1. Introduction

Anti-reflection coatings for solar cells are traditionally optimized to maximize the photocurrent production of the solar cell under a particular reference spectrum [1]. Forming an anti-reflection (AR) coating on the front surface of the solar cell using one or more dielectric films can achieve good broadband anti-reflection characteristics, provided the films have suitable refractive indices [2]. However, an AR coating consisting of only a few dielectric layers will inevitably reflect a small portion of the solar spectrum over some of the range of visible wavelengths. For this reason, dielectric coated solar cells are often not black in appearance, but have a distinct hue due to the reflected light. Color-tuning solar cells could enhance their suitability for a particular application, such as in a building integrated environment, where solar cells may be required to have a good aesthetic appearance as part of an architectural design [3]. Also, in military applications, colored and patterned coatings may improve the camouflage properties of solar cells when being used for remote power generation [4]. Recent work has shown that colored coatings can be produced by tuning the thickness of thin, strongly absorbing layers [5]. However, the films used in this work are transparent dielectrics in the visible wavelengths, which can retain a large transmission for applications as AR coatings for PV applications.

The variation in the color of thin films with thickness is a well-known phenomenon [6, 7]. Furthermore, work by other authors has demonstrated a procedure for calculating the perceived color of dielectric films under arbitrary illumination [8, 9]. The purpose of this work is to examine the relationship between the color of an AR coating and its performance on a solar cell. In particular, we have examined the design space and trade-offs associated with AR coatings which retain a large photocurrent when deposited on a solar cell, but which can be tuned over a wide range of colors. We designed and fabricated bilayer coatings on crystalline silicon wafers and used colorimetric analysis to model the perceived color of the coatings. Using data for the internal quantum efficiency of a Si solar cell we then calculated the loss in photocurrent if applied to a solar cell structure. Our results demonstrate that is possible to use a computational model to design high-performance colored coatings, avoiding the need for dyes and filters which can introduce significant loss. The predicted color closely matches the observed color under a solar simulator, allowing the design of a detailed patterned solar cell with strong color contrast and low reflectivity.

2. Colorimetric analysis

The Commission International de l’Eclairage (CIE) has standardized the measurement of color using dimensionless quantities known as color matching functions (CMF) [10]. The CMFs describe the relative intensities of three primary color lights required to produce the same color as a monochromatic light source of a given wavelength. In the CIE system, the measured red, green and blue CMFs are mathematically transformed into a convenient set of new CMFs denoted $\overline{x}\left(\lambda \right)$, $\overline{y}\left(\lambda \right)$ and $\overline{z}\left(\lambda \right)$. The transformed green color matching function, $\overline{y}\left(\lambda \right)$, is chosen to be identical to the eye-sensitivity function. The CIE 1931 CMFs, taken from reference [10], are shown in Fig. 1. The relative power of red, green and blue lights needed to match the color of an arbitrary spectrum, $P\left(\lambda \right)$, are denoted the tristimulus values, X, Y and Z, where

 

Fig. 1 The normalized CIE D65 illuminant spectrum and Oriel AM1.5 solar simulator spectrum. The solar simulator spectrum was dispersed using a translucent plastic sheet. CIE 1931 color-matching functions are also shown on the right-hand axis.

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The CIE also defines a series of standard illuminants. A common illuminant is the D65 illuminant, which corresponds roughly to midday sun in central/northern Europe. Figure 1 shows the normalized D65 illuminant with the normalized spectrum generated by an Oriel AM1.5 solar simulator, which demonstrates the similarity in the content of the two spectra. The solar simulator light was dispersed using a translucent plastic sheet and measured using a calibrated FieldSpec 4 Hi-Res Spectroradiometer made by Analog Spectral Devices Inc.

To visualize the color of a particular set of tristimulus values, we adopt the standard RGB color space, known as sRGB. The white point of this color space was defined using the D65 illuminant, and therefore the color of light reflected from the material of interest can be calculated by multiplying the D65 illuminant spectrum with the reflectivity spectrum of the material as follows;

The color space conversion maps the tristimulus values, calculated using the reflected part of the D65 spectrum and Eqs. (1)-(3), to sRGB values in the range [0, 255] which can be displayed on computer screens or in graphics files. The conversion procedure consists of two stages: the first step of the algorithm is a matrix multiplication to map the tristimulus values to corresponding linear RGB values in the range [0, 1];

Values of R_linear, G_linear and B_linear which lie outside of the range [0, 1] are truncated to lie within this range. The second stage of the algorithm is to transform the linear RGB values into gamma corrected values, which accounts for the non-linear nature of the human sensitivity to light. The transformation is identical for R, G and B values and is given by the following equation, shown here for the R value;

The values are rounded to the nearest integer and can therefore be used to display the color of the reflected spectrum $P\left(\lambda \right)$to a computer screen or be saved in an image format, such as a bitmap. To generate the sRGB values for the anti-reflection coatings in this work, the reflectivity of the layers was calculated and the reflected spectrum was evaluated using Eq. (4). This method then gives an accurate prediction of the actual color perceived when the real samples are illuminated under the solar-simulator spectrum.

