# Optical Studies in Red/NIR Persistent Luminescent Cr-Doped Zinc Gallogermanate (ZGGO:Cr)
## 3 Results
### Temperature-Dependent PL

Table 2: Peak position of the R-lines for ZGO:Cr and ZGGO:Cr samples measured at 15 K.  
stands for the activation energy that describes the observed thermal quenching. The values obtained for the best fit to the proposed models are listed in Table 3. The value of \(\sim\)4.8 meV is in good agreement with the energy separation of the R-lines mentioned above (Table 2), indicating that thermalisation occurs between the two electronic levels and thus the R2 becomes thermally populated at the expense of the R1 up to \(\sim\)90 K. Above this temperature, the two levels behave as one, as attested by the similar activation energy estimated for the depopulation processes (\(\sim\)47 meV). \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\Lambda_{exc}\) **(nm)** & **Lines** & \(E_{a,pop}\) **(meV)** & \(E_{a,dpop}\) **(meV)** \\ \hline
325 & R1 & - & 47.1 \(\pm\) 5.9 \\
325 & R2 & 4.8 \(\pm\) 0.2 & 47.7 \(\pm\) 6.0 \\
442 & R1 & 15.1 \(\pm\) 1.9 & 10.6 \(\pm\) 3.7 \\
442 & R2 & 7.6 \(\pm\) 1.2 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Activation energies obtained for the population/depopulation processes of R1- and R2-lines excited either with 325 nm or 442 nm. Figure 8: Temperature-dependent PL spectra of ZGGO:Cr obtained under (**a**) 325 nm and (**b**) 442 nm of excitation. (**c,d**) Corresponding enlarged spectra of the R-lines region upon subtracted baseline. When the sample is excited with 442 nm (blue symbols in Figure 9), both lines can be accounted for by the model of Equation (2), assuming no depopulation processes in the case of the R2-line, that is, only a thermal population assuming a Boltzmann function is considered. In this case, the thermal population of the R1-line is well accounted for with an activation energy of \(\sim\)15 meV, whereas it depopulates with an activation energy of \(\sim\)10 meV. In the case of the R2-line, the thermal population is described by an activation energy of \(\sim\)8 meV. The schematic representation in Figure 10 illustrates the phenomena occurring in these population/depopulation processes. As mentioned before, the R-lines are seen to widen and shift their peak position to lower energies with increasing temperature, as shown in Figure 11. This effect can be described by the electron-phonon coupling between the impurity levels and the lattice  
Figure 10: Schematic representation of the mechanism for the population/depopulation processes when ZGGO:Cr is excited under 325 nm and 442 nm. The curved arrows denote non-radiative processes, while the straight red ones correspond to radiative ones. The orange rectangles involving the \(\overline{E}\) and \(2\overline{A}\) states illustrate the R2/R1 thermalisation process. i, ii, and iii indicate different Cr\({}^{3+}\) centres present in the sample. The diagram is not to scale and it was assumed that the ground level was at the same energy location for all the Cr\({}^{3+}\) optical centres. Figure 9: Temperature dependence of the R-lines’ integrated intensity obtained under 325 nm and 442 nm photon excitation and correspondent fittings according to Equations (1) and (2). phonons. Accordingly, considering a simplified model where the energy shift is proportional to the phonon population number, the temperature dependence of the peak position, \(E(T)\), can be approximated to [11; 34],  
\[E(T)\ =E_{R}(0)-\frac{\beta}{exp(\hbar\overline{\omega}/k_{B}T)-1} \tag{3}\]  
where \(E_{0}\) is the line energy at 0 K, \(A\) corresponds to a proportionality factor, \(\hbar\overline{\omega}\) is the energy of the phonons involved, \(\hbar\) is the reduced Planck constant, \(k_{B}\) is the Boltzmann constant, and \(T\) is the absolute temperature. Table 4 indicates the parameters obtained for R-lines best fit to Equation (3). As a result, with 325 nm excitation, the energy of the phonons involved and \(\beta\) values are similar to the ones measured in ZGO:Cr pellets, being, however, reversed relatively to the R1- and R2-lines, meaning that a distinct vibrational coupling is observed in the here-studied ZGO:Cr.