# Defect Tailoring in HfO2/Si Films upon Post-Deposition Annealing and Ultraviolet Irradiation
## 3 Results
### Optoelectronic Properties
#### 3.4.2 UV-Visible Spectroscopy  
S1-S4 samples were analyzed by UV-Vis diffuse reflectance spectroscopy for a wavelength range of 200 to 800 nm. By applying the Kubelka-Munk function (FK-M), the optical absorption coefficient, \(\alpha\), was estimated using the following equation:  
\[\left[\alpha\sim\mathrm{F}\right]_{(K-M)}=\frac{\left(1-R\right)^{2}}{2R} \tag{1}\]  
where \(R\) is diffuse reflectance. To assess the electronic states near the absorption edge, the following expression as a function of FK-M was used:  
\[\left[\mathrm{h}\mathrm{v}\alpha\sim\mathrm{h}\mathrm{v}\mathrm{F}\right]_{( K-M)}\propto A\left(\mathit{h}\
u-Eg\right)^{n} \tag{2}\]  
where \(A\) is a constant that does not depend on the photon energy, \(h\) is blank constant, \(\
u\) is the frequency, \(Eg\) is the band gap, and \(\mathrm{n}\) can take the values 0.5 or 2 depending on if the band gap is direct or indirect [21]. The band gap for HfO\({}_{2}\) has been reported as indirect at ca. 6 eV [4] and direct at ca. 5.8 eV [11]. Figure 9 shows the analysis of the optical reflectance of the S1-S4 samples. Figure 9a shows the reflectance spectra, Figure 9b shows the Tauc plot (F(R)h\(\
u\))\({}^{0.5}\) vs. \(\mathit{h}\
u\), which corresponds to indirect transitions, and Figure 9c shows the Tauc plots (F(R)h\(\
u\))\({}^{2}\) vs. \(\mathit{h}\
u\) corresponding to the direct transitions for the S1-S4 HfO\({}_{2}\) samples, respectively [21]. These results, which show both direct allowed and indirect allowed transitions in HfO\({}_{2}\) films, are consistent with those reported by [PERSON] et al. [22] for HfO\({}_{2}\) powders, but this has not been reported in HfO\({}_{2}\) films, as far as revised in the literature. The reflectivity of the films decreases from higher to lower wavelengths according to the reported refractive index vs. wavelength [4]. From Figure 9a, it can be observed that film S1 has the highest reflectivity vs. wavelength behavior (%R from 5 to 80%). It has been reported that the refractive index increases with the temperature [4]. The other reflectance spectra have similar reflectivity values and features, also suggesting an increased density upon post-deposition treatments [4]. Figure 9b shows the optical behavior of the films when indirect transitions (F(R)h\(\
u\)\({}^{1/2}\) vs. energy plot) are assessed. In the plot, several linear regions are indicated with straight lines for each spectrum, indicating the presence of delocalized states within the band gap. It is evident that there is a difference in such states from the S1 sample to the samples with post-deposition treatment. In Figure 9c, the F(R)h\(\
u\)\({}^{2}\) vs. energy plot, which accounts for direct transitions, is shown. Several linear regions are indicated at around 5, 3.5-4.0, 2.6-3.0, and 2 eV. The gray arrows indicate the trend of the transition values. The spectrum of the S1 sample shows a defined transition at ca. 5.6 eV, which can be assigned to the direct band gap of HfO\({}_{2}\)[11], followed by another defined state at ca. 5 eV, the nature of which is discussed below. Correspondingly, the spectra of samples S2-S4 have similar features, but the fundamental transition is not observed,  
Figure 9: (a) Diffuse reflectance; Tauc plots (b) (F(R)h\(\
u\))\({}^{1/2}\) vs. h\(\
u\); and (c) (F(R)h\(\
u\))\({}^{2}\) vs. h\(\
u\) of samples S1-S4. possibly due to the spectral range where the transmittance was assessed [4]. The areas within dashed circles indicate extended absorption tails around 5.0 eV, 3.8 eV, and 2.8 eV, respectively, related to the disorder and widening of the density of available states around these energies within the mobility gap. Following [PERSON] and [PERSON] [21], the intersections where y = 0 in the plot are not necessarily an electronic transition but depend on the disorder degree and can be considered extrapolations from delocalized states to the zero of density states, according to the Davis-Mott model.