3. Modeled bilayer anti-reflection coatings

It is important to know the relationship between the color and transmission properties of the anti-reflection coating when designing practical solar cells, which we have investigated using a simple bilayer anti-reflection coating on crystalline Si. The reflectivity was calculated using a transfer matrix technique [11] assuming a vacuum ambient and a semi-infinite crystalline-Si substrate. To assess the coating performance, we calculated the short circuit current of a silicon solar cell under the ASTM air mass 1.5 global (AM1.5G) spectrum for a range of coating thicknesses, using the calculated external quantum efficiency (EQE). The internal quantum efficiency (IQE) of the silicon solar cell was not calculated, but instead deduced from literature data for the EQE and reflectivity for a world record Si solar cell, published by Zhao et al. [12] A modeled EQE curve was then calculated for a range of two layer SiO_x/SiN_x anti-reflection coatings using the following equation

The short circuit current density (J_sc) was evaluated for SiO_x and SiN_x thicknesses ranging from 10nm-160nm and is shown in Fig. 2(a). The optimum J_sc of approximately 41mA/cm² is achieved using an 80nm SiO_x and 65nm SiN_x coating. Figure 2(b) shows the rendered sRGB color calculated from the reflected spectrum for the D65 illuminant at normal incidence. For clarity, the J_sc contours of Fig. 2(a) are superimposed, which demonstrates that there is a wide range of colors available in the thickness range giving good photocurrent performance of 39mA/cm² or greater.

 

Fig. 2 (a) The calculated short circuit current under the ASTM AM1.5G spectrum for a bilayer anti-reflection coated Silicon solar cell with different thicknesses of SiO_x and SiN_x. The internal quantum efficiency of the solar cell was deduced from the data in reference [12]. The dots indicate the thicknesses of sample coatings deposited on pieces of crystalline Si wafers. (b) The modeled sRGB color observed for each coating thickness under the D65 standard illuminant. For clarity, the J_sc contours from Fig. 2(a) are superimposed. (c) The J_sc and sRGB color observed for a Si solar cell coated with a single layer of SiO_x or SiN_x.

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In comparison to the performance with bilayer coatings, the J_sc and color of Si coated with single layer SiO_x and SiN_x films is shown in Fig. 2(c). The SiO_x coating has a significantly lower J_sc than the optimal bilayer coating, reaching a maximum value of 37.2mA/cm². The range of colors available using the single layer coating is also limited in comparison to the bilayer coating. The SiN_x film is better matched to the refractive index of the Si and consequently can achieve higher J_sc values, with a maximum value of 39.5mA/cm². The higher index SiN_x film also offers a wider array of colors than the SiO_x film close to the maximum J_sc point. However, the variation in J_sc is significantly greater than the bilayer coating as the color is tuned due to the overall reflectivity changing rapidly as the thickness is changed. The bilayer coating therefore offers a scheme for tuning the coating color which is less detrimental to the performance of the coating.

4. Experimental sample preparation

Six crystalline-Si samples were coated with dielectric layers of different thicknesses. The coating thicknesses are shown on Figs. 2(a) and 2(b). The experimental points were chosen to encompass a broad range of coating colors ranging from deep blue for sample 1 to red for sample 6, but remaining close to the optimum short circuit range. Sequential layers of SiN_x and SiO_x were deposited using a commercial PECVD system (Plasmalab System 100 PECVD, Oxford Instruments Inc.). During deposition, the PECVD chamber temperature was set at 300°C. Prior to the deposition, all the silicon substrates were processed through standard degreasing and cleaning procedures. The thicknesses and the refractive index of the dielectric layers were monitored using a spectrophotometer (n&k 1280 Analyzer, n&k Technology, Inc.). The relative specular reflectance of the bilayer coatings was measured with a spectrometer (LAMBDA 750 UV/Vis/NIR Spectrophotometer, PerkinElmer Inc.).

In Fig. 3, the measured reflectivity spectra are compared to the model predictions of the coatings for each sample. The curves demonstrate excellent agreement across the whole wavelength range of interest between 250 and 1000nm. The calculated sRGB color is also shown for each of the samples, calculated from the normal incidence reflectivity spectrum. The total power density reflected by the coatings, P_ref, under the AM1.5G spectrum in the wavelength range of 280-4000nm is displayed for each coating as a percentage of the incident power density of 1000W/m². The total reflected power facilitates the comparison to other anti-reflection coated solar cells made from different materials, as opposed to comparing the short circuit current densities.

 

Fig. 3 The calculated and measured reflectivity at normal incidence for samples 1-6. The calculated sRGB color of each coating is also shown, along with the reflected power density, P_ref, under the ASTM AM1.5G spectrum as a percentage of the incident power density.

