected wavelengths are shown in figure 29. The Lambertian distribution as a

function of the specular intensity is plotted for comparison (I o

*cos(θ)). As expected, excellent scattering is observed. At wavelengths larger than 400 nm the angular intensity distribution is roughly equal to the Lambertian distribution.

Figure 29 Single wavelengths compared to the Lambertian distribution.

There can be noted that at 400 nm the distribution is slightly different from the Lambertian, this around the band gap of TiO

2

and the optical properties are influenced by some light absorption, for use as back reflector of solar cells this is irrelevant as this light will all be absorbed in a single pass. At

850 nm there is a little artefact of the detector is found.

30

3.3 Scattering properties at white paint-silicon interface

The scattering properties within a medium other than air is very difficult to measure, but the distribution can be estimated by simulations. Often in literature is assumed that the reference scattering into air suffices and those scattering values are used. However, the reflection of the light is also influenced by the refractive indices on either side of the interface. Inside the solar cell the white paint is deposited on either amorphous silicon or a layer of a transparent conductive oxide (TCO), and the refraction at this interface should be taken into account. In this research the distribution is determined with the help of Opticalculate simulations [22].

For this purpose this research includes a study on the behaviour of the white paint reflectance when it is measured through a double side polished c-Si wafer. This is used as model system, with high refractive index and perfectly flat interfaces. As the refractive indices of c-Si (n≈3.5) and a-Si (n≈4.0) are both much higher than materials at the other side of the interface, this model system can represent amorphous silicon as well. Reflection and transmission is measured through the wafer with

and without back reflector as indicated in figure 30.

Figure 30 Setup of measurements for Opticalculate study.

The different back reflectors included in this research are white paint with binder, white paint without binder, and the combination of silver nanoparticles with binder-free white paint. The white paint with binder is represented by a commercial correction fluid called Tipp-ex. In correction fluid a layer of the pigment TiO

2 is formed in a film layer of a polymer. This measurement is included as reference, to indicate the relevance of this research. The white paint without binder is dropcasted on the wafer as previously discussed. The silver nanoparticles are fabricated in the PVMD laboratory. A

21 nm Ag film was deposited on one side of the double side polished c-Si wafer. This film is annealed for one hour at 400

O

C. The particles have not been tested for size, shape and distribution.

31

First the Opticalculate model is validated by measuring the wafer only (3.3.1). Afterwards the difference in absorbance with white paint is shortly discussed in section 3.3.2. Then the different results found with the simulations are presented (3.3.3) and at the end of this chapter these results will be discussed in 3.3.4.

3.3.1 Validation of the Opticalculate model

In order to validate the model it has to be compared with experimental results. This is done by

measuring a double side polished c-Si wafer. This structure is also simulated and figure 31 shows that

Opticalculate can very accurately simulate the reflection and transmission effects at different wavelengths.

Figure 31 Simulation and measurement of double side polished c-Si wafer.

In this measurement it is shown how the light is reflected at the interfaces. At low wavelengths the reflection of the front side of the wafer is shown, the rest of the light is absorbed so no light is transmitted or reflected from the backside of the wafer. Above the band gap (1100 nm) there is an enhancement of reflection due to the fact that the wafer becomes transparent and that this additional reflection is due to the second interface at the back side of the wafer.

32

3.3.2 Absorption wafer and white paint

In figure 32 we observe the calculated absorption of the silicon wafer with and without white paint at

the back. The reflection (R) and transmission (T) are measured and the absorption is A = 1-R-T. There is an increase in absorption observed in wavelengths larger than 1000 nm with a 5 % absorption in wavelengths larger than 1200 nm. This is the sum of absorption of light in both the silicon wafer and the white paint.

The wafer was lightly n-doped with a concentration about 2 10

15

cm

-3

. The free carrier absorption coefficient is determined by [26]:

2

(7)

Where is given in cm

-1

, and are given in cm

-3

and in µm. Even if we take into account the free-carrier absorption in the lightly doped wafer, is about 0.009 cm

-1

and the penetration depth of wavelengths of larger 1200 nm is more than 1 m before it is absorbed. The wafer is only 300 µm thick, so this implies that the absorption in the wafer is negligible and the observed absorption for wavelengths larger than 1200 nm is almost entirely due to the white paint.

Figure 32 Absorption of wafer and wafer with white paint.

In the wavelength band between 1000 nm and 1200 nm a much larger increase of absorption is observed. The silicon wafer does absorb light in this band and the enhanced absorption is assumed to be due to increase of the path length due to the reflection of the white paint.

