## 3 Results and Discussion
### Photoluminescence Measurements
The operators \(m^{i}\) and \(p^{i}\) are associated with the magnetically correlated corrections. The corrections of the free ion including the crystal field were conducted using the crystal field theory [22]. The theoretical results and transition assignment, along with the experimental values, are given in Table 5. A good correlation between the experimental and theoretical values was found. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Temperature**} & \multicolumn{3}{c}{**Transition**} \\ \hline
**20 K** & **50 K** & **75 K** & **100 K** & **150 K** & **300 K** & & \\ \hline  & \multicolumn{4}{c}{**\(\lambda\) (nm)**} & & & **v (cm\({}^{-1}\))** & \\ \hline
743.9 & & & & & 13.443 & \({}^{5}\)D\({}_{0}\rightarrow\)\({}^{7}\)F\({}_{5}\)\({}^{*}\) \\
739.6 & & & & & & 13.521 & \({}^{*}\) \\
733.9 & & & & & & 13.626 & \({}^{*}\) \\
720.6 & 720.7 & 720.9 & 720.9 & 720.9 & & 13.872 & \({}^{*}\) \\
711.7 & 710.4 & 711.4 & 711.5 & 711.2 & 711.1 & 14.061 & \\
707.3 & 708.8 & 709.3 & 709.2 & 708.9 & 708.9 & 14.106 & \({}^{5}\)D\({}_{1}\rightarrow\)\({}^{7}\)F\({}_{6}\) \\  & 705.1 & 705.7 & 705.7 & 705.7 & 705.8 & 14.170 & \({}^{5}\)D\({}_{1}\rightarrow\)\({}^{7}\)F\({}_{6}\) \\
700.0 & 699.9 & 699.9 & 700.5 & 700.0 & 700.2 & 14.286 & \\
695.7 & & 696.4 & 696.2 & 695.9 & 696 & 14.370 & \({}^{**}\) \\
689.7 & 689.6 & 690.0 & 689.9 & 689.8 & 690 & 14.496 & \({}^{5}\)D\({}_{0}\rightarrow\)\({}^{7}\)F\({}_{4}\)\({}^{**}\) \\
672.3 & & 678.1 & 680.2 & 680.0 & 680.2 & 14.706 & \({}^{**}\) \\
666.9 & & 668.5 & 668.5 & 668.7 & 668.8 & 14.957 & \\
660.4 & 661.9 & 661.8 & 661.8 & 661.7 & 661.5 & 15.113 & \({}^{5}\)D\({}_{0}\rightarrow\)\({}^{7}\)F\({}_{3}\) \\
657.6 & 657.5 & 657.6 & 657.6 & 657.7 & 657.8 & 15.205 & \({}^{5}\)D\({}_{1}\rightarrow\)\({}^{7}\)F\({}_{5}\) \\
610.3 & 610.3 & 610.4 & 610.0 & 610.2 & 610.2 & 16.388 & \({}^{5}\)D\({}_{0}\rightarrow\)\({}^{7}\)F\({}_{2}\) \\
604.8 & 604.7 & 604.3 & 604.8 & 604.7 & 604.7 & 16.537 & \({}^{5}\)D\({}_{0}\rightarrow\)\({}^{7}\)F\({}_{1}\) \\  & 595.9 & 599.2 & & & & 16.781 & \({}^{5}\)D\({}_{2}\rightarrow\)\({}^{7}\)F\({}_{6}\) \\  & 544.4 & 544.0 & & & & 18.368 & \\  & 534.5 & 534.6 & & & & 18.705 & \({}^{5}\)D\({}_{1}\rightarrow\)\({}^{7}\)F\({}_{1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Photoluminescence spectra and transition assignment for the ZnSe:Eu\({}^{3+}\)/Yb\({}^{3+}\) semiconductor. \({}^{*}\), \({}^{**}\) cubic crystal field splitting. The rare earth ion Eu\({}^{+3}\) has a regular \({}^{7}\)F (\({}^{7}\)F\({}_{0}\)-\({}^{7}\)F\({}_{6}\)) multiplet as the ground level, followed by a \({}^{5}\)D multiplet \({}^{5}\)D\({}_{0}\)-\({}^{5}\)D\({}_{2}\). The ground level was split in seven levels \({}^{7}\)F\({}_{0}\)-\({}^{7}\)F\({}_{6}\) by the crystal field, as shown in Figure 10. The 5D was also split into four levels by the crystal field and only three levels were observed due to the wavelength of the excitation laser. These splitting levels have new splitting levels, as reported in Figure 10. [PERSON] [23] provides a complete list of levels for known Stark levels for the anhydrous chloride and ethylsulfate crystals. The values reported in this work were in good agreement with the values reported by [PERSON] using a different matrix, but the same rare earth ions. The values assigned with asterisks (Table 5) correspond to the excited ion level to crystal field splitting levels of the ground state. Figure 10 shows that the experimental values corresponded to the exited ion levels to the eight-splitted 3H ground state. Our results demonstrated that because of the Yb\({}^{3+}\) co-doping, the semiconductor was able to generate emission lines with higher intensity. The mechanism involved in the energy transfer between Yb\({}^{3+}\) and Eu\({}^{3+}\) ions is still unclear and needs further theoretical analysis and calculations.