## 3 Results and Discussion
In this context, the L-L relationship suggests that the observed increase in \(n\) in 650 \({}^{\circ}\)C-grown samples upon annealing is partly due to the observed thin-film thickness reduction (e.g., \(\sim\)22% between the AD and A3 samples; see Figure S1B). The film densification observed for the sample deposited at 700 \({}^{\circ}\)C is lower (\(\sim\)17%) and does not lead to an observable change in the index of refraction, within the error associated with the SE measurements and fitting. The values of \(k\) in the NIR region range from \(\sim\)10\({}^{-3}\) to 10\({}^{-6}\) depending on the fitting model used (CL and CU) (Table 1), irrespective of the amorphous or crystalline phase of the films. These findings underscore that the extracted \(k\) values and corresponding absorption coefficients are highly model-dependent, as expected from the inherently model-based nature of SE. While these \(k\) values are low, those below \(\sim\)10\({}^{-3}\) fall below the sensitivity limits [55] of \(k\) values in this range from other studies may similarly reflect model-dependent limitations and should be accompanied by a clear disclaimer regarding the sensitivity limits of SE and the assumptions of the fitting model, as they may not reflect true material absorption. Figure 4C presents the absorption coefficient values calculated from the TL and CL fits for the 650 \({}^{\circ}\)C and 700 \({}^{\circ}\)C AD films for photon energies \(\geq\) 1 eV. The \(E_{04}\) gap is denoted by the gray dashed line. For energies above this point, both models show identical absorption coefficient values. Below \(E_{04}\), the TL-derived absorption coefficient values go to zero at the energy corresponding to \(E_{g}\), as outlined in Equation (1a). Conversely, the CL models show non-zero absorption coefficient values extending from \(E_{g}\) into the NIR region. Nevertheless, both models produce nearly identical \(E_{04}\) and \(E_{g}\) values, with all extracted fitting parameters  
Figure 2:2 Spectroscopic ellipsometry of the SiC films: (**A**) Schematic illustration of mobility edge, optical gap (\(E_{g}\)), and band-tail states (\(E_{u}\)) in the energy (\(E\)) vs. density of states (DOS) diagram. The adjacent energy vs. absorption (\(\alpha\)) plot highlights the need for multiple models to describe absorption across different energy ranges. Inset: Comparison of model assumptions—while the Tauc-Lorentz (TL) model imposes zero absorption for E \(<\) E\({}_{g}\), the CL and CU models capture non-zero sub-gap absorption associated with Urbach tail transitions, with the CU model typically yielding a higher absorption near the optical bandgap. (**B**) Refractive index (\(n\)) and extinction coefficient (\(k\)) extracted from CL and TL fittings for AD and A3-annealed SiC films grown at (**i**) 650 \({}^{\circ}\)C and (**ii**) 700 \({}^{\circ}\)C, measured across the UV-Visible-NIR range. Inset: Data obtained from CU fitting. (**C**) Absorption coefficient in the energy range 1-3.75 eV, which is used to extract \(E_{04}\) values. (**D**) In the sub-bandgap Urbach tail region (0.7-1.1 eV), absorption is modeled using the CL and CU models. A standard 25 nm SiO\({}_{2}\)/Si reference sample is fitted by CU and CL models for reference. (**E**) Tauc’s plots with linear fits (dotted lines) used to extract Tauc’s optical gap (\(E_{g,\text{Tauc}}\)). summarized in Figure 2:3 Figure 4D highlights the absorption behavior in the NIR region (\(\sim\)0.7 eV-1.1 eV) for the 650 \({}^{\circ}\)C and 700 \({}^{\circ}\)C AD films, incorporating both the CL model and the corresponding CU fits discussed earlier. For reference, the fitting results for a pristine 25 nm thick reference SiO\({}_{2}\) film -- expected to be fully transparent below \(\sim\)7 eV --are also included. All models reproduced the expected refractive index of \(\sim\)1.48 for SiO\({}_{2}\) at 1550 nm (Table S3) [56]. Absorption in this region in the SiC films is below \(\leq\)10\({}^{3}\) cm\({}^{-1}\) in all cases.