Master_thesis_Johan_Blanker.

Master_thesis_Johan_Blanker.
TiO2 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 TiO2 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
TiO2 nanoparticles/air and TiO2 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 TiO2 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 TiO2 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 TiO2-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 TiO2: 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 pand 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 (Voc) of
approximately 0.9 V (compared to about 0.7 V for c-Si cells), but reduces the short circuit current
density (Jsc) to about 14.5 mA/cm2 where c-Si provides Jsc of about 42 mA/cm2 [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 JSC 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.
θ2
2
θ
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:
|
Where
|
{
}
{
is the modified refractive index adjusted for polarization of the light,
index of the material, and
}
(1)
is the refractive
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 41.8o 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 90o this indicates that the directional propagation of the transmitted lights is
closer towards the interface.
(2)
For angles
When
2
2
of 90o and larger angles no transmission occurs, and total internal reflection occurs.
is 90o,
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
2
leading to a maximum of
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
TiO2 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 TiO2 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 TiO2 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 TiO2 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 (neff) 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 neff ≈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 TiO2
nanoparticles to improve scattering. A high concentration of densely packed nanoparticles with air in
between them results in an neff ≈2. Due to this higher neff 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
TiO2 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 TiO2 as the material is initially an
insulator. Figure 9 below shows the conductivity of a rutile TiO2.2 film as a function of annealing time.
This result is found on a continuous layer in contrast to the TiO2 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 TiO2: 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 10O to overcome the problem of the specular
reflection otherwise cannot be measured. The distribution of the reflected light can be measured
from -90O to 90O degrees but a homogenous scattering distribution is assumed and therefore
measurements are restricted from 0O to 90o 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 10O to 90O 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 µm524 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 (cos2(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 cos2(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 TiO2 with Ag-nanoparticles is tested.
TiO2 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 TiO2 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 TiO2 nanoparticles there are a few variables: the
concentration of TiO2, 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 mm2, 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 TiO2, 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 TiO2 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 TiO2
nanoparticles mixed with ethanol. The high concentration mixture was a 10 % TiO2 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 TiO2 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 TiO2 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
yes
Yes
No
Yes
Spin-coating
No
Yes
No
No
Snow globe method
Yes
Yes
No
Yes
Pressure paste
yes
Yes
No
Yes
Table 1 Summarizing table of deposition methods.
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.
Thickness [µm]
1
2
3
4
5
6
7
13±5
17±5
18±3
30±8
33±3
45±5
50±10
Table 2 Thicknesses of white paint layers for different samples.
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 0O and 90O 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 (Io*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 TiO2 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 TiO2 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 OC. 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 1015 cm-3. The free carrier absorption
coefficient is determined by [26]:
2
Where
is given in cm-1,
and
are given in cm-3 and
free-carrier absorption in the lightly doped wafer,
(7)
in µm. Even if we take into account the
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 18O 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 20O 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 75O.
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 TiO2 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]
Front contact
ITO [75nm]
P-layer a-SiC
P-layer a-SiC
Substrate [3mm]
(Corning glass)
I-layer a-Si(i)
[310nm]
[310nm]
P-layer µc-Si [5nm]
P-layer a-SiC [7nm]
Buffer SiC [5nm]
N-layer a-Si [20nm]
N-layer a-Si [20nm]
Protective layer
AZO [30nm]
Substrate [3mm]
Asahi SnO:F layer
P-layer µc-Si [5nm]
P-layer a-SiC [7nm]
Buffer SiC [5nm]
I-layer [300nm]
Substrate [5mm]
(Asahi glass)
Back reflector
Protective layer
AZO [30nm]
I-layer i-Si [300nm]
Back contact
AZO [1100nm]
(Corning glass)
(Asahi glass)
Asahi SnO:F layer
Front contact
AZO [1100nm]
I-layer a-Si(i)
Substrate [5mm]
Back reflector
N-layer a-Si [20nm]
N-layer [20nm]
N-layer SiOx [30nm]
N-layer SiOx [30nm]
Back contact
ITO [200nm]
Back contact
ITO [200nm]
Back reflector
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 TiO2 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 cm2. 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 JSC 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 JSC 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 JSC
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 Voc 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
[cm2]
FF
[-]
VOC
[V]
JSC(EQE) Ag
[mA/cm2]
JSC(EQE) WP
[mA/cm2]
Efficiency
Ag [%]
Efficiency
WP [%]
Rough PIN cell
0.16
0.686
0.849
16.4
16.4
9.90
9.90
Flat PIN cell
0.16
0.670
0.859
12.8
12.5
7.40
7.23
Rough NIP cell
0.16
0.619
0.85
13.9
14.2
7.58
7.74
Flat NIP cell
0.16
0.607
0.761
14.4
14.7
6.35
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 TiO2
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 NIPcell, 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 20O. This was a broader distribution than Tipp-ex
which has been simulated to have a distribution with a diffuse angle of 18O.
