University of Amsterdam
MSc Physics and Astronomy
Track: Science for Energy and Sustainability
Master Thesis
Influence of random upright pyramid
substrate surface texture on the colour
appearance of dielectric thin film coated
silicon PV
by
Nathan Roosloot
10780947
June 2020
60 ECTS
19 August 2019 - 28 June 2020
Supervisors
Prof. Dr. Erik Stensrud Marstein
Verena Neder, MSc
Examiners
Prof. Dr. Albert Polman
Prof. Dr. Erik Stensrud Marstein
Abstract
In this work, the colour appearance and stability of dielectric thin film coated planar silicon substrates are compared to those of silicon substrates with random upright pyramid textures with different pyra-mid size distributions, coated by identical dielectric thin film layers deposited by plasma enhanced chemical vapour deposition. Dielectric colouring on the former substrate has been researched exten-sively, while this has barely been done for the latter, even though most commercial monocrystalline silicon-based photovoltaics use silicon that is textured in this way. A modeling framework is created to translate the target colours red, blue and green to the appropriate thin film depositions on pol-ished substrates. By angle dependent reflectance, it is shown that colours of the textured samples are generally less saturated, darker, and more stable against changes in the angle of incidence than colours of planar samples as a result of the different substrate surface geometries. Angle-resolved re-flectance measurements under normal incidence demonstrate that the colour appearance of textured samples can be observed from a wider range of angles than that of planar samples, due to the angle-resolved reflectance of the textured samples being relatively broader. For both angle dependent and angle-resolved reflectance, no influence of the pyramid size distribution on the reflectance of textured samples is observed. Because of the combination of lower average reflectance, higher colour stability as a function of the angle of incidence and reflectance over a wider range of angles, silicon substrates textured with upright random pyramids are more suitable for building-integrated photovoltaic appli-cations that based on dielectric colouring than polished silicon substrates, where colour stability is often desired.
Acknowledgements
Firstly, I am extremely grateful to my supervisor at IFE, Erik Marstein, for welcoming me at IFE with open arms and showing me the wonderful world of coloured solar cells and BIPV. I have greatly enjoyed my time at IFE and am extremely happpy to have been part of the SOL department over the last year. Your continuous enthusiasm and trust in my capabilities have given me the confidence that I belong in research.
Secondly, I owe great thanks my supervisor at AMOLF, Verena Neder, for always taking the time and effort to help me from a distance, and keeping me critical of my own work. Special thanks to Albert Polman as well, for aiding in steering this work in the right direction at difficult times.
I wish to show my gratitude to Halvard Haug for helping me with modeling tasks, which would have taken much more time without your assistance. Furthermore, I want to thank Chang Chuan You for showing me the ropes in the lab and assisting me with practically every piece of lab equipment I have touched in the past year, as well as always being open for discussions related to my work. Thanks also to Bent Thomassen for helping me with KOH etching, Simona Palencsar and Samson Lai for assistance with SEM measurements and Annett Thøgersen for carrying out and analysing the TEM measurements.
I want to thank my friends and family for making this year in Norway a great one while missing all of you that are in the Netherlands as well. I am forever grateful to my parents and sister for their unconditional support, no matter where in the world I am located.
Contents
Abstract 1
Acknowledgements 2
1 Introduction 4
2 Theoretical background 7
2.1 Quantifying human colour perception . . . 7
2.2 Creating colour with planar thin films . . . 9
2.3 Random upright pyramid surface texture . . . 10
3 Modeling colour of planar thin films 13 4 Experimental methods 17 4.1 Used substrates . . . 17
4.1.1 Characterisation of pyramid size distribution . . . 17
4.2 Thin film deposition . . . 17
4.3 Thin film characterisation . . . 18
4.3.1 Ellipsometry . . . 18
4.4 Reflectance measurements . . . 19
4.4.1 Angle dependent reflectance . . . 19
4.4.2 Angle-resolved reflectance . . . 20
5 Results and Discussion 22 5.1 Pyramid size distributions . . . 22
5.2 Thin film depositions . . . 24
5.3 Angle dependent reflectance . . . 26
5.3.1 Uncoated substrates . . . 26
5.3.2 Coated substrates . . . 29
5.3.3 Angle dependent colour appearance . . . 35
5.4 Angle-resolved reflectance . . . 41 5.4.1 Uncoated substrates . . . 41 5.4.2 Coated substrates . . . 43 6 Conclusion 47 References 52 7 Appendices 53 7.1 Appendix A: Ellipsometric measurement parameters . . . 53
7.2 Appendix B: Images of TEM measurements . . . 53
7.3 Appendix C: Sample rotation for angle-resolved measurements . . . 55
7.4 Appendix D: Angle dependent reflectance spectra and colour appearance of sample R2 57 7.5 Appendix E: Sample images . . . 59
1
Introduction
As more than a third of the world’s final energy consumption is attributable to buildings, it has become a great challenge to make buildings as energy efficient as possible [1]. Building-integrated photovoltaics (BIPV) provide a possible pathway for increasing the energy efficiency of buildings by producing electricity while functioning as construction materials. The global BIPV market is rising fast, with an annual growth rate of around 40% over the last five years [1]. However, many BIPV products still face important challenges that must be resolved to unlock the full potential of the market. Two key aspects of BIPV elements are their aesthetics and power output. Ideally, BIPV elements are desired components of a building from an aesthetic point of view, while also producing as much power as possible. In the case of coloured BIPV, these two aspects are often conflicting. Commercial solar cells are as black as possible within existing cost restraints to maximize transmission of light to the active layer, limiting the scope of possible architectural design with these cells. Creating cells with different colours therefore widely increases this scope. However, coloured solar cells will always reflect some portion of light that would otherwise be transmitted to the active layer of the cell, which results in a decrease in their current output. It is thus an important challenge to create solar cells with a wide range of possible colours at minimized optical losses. As the both the PV and BIPV market are dominated by crystalline silicon (c-Si) technologies [1], it is especially important to create cheap and efficient ways to colour c-Si based solar cells.
Most c-Si based coloured BIPV products that are currently present on the market are based on printing techniques, which colour one or more elements of the solar module [1]. Although cheap and easily integrated into the PV manufacturing process, these techniques come with high optical losses, which decreases the current output of the cells drastically [2]. A more efficient way to colour c-Si cells is to deposit a thin film coating on top of the silicon substrate. Such coatings have spectrally selective reflectance spectra due to interference. By varying the thickness and refractive index of this film, a wide variety of colours with minimized optical losses compared to c-Si cells with a standard anti-reflective coating (ARC) can be achieved [3], [4], [5], [6], [7]. In particular, films made of
sili-con nitride (a-SiNx:H, also called SiNx) or silicon oxynitride (a-SiOxNy:H or SiOxNy), deposited by
plasma-enhanced chemical vapour deposition (PECVD) allow for immediate large scale production of coloured solar cells, as they are already deposited onto c-Si solar cells in standard manufacturing
as the ARC. It has been shown that using SiNx as ARC material comes with additional benefits
of surface- and bulk passivation of silicon PV [8], [9], [10]. Depositing coloured coatings using this technique is cheap and easy, as just changing the thickness of the standard ARC already results in different coloured solar cells. This is a major benefit of this technique over a variety of other novel solar cell colouring techniques based on for example scatterers [11], [12], plasmonic structures [13], photonic structures [14], and other nanostructures [15], [16], [17], which have also shown to colour solar cells with little optical losses, but are not yet ready to be implemented on a factory scale. In this work, I will therefore focus on the colouring of c-Si solar cells using thin film coatings based on
SiNxor SiOxNy deposited by PECVD. In this field, a lot of possibilities have been explored, and there
is not much room for innovative research. This is especially the case for planar substrates, as the fundamental physics behind this colouring mechanism on these substrates are well understood and described. However, almost all installed c-Si PV is based on substrates that are not planar, but have some surface texture. In the case of monocrystalline silicon, a random upright pyramid texture is most
commonly used [18], [19], [20], [21]. This texture reduces reflectance and increases light trapping, and thus contributes to an increase in the current output of the solar cell, as for example mentioned by [18], [22], [23], [24], and is actually cheaper to realize than a perfectly planar substrate surface. However, little research has focused on the combination of textured silicon substrates and thin film coatings to create coloured solar cells, while this has clear potential benefits over colouring on planar substrates. Firstly, since substrates with a random upright pyramid texture have reduced reflectance compared to polished substrates, textured substrates coloured by thin films will have lower overall reflectance than their coloured polished counterparts as well, increasing the current output of the cell.
