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Abstract
We compare two model approaches for the ray optical description of PV modules with coloring based on an interference layer system on the inside of the cover glass. The light scattering is described by a microfacet-based bidirectional scattering distribution function (BSDF) model on the one hand and ray tracing on the other hand. We show that the microfacet-based BSDF model is largely sufficient for the structures used in the context of the MorphoColor application. A structure inversion shows a significant influence only for extreme angles and very steep structures showing correlated heights and surface normal orientations. Regarding an angle-independent color appearance, the model-based comparison of possible module configurations shows a clear advantage of a structured layer system compared to planar interference layers in combination with a scattering structure on the front side of the glass.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The acceptance of photovoltaics (PV) plays a key role in the decision-making process of whether or not to build or integrate a system. Particularly in the areas of vehicle-integrated PV (VIPV) and building-integrated PV (BIPV), the usual design freedom should be retained despite PV integration, so that PV can be adapted to existing environments or offer the possibility of highlighting it as an active design element. Accordingly, the demand for color customizable PV is frequent. In addition to a selection of saturated colors that appear homogeneous for possible illumination and viewing angles, as well as an option to avoid glare, the efficiency of the module should be affected as little as possible by the color. A detailed overview of existing concepts for the color design of PV is given in [1–3]. Focusing on systems with module-level coloring, the main disadvantages are high efficiency losses [4,5], only low-saturated colors [4,5], and inflexible [6] or cost-intensive and time-consuming production [7].
With an industrially well scalable production, the MorphoColor technology [8] overcomes these problems and enables a broad range of saturated and angular stable colors while maintaining high PV efficiency. Inspired by the Morpho butterfly effect [9,10] and described by Bläsi et al. in [11], MorphoColor consists of an interference layer system on a structured PV module cover glass, optimized for high color saturation and color stability by using a higher harmonic reflection order and a high average refractive index. In [12], Wessels et al. present a model combination based on a statistical representation of the structured surface using a discrete microfacet-based BSDF, hereinafter abbreviated as mb-BSDF. They use it to describe an overall MorphoColor system and exemplarily investigate the influence of the positioning of the interference layer system on the outer interface (position 1 configuration) or the inner interface (position 2 configuration) of the module cover glass as illustrated schematically in Fig. 1. A clear advantage for position 2 was shown in terms of angular color stability.
Fig. 1. Comparison of the two configurations with different positioning of the MorphoColor layer system on the module cover glass.
The scope of this work is to present an alternative approach to optically describe interference layer systems on structured surfaces as well as an embedding of these into more complex optical systems. Instead of describing the scattering behavior by means of a mb-BSDF, direct ray tracing is used so the information of the spatial arrangement of the structural elements relative to each other is preserved. Thus, effects such as masking and shadowing are mapped directly and are not subject to assumptions such as a Smith microfacet profile. Furthermore, the effect of a structure inversion, which can not be mapped in the mb-BSDF approach due to the invariance of the resulting microfacet angle distribution, is mapped in ray tracing and is part of the investigation. In the context of MorphoColor this is important when a module cover glass is installed with the coating at position 2 and thus is flipped relative to the orientation during coating. Finally, a selection of system configurations for the color design of PV modules is compared using both model approaches, so that conclusions can be drawn regarding both the applicability of the models and the optical properties of the configurations.
2. Material and methods
2.1 Sample preparation and characterization
All used glasses are structured on one side. The sample preparation and characterization is similar to that in [12], both in terms of the used equipment and the methodologies applied. The most essential aspects are briefly described below.
- • Topographic characterization of the glass structures is performed using an Olympus 3D Measuring Laser Microscope LEXT OLS4000 with an 100x objective lens and stitching mode resulting in a measured area of approximately 580 $\mathrm{\mu}$m $\times$ 580 $\mathrm{\mu}$m with a 125 nm grid point distance. Unintentional tilting of the sample in the measurement setup is compensated by plane fitting.
- • The layer system consists of substrate/Si3N4/TiO2/Si3N4/TiO2/Si3N4/SiO2 and is applied by MF Magnetron sputtering using dual rotatable tube cathodes. The respective thicknesses correspond to those given in [11] with a maximum deviation of 7 nm.
- • Reflectance and transmittance measurements for layer analysis are performed using a Bruker VERTEX 80 Fourier spectrometer equipped with an integrating sphere. The refractive index data is then obtained using a exponential Cauchy model. The physical layer thicknesses are fitted using the transfer matrix method (TMM).
