## 3 Results
### Characterization of ALD TiO\({}_{2}\) Thin Films
According to the results from other groups [33; 34], the crystalline size of anatase TiO\({}_{2}\) embedded in 66-nm-thick film should be larger than the critical size (\(\sim\)20 nm). This estimation is also consistent with our TEM result shown in Figure 1d. The 66-nm-thick TiO\({}_{2}\) film was also analyzed by spectroscopic ellipsometry. The software CompleteEASE (Version 4.48, J.A. Woollam Co., Lincoln, NE, USA, 1999-2010) was used to fit the experimental data. To extract the optical constants of deposited TiO\({}_{2}\) film, we tried to use one, two, and three optical dielectric layers to model this single deposited layer. To simplify our fitting, the Cauchy function provided by CompleteEASE was used for the optical dielectric layers. For the fitting of optical dielectric layers, the parameters of the Cauchy function (A, B, and C) and the thickness are allowed to fit. Initially, the parameter of k amplitude, which is related to the strength of the extinction coefficient, was fixed at zero in consideration of the bandgap of TiO\({}_{2}\). Then, in order to improve the fitting (further minimizing the mean square errors (MSE) value), the k parameter of the upper layer was allowed to fit. The obtained MSEs for the one-, two-, and three-layer models are 8.26, 2.64, and 2.48, respectively. By comparing it with the MSE value of the two-layer model, the three-layer model only improved a little, which indicates that the two-layer model is enough. Among the different fitting models, we can find the best one as shown in the inset of Figure 4. The fitting results were composed of a surface roughness layer (5.8 nm), an upper layer (20.4 nm), a lower layer (50.3 nm), and a Si substrate. Adding more layers in the model does not improve the fitting results. The thickness of the surface roughness (5.8 nm) is close to the atomic force microscopy results of the 66 nm film (4.01 nm) [32]. The total thickness (upper and lower layer) of TiO\({}_{2}\) around 70 nm is consistent with our estimation of 66 nm based on the growth rate of our ALD system. Moreover, the two-layer model of the TiO\({}_{2}\) film and its individual thickness agree with the TEM result in Figure 1d. From the TEM image, the darker region from the top of the TiO\({}_{2}\) layer is related to the upper layer of the ellipsometry model. Since most of the measured spectral range is below the bandgap of TiO\({}_{2}\), the optical dispersion of the upper and lower layers is fitted by the Cauchy dispersion functions. The extracted indices of the refraction (\(n\)) and the extinction coefficient (\(k\)) of the upper and lower layers as functions of wavelength are shown in Figure 4. The refractive index of the lower layer closes to the refractive index of the anatase TiO\({}_{2}\)[35]. The upper layer shows a lower value of the refractive index and a larger value of the extinction coefficient because of its amorphous phase. Besides, this double-layer structure is better for light harvesting than the one-layer structure [36]. To show this concept, we calculated the reflectance values for one layer of 70.7-nm-thick TiO\({}_{2}\) (with \(n\) and \(k\) values of the lower layer) and the two-layer TiO\({}_{2}\) composed of an upper layer (20.4 nm) and a lower layer (50.3 nm) on top of a planar Si wafer. By loading our extracted values of \(n\) and \(k\) and using OPAL 2, an optical calculator hosted on the PV Lighthouse website [37], the average reflectance  
Figure 3: Raman spectra of 66-nm-thick TiO\({}_{2}\) film and a Si wafer. The inset shows a zoom-in around the wavenumber of 200 cm\({}^{-1}\). values for the spectral range of 380-890 nm, which is the measured spectral range of ellipsometry, are 13.8% and 11.2% for the one-layer and two-layer TiO\({}_{2}\), respectively.