Secondly, cells coloured by thin films on planar substrates can vary in colour as a function of the angle of incidence of the light source. As this angle varies, the effective thickness of the thin film changes, which impacts at which wavelengths interference occurs, thus causing a shift in the position of the reflectance minima and maxima. This alters the perceived colour of the cell. For textured substrates, light is reflected along different paths, which all consist of one or multiple interactions of light with the substrate under different angles of incidence. Therefore, a change in the angle of incidence does not necessarily have to impact the effective thickness of the thin film and thus the colour appearance of the cell. For BIPV purposes, it is often desired that the colour of a cell is stable, for example because cities may have a certain colour pattern to which buildings must adhere [25]. For planar substrates with thin film coatings, this would not be possible as the incoming angle of the sun changes throughout the day, and substrates with a random upright pyramid surface texture might be preferred instead.
Lastly, as planar substrates are known to have specular reflectance, the intended colour of a BIPV element might not be observed by viewers from different positions. Surfaces with a random upright pyramid texture have a broader angular reflectance spectrum than planar surfaces [18], [19], [26], which could lead to a more uniform colour appearance for observers from different positions.
The goal of this work will therefore be to compare the colour appearance and stability of planar silicon substrates with that of silicon substrates with an upright pyramid texture, both coated by
identical SiNx or SiOxNy layers. For planar substrates, monocrystalline polished silicon wafers will
be used. Substrates with a random upright pyramid texture are created by etching monocrystalline polished silicon substrates in a potassium hydroxide (KOH) based solution. To further investigate the influence of the pyramid size distribution of the surface texture on the colour appearance of the samples, substrates will be etched at varying times.
In order to select the colours of the thin films coatings that will be deposited onto the different substrates, a modeling framework will first be established which allows the translation of selected colours of dielectric films on planar substrates to thin film deposition parameters. This model will be used to set target colours for the samples and find the according thin film deposition parameters. The target colours of the samples will be the primary colours red, green and blue. Although it has been shown that using a stack of thin film layers instead of a single layer can increase the selection of possible colours while decreasing optical losses [4], [7], only coatings consisting of a single thin film will be considered in this work for the comparison of the respective substrates.
After depositing the modeled thin film coatings by PECVD, the colour appearance of all samples at different angles of incidence will be quantified by angle dependent reflectance measurements. By look-ing at the reflectance spectra and accordlook-ing colours of planar and textured substrates, a comparison of the colour stability of the substrates with changing angle of incidence will be made. Furthermore,
these spectra will be used to compare the total reflectance of the substrates, which are seen as a measure of their current output.
Additionally, the angle-resolved reflectance of all samples under normal incidence will be measured. By considering the angular distribution of these spectra, information will be deduced on the colour appearance of the cells from different points of view.
Altogether, these steps allow for an in-depth comparison of the colour appearance of coated pla-nar silicon substrates and those with a random upright pyramid texture. Since this has not been researched before, this work forms an important first step in identifying and understanding the pos-sible benefits of using textured instead of planar substrates when colouring solar cells with thin film coatings.
2
Theoretical background
In this section, some important concepts will be covered that provide the necessary information to understand colour appearance on planar and textured substrates. Firstly, the ways in which colour can be quantified will be explained. Next, the calculation of reflectance on planar thin films will be covered, and lastly, reflectance on random upright pyramid textures will be touched upon.
2.1
Quantifying human colour perception
The human eye consists of two different kinds of light receptors: cone and rod cells. Cone cells are sensitive to colour, whereas rod cells respond to low levels of illumination, where colour perception diminishes [27]. There are three types of cone cells, each with a different spectral response. Their response functions have spectral sensitivity peaks in either the short, middle or long wavelength range, as can be seen in figure 1.
0 0.2 0.4 0.6 0.8 1.0 400 450 500 550 600 650 700
S M
L
Figure 1: Response functions of the cone cells in the human eye, with peaks in the short (S), medium (M) and long (L) wavelengths. On the x-axis is the wavelength in nm and on the y-axis is the normalized spectral sensitivity (a.u.). Image from [28].
Any colour we observe is thus the product of a certain level of stimulus in each of the three types of cone cells. These cells can therefore be seen as three primary colours, of which all colours can be created by mixing. This has allowed for the creation of three dimensional colour spaces that cover all colours, based on three primary colours. Next, I will cover the colour spaces that are used later in this work.
There are many different systems in which colour can be represented, but the CIE 1931 XYZ and xyY colour spaces established by the Commission Internationale de l’Eclairage (CIE) in 1931 are the most universal [27]. These spaces are based on three colour matching functions, x(λ), y(λ) and z(λ), which were experimentally derived and represent the necessary amount of light from three different primary light sources to match the colour of a monochromatic light source [29]. By calculating how the visible wavelength range of a spectral power distribution overlaps with each of these response functions, it is possible to represent the resulting colour of the distribution in terms of three coordinates: X, Y
and Z, which are called the tristimulus values. All colours can be defined by these tristimulus values, which make up the CIE 1931 XYZ colour space. In the case of reflectance or transmittance, the light source affects the spectral power distribution and thus colour of the object. To avoid ambiguity of XYZ values, a set of reference illuminants were defined by the CIE [29]. In this research, the CIE standard illuminant D65 is used, which represents the average midday light in Western and Northern Europe [30].
Since it is complicated to visualize colour in a three-dimensional colour space, the CIE handily chose the tristimulus values so that they can also represent colour in terms of its brightness and chromatic-ity, which specifies the quality of a colour regardless of the brightness. This allows us to introduce the CIE 1931 xyY colour space, where x and y are the normalized values of X and Y:
x = X
X + Y + Z
y = Y
X + Y + Z
(1)
In this colour space, the values x and y make up the chromaticity of the colour, while Y stands for the brightness. When using the D65 illuminant, Y is scaled so that when all visible light is reflected, Y = 1, and when no visible light is reflected, Y = 0. The chromaticity of a colour can be represented in a chromaticity diagram, as shown in figure 2. Around the curved boundary of this diagram, the chromaticities of monochromatic light, which are most saturated, can be found. In the middle is the chromaticity of white light when using the D65 illuminant as reference.
Figure 2: Chromaticity diagram with the sRGB space outlined by the blue line. The white dot
represents the reference white point of the D65 illuminant. As the xyY space covers the entire
diagram, it is clear that the sRGB space is significantly smaller.
Although the xyY space covers all possible colours, it is not used by most monitors and printers or on the internet. Instead, the standard Red Green Blue (sRGB) colour space is preferred, which
is comprised of less saturated chromaticities. This is shown in figure 2, where the chromaticities in the sRGB space are outlined. In this space, colours are represented by the three primaries red (R), green (G) and blue (B), which take on values between 0 and 255. RGB values can easily be derived from XYZ values by matrix multiplication followed by gamma correction, which corrects for the light intensity. Values are then clipped to the 0-1 range and multiplied by 255 before being rounded to the nearest integer [31].