33

3.3.3 Simulation of the reflectance and the diffuse angle

Simulations were done with three different type of reflectors. With the different simulations the diffuse angle ( ) and reflectance of the back reflector material is varied until the best fit is found when compared with the measurements. The measurements are done with the integrating sphere, and the simulations were compared with 1-reflection. In previous researches absorption is often simulated, but in that case transmission is assumed to be inexistent, which is not true for this material. As absorption and transmission in the reflector layer cannot be simulated separately, here

1-reflection measurements are used for simulations.

First presented are the results of the simulations done of white paint with binder, represented by a

correction fluid (Tipp-ex). The results of the measurement and simulation are found in figure 33. The

best fit with Tipp-ex indicates an angular intensity distribution with a diffuse angle of 18

O

and a reflectance of the material of 96 %.

Figure 33 Simulations and measurement with Tipp-ex.

34

Simulations based on the white paint measurements were compared to two different samples. The difference in the two samples lies in the thickness, where measurement 1 is roughly 90 µm thick and measurement 2 only 50 µm, as shown in Appendix 2.

Figure 34 Transition simulated for wafer with white paint.

In figure 34 the best obtained fit with the white paint measurement is presented. This corresponds to

an angular intensity distribution with a diffuse angle of 20

O

and a reflectance of 96 %. Compared to the Tipp-ex experiment it can be observed that the reflectance has not changed and the distribution is slightly broader.

However, it is significantly narrower distribution than the Lambertian distribution obtained in the

white paint-air interface previously observed in section 3.2.3 in figure 29.

35

Due to the plasmonic effect silver nanoparticles (Ag NPs) can scatter light outside the critical angle and Basch et al [27] suggested that a combination of Ag NPs and white paint can prevent refraction and improve the angular intensity distribution of the reflected light [27].

The silver nanoparticles are measured through the wafer and the results of the simulations are

shown in figure 36. There are different interesting aspects in this simulation. First, it must be noted

that angular intensity distribution is as high as 75

O

, which corresponds to a distribution broader than the Lambertian distribution.

Figure 35 Simulation transition phase of wafer with silver nanoparticles

Secondly, the reflection is very low for a back reflector. Note the difference in scale on the vertical axis in comparison to the other measurements. The reflectance of the back reflector is only 70%, due to absorption and transmittance. The nanoparticles are island-like structures and there is no full coverage of the surface.

36

The combination of using the reflectivity of the white paint with the broad distribution of silver

nanoparticles has also been investigated by experiment and simulation. In figure 36 the results of the

combination of silver nanoparticles the white paint are shown. The combination indeed showed a very broad distribution. The best fit resulted also showed a diffuse angle of 75

O

.

Figure 36 Simulation transition phase of wafer with white paint and nanoparticles.

It can be observed that the reflectance of this material is 94 %. Compared to the results of the simulations of the white paint only, this is a decrease of 2%, which considered to be due to plasmonic absorption of the silver nanoparticles. Compared to the simulations of the silver nanoparticles it can be seen as an increase of reflectance of 24% while it has no influence on the angular intensity distribution.

37

3.3.4 Conclusions optical properties white paint

White paint is suggested to be a Lambertian scatterer. It has been illustrated that this is true for scattering in air. However, the scattering properties are significantly influenced by changing the

interface as shown in figure 37. The cosine approximations deduced with the Phong model of the

different distributions are shown in this figure. That the angular intensity distribution is strongly influenced by the difference in refractive index is in agreement with Cotter’s model [22]. It can be seen that the angular intensity distribution of a white paint back reflector on a c-Si wafer is slightly broader than the scattering of white paint with binder, such as Tipp-ex. This improvement is already considered a very useful improvement but compared to the Lambertian distribution there is still much to be gained.

Figure 37 The different scattering distributions based on the simulations.

It is a big discovery to see how much improvement the combination of silver nanoparticles with white paint contributes to the distribution, it shows very clearly that the distribution can much stronger be influenced with this combination rather than binder-free material only.

It must be noted that the approximations of angular intensity distributions are based on

Opticalculate simulations, which is a 2D scattering model, which is not accurate enough to prove that the true three-dimensional distribution is indeed wider than the Lambertian distribution, but it does at least show significant broader distributions compared with white paint only.

In this research there are no cells produced with this back reflector. This is because problems in cell configuration need to be overcome before this can be realized. For instance, the silver nanoparticles are fabricated at a higher temperature than the solar cells can manage and they cannot be deposited on the white paint layer. However, expectations are that this combination can be a very successful back reflector.

