Wavelength and angle resolved reflectance measurements of pyramidal textures for crystalline silicon photovoltaics

Wavelength and angle resolved scattering (WARS) reflectance measurements are attractive to the photovoltaic (PV) industry as a means of characterizing the light‐trapping properties of a textured front surface. Moreover, at the PV module level, where a stack comprising encapsulants and glass is present, large angle scattering can promote total internal reflection at the interfaces and redirect light back towards the solar cell, thus increasing the photocurrent of the device. In this work, we present WARS measurements of a potassium hydroxide (KOH)etched random pyramid surface in the 6°–90° range and identify the main paths the photons experience through reflections from various facets of the pyramids. Our results, combined with ray‐tracing predictions, show that a reassessment of the morphology for simulation inputs is advised for a more comprehensive description of the experimental light paths due to a distribution of power across multiple scattering angles and a lower average pyramid base angle. In addition, we discuss the implications on the total amount of light trapped at the glass‐air interface and show that for a typical encapsulant refractive index of 1.5, approximately 14.5% of the scattered light is predicted to be trapped by the fabricated pyramidal texture. This is a significant increase over the 3.8% calculated to be trapped when assuming a dihedral base angle fixed to 54.74°.


| INTRODUCTION
Photo-generation inside the substrate of a silicon solar cell can be enhanced by addressing the optical losses associated with top surface reflectance and poor absorption of low energy photons inside the bulk. 1,2 Micron-scale texturing combined with a thin film antireflection coating is the crystalline silicon photovoltaics (PV) industry standard for addressing these losses. Texturing is achieved through either an acidic etching process for multicrystalline silicon or an alkaline etching process, based on KOH or tetramethylammonium hyroxide (TMAH), for mono-crystalline silicon. 3 The latter results in randomly distributed, upright, micron-sized pyramids with a theoretical base angle of 54.74 corresponding to the dihedral angle between the (100) surface of the wafer and the slower etching {111} crystallographic planes.
Light reflected from a flat silicon surface is directed away from the cell; however, light reflected from an inclined facet of a pyramid may be redirected onto an adjacent facet, providing additional interactions of light with the cell surface and thereby increasing the overall amount of light coupled into the cell. In combination with an approximately 80-nm SiN x anti-reflective coating (ARC), this reduces the surface reflectance to below 10% in the 300-1100 nm wavelength range. 4,5 Improving the optical path length through scattering of light to higher angles as it is coupled into the silicon leads to more absorption of light for a fixed substrate thickness. [6][7][8] Alternatively, the thickness of the substrate can be reduced while maintaining the amount of light absorbed, reducing the amount of material required in the device and therefore the cost. 9 Furthermore, when encapsulated to form a PV module, additional interfaces are created between the solar cell and the surrounding environment. Total internal reflection (TIR) can occur if the light is scattered by the silicon surface so that it is incident at an angle greater than the critical angle at these interfaces. This mechanism will cause light to be redirected back onto the cell, increasing the overall amount that is coupled into the device. 5,10,11 Characterizing the wavelength and angular scattering profile of solar cell surfaces can therefore help to quantify the light trapping properties of various textures that complement their antireflective properties.
Diffuse reflectance can be measured using an integrating sphere by eliminating the specular reflection, and thus, the reflectance haze can be calculated as a means of quantifying the percentage of the total light scattered from a surface. 12 However, this provides no information on the angular distribution of scattered light, a key consideration when determining the proportion that will undergo TIR at the glass-air interface. Few setups and methods have been proposed so far to capture such dependencies. 10,11,[13][14][15][16][17] Baker-Finch and McIntosh 11 reported scattering measurements on random pyramid textures that showed the peak in the scattering angle is much lower than that predicted from ray-tracing on {111} facetted pyramids of characteristic dihedral angle 54.74 . Yang et al. 10 presented angle resolved reflectance measurements of pyramid textured surfaces for a single wavelength by capturing the reflection on photographic paper. Similarly, they found a peak in the scattered reflections at angles much lower than those predicted by simulations. This supports reports 5,18,19 that the characteristic angle of most random pyramid textured surface is less than 54.74 and means that the proportion of reflected light trapped at the air-glass interface and redirected back onto an encapsulated cell will be reduced. More recently, Fung et al. 20  is also presented, along with a discussion of the fraction trapped by TIR at the glass-air interface in an encapsulated texture.

| THEORETICAL BACKGROUND
The interaction of photons with micron-scale pyramids is theoretically well understood and can be simulated using geometric ray tracing to obtain angular information on the surface reflections, as the wavelengths of the incident photons are well below the feature size. [5][6][7]21 Light can experience up to seven distinct paths upon interaction with the {111} facets. 4,21 These paths present different reflectance weightings and each result in rays that exit in a direction that can be defined by a polar scattering angle and an azimuth angle. In this work, a custom Matlab script was used to define the vector of the incident light, as well as the pyramidal plane normals, for calculations of both the polar and azimuth exit angles for different photon paths. The results are summarized in Table 1, with the polar scattering angles T A B L E 1 Calculated polar and azimuth exit angles for photon Paths A-G for pyramids with base angle of 54.74 Path Reflection angle ( ) <plane number> (see Figure 1A)
This was followed by a thorough de-ionised water rinse and then a 5-min dip into a 7:1 H 2 O:HF solution for native silicon dioxide removal. The alkaline etching of the micron-scale pyramids was carried out in a 0.2-M KOH and 5% isopropyl alcohol (IPA) mixed solution heated at 80 C for 60 min 14 and followed by a rinse in deionised water.