In this work, I will represent the colours of my samples by their chromaticity and brightness and by colour patches that are generated by using RGB values. Combining these two representations gives a comprehensive view of how samples are coloured and change in colour as a function of the angle of incidence.
2.2
Creating colour with planar thin films
Because reflected light from a single thin film on top of a substrate consists of two beams, as shown in figure 3, interference of light occurs. By tuning at which wavelengths this happens, the colour appearance of the film can be modified.
Figure 3: Path of light incident through medium with refractive index n0 on thin film material with
index n1 covering substrate with index n2. Since the reflected light is a combination of two beams,
reflectance can be decreased or enhanced by destructive or constructive interference, respectively. Image from [27].
For destructive interference to occur, the optical path difference between the two reflected beams
should be equal to (m1+ 12) times the wavelength of light, with m1 = 0, 1, 2, .... Therefore, one can
easily derive that for a thin film of thickness d, destructive interference occurs at wavelengths
λmin = 2n1d (m1+12) r 1 −n0 n1 2 sin2(θ) (2)
where n0 and n1 are the refractive indices as indicated in figure 3, and θ is the angle of incidence
on the thin film. In this work, it is always assumed that the incident medium is air, so we can fix
interference occurs, one can simply substitute (m1+12) in equation 2 for m2 with m2 = 1, 2, 3, .... This demonstrates that at a fixed angle of incidence, the wavelengths at which constructive and destructive interference occur are fully determined by the refractive index and thickness of the thin film. Simply changing these two parameters thus affects the colour of a thin film. Since thin films have a regular pattern of constructive and destructive interference, it is impossible to have high reflectance for a certain visible wavelength and minimized reflectance at all other wavelengths. This would be the ideal case of creating a colour, in which optical losses are minimized. Instead, there will always be some optical losses caused by reflectance maxima, which could be reduced by using a substrate with an upright pyramid surface texture rather than a planar one, as this reduces overall reflectance. For planar systems, the exact reflectance, transmittance and absorptance of thin film stacks of N discrete layers on top of an arbitrary substrate can also be described in formula form. These formulas are a part of the model used in this work to calculate the colour of thin films on top of planar silicon substrates. The full derivation of these formulas is based on the transfer matrix method, and can be found in chapter four of [27], so will not be repeated here. Rather, the final formulas are given. The reflectance of a stack of planar thin films is described by
R =η0B − C η0B + C η0B − C η0B + C ∗ (3)
with η0 the optical admittance of the incident medium, which amongst other things contains the
indicent angle of light on the thin film stack. The quantities B and C are described by B C = N Y r=1 cos δr (i sin δr)/ηr
iηrsin δr cos δr
1
ηm
(4)
where N stands for the amount of thin film layers, δr describes a phase difference between EM waves
at identical positions on the two boundaries of the thin film r and ηm is the optical admittance of
the substrate. Similarly, the transmittance and absorptance of a stack of planar thin film filters are described by T = 4η0Re(ηm) (η0B + C)(η0B + C)∗ (5) and A = 4η0Re(BC ∗− η m) (η0B + C)(η0B + C)∗ (6) We now have an understanding of how the thickness and refractive index of a thin film influence its reflectance spectrum and colour, and how the full reflectance, transmittance and absorptance spectra of a stack of planar thin films are calculated. To conclude the theory, we will look at how reflectance is influenced by a random upright pyramid surface texture.
2.3
Random upright pyramid surface texture
Monocrystalline silicon substrates are made of wafers with a (100) orientation. By anisotropic etching in alkaline solutions, based on for example KOH, texture can be created on the front and back surfaces. This form of etching has a much higher etch rate in the (100) direction than the (111) direction, exposing the (111) planes. This creates a surface texture consisting of upright pyramids with facets in the (111) direction. These pyramids have random positions and heights, but ideally
have a constant base angle [21]. This base angle is 54.7◦, as determined by the angle between the (111) and (100) planes. Incident light on this texture hits the substrate at least twice, as is demonstrated in figure 4, which reduces reflectance as light has multiple chances to be transmitted into the substrate. Furthermore, light trapping is increased by this texture, as light is transmitted at a non-perpendicular angle. Because of this, overall reflectance is decreased considerably compared to a planar substrate where light only hits the substrate once.
Figure 4: Possible paths of light incident on a silicon substrate with a random upright pyramid surface texture. The reflected beam will hit the substrate at least twice, causing reduced reflectance, while light transmitted in the substrate is trapped by the surface texture.
The exact path that a light beam incident on this texture takes depends on the exact surface geometry of the substrate, and the initial position and angle of incidence on a pyramid [18]. As a result, total reflected light is made up of beams following a large amount of discrete paths, which each have one or multiple interactions with the substrate under different angles of incidence. Because of this, reflectance on such substrates can not be modeled using the transfer matrix method. However, as long as the surface geometry of these substrates is known, and feature sizes are much larger than the wavelength of light, reflectance can be calculated by identifying all reflected paths, and solving the Fresnel equations at each interface for each path. Since the pyramids have a size that is typically of the order of several micrometers [20], reflectance is modeled in this way via ray tracing [18], [32]. One issue with ray tracing is that such models often assume an ideal upright pyramid surface texture as described before. However, it has been observed that the pyramid base angles, which are ideally
constant, often have a distribution of values below 54.7◦ as a result of non-ideal etching [19], [20],
with an orthogonal base, rather than of pyramids, making ray tracing approximations less exact [26]. Lastly, shorter etching times can result in pyramids with sizes around the wavelength of light, where light scattering and/or diffraction can occur. Such effects are not taken into account in most tradi-tional ray tracing [33], [34]. So although ray tracing provides a good way to model reflectance of thin films on substrates with ideal textures, modeled and measured reflectance of real samples are often not equal. In this work, ray tracing will therefore not be used to model the reflectance of textured samples. Now that we have a full understanding of the basic physics behind reflectance of planar and tex-tured substrates, we will take a look at the modeling framework of this thesis.
3
Modeling colour of planar thin films
In order to create thin film coated samples with desired colours, it is crucial to calculate how the colour appearance of these samples depends on thin film thickness and refractive index. For this, I have developed a Matlab model, based on an existing model [35] for thin film ARC optimization on planar substrates.
The model uses the transfer matrix method, which essentially consists of formulas 3, 5 and 6, to cal-culate reflectance, transmittance and absorptance of a given thin film stack with defined thicknesses and complex refractive indices on top of a planar substrate under any given angle of incidence. The calculated reflectance of a sample is used in combination with the D65 light source to find the sample’s colour appearance, using the colour spaces explained in section 2.1. Although the model is able to calculate colours of a thin film stack, with which I have worked as well, only thin film coatings of a single layer are covered in this work for the aforementioned reasons. A schematic overview of the model is shown in figure 5.
θ d1 dN d2 N2(λ) N1(λ) NN(λ) Nsub(λ) T(λ) P(λ) R(λ) [R G B] [X Y Z] [x y Y]
(a)
(b)
(c)
Figure 5: Setup of the model: a thin film stack is designed (a), for which the reflectance, transmittance and absorptance spectra are calculated (b), of which the reflected spectrum is used to calculate the colour of the stack (c).
For all samples, the incident medium of air (n = 1) is selected. The substrate, which is monocrys-talline silicon, is defined as the emergent medium, so that its thickness has no influence on the cal-culated reflectance, transmittance or absorptance. The refractive index of the substrate is acquired by ellipsometric characterisation of the used polished silicon substrates, a technique that is covered in section 4.3.1.