38

4 Simulation and fabrication of solar cells

In this chapter the focus is turned to simulation and fabrication of complete solar cells. All cells are made in the PVMD laboratory with plasma enhanced chemical vapour deposition (PECVD), where the different materials are deposited on a substrate. To prevent contamination all layers are deposited in a vacuum and different layers are deposited in different deposition chambers.

In the first section of this chapter the different solar cell configurations are considered. In section 4.2 the predictions of the ASA simulations are discussed. In the section 4.3 the results from the solar cells are shown and in the final section of this chapter these are compared with the ASA simulations and there is an overall discussion about the scattering, modelling and prospects.

4.1 Solar cell designs

For fabrication of the solar cells it must be considered that the TiO

2

nanoparticles form an electrically insulating layer. This has as consequence that it must be placed behind the back contact in contrast to conventional metal back reflectors that can serve both the function of back contact and back reflector. For white paint back reflectors a transparent conductive oxide is needed to conduct the electricity. In section 3.1 was established that no white paint layer could be made homogenous enough to deposit the rest of the solar cell on top of this layer.

These restrictions taken into account, different configurations were manufactured in the PVMD lab.

These different configurations are schematically shown in

figure 38

below. Both the PIN-structure and the NIP structure are presented. Both structures are fabricated on both Corning glass and Asahi glass to make a flat and rough cell, respectively. As the Asahi substrate consists of glass layer with a deposition of roughened SnO:F on the one side, the difference between these cells is that the light in rough cells are already scattered at the substrate interface. This is schematically shown with the pyramids in the figure. Note that the roughness of the substrate the only difference between the rough and the flat cell configuration. The roughness of the substrate influences all layers that are deposited on top of it. All layers will have some texturing, but the roughness will decrease and the surface will smoothen with increasing thickness of cell.

The glass layer in the Asahi construction is thicker than the Corning glass, but this has no optical effect as both glass substrates are significantly thicker than the order of magnitude of the considered wavelengths.

39

The back reflector in the NIP-structure was moved to behind the glass substrate. The transparent conductive oxide (TCO) as back contact conducts the electricity to the side of the substrate strip, where an aluminium strip is placed for further conduction. This prevents losses as the resistance of a

TCO is higher than a metal conductor. The thickness of the different layers are optimized thicknesses based on experimental results in the PVMD research group. As the white paint can easily be washed off the surface and the silver can be deposited later it is possible to measure the exact same sample without back reflector, with white paint as back reflector and with silver as back reflector by measuring it in this order.

Front contact

ITO [75nm]

P-layer a-SiC

I-layer a-Si(i)

[310nm]

N-layer a-Si [20nm]

Back contact

AZO [1100nm]

Substrate [3mm]

(Corning glass)

Back reflector

Front contact

ITO [75nm]

P-layer a-SiC

I-layer a-Si(i)

[310nm]

N-layer a-Si [20nm]

Protective layer

AZO [30nm]

Asahi SnO:F layer

Substrate [5mm]

(Asahi glass)

Back reflector

Substrate [3mm]

(Corning glass)

Front contact

AZO [1100nm]

P-layer µc-Si [5nm]

P-layer a-SiC [7nm]

Buffer SiC [5nm]

I-layer i-Si [300nm]

N-layer a-Si [20nm]

N-layer SiO x

[30nm]

Back contact

ITO [200nm]

Back reflector

Substrate [5mm]

(Asahi glass)

Asahi SnO:F layer

Protective layer

AZO [30nm]

P-layer µc-Si [5nm]

P-layer a-SiC [7nm]

Buffer SiC [5nm]

I-layer [300nm]

N-layer [20nm]

N-layer SiO x

[30nm]

Back contact

ITO [200nm]

Back reflector

Figure 38 Schematics of the different configurations, (L to R): flat NIP, rough NIP, flat PIN, rough PIN.

It must be noted that the back contact is in both situations the transparent conductive oxide, that conducts worse than a metal back contact. In an ordinary NIP cell with a silver back contact the silver can serve as both the back contact and back reflector and could thus reflect directly in the silicon layer where it now has to pass two other interfaces first. However, that configuration is not possible for TiO

2

as back reflector. Therefore it was chosen to put the silver on the backside of the glass as well, which allows for better comparison.