- • Angle-dependent reflection measurements are carried out using an Agilent Cary 5000 spectrometer with the diffuse reflectance accessory (DRA) for hemispherical integration and with the universal measurement accessory (UMA) for goniometric integration over a circular aperture with 6 $|^{\circ }$ half angle, adjustable in polar angle. For measuring the scattering behavior of uncoated glasses, the unstructured side is blackened as depicted in Fig. 2 on the left. Coated glasses are measured in position 2 configuration with the coated back side blackened as shown in Fig. 2 on the right. In both cases, blackening is done with a highly absorbent coating of Nigrin 74117 and serves to suppress back-surface reflection.
Fig. 2. Schematic illustration of the measured sample types. During the measurement, the incident light hits the unblackened side. Glass is shown in gray and the absorbent coating in black. Left: Uncoated glass. Right: Coated glass with layer system in position 2 configuration. Si3N4, TiO2 and SiO2 are depicted in green, blue and coral, respectively.
2.2 Color calculation
The calculation of the CIE color values is performed using the CIE 1931 colorimetric standard observer according to [13]. The subsequent conversion to sRGB is executed according to [14].
For the color calculation from goniometric measurement data or goniometrically evaluated simulation data, the reflectance data are normalized to the aperture size and the respective aperture position according to [15]. For the corresponding normalization factor applies:
with $\alpha$ as half the aperture opening angle and $\theta$ the polar angle of the aperture position.3. Models used for the optical description of colored PV modules
The structures studied in this work are etched in glass. Considering the structure size, which is similar to that of the structures in [12], purely ray optical models are applied to describe the scattering behavior.
3.1 Statistical representation of the structured surface
The basic design and functioning of the combination of a discrete mb-BSDF model with the TMM to describe the optical properties of interference layer system on structured surfaces as well as a further combination with the Optical Properties of Textured Optical Sheets (OPTOS) [16–18] formalism to describe more complex optical systems with multiple incoherent coupled interfaces, is described in [12]. In the context of this work the implementation is used as described there.
3.2 Direct use of the 3D structural surface characteristics
For ray tracing the software Raytrace3D [19] is used. In terms of acceptable computation times and RAM capacities, the maximum number of pixels that can be simulated is defined for each configuration. Based on this an optimization is performed with regard to the resolution ($res_s$) and area ($A_s$) used. The corresponding values will be given for each simulation. Each triangulated structural element is assigned the information of the interference layer system. Thereby, the adjustment of the physical layer thicknesses is performed according to the individual polar angle of the structural element, taking into account a non-uniform angle distribution during the sputtering process as described in [12]. As in the statistically based model approach, the optical behavior of the layer systems is calculated using the TMM.
4. Comparison of model results and measurement
4.1 Scattering characteristics of uncoated substrates
In order to compare the ray tracing results with measured data and at the same time highlight possible differences between the two model approaches, the measured and simulated scattering behavior of two uncoated glass structures as in the left of Fig. 2 is compared in Fig. 3. Glass A is the same as glass A in [12]. In comparison, the surface structure of Glass B is significantly steeper sloped and accordingly shows much larger structural angles. For laser microscope images as well as polar angle distributions of both structures, please refer to Sec. 1 of the Supplement 1. Looking at glass A first, there is a very good agreement between the models. Only in the area of the direct reflection at an incident angle of -75 $|^{\circ }$ a slight deviation can be seen. The comparison with the measured data also shows how well both simulation methods qualitatively reproduce the scattering behavior. Quantitatively, a slight systematic overestimation of the reflectance can be observed, with the exception of the angular range just described at an incident angle of -75 $|^{\circ }$. Since this is almost identical for both models, it is unlikely that the effect is caused by a model-specific parameter choice. Rather, the data suggests a systematic difference between measurement and simulation. It is conceivable that edge effects of the aperture or unexpected scattering or absorption effects occur in the real case, which are not represented by any of the models. Considering the small deviations in absolute terms, however, we stopped further investigation of the effects at this point. Despite the very low overall intensities for glass B, both models reproduce the reflectance behavior of the real sample well. However, a closer look reveals clearer differences between the models in relative terms. Especially for an angle of incidence of -60 $|^{\circ }$ the ray tracing seems to provide a better agreement in comparison with the measured data. This is supported by the general scattering shape as well as the absolute position of the reflection maximum. The reason for these deviations, which can be observed especially for structures with steep slopes and large angles, are probably errors in the statistically based determination of shadowing and masking in the mb-BSDF model. With the use of a Smith microfacet profile, it is assumed that the spatial arrangement of the structural elements relative to each other can be neglected. However, real etched structures do not always fully satisfy this assumption. The ray tracing model is able to actually represent shadowing and masking effects.
