## 3 Results
### Reflectivity and Surface Passivation of TiO\({}_{2}\)/SiN\({}_{x}\) Stacks  
Figure 8 shows the reflectivity as a function of wavelengths from 300 nm to 1200 nm for Si wafer; 8-nm-thick, 15-nm-thick, 35-nm-thick, and 66-nm-thick TiO\({}_{2}\) films; and TiO\({}_{2}\)/SiN\({}_{x}\) stacks on Si. For samples with TiO\({}_{2}\) films deposited on the Si wafers, their reflectivity decreases as the thickness of the TiO\({}_{2}\) films increases. According to the theory of quarter-wavelength anti-reflection coating (\(d=\lambda/4\pi\)TiO\({}_{2}\), \(d\) is the thickness and \(\pi\)TiO\({}_{2}\) is the refractive index of TiO\({}_{2}\)), the (first-order) wavelength at minimum reflection red-shifts as the film thickness increases. As the wavelength at minimum reflection for the thicker TiO\({}_{2}\) films on Si shifts closer to the wavelength of the peak intensity of the solar spectrum for the thicker TiO\({}_{2}\) films on Si, they can have a better ability to harvest light. The results show that the 66-nm-thick TiO\({}_{2}\) film can be a good anti-reflection coating layer for Si solar cells. However, the phase transformation and post-deposition annealing could cause the surface passivation of 66-nm-thick TiO\({}_{2}\) film to decline.  
In this paragraph, we go further to study the optical properties and surface passivation of TiO\({}_{2}\)/SiN\({}_{x}\) stacks on Si for future applications on the front side of \(p\)-type c-Si solar cells. TiO\({}_{2}\)/SiN\({}_{x}\) stacks are composed of an 8-nm-thick TiO\({}_{2}\) film deposited by ALD and a 72-nm-thick SiN\({}_{x}\) film deposited by plasma-enhanced chemical vapor deposition (PECVD). From the measured reflectivity  
Figure 8: Reflectivity of Si wafer, Si with different thicknesses TiO\({}_{2}\) layers and TiO\({}_{2}\)/SiN\({}_{x}\) stacks as function of wavelengths from 300 nm to 1200 nm.  
Figure 7: Minority carrier lifetime as function of carrier density for two TiO\({}_{2}\) films: One is deposited for 250 cycles without post-deposition annealing, and another is deposited for 250 cycles with post-deposition annealing at 200 \({}^{\circ}\)C for more 6000 s in the chamber.  
shown in Figure 8, TiO\({}_{2}\)/SiN\({}_{x}\) stacks have reflectivity as low as 66-nm-thick TiO\({}_{2}\) films which can serve as an anti-reflection coating layer for Si solar cells.  
SiN\({}_{x}\) thin film deposited by PECVD not only is the mainstream option for anti-reflection coatings in c-Si solar cells, but it also serves as the passivation layer due to the atomic hydrogen in the film. During the process of solar cells, hydrogen atoms can diffuse and serve in the chemical passivation [40]. For the silicon surface passivation of TiO\({}_{2}\)/SiN\({}_{x}\) stacks, Figure 9 shows the effective carrier lifetimes of bare Si wafer, TiO\({}_{2}\)/SiN\({}_{x}\) stacks, 80-nm-thick SiN\({}_{x}\) films deposited by PECVD, and 66-nm-thick TiO\({}_{2}\) films deposited by ALD on Si at the injection level of 1.0 \(\times\) 10\({}^{15}\) cm\({}^{-3}\). The error bar of the effective carrier lifetime is the standard deviation of six samples for individual conditions. Some degree of silicon surface passivation by TiO\({}_{2}\)/SiN\({}_{x}\) stacks can be found, and the stacks have a better performance of surface passivation than that of SiN\({}_{x}\) and TiO\({}_{2}\) layers. TiO\({}_{2}\)/SiN\({}_{x}\) stacks have excellent optical properties and effective Si surface passivation so they can be a potential material for c-Si solar cells. Compared with 8-nm-thick TiO\({}_{2}\) film, the effective lifetime decreases after the capping layer of SiN\({}_{x}\). The reason might be similar to that for 66-nm-thick TiO\({}_{2}\) film. Stress effects, phase transformation of TiO\({}_{2}\) films and the thermal budget effect induced by the PECVD process make the performance of the surface passivation decrease. For further applications on c-Si solar cells, lower-temperature deposition of the SiN\({}_{x}\) capping layer and forming gas annealing of TiO\({}_{2}\)/SiN\({}_{x}\) stacks might be better.