40

4.2 Fabricated solar cell results

In this chapter the best results of the different complete solar cells are presented. All the cells produced are placed on strips of substrate containing 24-30 individual cells and all cells have a surface area of 0.16 cm

2

. The best results are shown and are compared.

4.2.1 Flat NIP cell

The EQE was measured and results of the flat NIP structured cell are shown in figure 39. There is a

very clear and expected improvement seen in the case of a back reflector when compared with the cell without back reflector.

Figure 39 Measured EQE of flat NIP cell with and without white paint and silver back reflector.

In this cell the white paint also outperforms the silver back reflector, especially in the range of wavelengths of 660-710 nm. This improvement was expected as the flat silver back reflector reflects the light specularly, while the paint scatters the light diffusely, improving the path lengths. In relation to the reference cell, the silver back reflector improves the current with 10.7 % where the white paint increases the current with 13.7 %.

41

4.2.2 Rough NIP cell

The results of the EQE measurements of the rough NIP cell are found figure 40 and figure 41 below.

The first figure shows the improvement of white paint relative to the reference cell without back reflector. The cell was re-measured, but for some unknown reason efficiency had dropped. Therefore

the results of the reference cell have been reduced to 95 % in figure 41. This was the reduction of the

measured EQE with the white paint as back reflector and the absorption is equal to the other EQE values for wavelengths below 500nm, where the back reflector has no effect.

Figure 40 Measured EQE of rough NIP cell with and without WP and Ag back reflector.

Figure 41 Measured EQE of rough NIP cell (with adjusted No BR).

42

In the rough NIP cells there was no clear difference between the white paint and the silver as back reflector. As the light reaches the back reflector already in a diffuse state, the reflectors both reflect the light and the reflection is diffuse in both situations. Based on these results it can be stated that white paint shows a performance comparable to silver as a back reflector in these type of solar cells.

The improvement in J

SC

based in relation to the reference cell is 7.4 % for silver and 6.7 % for the white paint back reflector, but looking at the EQE, this difference is found in wavelength range between 400 and 500 nm and is negligible.

43

4.2.3 Flat PIN cell

The flat PIN cells were deposited and measured for EQE without back reflector, with white paint

directly on the TCO back contact, and with silver as back reflector. The results are shown in figure 42.

In the PIN cells much interference is seen. This figure clearly shows that the interference is stronger in the cell with the silver back reflector. The interference below 550 nm originates from the TCO layer at the front of the cell. At larger wavelengths the peaks become broader, which is due to interference from the TCO of the back contact. This interference results in a higher EQE.

The figure also shows that the white paint back reflector outperforms the silver in the destructive interference regions around 575 nm and 650 nm. This shows that the white paint does scatter the light better than the flat silver back reflector, as scattering decreases the interference. The white paint reflector improves the J

SC

with 13.8 % relative to the reference cell. The cell with the reflector produces a 20.4 % higher current density.

Figure 42 Measured EQE of a flat PIN solar cell without and with silver and white paint back reflector.

It must be noted that the difference in current density between the white paint and silver as back reflector is also partially generated at wavelengths below 550 nm, where the back reflector has no effect. This is due to that not the same cells were measured in this experiment and that the cell with white paint as back reflector was of a lower quality.

44

4.2.4 Rough PIN cell

In the rough PIN cell the difference between white paint and silver is very clearly demonstrated

(figure 43). Where the silver back reflector outperforms the white paint at 620 nm due to

interference, the white paint has a higher enhancement in EQE, when all other wavelengths larger than 550 nm are compared. In this experiment also different cells were measured for silver and white paint as back reflector, but as seen that the EQE overlaps at the lower wavelengths these cells were of a comparable quality.

Figure 43 EQE of a rough PIN solar cell without and with silver and white paint back reflector.

As overall result the white paint reflector slightly outperformed the silver, with current enhancements 7.2 % for white paint opposed to 6.5 % for the silver, when compared to the J

SC without the back reflector. Enhancements are slightly lower than the ones found in the flat cells, due to scattering at the front interface.

45

4.3 ASA Simulations

The ASA studies focus on the simulation of entire solar cells. Complete solar cells are simulated both optically and electrically and the theoretical changes of white paint in the previously introduced cells is discussed. First the cells with silver back reflectors were simulated. In these simulations white paint as back reflector was simulated by using the material properties as obtained from the wafer experiments, and the related effective refractive index-values are extracted from the Opticalculate simulations. The used parameters in ASA are found in appendix 4.

Figure 44 ASA simulations of flat cells: absorption in different layers (l) and EQE of white paint and silver BR (r).