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 75o, 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 Jsc 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
Literature
[1] B. S. Honsberg C., "PV Education," [Online]. Available: http://www.pveducation.org/. [Accessed
2012].
[2] "Thin film solar cells," in Solar cells, Textbook - course solar cells, TU Delft , pp. 7.01-7.30.
[3] R. Santbergen, "Optical Absorption Factor of Solar Cells for PVT Systems," Eindhoven University,
PhD thesis, 2008.
[4] W. Beyer, "Voids in hydrogenated amorphous silicon materials," Journal of Non-Crystalline
Solids, no. nr 358, pp. 2023-2023, 2012.
[5] A. Smets, "Vacancies and voids in hydrogenated amorphous silicon," Applied physics letters, vol.
Volume 82, no. Number 10, 2003.
[6] T. Soderstrom, "Optical developments for silicon thin film solar cells in the substrate
configuration," Infoscience, no. PV-LAB-CONF-2008-003, pp. IMT-NE Number: 483 , 2008.
[7] L. Forbes, "Textruing, reflectivity, diffuse scattering and light trapping in silicon solar cells," Solar
cells 86, pp. 319-325, 2012.
[8] D. Hahn, "Light Scattering Theory," Department of Mechanical and Aerospace Engineering,
Uniersity of Florida, July 2009.
[9] B. Lee, "Light trapping by a dielectric nanoparticle back reflector in film silicon solar cells,"
Applied Physics Letters 99, p. 064101, 2011.
[10] E. Yablonovitch, "Intensity Enhancement in Textured Optical Sheets for Solar Cells," IEEE
Transactions on electron devices, pp. volume ED-29, NO2, February 1982.
[11] P. P. Agrawal M., "The physical limits of light trapping in thin-films and photonic structures that
operate the limit," 2010. [Online]. Available:
http://www.stanford.edu/~mukul/publications/34IEEEPVSC2009.pdf. [Accessed 09 02 2012].
[12] "Economically viable solar power," Tokyo Electron, 2012. [Online]. Available:
http://www.solar.tel.com/.
52
[13] S. Valencia, "Study of the Bandgap of Synthesized Titanium Dioxide Nanoparticules Using the
Sol-Gel Method and a Hydrothermal Treatment," The Open Materials Science Journal, vol. 4, pp.
9-14, 2010.
[14] B. Lipovšek, "Modeling and optimization of white paint back reflectors for thin-film silicon solar
cells," Journal of applied physics 108, p. 103115, 2010b.
[15] B. Lipovšek, "Analysis of thin-film silicon solar cells with white paint back reflectors," Physica
Status Solidi C, pp. 1-4, 2010a.
[16] J. Meijer, "Back contact and Back reflector for thin film solar cells". USA Patent
WO2005/076370A2, 2005.
[17] O. Berger, "Commercial white paint as back surface reflector for thin-film solar cells," Solar
Energy Materials & Solar Cells, vol. 91, pp. 1215-1221, 2007.
