# Angular Dependence of Photonic Crystal Coupled to Photovoltaic Solar Cell
## 2 Materials and Methods
### Experimental Measurements  
Thickness was measured using a mechanical profilometer (KLA Tencor model P-6, Millice Pte Ltd, Singapore, Singapore). Refractive index was characterized using a spectroscopic ellipsometer with a rotating polarizer and a fixed analyzer (Semilab GE S6E, Yorba Linda, CA, USA), with a spectral range of 250 to 1700 nm. Transmissivity and reflectivity of the 1 DPC were characterized by a UV-VIS spectrometer setup, including Xe-lamp (Newport model 71228, CA, USA), Monochromator (Oriel Cornerstone 260, Irvine, California), integer sphere (Labsphere 3P-GPS-030-SF, North Sutton, NH, USA), and UV-VIS detector (Newport 71610, CA, USA). Signal was recorded using a Dual Lock-in amplifier (Stanford Research SRS-830, Sunnyvale, CA, USA). Refractive index and thickness selected for TiO\({}_{2}\) were n\({}_{2}\) = 2.32 and d\({}_{2}\) = 70 nm. For SiO\({}_{2}\), values selected were n\({}_{1}\) = 1.41 and d\({}_{1}\) = 100 nm.  
To evaluate the angular response of the 1 DPC in outdoor conditions, it was coupled to one silicon solar cell calibrated by an external certified laboratory (Table 2). A similar solar cell without 1 DPC was used as a reference sample. Optoelectronic characteristics of the solar cells were recorded continuously using an Agilent data logger (model 34970A, Santa Clara, CA, USA). Environmental conditions (irradiance, temperature, wind speed, etc.) were also monitored using a meteorological station (Geonica MTD 301). Samples were located outdoors on a fixed structure at 20\({}^{\circ}\) inclination, oriented to the south without any neighbor shadows. Photovoltaic measurements were performed at Seville (Spain) during the autumn (from September to November 2019).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample ID**} & \multirow{2}{*}{**Layer Sequence**} & \multicolumn{2}{c}{**Dielectric Material 1: SiO\({}_{2}\)**} & \multicolumn{2}{c}{**Dielectric Material 2: TiO\({}_{2}\)**} \\ \cline{3-6}  & & **Thickness** & **Refractive** & **Thickness** & **Refractive** \\  & & **[nm]** & **Index at 600** & **[nm]** & **Index at 600** \\  & & **nm** & **nm** & **nm** \\ \hline Objective & 1 21 21 21 21 21 21 & 100 & 1.41 & 70 & 2.32 \\ PC-03 & 1 21 21 21 21 21 21 & 90 & 1.41 & 50 & 2.32 \\ PC-02 & 1 21 21 21 21 21 & 140 & 1.41 & 70 & 2.32 \\ PC-04 & 1 21 21 21 21 21 & 70 & 1.41 & 50 & 2.32 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Properties of 1 DPC fabricated during calibration process.  
Figure 3: (**a**) Reflectance modeling response from the objective 1 DPC and picture of one of the prototypes tested. (**b**) Refractive index measured with one ellipsometer during the calibration process.  
The 1 DPC has been designed to reflect in the visible solar spectrum, so its maximum reflectivity is centered at approximately 650 nm and Bragg peak deal with 300 nm width (Figure 3a). Spectroscopy ellipsometry also provided an accurate measurement of refractive index data of the dielectric layers used (SiO\({}_{2}\) and TiO\({}_{2}\)) to manufacture the 1 DPC. Cauchy dispersion relation was selected as a theoretical model for the experimental data fitting (Figure 3b). 1 DPC was finally achieved considering 13 dielectric layers alternating periodically SiO\({}_{2}\) and TiO\({}_{2}\).  
Reproducibility and repeatability of the study was confirmed by processing a batch of 10 identical samples, each sample of \(300\times 300\) mm\({}^{2}\). The same characterization was done measuring at five points per sample (center and corners). The influence on the Bragg peak position was also studied when the thickness of the dielectric layers was modified in the range of +/- 10%, with negligible relevance on the optical properties within this interval.