Based on these simulations (figure 44) the effect of white paint has on the solar cell is also

determined. The flat NIP solar cells can be expected to have an overall improvement at wavelengths larger than 550 nm based on these simulations. In the PIN flat cell also the interference is decreased, as also observed in the measured cell.

46

In the rough cells not too much is changed by the white paint. Looking at the flat PIN cell, it seems that the influence of interference decreases slightly, which makes sense as the paint scatters the light better and interference from the reflected light is likely to be reduced.

Figure 45 ASA simulations of rough cells

It must be noted that these simulations are less accurate as the roughness influences the simulation and absorption, reflection and transmission do not cumulate to 1. Furthermore, the change of the back reflector influences the EQE at wavelengths below 550nm, which is not to be expected as this light is absorbed in a single pass.

47

4.4 Discussion

In the table below the results from the JV-measurements are displayed showing that the cells produced were of a decent quality. The results in the table are measured with silver as back reflector.

The efficiency is corrected based on the obtained current from the EQE-measurement as the results from the JV-measurements contain more uncertainty in relation to light intensity and illuminated area. The fill factor and V

oc

are considered to be independent of different illumination intensities, as opposed to the current density, so this parameter is taken from the EQE measurements.

Cell

Area

[cm

2

]

FF

[-]

V

OC

[V]

Rough PIN cell

0.16 0.686 0.849

J

SC

(EQE) Ag

[mA/cm

2

]

16.4

J

SC

(EQE) WP

[mA/cm

2

]

16.4

Efficiency

Ag [%]

9.90

Flat PIN cell

0.16 0.670 0.859

Rough NIP cell

0.16 0.619 0.85

12.8

13.9

12.5

14.2

7.40

7.58

Flat NIP cell

0.16 0.607 0.761 14.4 14.7

6.35

Efficiency

WP [%]

9.90

7.23

7.74

6.48

Table 3 Parameters of the different cells.

Silver seemed to outperform the white paint as back reflector in the flat PIN cells due to extra absorption in regions of constructive interference. However, the cells were not of an equal quality and the white paint might still be competitive even while it reduces the interference. The fact that there is less interference at least complies with a broader range in AID of the reflected light.

The white paint can already be considered competitive with the silver back reflector, based on the results presented in table 2 above while scattering is not ideal. The effective refractive index of the white paint is suggested to be about 2.0, but is strongly dependent on the concentration of TiO

2 nanoparticles and the air in between the particles. In solar cells the reflected light will pass at least two interfaces before reaching the silicon layer as the white paint is non-conductive. First the white paint-back contact interface is passed followed by the back contact-silicon interface.

In this research is noted that the effect of passing interfaces with a higher refractive index strongly reduce how broad the light is scattered. The suggested 2.0 effective refractive index is much like the

TCOs used in solar cells. In this case the light will pass through this interface with a very broad distribution. However, if the effective refractive index of the white paint is lower, than the light will be refracted twice before entering the absorber layer, making it very difficult to predict the distribution.

48

In figure 46 the measured EQE values of the white paint and the silver back reflector are indicated

together with the simulated EQE. Most attention has gone to accurate simulate EQE of the flat NIP-

cell, which has also returned the best result as seen in figure 46. Between wavelengths 370-470 nm

and 600-650 nm the simulation slightly overestimates the output. At all other wavelengths it proves that it can simulate both the cell with silver as the white paint back reflectors accurately.

Figure 46 Measurements and simulations compared.

The trends found in the simulations and the trends in the measurements, (black lines in figure 46) it

can be noted that expectations can be formed based on the ASA simulations, by simply adjusting the refraction index-values of silver into the white paint. No values for scattering were adjusted in these simulations, because results showed a worse fit than with only adjusting the refractive index-values.

49

5 Conclusions and recommendations

The objective was to analyse binder-free white paint, by determining the best deposition methods, find the scattering properties of the material and the effect on the different solar cells. Furthermore the goal was to create input variables that can represent the white paint for the simulation tools.

Conclusions

In this research the deposition methods dropcasting, spin-coating, snow globe method and the pressure paste method have been investigated. It turns out that none of the methods is suitable for creating homogenous layers that fulfil the requirements to deposit other layers on top. Dropcasting is considered to be the most suitable deposition method because of its simplicity and it serves its task just as good or better than its competitors.

The optical properties of the binder-free white paint have been investigated with both air and a c-Si wafer on the other side of the interface. Lambertian scattering has been observed in when light was scattered on the white paint-air interface.