[18] A. Basch, "Enhanced light trapping in solar cells using snow globe coating," PROGRESS IN
PHOTOVOLTAICS: RESEARCH AND APPLICATIONS, vol. 20, pp. 837-842, 2012.
[19] M. Radecka, "The influence of thermal annealing on the structural, electircal and optical
properties of TiO2-x thin films," applied surface science, vol. 65/66, pp. 227-234, 1993.
[20] PerkinElmer, "LAMBDA 950 UV/Vis/NIR Spectrophotometer," PerkinElmer, 2012. [Online].
Available: http://www.perkinelmer.com/Catalog/Product/ID/L950.
[21] Perkinelmer, "Technical Specifications for the LAMBDA 1050 UV/Vis/NIR and LAMBDA 950
UV/Vis/NIR Spectrophotometers," PerkinElmer, 2007. [Online]. Available:
http://www.perkinelmer.com/CMSResources/Images/4474789SPC_LAMBDA1050LAMBDA950.pdf.
[22] J. Cotter, "Optical intensity of light in layers of silicon with rear diffuse reflectors," Journal of
Applied physics, vol. 84, p. 618, 1998.
[23] A. R. Burgers, “New Metallisation Patterns and Analysis of Light Trapping for Silicon Solar Cells,”
Energieonderzoekcentrum Nederland, Proefschrift Universiteit Utrecht, 2005.
[24] T. Phong, "Illumination for Computer Generated Pictures," Communications of the ACM, pp.
volume 18, number 6, 1975.
53
[25] K. Jaeger, "A scattering model for nano-textured interfaces and its application in opto-electrical
simulations of thin-film silicon solar cells," Journal of applied physics, vol. 111, no. 083108, pp. 19, 2012.
[26] M. Green, Silicon solar cells: advanced principles & practice, Kensington: ISBN 0733409946,
1995.
[27] A. Basch, "Combined plasmonic and dielectric rear reflectors for enhanced photocurrent in solar
cells," Applied physics letters, vol. 100, no. doi: 10.1063/1.4729290, 2012.
[28] A. E. Braundmeier A.J., "Effect of surface roughness on surface plasmon resonance absorption,"
Physical Chemical Solids, pp. 517-520, 1974.
[29] Y. S. Huiying Xu, "A physically based transmission model of rough surfaces," Journal of virtual
reality and broadcasting 5, p. 9, 2008.
[30] H. Swatland, "Basic Science for Carcass grading," University of Guelph, Ontario, Canada, Guelph,
http://www3.sympatico.ca/howard.swatland/Brazil.htm.
[31] Z. Yu, "Fundamental limit nanophotonic light trapping in solar cells," PNAS 107, pp. no. 41
(17491-17496 +3 pages 'support information'), 2010.
[32] Z. Yu, "Nanophotonic light-trapping theory for solar cells," Applied Physics A 105, pp. 329-339,
2011.
[33] Tobytam, "Accelerated study notes - IGCSE Coordinated Sciences: Refraction of Light," Free iGCE
an IB Revision Notes, 2012. [Online]. Available:
https://www.acceleratedstudynotes.com/2012/05/12/igcse-coordinated-sciences-refraction-oflight/.
[34] GianniG46, "Diffuse reflection," Wikipedia, 2012. [Online]. Available:
http://en.wikipedia.org/wiki/Diffuse_reflection.
