## 3 Results and Discussion
A typical SSPC spectrum for Ni/GaN SBDs measured at T = 293 K is shown in Figure 4, where the Y-axis was recalculated to represent the trap concentration (N\({}_{\text{T}}\)) using the formula:  
\[\text{N}_{\text{T}}=2\text{N}_{\text{D}}(\Delta\text{C}_{\text{ss}}/\text{C}) \tag{2}\]  
where N\({}_{\text{D}}\) is the net donor concentration, \(\Delta\text{C}_{\text{ss}}\) is the change in the steady-state photo-capacitance transient, and C is the capacitance measured with the bias applied to the sample, here, U\({}_{\text{R}}=-0.5\) V. The capture cross-section data obtained from the DLOS measurements calculated from (1) and plotted as empty squares are presented in the inset of Figure 4. The red solid lines in the inset illustrate the Lucovsky model (d\({}_{\text{FC}}\) = 0) fitted to the experimental data points according to the theoretical model given by  
\[\text{e}_{\text{e}}^{0}(\text{hv})\,\sim\frac{\left(\text{hv}-\text{E}_{\text {T}}\right)^{\frac{3}{2}}}{\left(\text{hv}\right)^{3}} \tag{3}\]  
Figure 3: DLTS spectrum for a rate window of 20 s\({}^{-1}\) measured for Ni SBD for a filling time t\({}_{\text{P}}\) = 1 ms.  
where \(\rm E_{T}\) represents the trap level position in the bandgap with respect to the conduction band edge, and \(\rm hv\) is the photon energy. Accordingly, the \(\rm E_{T}\) values modeled with the Lucovsky approach were found to be \(\rm E_{C}\)-2.05 eV, \(\rm E_{C}\)-2.75 eV, and \(\rm E_{C}\)-3.33 eV, respectively. For n-type materials, the positive onsets in the SSPC spectra, as shown in Figure 4, correspond to the trap level positions relative to \(\rm E_{C}\)[5]. However, due to phonon-lattice coupling effects in GaN that are visible as broad steps (or plateaus) in the SSPC spectra, it is difficult to estimate the exact trap level position solely from them. Moreover, since no information about coupling can be deduced from this approach, trap levels' positions derived in this manner can be considered only as vague approximations. Therefore, theoretical models describing photoionization processes have to be used for the accurate determination of deep-level parameters, such as \(\rm E_{T}\) and \(\rm d_{FC}\). In Figure 5a, the spectral dependencies of the electron photoionization cross-section for three trap levels detected in the Ni/GaN SBDs are shown. Figure 5b-d present the same spectral dependencies as shown in Figure 5a but focus on the individual trap levels only and are displayed over a limited energy range for clarity and visualization purposes. Moreover, the levels positions shown in Figure 5a-d highlighted in the red color correspond to the \(\rm E_{T}\) derived from the Lucovsky model fitting (\(\rm d_{FC}=0\)). It is clear from Figure 5a-d that the experimental data of the capture cross-section for traps with Ec-2.75 eV and Ec-2.05 eV correspond to a significantly broader range than suggested by a purely electronic excitation model. The unusually large extension of the low-energy tail observed for these traps indicate a strong electron-lattice coupling. Therefore, the lines in Figure 5a-d were fitted to the experimentally determined optical capture cross-sections based on the models proposed by [PERSON] (red), [PERSON] (blue), and [PERSON] (green). The [PERSON] fit in Figure 5a-d was obtained using (3), while the Passler and Chantre-Bois fits were modeled using the following formulas:  
Figure 4: SSPC spectrum for Ni/GaN SBDs measured at T = 293 K with Y-axis recalculated to trap concentration \(\rm N_{T}\). Inset shows capture cross-section data determined from DLOS measurements using (1) and fitted with [PERSON] model (\(\rm d_{FC}=0\)).