The optical properties at the interface of white paint and c-Si wafer has been determined by an optical model, using the wavelengths in the range of the band gap of silicon. The slope of the measured reflection at wavelengths near the transition between absorbing material and transparent material have been simulated where the angular intensity distribution (AID) was approximated with

Phong’s diffuse reflection model. The distribution within the wafer material can be approximated by varying the reflectance and diffuse angle of the reflector material. Close fits were found with much narrower distributions than the Lambertian distribution in wafer. The best found simulation approached the distribution with a diffuse angle of 20

O

. This was a broader distribution than Tipp-ex which has been simulated to have a distribution with a diffuse angle of 18

O

.

Preliminary results showed excellent scattering properties in the wafer material when the white paint was combined with silver nanoparticles. The simulations showed an angular intensity distribution with a diffuse angle of 75 o

,

well over the Lambertian distribution. However, these are results from 2D-simulations and this does not confirm that the Lambertian limit was indeed surpassed. Approximations on AID and comparisons between the AID of different back reflectors can be done on 2D modelling, but in very broad distributions there are some differences between the 2D simulation and the real three dimensional scattering. A suitable 3D model was not available, so there can only concluded that there was a really broad distribution with promising research perspective for the future.

50

The external quantum efficiency of different solar cell results have been simulated with ASA and white paint has been simulated with parameters found in the wafer experiments. It is shown that the

ASA software could make reasonably realistic predictions of the effect of white paint in solar cells.

Tests in different solar cells showed that white paint is competitive with silver as back reflector in different type of solar cells. It shows that it can outperform silver in flat NIP cells and can perform just as good as silver in roughened NIP cells. In PIN cells the interference give an advantage to the silver as back reflector, confirming that white paint scatters the light better, but resulting in worse results for the flat solar cells. In the roughened PIN-cell the broader scattering of the white paint results in better EQE results than silver back reflectors.

Recommendations

For future research there are still many opportunities to perform measurements on different type of solar cells, such as micro-crystalline Si solar cells. As the back reflector has most influence on larger wavelengths, the J sc

improvement due to the white paint can probably be well demonstrated in those cells.

Phong’s reflection model gives a good insight in global distribution, but this model is not very suitable for determining the critical angle, that would show a cut off in the distribution. Advice is to separate the diffuse and specular components of the reflection can be separated for narrow distributions.

While simulations of ASA seem to be able to predict the effect of white paint as back reflector material, not all simulations were very accurate when compared to the experimental cells and refractive index-values were adjusted but best fits were found with the same scattering input files.

For further research is suggested to try to simulate the experimental results, with different scattering parameters and varying the layer thicknesses more accurately simulate the cells can help to improve the input files.

The combination of the white paint and silver nanoparticles showed excellent scattering in a silicon wafer. The present results are still very preliminary. For future research (1) 3D-modelling could determine the distribution better, as 2D models cannot serve as proof of surpassing the Lambertian distribution. Also, (2) solar cells could be developed with the combination of white paint and silver nanoparticles as back reflectors. Furthermore, (3) the absorption of the Ag should be determined over different wavelengths, as white paint does not absorb light in the larger wavelengths this is kept outside the scope of the research, but surface plasmon resonance of the Ag-NP should be taken into account and its effects should be investigated. (4) The conductivity of the nanoparticle layer can also be investigated. If this layer is conductive enough the it could possibly replace the TCO-back contact.

51

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54

Appendix 1: ASA input file

(capital C deactivates the rest of the input line)

C DEVICE DEFINITION;

layers grid[f.1] grid[3] grid[b.1] grid[b.2] electrical=3 front=2 back=4; d=70e-9; C spaces=200; grid[1] d=20e-9 dx.t=1e-9; grid[2] d=310e-9 dx.t=5e-9; d=14e-9 dx.t=1e-9; d=1200e-9; C spaces=200; d=0.001;

C TCO

C p-asi;

C i-aSi;

C n-aSi;

C TCO

C glass; grid[b.3] d=300e-9; C Silver;

C OPTICAL PARAMETERS OF LAYERS AND INTERFACES;

optical[f.1] lnk.file=nk/ito_2.nk; C TCO layer optical[1] lnk.file=nk/tud_p-aSiC.nk; optical[2] lnk.file=nk/tud_i-aSi.nk; optical[3] lnk.file=nk/tud_n-aSi.nk;

C p-layer;

C i-layer;