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The samples were photographed in the laboratory under illumination by an Oriel solar simulator, filtered to resemble the AM1.5G spectrum, which is close in spectral content to the D65 standard illuminant, shown in Fig. 1. The samples were photographed at two angles, 39.7 ± 1.0° and 57.3 ± 0.6°, relative to the normal of the sample face. The angles were determined from the aspect ratio of the imaged samples. Figure 4 shows the images of the samples adjacent to bitmap images rendered using the R, G and B values computed using the colorimetry model. The coating color is reproduced accurately for all the samples, which is evident in the close agreement of the modeled and the actual reflectivity of the coatings. The main sources of uncertainty leading to any discrepancies in the observed and predicted colors are the difference in the illumination source to the D65 standard illuminant, in addition to the response of the camera. However, Fig. 4 does demonstrate that even with the uncertainty associated with the illumination conditions, the colorimetric model approach is valuable for designing colored and patterned solar cells for being able to closely predict the final color of the coated solar cell under solar irradiation.

 

Fig. 4 Photographs of samples 1-6 at two different angles of incidence. The samples were illuminated using diffuse light from an Oriel AM1.5G solar simulator. The model prediction for the coating color under the D65 illuminant spectrum is also shown for each sample.

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5. Oblique incidence

The dependence of the coating color on the angle of incidence can be established by considering the reflectivity of the coatings over a range of angles. The hues of the coatings change as the samples are tilted, which is evident in the images of Fig. 4 for two different angles of incidence. The hue angle is a convenient metric for describing a color, quantifying how similar an arbitrary color appears to one of the unique hues, which are defined as red, yellow, green and blue. The hue angles were calculated from the sRGB values using the algorithm given in reference [13], which for brevity is not reproduced here. In Fig. 5(a), the calculated hue angle for each of the samples 1-6 is shown as a function of incident angle, along with a color bar depicting the true color associated with each hue angle. It should be noted that the fact the hue angle curves are not smooth is due to the rounding of the integer sRGB values.

 

Fig. 5 (a) The hue angle as a function of the angle of incidence for samples 1-6. Note the hue angle variation is not a smooth function, as the sRGB values from which it is calculated are rounded integer numbers. (b) The sRGB color for each sample as a function of incident angle.

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Up to angles of around 30° the hue changes relatively little for all the samples, but varies considerably more for wider angles of incidence. The most rapid variations in hue angle occur when the R, G and B values become very similar. A color with R = G = B is known as a neutral color. Here the R, G and B components are combined in the same proportions as the white point of the particular color space and therefore appears as varying shades of gray, depending on the R, G and B value. The sRGB color representation of each sample as a function of angle is shown in Fig. 5(b). This plot illustrates the variation in color for each of the samples under the standard illuminant, which is relatively insensitive to angle for all the samples below approximately 30°. However, at very wide angles of incidence the coatings become increasingly white, as the reflectivity approaches unity for all wavelengths.

5. Experimental sample preparation

To illustrate the potential for using the color hue of an anti-reflection coating to pattern the front surface of a large area solar cell, we fabricated 2⌋ × 2⌋ samples with the Naval Research Laboratory emblem on the front surface (inset Fig. 6(a)). Instead of conventional photolithograph masks, a photolithograph mask was created by laser printing (Xerox Docucolor 700) a black and white version of the emblem logo on to highly transparent and flexible films (3M Write-On Transparency Film AF4300), shown in Fig. 6(b). As described earlier, a bilayer film of SiN_x (50 nm)/SiO_x (140 nm) was first deposited atop the Si substrate. After standard photolithography using the laser printed mask, the SiO_x layer was then etched using an Ar plasma reactive ion etching for about 26 min to remove 85nm of SiO_x. After etching, the resulting thickness of SiN_x and SiO_x is 50nm and 55nm, respectively. The etched film was photographed outdoors at the Naval Research Laboratory and is shown in Fig. 6(a). Both the blue and yellow areas of the mask have calculated J_sc values in excess of 39mA/cm⁻², reiterating that excellent anti-reflection characteristics are possible in patterned solar cells, even in a sample with large color contrast as in the wafer demonstrated here.

 

Fig. 6 (a) A patterned crystalline Si wafer with a bilayer SiO_x/SiN_x AR coating, patterned using a photolithography and reactive ion etch technique. The inset shows the emblem of the Naval Research Laboratory for comparison. (b) The laser printed mask, printed on a flexible, transparent film.

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6. Conclusion

In this work we have investigated the use of dielectric anti-reflection coatings to produce multicolored solar cells which maintain a high short circuit current. Using a reflectance model combined with colorimetric analysis, we were able to make accurate predictions of the color observed for a Si wafers coated with a bilayer SiO_x/SiN_x anti-reflection coating illuminated by a solar simulator. Six samples were prepared by depositing bilayer coatings on Si using PECVD and the measured reflectivity and color were compared to model predictions and found to be in good agreement. To demonstrate a patterned solar cell anti-reflection coating with high-contrast coloration, a Si wafer was coated with a bilayer coating and an inexpensive printing technique was used to fabricate a photolithography mask for patterning the coating. The emblem of the Naval Research Laboratory was patterned on the wafer, with only a small reduction in the calculated value of short circuit current. This method of producing patterned solar cells is anticipated to have a wide range of applications, including building integrated photovoltaics and camouflage for military applications.