To accurately model the colour appearance of thin films, input of refractive index profiles of these
films is needed. To acquire these data, SiNx and SiOxNy films are deposited by PECVD under
vary-ing gas flows, which creates films with refractive indices rangvary-ing from values as low as that of glass
(n630nm = 1.5) up to values as high as that of amorphous silicon (n630nm = 3.6). In section 4.2,
PECVD is explained more in-depth. The refractive indices of the films are found by ellipsometric characterisation.
In total, 16 different depositions, of which four SiOxNy and the other 12 SiNx, are used as input
data. By ranking the refractive indices by increasing n value, the model is able to interpolate between different refractive indices via spline interpolation. In this way, all realistic refractive index profiles between the indices of glass and amorphous silicon are represented in the model. Futhermore, by assigning a single coordinate, called x, to the gas flows of the input data, any interpolated refractive index can easily be translated to the gas flows that are required to deposit a thin film layer with said index. In figure 6, one can see the real (6a) and complex (6b) parts of the refractive indices used as model input at 630 and 300 nm, respectively, as well as the spline interpolation the model uses to interpolate between these data.
0 4 8 1 2 1 6 2 0 2 4 2 8 3 2 1 , 5 0 1 , 7 5 2 , 0 0 2 , 2 5 2 , 5 0 2 , 7 5 3 , 0 0 3 , 2 5 3 , 5 0 3 , 7 5 n (6 3 0 n m ) S i H 4 / N H 3 / N 2O c o m p o s i t i o n ( s c c m ) ( 1 0 + 1 0 x ) S i H 4 / ( 5 x ) N H 3 / ( 3 0 0 - 7 5 x ) N 2O ( 5 x - 1 5 ) S i H 4 / ( 5 0 ) N H 3 ( 1 0 ) S i H 4 / ( 1 0 0 - 1 0 x ) N H 3 ( 1 0 x - 7 0 ) S i H 4 / ( 2 0 ) N H 3 ( 5 0 ) S i H 4 / ( 3 2 - x ) N H 3
(a) Real part of refractive index at 630 nm
0 4 8 1 2 1 6 2 0 2 4 2 8 3 2 0 , 0 0 0 , 2 5 0 , 5 0 0 , 7 5 1 , 0 0 1 , 2 5 1 , 5 0 1 , 7 5 2 , 0 0 2 , 2 5 2 , 5 0 k (3 0 0 n m ) S i H 4 / N H 3 / N 2O c o m p o s i t i o n ( s c c m ) ( 1 0 + 1 0 x ) S i H 4 / ( 5 x ) N H 3 / ( 3 0 0 - 7 5 x ) N 2O ( 5 x - 1 5 ) S i H 4 / ( 5 0 ) N H 3 ( 1 0 ) S i H 4 / ( 1 0 0 - 1 0 x ) N H 3 ( 1 0 x - 7 0 ) S i H 4 / ( 2 0 ) N H 3 ( 5 0 ) S i H 4 / ( 3 2 - x ) N H 3
(b) Complex part of refractive index at 300 nm Figure 6: Real (a) and complex (b) part of the refractive index, at 630 and 300 nm, respectively, of matlab input data versus used deposition gas flows, with spline interpolation between the values.
The black lines interpolate between the SiOxNy input data, while the red lines interpolate between
the SiNx input data. Colours of the datapoints correspond to the specific domain of used gas flows.
Table 1 shows exactly how the interpolation coordinate x is translated to the deposition gas flows for the entire range of refractive indices. Since not all input data could be achieved under a single linear change of gas flows, the coordinate consists of different linear domains.
Domain Gas flow function 0 ≤ x ≤ 3 (10 + 10x) SiH4 / (5x) NH3 / (300 - 75x) N2O 4 ≤ x ≤ 5 (5x - 15) SiH4 / (50) NH3 5 ≤ x ≤ 8 (10) SiH4 / (100 - 10x) NH3 8 ≤ x ≤ 12 (10x - 70) SiH4 / (20) NH3 12 ≤ x ≤32 (50) SiH4 / (32 - x) NH3
Table 1: Domains of the interpolation coordinate and according functions that are used to calculate deposition gas flows from this coordinate.
Since figure 6 only shows interpolation at a single wavelength, figure 7 demonstrates an example of an interpolated complex and real refractive index at all wavelengths.
300 400 500 600 700 800 900 1000 Wavelength (nm) 1.5 2 2.5 3 3.5 4 4.5 n
(a) Real part of refractive index
300 400 500 600 700 800 900 1000 Wavelength (nm) 0 0.5 1 1.5 2 2.5 k
(b) Complex part of refractive index
Figure 7: Real (a) and complex (b) part of the refractive index of matlab input data versus at all wavelengths (dotted lines), with interpolated spectra (blue line) belonging to x = 9.5.
Besides calculating the colour of a given thin film stack, the model is also capable of optimizing the thicknesses and refractive indices of a thin film stack to match its colour to a given target colour. By varying the thicknesses and refractive indices of the thin film layers using the interpolation coordinate from given starting thicknesses and refractive indices, the model looks for the minimum of a function that defines the difference between the RGB coordinates of the target colour and those of the modeled stack:
f (R, G, B) =p(RT − RM)2+ (GT − GM)2 + (BT − BM)2 (7)
Here, XT is the target value and XM is the modeled value. Apart from the thickness and refractive
index, all other parameters are fixed during optimalization. Because thin films of different thicknesses can share reflectance maxima and minima, as expressed before in function 2, films with different thicknesses will have similar colour appearances. This is shown in figure 8 for the case of a thin film stack consisting of two layers.
Figure 8: Calculated RGB colours for thin film stack of two layers, with different thicknesses d(1) and d(2) in nm. Refractive index of both layers is fixed.
This can lead to the model getting stuck in a local minimum of function 7 during optimization, rather than finding the absolute minimum. To avoid local minima, a sweep of target thicknesses and/or refractive indices is performed first, and optimization is carried out with the starting thick-ness and refractive index close to the actual minimum. This procedure is difficult to carry out for stacks of thin film layers, as a sweep over more than two parameters is hard to visualize, but works well when only one layer is used. When a minimum of function 7 is found, the model gives the according film thicknesses and interpolation coordinates, which are translated to deposition gas flows. As the growth rate in the PECVD has a non-linear dependence on the gas flows, a film with arbitrary thickness must first be deposited with the correct gas flows to find out the growth rate of said film. In a second deposition, the film with correct thickness can then be deposited.
This model forms the basis of this work, as it makes it possible to find the deposition recipes that lead to films closest to the selected target colours red (RGB coordinates [255 0 0]), green (RGB coordinates [0 255 0]) and blue (RGB coordinates [0 0 255]).
Now that both the relevant theory and the used model are explained, we will continue with a de-scription of the experimental methods, which consist of an overview of the used substrates, the used deposition method, the characterisation tools used to measure the thickness and refractive index of the thin films and the characterisation tools used to find the angle dependent and angle-resolved reflectance of the samples.
4
Experimental methods
4.1
Used substrates
As planar substrates, p-type (100) double side polished monocrystalline silicon wafers grown by the Czochralski method were used. The wafers have a thickness of 275 ± 20 µm and a resistivity of 1-10 Ohm-cm. Wafers were cut in square 30x30 mm pieces by a laser cutter before use, as this is the rec-ommended size of samples inside the integrating sphere which is used for angle dependent reflectance measurements.
To create substrates with a random upright pyramid texture on both sides of the wafer, the polished wafers were etched in a KOH based solution. This solution is based on a standard recipe developed at the Institutt for Energiteknikk (IFE) and consists of water, a 48% KOH solution, a proprietary
buffering agent and a texturizer additive. The temperature of the solution was 80 degrees ◦C and a
nitrogen bubble flow was present in the solution during the entire etching process to promote chemical mixing. To create samples with different texture sizes, etching time inside the solution was varied. Wafers were either etched for 20, 30 or 40 minutes. After etching, wafers were consecutively rinsed in baths of deionized (DI) water, hydrochloric acid solution and DI water, before being dried under a nitrogen gas flow. Again, wafers were cut by the laser cutter before use. The textured samples shown in this work have a quarter circle shape with a radius of 30 mm.
