## 1 Introduction  
It is commonly accepted that due to significant electron-phonon interactions in nitrides, the photoionization processes of deep trap levels in GaN (Eg = 3.4 eV) and Al\({}_{\mathrm{x}}\)Ga\({}_{\mathrm{1-x}}\)N alloys should be strongly coupled to the lattice [1; 2; 3; 4]. Experimentally, the electron-phonon coupling phenomenon is manifested i.e. through a much higher optical ionization energy threshold (E\({}^{0}\)) required to promote electrons captured on a trap level to the conduction band (C\({}_{\mathrm{B}}\)) observed in absorption measurements such as SSPC (Steady-State-Photo-Capacitance) [5] and DLOS [6; 7] than it would solely result from the position of a trap level in the bandgap. Therefore, the photoionization energies measured in GaN are typically shifted to higher energies by a Franck-Condon factor (d\({}_{\mathrm{FC}}\)), which is related to lattice deformation around a defect that changes its charge state after the photoionization process [8; 9]. As previously proposed in numerous papers [8; 10], the electron-phonon interaction can be conveniently described in terms of a configuration coordinate diagram (CC) shown schematically in Figure 1. In general, the CC diagram represents the total potential energy of the electronic and lattice vibration subsystems, which are represented by parabolas and horizontal lines within the parabolas, respectively. In this simple model, a defect can be described by a generalized coordinate Q that is proportional to the bond length around the impurity. Thus, the energy of the system can be expressed by a simple relation where energy is approximately proportional to Q squared (E-Q\({}^{2}\)) as the bonds behave like a harmonically vibrating spring. Furthermore, the CC model assumes that the electron-lattice coupling is a linear function of Q. Therefore, the minima of both parabolas shown in Figure 1 are horizontally displaced and correspond to the generalized coordinates Q\({}_{1}\) and Q\({}_{2}\) in two different defect charge states, respectively. It is also important to note that in the CC model, optical transitions occur instantly and vertically, whereas thermal transitions are much slower processes that occur laterally through phonon emission or absorption. This depends on the difference between the initial and the final phonon states, represented as horizontal lines in Figure 1. If phonon states are equally distributed in both charge states, the parabolas' minima are vertically shifted by a factor E\({}_{\text{therm}}\), which is the thermal activation energy commonly measured with a deep-level transient spectroscopy technique (DLTS) [11]. It can be shown that in thermodynamic equilibrium, the total energy of the system with the electron occupying the trap level is minimized for a given Q\({}_{1}\) value (left parabola in Figure 1). However, this situation is remarkably different when a photon is absorbed (E\({}_{\text{abs}}\)) and the electron is promoted to the conduction band. This process is depicted as an optical transition (blue vertical arrow) in Figure 1. In the case of an acceptor trap level (as discussed in this example), this transition results in a change in the charge state from negative to neutral. Since the defect has changed its charge state, the bond lengths are slightly different than in the initial Q\({}_{1}\) state, and the excess energy in the form of phonons (d\({}_{\text{FC}}\)\({}^{\text{e}}\)) is transferred to the lattice, which results in plastic deformation around the impurity and a new equilibrium state, denoted now as Q\({}_{2}\) (minimum of the right parabola in Figure 1), is obtained. Similarly, if the electron is recaptured into the trap level, the process is reversed, and the system recovers to its initial Q\({}_{1}\) state through the emission of photons with a characteristic energy (E\({}_{\text{em}}\)), which can be measured by the photoluminescence technique (PL).