Fig. 3. Comparison of simulated and measured angle-dependent reflectance at 500 nm and given incident angles. Please note that the values on the y-axes are multiplied by 103. For both glasses $A_s$ = 500 $\mathrm{\mu}$m $\times$ 500 $\mathrm{\mu}$m and $res_s$ = 250 nm. Since surface area and resolution are no constraints for the mb-BSDF model, the original laser microscope image is used. With given parameterization, the computation time could be reduced from several hours with the ray tracer to a few seconds with the mb-BSDF model. Left: For glass A. Right: For glass B.
Further, the comparison between ray tracing and measured data in the form of the spectrally resolved angle-dependent reflectance behavior of coated samples in position 2 configuration, as shown on the right in Fig. 2, shows good agreement. For the illustration of the corresponding results for glass A as well as glass B, refer to Sec. 2 of the Supplement 1.
5. Influence of the inversion of a structure
As described earlier, a configuration with the interference layer system at position 2 causes an inversion of the structure. Therefore, it is crucial to classify the significance of possible inversion effects and their impact on the optical properties of the system for the structures used here. Fig. 4 shows the corresponding ray tracing simulation results.
Fig. 4. Comparison of ray traced angle-dependent reflectance at 500 nm and given incident angles for non inverted reference and inverted structures. Please note that the values on the y-axes are multiplied by 103. For both glasses $A_s$ = 500 $\mathrm{\mu}$m $\times$ 500 $\mathrm{\mu}$m and $res_s$ = 250 nm. Left: For glass A. Right: For glass B.
For glass A there is no significant influence of the inversion on the scattering behavior in any case. Even for the steeper sloped glass B, a relevant influence is only evident at an incidence of light from -75 $|^{\circ }$. To explain the observed deviations, the cross-sectional shape of the structural elements serves as an important factor. It can be derived both from the laser microscope image in Sec. 1 of Supplement 1 and from the plot of the correlation of height and polar angle of all triangulated structural facets in Sec. 3 of Supplement 1. While the non-inverted reference has convex (hill-like) elements, the inverted case results in concave (valley-like) shapes. Taking this into account, a qualitative explanation can be provided as shown schematically in Fig. 5.
Fig. 5. Qualitative explanation of the observed difference in reflected scattering behavior caused by a structure inversion of glass B. Left: Schematically illustrated comparison of possible light paths for valley-like and hill-like structures at large angles of incidence. Right: Associated schematic comparison of the difference in the resulting scatter distribution.
In the case of the valley-like structure, when light is incident from large angles, a significant fraction of the structural elements is shaded, specifically the one that would cause reflection to large angles. For the hill-like structure, this is not so much the case and reflection in large angles occurs less restricted, which explains the observed difference in the scattering behavior. In the context of the structures used for the MorphoColor application, since the effects only occur with very steep structures and extreme angles the effects have no significant relevance.
6. Model-based comparison of different system configurations
The module configurations shown schematically in Fig. 6 are compared regarding their optical properties using both model approaches. As a simple but representative description of the visual impression of a solar cell, the blackened back is modeled as fully absorbing. Additional effects, for example due to the highly reflective front contacts of many solar cells, are not considered here. It should also be noted that, as shown in Fig. 1, an encapsulant follows the layer system in the real module. Due to the optically very similar properties to glass, the latter is used in the simulation. If position 1 has a structure, it is that of glass A. If position 2 is structured, the inverse of glass A is used. As already shown in the previous part, no significant effect of the inversion is to be expected for glass A. However, due to the different parameters $A_s$ and $res_s$ chosen in these simulations, possible effects shall be considered here.
Fig. 6. Schematic illustration of the four different module configurations simulated with the associated labels used in the following. Color coding as in Fig. 2.
Figure 7 shows the resulting spectral reflectance plotted over the possible angles of reflection for normal incidence after subtracting the specular band. The resulting sRGB colors are also displayed as a function of the reflection angle.
Fig. 7. Comparison of the angle-dependent spectrally resolved reflectance characteristics of the module configurations from Fig. 6 at 0 $|^{\circ }$ incidence based on glass A, each labeled with a small illustration. The fraction of the total reflectance resulting solely from interaction with the uncoated position 1 glass interface, appearing as a wavelength-independent specular band, was subtracted from the result in each case. The corresponding sRGB color for each angle is shown on the right. The difference in color appearance and its angular width seen in the cases planar-planar and structured-planar is caused by the special OPTOS binning [17]. The light color reflects glare effects in both cases. For all ray tracing simulations $A_s$ = 250 $\mathrm{\mu}$m $\times$ 250 $\mathrm{\mu}$m and $res_s$ = 750 nm. For the mb-BSDF model, the original laser microscope image is used again. Left: For ray tracing. Right: For the mb-BSDF model.