4.1.1 Characterisation of pyramid size distribution
To investigate the pyramid size distribution of the upright pyramids at different etching times, scan-ning electron microscope (SEM) images were taken of uncoated samples. Because of issues with the SEM, some samples were measured externally, and SEM settings thus vary for different samples. Analysis of pyramid size distribution was performed with the open software ImageJ. Because of large differences between pyramid sizes, all pyramid areas were determined manually, as any automated attempts either neglected smaller pyramids or split up larger pyramids into multiple smaller ones. For each etching time, the areas of 250 pyramids on a single SEM image were identified.
4.2
Thin film deposition
All thin films were created by PECVD. This process deposits solid thin films from a gas phase, and is used by almost the entire PV industry for the deposition of ARCs and surface passivation layers [36]. Therefore, the creation of coloured cells using this deposition method is immediately applicable on a large scale. Deposition occurs under relative low temperatures, is fast and creates homogeneous layers [36]. For further explanation of the mechanisms and some of the surface passivation benefits of PECVD, see for example [8] and [37].
All samples were deposited with an Oxford instruments plasmalab system 133 under a radio
fre-quency (RF) power of 40 W, a reaction chamber pressure of 800 mTorr and a temperature of 350◦C.
SiOxNy films are created using gas flows of SiH4, N2O and NH3, while SiNx is created from SiH4 and
NH3 gas flows. For both materials, a N2 background flow of 980 sccm was used for all depositions. The
other gas flows as well as the deposition time varied per sample, depending on the required refractive index and thin film thickness. Because the growth rate of the thin film is dependent on substrate
surface roughness, films with planar and textured substrates have varying growth rates. To achieve identical thin film thicknesses on all substrates, individual depositions on the different substrates were thus required. To remove the native oxide layer on the samples before depositions, all samples were put in a 5% hydrogen fluoride (HF) bath for two minutes and subsequently rinsed with DI water and then dried under a nitrogen gas flow.
4.3
Thin film characterisation
4.3.1 Ellipsometry
Ellipsometry is an optical technique used to deduce the optical and compositional properties of thin films, such as the refractive index, thickness and crystallinity [38], [39]. This is done by measuring changes in the polarization of an incident light source as a result of interaction with a sample’s surface. Ellipsometry is widely used in both research and industry, and is well understood physically, making it a reliable tool to characterise thin films [39]. The output of an ellipsometric measurement consists of two parameters, psi (Ψ) and delta (∆), which describe the aforementioned change in polarization of incident light. The physical parameters of a sample are thus not directly given, but can be deduced from psi and delta by modeling. A more in-depth description of this technique can be found in [40]. In this work, ellipsometry was used to find the thickness and n&k data of the thin films on pla-nar substrates. It was not possible to characterise the textured samples via ellipsometry as reflected light missed the detector. This is a result of non planar reflectance due to the surface texture. All measurements were carried out using a Variable Angle Spectroscopic Ellipsometer (VASE) from J. A. Woollam. All samples were characterised from 350 to 1000 nm with 5 nm intervals using the same measurement parameters, which can be found in appendix A.
For modeling of the ellipsometric data, the WVASE32 software from Woollam was used. In this software, individual layers represent the different layers making up the sample. Modeled data is then fitted to the experimental data via the Levenberg-Marquardt routine. In this work, three layers were used:
1) The silicon substrate was modeled by a c-Si layer from the Woollam materials library with a fixed thickness of 270 µm.
2) The dielectric thin film layer was modeled by either a Cauchy layer or a general oscillator layer, depending on whether the thin film absorbs light or not. An explanation of different fitting layers can be found in [38]. In case there is no light absorptance in the thin film, a Cauchy layer provides a good fit. For films where (UV) absorptance is present, a fitting procedure was followed based on information provided by Woollam. First, the transparent region of the layer is fitted with a Cauchy layer. After fixing the thickness that follows from this fit, n and k are fitted over the entire wavelength range by a point by point fit. Although fitting is accurate with this procedure, n and k have nonphysical profiles. Therefore, the Cauchy layer is turned into a general oscillator layer. Here, the real and complex part of the dielectric function of the film are modeled. The complex part of this function is fitted with a Tauc-Lorentz oscillator, which provides good fits for amorphous materials [38], [40]. The real part of the dielectric function is represented by a combination of two zero-width Lorentz oscillators, called poles. In this work, only one pole had to be fitted to obtain accurate results, while the second was fixed to the default values. With this method, realistic n and k profiles were acquired for absorbing thin films.
some surface roughness as a result of the gas flows turning off in the PECVD while layer growth might still carry on slightly after. This layer is made up of an effective medium approximation (EMA) of 50% thin film layer and 50% void. The modeled thickness of this layer was typically a couple of nm, while significantly improving model fits. For the total thin film thickness, the thicknesses of the thin film layer and surface roughness layer were added.
The fitting procedure as described here lead to good fits for all deposited planar thin films, pro-viding accurate values for film thickness and n&k spectra.
4.4
Reflectance measurements
4.4.1 Angle dependent reflectance
The angle dependent reflectance was measured with an integrating sphere setup. A Spectral Products QTH 30 W ASB-W-030 high stability tungsten-halogen light in combination with an Oriel Corner-stone 260 monochromator from Newport was used as light source. To modulate the intensity of the light beam and improve the signal-to-noise ratio, the beam was sent through a chopper and lock-in amplifier. The beam was then focused by a series of lenses and depolarized by a depolarizer before entering a 6 inch RTC-060-SF integrating sphere from Labsphere, in which samples were placed inside via a clip-style center mount sample holder. Reflected light was detected with a S1336-5BQ silicon detector from Hamamatsu. All measurements were performed between 350 and 1000 nm, with 5 nm intervals. It was observed that from 950 nm, reflectance increased for all samples as the substrates became partially transparent. Per the measurement handbook at IFE, all samples had a maximum size of 30x30 mm to minimize systematic errors. Reference measurements for all samples were carried out by rotating both the sphere itself and the sample inside the sphere so that the beam hits the wall of the integrating sphere and not the sample. The sample was kept inside of the sphere during reference measurements to take reflections from the sphere walls onto the sample surface into account. All samples were measured from the zenith angle θ = 10 to 80 degrees with 10 degrees intervals. The spot size on the samples had a rectangular shape of about 15 mm in height but only about 2 mm in width. This allowed measurements at angles up to 80 degrees to be taken, as from inspection with the naked eye, the light source did not seem to miss the samples. It should be noted that in real life, solar cells are covered by glass, which restricts the angle of incidence to about 60 degrees. However, to create a better understanding of reflectance on the different substrates, reflectance is still measured at all possible angles.
