## 1 Introduction
Again, this process is followed by the reconfiguration of atoms close to the defect and the transfer of energy in the form of phonons (d\({}_{\text{FC}}\)\({}^{\text{g}}\)) released into the lattice until an equilibrium state is achieved. If a large number of phonons participate in the photoionization process, the optical capture cross-section of electrons can be approximated by the Huang-Rhys approach [12]. This approach separates both the electron and phonon terms of the optical capture cross-section, and \(\sigma_{e}^{0}\) can be calculated as the product of the electronic part and a Gaussian  
Figure 1: Configuration coordinate diagram describing electron–phonon coupling for an acceptor defect state (0/\(-\)). The arrows represent optical transitions as well as specific energies used in CC model. function representing the phonon term, which takes into account the broadening effects related to lattice vibrations [13]. This approach has been successfully implemented in the Chantre-Bois [6] and Passler [7] models, commonly used for modeling the optical capture cross-section in nitrides and other materials. Meanwhile, if the electron-phonon coupling is negligible (\(\mathrm{d_{FC}}\to 0\)), the optical capture cross-section has a purely electronic character and can be approximated with the Lucovsky model [14]. In general, the processes of photoionization of deep trap levels can be described by the spectral dependence of the optical capture cross-section, where the photoionization energy is usually determined by fitting a theoretical model describing the photoionization process to the experimental data. In this procedure, \(\mathrm{E^{0}}\) and \(\mathrm{d_{FC}}\) are used as fitting parameters. It is evident that \(\mathrm{E^{0}}\), \(\mathrm{d_{FC}}\), and \(\mathrm{E_{T}}=\mathrm{E_{therm}}\) are characteristic and unique parameters that explicitly define any defect level within the bandgap. If these parameters are precisely identified, they can facilitate the accurate and unambiguous recognition of defects. As illustrated in Figure 1, all of the aforementioned parameters are self-dependent and can be expressed by the relation \(\mathrm{E_{abs}}=\mathrm{E_{0}}=\mathrm{d_{FC}}^{\mathrm{e}}+\mathrm{E_{T}}\). In this study, the optical capture cross-section was determined from the analysis of the photo-capacitance transients, as reported in our recent paper [15]. Accordingly, the [PERSON] [14], [PERSON] [6], and [PERSON] [7] models were fitted to the spectral shape of the optical capture cross-section that was experimentally determined using the formula:  
\[\sigma_{\mathrm{e}}^{0}(\mathrm{h}\upsilon)=\frac{\mathrm{e^{0}}}{\mathrm{ \phi(h\upsilon)}}=\frac{2\mathrm{N_{D}}}{\mathrm{\phi(h\upsilon)N_{T}C}}\frac{ \mathrm{d}\mathrm{C(t)}}{\mathrm{dt}}\bigg{|}_{\mathrm{t}\to 0} \tag{1}\]  
where C is the initial diode capacitance, \(\mathrm{N_{D}}\) is the net donor concentration, \(\mathrm{N_{T}}\) is the trap level concentration, and C(t) is the photo-capacitance transient, respectively. Below, we present the results of fitting the theoretical models to our experimental data, followed by a brief discussion of the defect parameters determined from the fitting procedure. Moreover, some variations in \(\mathrm{E_{T}}\) and \(\mathrm{d_{FC}}\) obtained from the Chantre-Bois and the Passler models are discussed, and a couple of possible reasons for these discrepancies between both models are given. We would like to emphasize that due to the lack of native GaN substrates essential for obtaining high-quality GaN films, numerous GaN and \(\mathrm{Al_{x}Ga_{1-x}N}\) layers studied with SSPC and DLOS techniques have commonly been grown on foreign, lattice-mismatched sapphire templates [2; 3; 4]. This practice may result in the formation of strained films and high dislocation densities in the overgrown layers, which significantly affect the experimental data and complicate the interpretation of results.