C n-layer; optical[b.1] lnk.file=nk/azo_juelich.nk; C TCO layer optical[b.2] ext.coeff=0 ref.index=1.55 incoherent; C glass layer; optical[b.3] lnk.file=nk/ag_palik.nk; C Silver layer

C Wavelength dependence of haze is read from a file; (deactivation results in specular propagation)

C **************************Air---ITO interface************************************;

C interface[i.1] adf.s.rf=noadf adf.s.rb=noadf adf.s.tf=noadf adf.s.tb=noadf; C DEACTIVATED

C interface[i.1] adf.h.rf=user adf.h.rb=user adf.h.tf=user adf.h.tb=user adf.h.file=nk/full_transmission.txt;

C **************************ITO---p-aSi interface**********************************;

interface[i.2] adf.h.rf=user adf.h.rb=user adf.h.tf=user adf.h.tb=user adf.h.file=scattering/Asahi_090414_512_haze.dat;

interface[i.2] adf.s.rf=user adf.s.rb=user

C

DEACTIVATED

C haze at TCO-Si interface; adf.s.tf=user adf.s.tb=user adf.s.file=scattering/Asahi_090414_512_aid.dat; C AID at TCO-Si interface;

C **************************p-aSi---i-aSi interface********************************;

C interface[i.3] adf.s.rf=noadf adf.s.rb=noadf adf.s.tf=noadf adf.s.tb=noadf; C DEACTIVATED

C interface[i.3] adf.h.rf=noadf adf.h.rb=noadf adf.h.tf=noadf adf.h.tb=noadf; C DEACTIVATED

C **************************i-aSi---n-aSi interface********************************;

C interface[i.4] adf.s.rf=noadf adf.s.rb=noadf adf.s.tf=noadf adf.s.tb=noadf; C DEACTIVATED

C interface[i.4] adf.h.rf=noadf adf.h.rb=noadf adf.h.tf=noadf adf.h.tb=noadf; C DEACTIVATED

C **************************n-aSi---TCO interface**********************************;

C interface[i.5] adf.s.rf=noadf adf.s.rb=noadf adf.s.tf=noadf adf.s.tb=noadf; C DEACTIVATED

C interface[i.5] adf.h.rf=noadf adf.h.rb=noadf adf.h.tf=noadf adf.h.tb=noadf; C DEACTIVATED

C **************************TCO---glass interface**********************************;

C interface[i.6] adf.s.rf=noadf adf.s.rb=noadf adf.s.tf=noadf adf.s.tb=noadf; C DEACTIVATED

C interface[i.6] adf.h.rf=noadf adf.h.rb=noadf adf.h.tf=noadf adf.h.tb=noadf; C DEACTIVATED

C **************************Glass---Back reflector interface***********************;

interface[i.7] adf.h.rf=user adf.h.rb=user adf.h.tf=user adf.h.tb=user adf.h.file=scattering/Asahi_090414_512_haze_si_ag.dat; C haze at Si-reflectorinterface; interface[i.7] adf.s.rf=user adf.s.rb=user adf.s.tf=user adf.s.tb=user adf.s.file=scattering/Asahi_090414_512_aid_si_ag.dat; C AID at Si-reflector interface;

C **************************Back reflector---air interface*************************;

C interface[i.8] adf.s.rf=cossq adf.s.rb=cossq adf.s.tf=cossq adf.s.tb=cossq; C DEACTIVATED

C interface[i.8] adf.h.rf=cossq adf.h.rb=cossq adf.h.tf=cossq adf.h.tb=cossq; C DEACTIVATED

55

C ELECTRICAL PARAMETERS OF THE DIFFERENT LAYERS

doping[1] e.act.acc=0.48; doping[3] bands[1] bands[2] bands[3] e.act.don=0.24; e.mob=1.93 e.mob=1.73 chi=3.950 chi=4.100 e.mob=1.73 chi=4.100 nc=5.0e26 nc=4.0e26 nv=4.0e26 epsilon=11.9; nc=4.0e26 nva=5.0e26 nv=4.0e26 epsilon=7.2; epsilon=11.9; mobility[1] mu.e=10.0e-4 mu.h=1.0e-4; mobility[2] mu.e=50.0e-4 mu.h=5.0e-4; mobility[3] mu.e=10.0e-4 mu.h=1.0e-4; vbtail[all] vbtail[1] e.range=1.0 levels=20 c.neut=0.7e-15 c.posa=0.7e-15; n.emob=5.0e27 e.char=0.08; vbtail[2] vbtail[3] cbtail[all] n.emob=1.0e27 e.char=0.040; n.emob=1.0e27 e.char=0.040; e.range=1.0 levels=20 c.neut=0.7e-15 c.neg=0.7e-15; cbtail[1] cbtail[2] cbtail[3] dbond[all] n.emob=5.0e27 e.char=0.07; n.emob=1.0e27 e.char=0.03; n.emob=1.0e27 e.char=0.03; levels=15 e.corr=0.2 d.e=0.15 e.range=6.0 ce.neut=0.8e-15 ch.neut=0.4e-15 ce.pos=80.0e-15 ch.neg=20.0e-15; dbond[1] ep.def.pool=1.24 sigma.def.pool=0.17 n.h=5e27; dbond[2] dbond[3] ep.def.pool=1.10 sigma.def.pool=0.17 n.h=5e27; ep.def.pool=1.10 sigma.def.pool=0.16 n.h=5e27;