As mentioned in the previous section, textured samples could not be characterised by ellipsometry. Since the same deposition recipes are used for planar and textured substrates at varying deposition times, it is assumed films deposited with the same parameters will have the same n&k data on all substrates. Because of this, it is not necessary to also characterise the n&k spectra of textured sam-ples. However, it is necessary to measure the thickness of the thin films on textured substrates. In equation 2 it is shown how the thickness of a planar thin film can be calculated from the po-sition of the reflectance minimum, when knowing the angle of incidence and the refractive index at the corresponding wavelength. It is demonstrated by [41] that this method also works well to determine thin film thickness on textured samples. Therefore, angle dependent measurements were performed on textured samples to calculate the thin film thickness. Samples were again measured from angles of 10 to 80 degrees with 10 degrees intervals. Measurements were performed around the
reflectance minimum with 5 nm steps. For each angles of incidence, the thin film thickness was calcu-lated using equation 2, with the refractive index at the wavelength of minimum reflectance acquired by ellipsometric measurement of the according planar sample. The average of the thicknesses found at these angles of incidence was taken as final film thickness. Measurement uncertainty was taken as the largest difference between an individual thickness value and average value. To verify that this method determines thin film thickness accurately, two samples were sent out to be measured with transmission electron microscopy (TEM), called sample A and sample B. Sample A consisted of a thin film deposited on a textured surface etched for 20 minutes, while sample B was a different thin film deposited on a textured surface etched for 40 minutes. The according TEM images can be found in appendix B. As demonstrated in table 2, these measurements confirmed that the thicknesses of both films were accurately determined with angle dependent reflectance measurements up to a couple of nm. Therefore, the thin film thickness of every textured sample was determined in this way.
TEM (nm) Angle dependent reflectance (nm)
Sample A 78.667 ± 2.333 79.529 ± 3.833
Sample B 86.667 ± 1.667 83.292 ± 4.793
Table 2: Thickness of thin film layer of sample A and B in nanometer, as determined by TEM and angle dependent reflectance measurements.
One important thing to note is that in order to calculate thin film thickness with angle dependent reflectance measurements, the reflectance minimum should be in the wavelength range of 350 to 950 nm, where measurements are accurate. Using equation 2 at normal incidence shows that a thin film with n = 2 at all wavelengths should have a film thickness of 43.75 − 118.75 nm for the reflectance
minimum to be between 350 and 950 nm. This is under the assumption that m1 = 0 in formula 2.
Indeed, films of higher thickness can still have reflectance minima of higher orders (m1 = 1, 2, ...)
within the appropriate wavelength range. However, without any knowledge of the thin film growth rate or approximate thickness, this can lead to incorrect determination of thin film thicknesses on
textured substrate when an incorrect value of m1 is chosen. This is why the thin films used in this
work have targeted thicknesses of 43.75 − 118.75 nm.
4.4.2 Angle-resolved reflectance
To measure the angle-resolved reflectance, a new experimental setup was created. Since there were no other suitable light sources available at IFE, the focused beam of the angle dependent reflectance setup was used. After the beam exited the path of focusing lenses and depolarizer, a 45 degree mirror was used to deflect the light from the entrance of the integrating sphere. After hitting a black screen with a pinhole of 3 mm in radius, the light source hits a sample mounted on a clip-style sample holder under normal incidence. Since the beam is focused, the screen with a pinhole has the function of decreasing the spot size that hits the sample. The silicon detector also used in the angle dependent setup is mounted on a rotating stage at the same height as the sample, and is able to measure reflected
light at all zenith angles around the sample. The detector has an aperture of 1.25◦. To avoid stray
light from the light source hitting the detector, a series of light blocking screens is placed along the series of lenses. A schematic overview of this setup is given in figure 9.
Figure 9: Schematic overview of angle-resolved reflectance measurement setup
To ensure normal incidence on the sample, mirrors were used for alignment. Because the detector is at the same height as the sample and the incoming light beam, measurements are not possible
between detector angles of -12 and +12◦, as the detector blocks the incoming beam at these angles.
Since a focused and not a collimated light source is used, the incoming light does not hit samples
under perfect normal incidence, but rather at angles ranging 2.2◦ around normal incidence. In the
case of upright pyramids, this causes broadening of the reflected beam. As a result, reflected light is distributed over a range of angles larger than the detector aperture, which causes broadening of measured reflectance peaks [26]. This should not be an issue in this work, as qualitative assessment and comparison of reflectance distributions is still possible.
All measurements are carried out from -90 to +90◦ with a 5◦ step size. Reflectance is measured
at 750 nm, since all samples had high enough reflectance around this wavelength. It was only possible to measure at wavelengths with relatively high reflectance, as at other wavelengths the detected signal was heavily influenced by background noise. In order to compare the angle-resolved reflectance data
of different samples, each sample’s data are normalized to the value at +12◦. It should be noted
that the rotation of a sample about the incoming light beam should be taken into account when measuring angle-resolved reflectance, as this can impact the measured spectrum. For these samples, however, little dependence of the sample rotation on the angle-resolved reflectance was found. More information on this is given in appendix C.
Now that all experimental methods have been explained, the resulting substrates, thin film coat-ings and reflectance spectra of the samples will be discussed in the coming section.
5
Results and Discussion
This section is split up in three parts: first, the pyramid size distributions of the textured substrates will be discussed, along with the potential impacts of these distributions on angle dependent and angle-resolved reflectance. Next, the deposited thin films, as selected by model optimization, will be covered. Lastly, the angle dependent and angle-resolved reflectance of all uncoated and coated substrates will be discussed, with special attention to the colour appearance of the samples.
5.1
Pyramid size distributions
In figure 10, one can see SEM images of the textured substrates at different etching times, which are representative for the respective samples used in this work. As can be seen, all substrates are completely covered by pyramids, with no planar surfaces present. As the SEM images were taken with different instruments, the quality and magnification of the images differs. The ’dust’ visible on the pyramids of the 20 minutes etch is likely caused by poor handling in transport, as it was not observed on any samples measured at IFE.
(a) 20 min etch (b) 30 min etch (c) 40 min etch
Figure 10: SEM images of 20 (a), 30 (b) and 40 (c) minutes etched textured silicon substrates. These three images were used to identify the size distribution of the pyramids for each etching time, following the method explained in section 4.1.1. In figure 11, one can find the pyramid area distributions of the three respective samples.
0 , 0 0 , 1 0 , 2 0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0 0 2 0 4 0 6 0 8 0 1 0 0 2 0 m i n 3 0 m i n 4 0 m i n 2 0 m i n 3 0 m i n 4 0 m i n P y r a m i d a r e a ( µ m 2) C u m u la ti v e p e rc e n ta g e o f to ta l p y ra m id s ( % ) 0 5 1 0 1 5 2 0 2 5 Cu m u la tiv e p e rc e n ta g e o f t o ta l a re a ( % )
(a) Area distribution for pyramid areas 0 to 1 µm2
0 , 0 0 0 , 0 1 0 , 0 2 0 , 0 3 0 , 0 4 0 , 0 5 0 , 0 6 0 , 0 7 0 , 0 8 0 , 0 9 0 , 1 0 0 2 0 4 0 6 0 8 0 2 0 m i n 3 0 m i n 4 0 m i n 2 0 m i n 3 0 m i n 4 0 m i n P y r a m i d a r e a ( µ m 2) C u m u la ti v e p e rc e n ta g e o f to ta l p y ra m id s ( % ) 0 2 4 6 C u m u la tiv e p e rc e n ta g e o f t o ta l a re a ( % )
(b) Area distribution for pyramid areas 0 to 0.1 µm2
Figure 11: Analysis of pyramid area distributions of 20, 30 and 40 minutes KOH etched polished silicon wafers. The left y-axis (bars) shows the cumulative percentage of total pyramids with a certain area, while the right y-axis (lines) shows the cumulative percentage of total surface area covered by
pyramids with this area. Figure (a) shows pyramid areas 0 to 1 µm2, while figure (b) zooms in on
pyramid areas 0 to 0.1 µm2.
From figure 11 one can conclude that the size distributions of the pyramids shift to larger values with increasing etching time. For example, almost 80% of the pyramids of the 20 minutes etched
sample have an area of maximum 0.1 µm2, while about 70% and 30% of the pyramids on the 30 and
40 minutes etched substrates have this maximum area, respectively. This is a trend that continues
up to a pyramid area of 0.5 µm2, from where we see that the cumulative percentages of the 20 and
30 minutes etches become practically equal.