| Characterization
Morphological characterization of the textures was carried out using detector. The collection arm is aligned to the center of rotation of the sample on both the polar and azimuth axes and to the laser beam path. For this study, the textured sample was illuminated at normal incidence (0 ) and the detector is swept around the sample in an arc from 6 to 90 as depicted in Figure 2. The WARS measurements were carried only with p-polarized light incident on the sample. More complete data can be obtained by averaging signals arising from both s and p polarization. However, it is expected that minimal changes would occur in the collected data when the polarization is changed under normal incidence.
The collected data were normalized with respect to the direct beam measurement of the laser source and then geometrically corrected as in Equation 1 to account for the in-plane movement of the detector, which captures a smaller amount of the total light scattered at large angles. Here, a is the distance between the detector and the sample (15 cm), θ is the polar scattering angle, and R is the radius of the detector aperture (600 μm).
The integration time of the spectrometer is assumed to scale linearly to the spectrometer counts in the detected signal and is chosen such that the signal to noise ratio of the data is maximized. Data are collected for every 1 movement of the detector. In addition, for azimuth rotations of the texture, data are collected for every 5 azimuth. The angular resolution of the system is ±0.4 , which is sufficient to prevent overlapping of the data in consecutive measurements.

| Hemispherical reflectance and haze
The total hemispherical reflectance spectrum, measured from the pyramidal textured surface is shown in Figure 4 as a solid black line,

| WARS
A WARS measurement of the random pyramid sample, with p-polarized light incident normal to the sample surface, is presented in Figure 5. The largest signal across the wavelength range occurs at approximately 28 , which is contrary to the 39 calculated in Table 1.  Table 2, Column 6). The results in Table 2 give a more accurate description of the distribution of light scattered from fabricated random upright pyramids textures compared with the calculation results in Table 1.
In order to verify the angle ranges from Table 2

| Impact of azimuthal rotations
Measurements at other azimuthal rotations for this texture are relevant for observing other photon paths that could travel in a direction away from the horizontal plane (see Table 2). Therefore, measurements were carried out every 5 azimuth rotation in the 0 -90 azimuth range. The intensity, integrated over the wavelength range, is plotted in Figure 8A Table 2). Figure   T A B L E 2 Calculated angle ranges for Paths A-G for pyramids with experimental measured base angles of 51 -53.2 . Paths B, E, and G are no longer allowed for this new dihedral base angle range. The calculated relative intensities of these disallowed paths, taken from other studies, 4,21 have been added to the remaining paths to approximate the proportion of total reflected power in each remaining path Path Reflection angle ( ) <plane number> (see Figure 1A) Approximate proportion of total reflected power (%) within the same pyramid may be slanted at different angles and not be identical. No peaks can be seen in Figure 8B) corresponding to paths other than Path A, for example there is no evidence of a peak corresponding to the Path C azimuth exit angle of 39.6 -37.9 . This is thought to be due to the large and broad peak in the integrated data corresponding to Path A masking any smaller signals that may be present from the other paths predicted in Table 2.
A comprehensive description of the surface reflections from any type of texture can be represented using polar coordinates, as shown in Figure 9 for a 0 -90 azimuth range, Inset 1 for the entire azimuth F I G U R E 8 Measured data integrated over wavelength range to show: (A) five increasing azimuth rotations, solid blue trace corresponding to Path A, solid black trace corresponding to Path C, and their scattering angle peak, in good agreement with results in Table 2; (B) also integrated over scattering angle to show symmetry around azimuth [Colour figure can be viewed at wileyonlinelibrary.com] encapsulated cell will be much less than predicted, which motivates the need for alternative surface textures that scatter light to higher angles. These measurements can also provide insights into the texture morphology and its distribution within the sample, especially when analyzing the position and width of the largest signal corresponding to path A.

| FRACTION OF SCATTERED LIGHT TRAPPED
As solar cells are encapsulated to protect the substrate from moisture and damage, the measurements presented in this study can be of interest when analyzing TIR at the glass-air interface and assessing the texture's capability to trap light and redirect it back to the solar cell.
The critical angle at the encapsulant-glass interface is always lower than the critical angle at the glass-air interface; therefore, the dominant critical angle to satisfy TIR in the stack is at the virtual encapsulant-air interface, as shown in Yang et al. 10 The  Figure 10 shows the evolution of f T for the fabricated random pyramidal texture (blue trace) with increasing encapsulant refractive index from 1 to 4, corresponding to a critical angle range from 90 -14.5 , along with f T calculated for "theoretical" random pyramids (black trace) described in Table 1 with α = 54.74 (where reflectance weightings for each path were taken from other studies 4,21 ). Also plotted is f T calculated from the pyramidal texture and the paths described in Table 2 (orange trace), where a range of dihedral base angles from 51 -53.2 was considered, with reflectance weightings approximated from the power redistribution triggered by the disappearance of Paths B, E, and G (see Section 4.3 and Table 2). The pyramidal random texture with α = 54.74 (black trace) presents steps at fixed known scattering angles corresponding to various photon paths. In contrast, the fraction trapped for the experimentally measured pyramidal texture (blue trace) yields lower values for high refractive indices, and it is a much more continuous function.
This is due to the wider scattering angle distribution, as well as the peak shift to lower scattering angles than those calculated. Moreover, the orange trace calculated according to the texture described in order to prevent high reflectance and absorption from these layers. While simulations predict that the fraction of light trapped is only 3.8% for a typical encapsulant with 1.5 refractive index, our experimental results show that this value is 14.5% due to reflections arising at scattering angles >50 .