# Angular Dependence of Photonic Crystal Coupled to Photovoltaic Solar Cell
## 2 Materials and Methods  
### 1 DPC Design and Manufacturing  
This case of study considers a 1 DPC acting as a back reflector (Figure 1b). Thus, 1 DPC structures were designed to reflect maximum energy within the visible spectral range, because the spectral  
Figure 1: (**a**) One-dimensional photonic crystal (1 DPC) designed to minimize solar cell overheating by reflecting nonabsorbed infrared photons. (**b**) 1 DPC designed to act as back spectral selective mirror or beam splitter: Visible solar spectrum is reflected. Dashed red line: photonic crystal transmittance; blue dots: silicon solar cell spectral response.  
response of the solar cell is maximized at this spectral region. For that purpose, periodic dielectric structure was defined as 13 alternating layers of SiO\({}_{2}\) (1) and TiO\({}_{2}\) (2), resulting the sequence 1 2 1 2 1 2 1 2 1 2 1. Dielectric layers were deposited by DC magnetron sputtering using ceramic targets (99.999%) with an area of \(500\times 100\) mm\({}^{2}\). Float glass was used as substrate, with an area of \(300\times 300\) mm\({}^{2}\). To avoid any contamination from the glass substrate, it was cleaned using a glow discharge at load-lock chamber. The processing chamber was evacuated below \(5\times 10^{-7}\) mbar prior to any deposition, and all depositions were carried out using Ar/O\({}_{2}\) mixture under constant pressure (\(2\times 10^{-3}\) mbar). The O\({}_{2}\) flow rate was selected in order to operate beyond the transition region of the cathode voltage versus oxygen flow curve, where the deposition fully works in the oxide mode. The process was performed at plasma temperature.  
Before the creation of the dielectric multilayer stack, the TiO\({}_{2}\) and SiO\({}_{2}\) deposition rates and their optical properties were calibrated by deposition of a single layer of the titanium oxide on glass and silicon oxide on top of titanium oxide/glass. Thickness and refractive index of both dielectric materials were characterized, and finally, the optical properties of the 1 DPC were characterized at normal incidence and compared with the initial design modeling.  
The thickness of the dielectric layers used to manufacture the 1 DPC was a critical parameter. Figure 2 shows that differences in the thickness of these layers implied significant differences in the optical performance of the samples: three samples (from left to right, PC-03, PC-02, and PC-04) with the same dielectric material structure but different thicknesses (Table 1) were used to validate the design specifications of the photonic crystal. Figure 2a shows the reflection spectrum, explaining the different colors obtained depending on the thickness used for each dielectric layer. In the backside, the transmission of the same samples using a mirror located at the rear side of the samples is shown. It can be observed that front and back color for each sample was different, due to the different thicknesses employed. Reflectance spectrum for the objective of this research is shown in Figure 3. According to the results summarized in Table 1 and Figure 2, when SiO\({}_{2}\) thickness differs 30% from the objective one, the Bragg peak shifts to lower wavelengths with undesired effects on the optical properties: transparency is lost in favor of blue-violet colors.  
Figure 2: (**a**) 1 DPC samples processed by DC sputtering during the calibration process. Modification in the layer thickness induced different reflection and transmission spectra, and consequently, color varied from one sample to another. (**b**) Reflectance spectrum of each sample (from left to right: PC1-03, PC-02, and PC-04), explaining that the color shifted as a function of the dielectric layer thickness.