For all three substrates, we see that more than 75% of the total pyramids have an area below 1
µm2. Assuming perfect pyramids with a square base, this translates to pyramids with a base size
of maximum 1000 nm. Together, these pyramids cover about 25% of the total surface area. Since a significant fraction of the total surface area is covered by pyramids with a size comparable to the wavelength of light, it is reasonable to expect that scattering or diffraction effects might occur. These effects could influence the angle dependent and angle-resolved reflectance of the samples. It has for ex-ample been demonstrated that reflectance of these textured sex-amples does not depend on pyramid size or distribution, as long as pyramid sizes are in the geometrical optics limit [18], [42], [43]. However, reflectance increases significantly for pyramid sizes of for example 200 nm, where the geometrical optics limit is not valid any longer [43]. The reflectance of such pyramids is not accurately mod-eled with conventional ray tracing methods and traditionally requires computationally heavy rigorous methods [44]. Alternatively, it has been shown that reflectance of submicron pyramids can accurately be modeled by representing pyramid textures as diffraction gratings [45], or possibly by integrating an EMA into ray tracing [44]. This shows both the potential influence that small pyramids can have on the reflectance, and strengthens the point that conventional ray tracing is not an appropriate way to model these samples. Other literature has pointed to the fact that scattering can indeed occur at pyramids [33], [34], influencing angle-resolved reflectance. Including scattering in ray tracing can therefore improve modeled angle-resolved reflectance [46].
5.2
Thin film depositions
As mentioned, the Matlab model was used to find single layer thin film coatings to create a red, green and blue sample under normal incidence, with [255 0 0], [0 255 0], [0 0 255] as respective RGB target coordinates. For reasons mentioned earlier, optimization was carried out for target film thicknesses between 43.75 and 118.75 nm. In table 3, one can find the optimized colour coordinates and according deposition parameters that were found by the model. These coordinates are relatively far off the target ones, but should still create samples with red, green or blue colour appearances.
Sample name Target RGB colour Optimized RGB colour Gas flows (SiH4 / NH3) (sccm) Film thickness (nm) Red 1 (R1) [255 0 0] [109 81 23] (30 / 20) 46 Red 2 (R2) [255 0 0] [170 116 72] (30 / 20) 156 Green 1 (G1) [0 255 0] [163 155 59] (30 / 20) 139 Blue 1 (B1) [0 0 255] [0 68 145] (20 /20) 81
Table 3: Target RGB colours and RGB colours found by matlab optimization with according depo-sition parameters.
The used gas flows shown in table 3 were a couple of sccm different than those found by optimiza-tion. Since this difference has a minor influence on the n&k data of the films, and because the growth rates of films on planar substrates using the flows from table 3 were already known from previous depositions, it was decided to use these gas flows instead.
For the red target colour, two optima were found. Because both films have thicknesses around the minimum and maximum of the appropriate thickness range, there might be a risk of not accurately determining the thickness of either film. It was therefore decided to deposit both red films. It is expected, however, that for films with thickness larger than the target maximum (R2 and G1), the thin film thickness on textured samples can still be identified with angle dependent reflectance
mea-surements, using the reflectance minimum for m1 = 1 rather than m1 = 0 (see equation 2). This is
only possible because the growth rate of the thin films is already known, providing information on
the approximate film thickness. Otherwise, it would be unknown which value of m1 leads to accurate
determination of the thickness.
After finding the correct deposition parameters for the target colours, the target films of table 3 were deposited on a polished and the three textured substrates, using the growth rates that had been determined earlier for planar substrates. This should lead to coated polished substrates with the target thin film thickness, and textured substrates with different thin film thicknesses. To ensure the same coating process, all four substrates were put in the reaction chamber simultaneously. All pol-ished substrates were then characterised by ellipsometry, while textured samples were characterised by angle resolved reflectance measurements. In some cases, n&k data of the polished films differed slightly from what was found before for the same gas flows, but effects on reflectance were negligible. After finding the growth rate on the textured substrates, a second set of depositions on textured films followed to also acquire the target thin film thicknesses on these substrates. As the growth rates on all textured substrates were almost identical, the three types of textured substrates were put in the reaction chamber together. Thin film thickness was again measured via angle dependent reflectance measurements. In table 4, one can find an overview of all samples and their realized thicknesses.
Sample name Substrate Target film thickness (nm) Realized film thickness (nm) Polished 44.167 ± 0.358 Textured 20 min 39.918 ± 1.494 Textured 30 min 39.902 ± 1.534 Red 1 (R1) Textured 40 min 46 39.605 ± 1.808 Polished 142.317 ± 0.176 Textured 20 min 136.838 ± 7.583 Textured 30 min 137.912 ± 8.657 Red 2 (R2) Textured 40 min 156 139.523 ± 8.246 Polished 125.310 ± 0.136 Textured 20 min 124.046 ± 6.713 Textured 30 min 123.010 ± 6.058 Green 1 (G1) Textured 40 min 139 125.685 ± 8.352 Polished 73.561 ± 0.171 Textured 20 min 73.612 ± 4.955 Textured 30 min 74.053 ± 4.741 Blue 1 (B1) Textured 40 min 81 74.302 ± 3.681
Table 4: Thicknesses of thin films on polished and textured substrates, determined by ellipsometry and angle dependent reflectance measurements, respectively.
As shown in table 4, realized thin film thicknesses are lower than the targeted values. It was assumed all thin film growth rates are perfectly linear, which is ostensibly not the case. However, since the main goal is to compare textured and planar samples, it is only important that the different substrates of the same sample have identical thin film thicknesses. We see that for all samples, the maximum difference in thin film thickness between different substrates is just over 5 nm. Using equation 2, we can express the shift in reflectance minimum as a function of the change in thin film thickness under normal incidence:
∆λmin =
2n1∆d
(m1+ 12)
(8)
For a film with n1 = 2 at all wavelengths, this means that a thickness difference of 1 nm leads to a shift
in the reflectance minimum of 4 nm at the first order reflectance minimum (m1 = 0) and to a shift of
1.33 nm at the second order reflectance minimum (m1 = 1). So, even a thickness difference of just 5
nm can shift a reflectance spectrum by about 20 nm, which can influence the colour of thin films. This will not change the colour entirely, but can have impact on its shade. However, it is not possible to deposit thin films with a higher accuracy than performed on this specific equipment without extensive research on how the growth rates of the thin films change with deposition time. We will therefore continue to use these samples. Furthermore, samples G1 and B1 have practically identical thin film thicknesses on all substrates, so in-depth comparison is certainly possible for these samples. In figure 12, one can see images from nearly directly above the samples, with near normally incident office lighting as illuminant. For the etched samples, the colour is hard to distinguish from this angle, as reflectance at zero degrees is relatively low. It must be noted that the white background and high reflectance from the planar samples can impact the colour appearance of the samples. Therefore, additional photographs of the samples are added in appendix E.
(a) R1 (b) R2
(c) G1 (d) B1
Figure 12: Samples R1, R2, G1 and B1 from almost directly above on a white background under illumination of near normally incident office lighting. For each image, the substrates are positioned as follows: polished top left, 20 minutes etch top right, 30 minutes etch bottom left, 40 minutes etch bottom right.
5.3
Angle dependent reflectance
For both the angle dependent and angle-resolved reflectance, measured data will first be shown for uncoated substrates and after for coated substrates. Doing this makes it possible to distinguish the influence of the thin film coatings and that of the substrates on the respective reflectance spectra.