Interpreting the results with respect to the comparison of the two models, it can be said that ray tracing does not provide any advantage over the mb-BSDF model for the selected structures. All results agree very well. This corresponds nicely with the findings of the previous section, that differences only occur for very steep structures and extreme angles.
Accordingly, when comparing the module configurations, both models show a clear advantage of the combination of interference layer system and structuring at position 2, as present in the planar-structured and structured-structured case. As can be seen from the significantly increased angular width of the sRGB colors, the color is distributed over a larger angular range, resulting in a more homogeneous appearance. Another interesting conclusion is that a structure at position 1 has only a very limited influence on the angular color distribution. While the change can still be seen when comparing the planar-planar and the structured-planar configurations due to the smearing of the hard boundary of the direct reflection, no significant change is noticeable with a structure already present at position 2. Thus, the effect of the structure at position 1 in the PV module is limited to the anti-glare function by scattering the light reflected directly at this first interface. However, due to the subtraction of the specular band, the anti-glare effect is not visible in the data presented here.
To extend the model comparison to the steeper sloped glass B, it is sufficient to consider the planar-structured configuration. A re-simulation of the planar-planar configuration is trivial and the influence of a structure on the front side has already been described on the basis of the previous results with glass A. Figure 8 accordingly shows the results for the planar-structured configuration with the inverse of glass B on position 2. As expected from the previous investigation of the scattering characteristics of uncoated substrates, a very good agreement of the model results is also shown here. Only at large angles of incidence, clearer deviations are to be expected. In the case of ray tracing, the influence of the choice of the parameters $A_s$ and $res_s$ becomes apparent. With the available computing power, glass B at position 2 could only be simulated with $A_s$ = 150 $\mathrm{\mu}$m $\times$ 150 $\mathrm{\mu}$m and $res_s$ = 500 nm. With these parameters, first minor anisotropy effects appear in the form of an underrepresented reflection in the angles around 13$|^{\circ }$.
Fig. 8. Comparison of the angle-dependent spectrally resolved reflectance characteristics of the planar-structured module configuration from Fig. 6 with glass B, simulated for an angle of incidence of 0 $|^{\circ }$. Please note that the reflectance is multiplied by 103. As explained for Fig. 7, the specular band was subtracted from the result and the sRGB colors are given on the right in each case. For the ray tracing $A_s$ = 150 $\mathrm{\mu}$m $\times$ 150 $\mathrm{\mu}$m and $res_s$ = 500 nm. For the mb-BSDF model, the original laser microscope image is used again. Left: For ray tracing. Right: For the mb-BSDF model.
7. Conclusion
The description of the optical properties of interference layer systems on structured substrates in the application of colored PV modules by means of a combination of ray tracing and TMM presented in this work was successfully validated on the basis of measurement data. The comparison of this method with the model combination previously presented in [12] shows that the mb-BSDF model is largely sufficiently accurate for the systems considered here. Only in the case of a combination of very strongly scattering structures and large angles, the mb-BSDF model shows clear deviations. These deviations are probably due to an inaccuracy in the estimation of shadowing and masking and, more concretely, to a strong correlation of the height and angle of the structural elements. The effect of this correlation is also clearly visible in the context of the investigations on the effect of the inversion of a structure. While this is not represented by the mb-BSDF model, ray tracing can be used to identify and qualitatively explain a significant variation in the scattering behavior in the case of steep structures and large angles. In summary, we recommend the mb-BSDF model for standard cases and ray tracing for the mentioned special cases.
In the context of the comparison of different PV module configurations for colored PV based on interference layer systems at position 2, it proves to be clearly advantageous to apply the coating on a structured substrate. When viewed from different angles, this results in a significantly more homogeneous appearance. Structuring at position 1 can optionally be added for an anti-glare effect, but has no significant influence on the angular spread of the color appearance.
Funding
Bundesministerium für Wirtschaft und Energie (03EE1049A, 03ETW007A); Deutsche Bundesstiftung Umwelt.
Acknowledgments
The authors thank Dr. Andreas Gombert and Prof. Dr. Stefan Glunz for their helpful input, discussions and supervision. Andreas Wessels and Adrian Callies gratefully acknowledge scholarship support from the Deutsche Bundesstiftung Umwelt (DBU).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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