C GENERAL SETTINGS FOR ASA AND CALCULATION OF DIFFERENT OUTPUTS

settings newton gummel.starts=2 max.step.reduc=0; settings damp=6 max.iter=50; model model amorphous external; powell.deane.1996.mod; settings Rs=8.5e-4 Rp=100.e1;

C CALCULATING GENERATION PROFILE, ABOSORPTION PER LAYER; opticgen print spectrum=am15.dat gp3; C Genpro 3 model; gnuplot absorptance file=sim01/abs.abs;

C CALCULATING SPECTRAL RESPONSE; settings sr.flux=1.0e20; solve equil; solve print sr wl.start=350nm wl.step=5nm wl.end=850nm v.bias=0.0; sr file=sim01/sr.dat gnu headers=false;

C CALCULATING DARK J-V; variable v_start=0 v_end=1; model solve poole.frenkel; equil; solve v.start=v_start v.end=v_end n.step=36;

C CALCULATING ILLUMINATED J-V (AM1.5 simulation); variable model v_start=0; poole.frenkel=off tat=off;

C Trap-assisted tunnelling is set automatically when Poole-Frenkel is set;

C settings Rs = 10.0; solve equil; solve print headers=false; v.start=v_start v.end=v_end n.step=36 illum; gnuplot jv file=sim01/jv.asp

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Appendix 2 Dektak results dropcasted samples

Samples on Corning glass: sorted thin to thick

(L-top, R-top, L-bottom, R-bottom: etched 30s, 60s, 5s, unetched)

Samples on Asahi glass: sorted thin to thick

(L-top, R-top, L-bottom, R-bottom: etched 60s, 5s, 30s, and unetched)

57

Samples on crystalline silicon wafer: sorted thin to thick (all unetched), with some extra drops,

(used only for testing to deposit the required thickness, not used in 3.2.2)

The wafer samples below were used for the white paint measurements to determine the reflectance and AID:

58

Appendix 3 Scattering WP with different thicknesses

The different tested glass samples with varying thicknesses, all with comparable trends:

ISRT (white paint samples with different thicknesses):

ARTA (AID at white paint – air interface):

59

Appendix 4 ASA parameters in simulations

Flat NIP cell Rough NIP cell Flat PIN cell Rough PIN cell

Thickness layers front

Thickness electrical layers

Thickness layers back

1 st

Scattering interface/ AID

1 st

Scattering interface/ AID

ITO:58+1 nm ITO:80+1 nm

Glass: 1 mm

AZO: 200 nm

Glass: 1 mm

AZO: 200 nm

P: 20 nm

I: 310 nm

N: 14 nm

P: 30 nm

I: 310 nm

N: 14 nm

P: 30 nm

I: 310 nm

N(a-Si): 20 nm

P: 30 nm

I: 310 nm

N(a-Si): 14 nm

AZO: 1100 nm

Glass: 1 mm

Ag: 300 nm

WP: 1µm

AZO: 1100 nm

Glass: 1 mm

Ag: 300 nm

WP: 1µm

AZO: 1100 nm

Glass: 1 mm

Ag: 300 nm

WP: 1µm

AZO: 100 nm

Ag: 300 nm

WP: 1µm

Glass/BR:

AID: TCO-Si

Haze: Si-Ag

- n-aS/TCO:

AID: TCO-Si

Haze: TCO-Si

-

Glass/BR:

AID: cos

2

(θ)

Haze: cos

2

(θ)

- n-aS/TCO:

AID: TCO-Si

Haze: TCO-Si

Glass/BR:

AID: Si/Ag

Haze: Si/Ag

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