5.3.1 Uncoated substrates
In figure 13a, one can see the full angular dependent reflectance spectra of the uncoated textured silicon substrates. This figure shows that the reflectance spectra of the 20 and 30 minutes etched sub-strates are generally very similar, while the reflectance of the 40 minutes etched substrate is higher than both. This demonstrates 40 minutes is past the optimal etching time. Secondly, reflectance of the 20 minutes etched substrate is not higher than that of the other etching times. This shows that the small pyramids present on the 20 minutes etched substrate do not increase reflectance as
might have been expected from [43] and [45], which demonstrates that the small pyramids do not cover enough surface area on the substrate to increase reflectance significantly. This also confirms that there is no case of incomplete etching, in which case reflectance would be increased by planar surfaces. This finding is in accordance with the SEM images of the substrate.
From figure 13a, it can also be seen that the reflectance for angles of incidence 40 and 50 degrees is very similar. This is caused by the fact that a fraction of the pyramids have a base angle around these angles, causing some light to reflect perpendicularly and leave the integrating sphere, thus decreasing measured reflectance. 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 R e fl e c ta n c e ( % ) W a v e l e n g t h ( n m ) 1 0 d e g - K O H 2 0 m i n 1 0 d e g - K O H 3 0 m i n 1 0 d e g - K O H 4 0 m i n 2 0 d e g - K O H 2 0 m i n 2 0 d e g - K O H 3 0 m i n 2 0 d e g - K O H 4 0 m i n 3 0 d e g - K O H 2 0 m i n 3 0 d e g - K O H 3 0 m i n 3 0 d e g - K O H 4 0 m i n 4 0 d e g - K O H 2 0 m i n 4 0 d e g - K O H 3 0 m i n 4 0 d e g - K O H 4 0 m i n 5 0 d e g - K O H 2 0 m i n 5 0 d e g - K O H 3 0 m i n 5 0 d e g - K O H 4 0 m i n 6 0 d e g - K O H 2 0 m i n 6 0 d e g - K O H 3 0 m i n 6 0 d e g - K O H 4 0 m i n 7 0 d e g - K O H 2 0 m i n 7 0 d e g - K O H 3 0 m i n 7 0 d e g - K O H 4 0 m i n 8 0 d e g - K O H 2 0 m i n 8 0 d e g - K O H 3 0 m i n 8 0 d e g - K O H 4 0 m i n U n c o a t e d t e x t u r e d S i
(a) Measured angle dependent reflectance spectra of uncoated textured silicon substrates
4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 5 2 0 2 5 3 0 3 5 4 0 R e fl e c ta n c e ( % ) W a v e l e n g t h ( n m ) 2 0 m i n e t c h 3 0 m i n e t c h 4 0 m i n e t c h R a y t r a c i n g p y r w i d t h 2 µ m R a y t r a c i n g p y r w i d t h 1 0 µ m R a y t r a c i n g p y r w i d t h 5 0 µ m R a y t r a c i n g p y r w i d t h 1 0 0 µ m R a y t r a c i n g O P A L 2 M o d e l e d a n d m e a s u r e d t e x t u r e d S i - 4 0 d e g
(b) Modeled and measured reflectance of uncoated tex-tured silicon substrates under 40 degrees angle of inci-dence
Figure 13: Measured reflectance of uncoated textured silicon substrates (a), and measured and mod-eled reflectance under 40 degrees using ray tracing methods (b).
In figure 13b, one finds a comparison of measured and modeled reflectance spectra of these sub-states under and angle of incidence of 40 degrees. The modeled data is acquired via the OPAL 2 and wafer ray tracer models, which are both ray tracing methods available online on [47], [48]. For an explanation of the OPAL 2 ray tracer, see [32]. In the wafer ray tracer model, a surface morphology of both front and rear random upright pyramids was selected, with varying widths as indicated in figure 13b. The default c-Si substrate was selected with a thickness of 275 µm. No front or rear films were added and the incident medium was air. The default AM1.5G spectrum was selected as light source. Modeled reflectance is not a straight line due to a limited number of available rays being available in the simulation. For the OPAL 2 ray tracing, again a surface morphology of random upright pyramids was chosen, with 0% planar fraction and the default characterisation angle. Here, the size of pyramids could not be selected. All other input parameters were the same as for the wafer ray tracer. Any parameter not indicated here was left at the default value.
One can clearly see that as explained before, ray tracing does not model the reflectance of the samples accurately, and is therefore not used further in this work. Most importantly, the differences in re-flectance between the individual substrates cannot be explained with ray tracing, thus not providing
useful information on the influence of pyramid size on reflectance.
The modeled and measured angle dependent reflectance of uncoated polished silicon are shown in figure 14. 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 3 0 3 5 4 0 4 5 5 0 5 5 R e fl e c ta n c e ( % ) W a v e l e n g t h ( n m ) 1 0 d e g - m e a s u r e d 1 0 d e g - m o d e l e d 2 0 d e g - m e a s u r e d 2 0 d e g - m o d e l e d 3 0 d e g - m e a s u r e d 3 0 d e g - m o d e l e d 4 0 d e g - m e a s u r e d 4 0 d e g - m o d e l e d 5 0 d e g - m e a s u r e d 5 0 d e g - m o d e l e d 6 0 d e g - m e a s u r e d 6 0 d e g - m o d e l e d 7 0 d e g - m e a s u r e d 7 0 d e g - m o d e l e d 8 0 d e g - m e a s u r e d 8 0 d e g - m o d e l e d U n c o a t e d p o l i s h e d S i
Figure 14: Modeled and measured reflectance of an uncoated polished silicon substrate. Here, we see that modeled and measured data are in good agreement up to 50 degrees. For angles of 60 and 70 degrees, the measured data is higher than modeled data, while for 80 degrees, measured data is substantially lower than modeled data. This seems to be a systematic error, as this is also seen for the coated polished samples which will be discussed in the coming section. One possible reason for this is that at large angles of incidence, a part of the light beam might miss the sample, artificially increasing reflectance. This was checked for all samples by the naked eye and did not seem to occur, but it might be possible that some part of the light with an intensity too low to see still missed the sample. At 80 degrees incidence, it was observed that a part of the reflected beam hits a part of the sample holder. Because of this, light can possibly be reflected off the sample a second time before reaching the detector, decreasing reflectance.
Furthermore, it can be observed that data at long wavelengths seem relatively unstable, especially for larger angles of incidence. This again seems to be a systematic error in the setup, as this too is observed for coated polished samples.
By comparing the overall reflectance of the textured and polished substrates, one can see that re-flectance of the textured substrates continuously increases with an increase in the angle of incidence, while that of the polished substrates is almost equal for angles up to 40 degrees. Reflectance of the textured samples increases with increasing angle of incidence as more light starts following paths with a single bounce rather than ones with multiple bounces at greater angles of incidence. Meanwhile, all light reflected off the polished substrate follows a single path. Therefore, reflectance is fully domi-nated by the Fresnel equations of this single path, which only leads to increased reflectance at angles of incidence of 50 degrees and up.
surface texture influences reflectance, and that modeling reflectance with ray tracing does not repro-duce the different reflectance spectra accurately. For the polished substrate, it has been shown that modeling does reproduce reflectance data accurately up to angles of incidence of 50 degrees, as sys-tematic errors influence the measured reflectance at larger angles of incidence. However, the overall shape of reflectance is still modeled correctly at these angles. Now that this has been established, we will move on to the reflectance spectra of coated samples.
5.3.2 Coated substrates
In the following figures, the angle dependent reflectance data from samples B1, G1 and R1 on planar and the three textured samples are shown. For the planar samples, reflectance modeled in matlab is plotted along with the measured reflectance. Modeled spectra are based on the ellipsometric data of these films. In all figures, the change of position of the wavelength with minimum reflectance is indicated with a black arrow. Since most conclusions based on these spectra apply to all samples, they are all discussed at once. This is also the reason why the reflectance spectra of sample R2 are not shown here, but in appendix D.
