## 3 Results and Discussion
For the [PERSON] model,  
\[\sigma_{\rm e}^{0}(\rm h\upsilon,T)\sim\frac{1}{\rm h\upsilon\sqrt{2\pi d_{\rm FC }\varepsilon}coth(\varepsilon/2k_{\rm B}T)}\times\int_{0}^{\infty}dE_{k}\frac{E_ {k}^{3/2}}{\left(E_{k}+E^{0}-d_{\rm FC}\right)^{2}}\times\exp\left[-\frac{ \left(\rm h\upsilon-E^{0}-E_{k}\right)^{2}}{2d_{\rm FC}coth\left(\frac{ \varepsilon}{2k_{\rm B}T}\right)}\right] \tag{4}\]  
For the Chantre-Bois model,  
\[\sigma_{\rm e}^{0}(\rm h\upsilon,T)\sim\frac{1}{\rm y\theta^{1/2}}\times\int_{ 1}^{\infty}dx\frac{\left(x-1\right)^{1/2}}{\left(x-1+E^{i}/E^{0}\right)^{2}} \times\exp\left[-\frac{\left(y-x\right)^{2}}{\rm\theta}\right] \tag{5}\]  
where \(\rm\theta=\frac{4d_{\rm FC}k_{B}T}{E^{0}}\), \(\rm y=\frac{h\upsilon}{E^{0}}\), and \(\rm E_{i}=\frac{h^{2}\alpha^{2}}{2m}\), where \(\rm m^{*}\) is the electron effective mass of 0.22 m\({}_{0}\), \(\rm E^{0}\) is the optical ionization energy, and \(\rm d_{\rm FC}\) is the Franck-Condon energy shift, and \(\rm E^{0}=d_{\rm FC}+E_{T}\). The nonnegative parameter \(\rm\theta\) corresponds to photon-phonon interactions, which are assumed to be proportional to a normal distribution, with a variance of \(\rm\theta/2\). If \(\rm\theta\) is low, either due to a low temperature or a small Franck-Condon shift, then the phonon contribution is limited, and the distribution is focused on the incident photon energy. Conversely, if \(\rm\theta\) is large, which implicates both a high temperature and Franck-Condon shift, then the distribution is broad, and the impact of the interaction with phonons becomes significant. Parameter \(\rm\theta\) in the Chantre-Bois model plays a similar role to the parameter \(\rm d_{\rm FC}\varepsilon\)coth\(\left(\frac{\varepsilon}{2k_{\rm B}T}\right)\) in the Passler model. However, these models are not equivalent,  
Figure 5: Spectral dependence of electron photoionization cross-section for (**a**) entire spectral range; (**b**) a trap with Ec–2.05 eV; (**c**) for a trap with Ec–2.75 eV; and (**d**) a trap with Ec–3.33 eV, respectively. The red, blue and green solid lines correspond to theoretical models of [PERSON], Chantre–Bois, and Passler, respectively. especially for a small Franck-Condon shift, as the Passler model is similar to the [PERSON] model, while the Chantre-Bois model is not (due to the 1/2 power in the numerator of the first term under the integral instead of 3/2). The E\({}_{\text{k}}\) parameter used in the Passler model corresponds to the kinetic energy of the excited electron [7]. The \(\alpha\) parameter used in the Chantre-Bois model is a fitting parameter that effectively adjusts the mass of the trapped electron, providing a means to fine-tune the model's accuracy. In Table 1, the parameters of the trap levels extracted from the DLOS data fitted with the three models are summarized. These include the optical ionization energy (E\({}^{0}\)), the trap level position (E\({}_{\text{T}}\)), and the d\({}_{\text{FC}}\) values for all identified trap states. In turn, the individual trap concentrations given in Table 1 were derived from the SSPC data shown in Figure 3.0  
One can notice that the results of the \(\alpha_{\text{e}}^{0}\) data fitted with the theoretical models, illustrated in Figure 5a-d, may lead to a few general remarks: (1) the Lucovsky model fits the experimental data quite well; however, the trap level positions (E\({}_{\text{T}}\)) determined from this approach appear to be consistently underestimated in comparison with the Chantre-Bois or Passler models for trap levels that are strongly coupled to the lattice, i.e., where d\({}_{\text{FC}}\) = 0.15-0.4 and 0.3-0.65 for the Ec-2.05 eV or Ec-2.75 eV trap levels, respectively; (2) in turn, the Lucovsky model applied to the trap level located relatively close to the valence band edge (Ec-3.33 eV) gives almost the same E\({}_{\text{T}}\) values as the two other models; and (3) significant discrepancies in the defect parameters determined from the Chantre-Bois and Passler models are observed for states with Ec-2.05 eV and Ec-2.75 eV.