54
Appendix 1: ASA input file
(capital C deactivates the rest of the input line)
C DEVICE DEFINITION;
layers
electrical=3 front=2 back=4;
grid[f.1]
d=70e-9; C spaces=200;
grid[1]
d=20e-9 dx.t=1e-9;
grid[2]
d=310e-9 dx.t=5e-9;
grid[3]
d=14e-9 dx.t=1e-9;
grid[b.1]
d=1200e-9; C spaces=200;
grid[b.2]
d=0.001;
grid[b.3]
d=300e-9;
C TCO
C p-asi;
C i-aSi;
C n-aSi;
C TCO
C glass;
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;
C p-layer;
optical[2]
lnk.file=nk/tud_i-aSi.nk;
C i-layer;
optical[3]
lnk.file=nk/tud_n-aSi.nk;
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
C
DEACTIVATED
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;
C haze at TCO-Si interface;
interface[i.2]
adf.s.rf=user
adf.s.rb=user
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]
e.act.don=0.24;
bands[1]
e.mob=1.93
chi=3.950
nc=5.0e26
nva=5.0e26
epsilon=7.2;
bands[2]
e.mob=1.73
chi=4.100
nc=4.0e26
nv=4.0e26
epsilon=11.9;
bands[3]
e.mob=1.73 chi=4.100
nc=4.0e26
nv=4.0e26
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]
e.range=1.0 levels=20 c.neut=0.7e-15 c.posa=0.7e-15;
vbtail[1]
n.emob=5.0e27 e.char=0.08;
vbtail[2]
n.emob=1.0e27 e.char=0.040;
vbtail[3]
n.emob=1.0e27 e.char=0.040;
cbtail[all]
e.range=1.0 levels=20 c.neut=0.7e-15 c.neg=0.7e-15;
cbtail[1]
n.emob=5.0e27 e.char=0.07;
cbtail[2]
n.emob=1.0e27 e.char=0.03;
cbtail[3]
n.emob=1.0e27 e.char=0.03;
dbond[all]
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]
ep.def.pool=1.10 sigma.def.pool=0.17 n.h=5e27;
dbond[3]
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
amorphous external;
model
powell.deane.1996.mod;
settings
Rs=8.5e-4 Rp=100.e1;
C CALCULATING GENERATION PROFILE, ABOSORPTION PER LAYER;
opticgen
spectrum=am15.dat gp3;
C Genpro 3 model;
print
gnuplot absorptance file=sim01/abs.abs;
C CALCULATING SPECTRAL RESPONSE;
settings
sr.flux=1.0e20;
solve
equil;
solve
sr wl.start=350nm wl.step=5nm wl.end=850nm v.bias=0.0;
print
sr file=sim01/sr.dat gnu headers=false;
C CALCULATING DARK J-V;
variable
v_start=0 v_end=1;
model
poole.frenkel;
solve
equil;
solve
v.start=v_start v.end=v_end n.step=36;
C CALCULATING ILLUMINATED J-V (AM1.5 simulation);
variable
v_start=0;
model
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
v.start=v_start v.end=v_end n.step=36 illum;
print
gnuplot jv file=sim01/jv.asp
headers=false;
56
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
Thickness layers front
Thickness electrical layers
Thickness layers back
1st Scattering interface/ AID
1st Scattering interface/ AID
Flat NIP cell
Rough NIP cell Flat PIN cell
ITO:58+1 nm
ITO:80+1 nm
Rough PIN cell
Glass: 1 mm
Glass: 1 mm
AZO: 200 nm
AZO: 200 nm
P: 20 nm
P: 30 nm
P: 30 nm
P: 30 nm
I: 310 nm
I: 310 nm
I: 310 nm
I: 310 nm
N: 14 nm
N: 14 nm
N(a-Si): 20 nm
N(a-Si): 14 nm
AZO: 1100 nm
AZO: 1100 nm
AZO: 1100 nm
AZO: 100 nm
Glass: 1 mm
Glass: 1 mm
Glass: 1 mm
Ag: 300 nm
Ag: 300 nm
Ag: 300 nm
Ag: 300 nm
WP: 1µm
WP: 1µm
WP: 1µm
WP: 1µm
Glass/BR:
n-aS/TCO:
-
AID: TCO-Si
AID: TCO-Si
AID: TCO-Si
Haze: Si-Ag
Haze: TCO-Si
Haze: TCO-Si
-
Glass/BR:
2
AID: cos (θ)
2
Haze: cos (θ)
60
-
n-aS/TCO:
Glass/BR:
AID: Si/Ag
Haze: Si/Ag
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement