## 3 Results and Discussion  
### Absorption Measurement Energy Band Gap Determination  
Theoretical analysis of the absorption coefficients \(\alpha\) for the ZnSe pure materials and the doped ones show that they obey the following relations [16]:  
\[\alpha=\frac{A}{h\upsilon}\sqrt{h\upsilon-E_{g}} \tag{1}\]  
where \(A\) is a parameter; \(E_{g}\) is the band gap of allowed transitions (eV); \(h\) is [PERSON]'s constant (6.63 \(\times\) 10\({}^{-34}\) Js); and \(\upsilon\) is the frequency of the light (s\({}^{-1}\)). The values of band gaps were obtained from the absorption spectra at room temperature using a UV-Vis spectrophotometer (Figure 2). In all samples, the absorption edge was very sharp and was located at about 465 nm, 496 nm, and 563 nm for ZnSe, ZnSe:Eu\({}^{3+}\)Yb\({}^{3+}\), and ZnSe:Eu\({}^{3+}\), respectively. The obtained values were in quite good agreement with the literature reports [17; 18]. In order to determine the values of the band gaps for the examined samples, we plotted the graph of \([\lambda h\upsilon]^{2}\) as a function of photon energy \(E=h\upsilon\). Extrapolation of the linear part of the graph gives the values of the band gap as the intercept with the abscissa axis, for which \([\lambda h\upsilon]^{2}=0\). The determined values of band gaps for all examined samples are presented in Table 1 and the procedure is shown for the ZnSe:Eu\({}^{3+}\) sample in Figure 3.  
Figure 2: Absorbance spectra of ZnSe (green line), ZnSe:Eu\({}^{3+}\)/Yb\({}^{3+}\) (blue line), and ZnSe:Eu\({}^{3+}\) (red line) at 300 K.  
From the results presented in Table 1, it is clear that the bandgap energy of the doped and co-doped semiconductors decreased compared with the host matrix ZnSe (2.67 eV). It is well known that impurities generate additional donor and acceptor levels in the host material, which can produce drastic changes in the optical behaviour and reduce the band-gap energy.  
The Varshni semi empirical relation [19] describes the energy band gap variation as a function of temperature for a doped semiconductor with different rare earths:  
\[E(T)=E_{0}(0)-\frac{\gamma T^{2}}{\beta+T} \tag{2}\]  
where \(E_{0}(0)\) is the energy band gap value at \(T\) = 0 K; \(\gamma\) is a parameter related to the electron-phonon interaction; \(T\) is the absolute temperature; and \(\beta\) is a parameter related to the Debye temperature. A routine to fit the experimental data to the Varshni semi empirical relation was developed using a genetic algorithm. All Varshni semi empirical relation parameters were obtained using the developed routine, and are listed in Table 2. The energy band gap dependence with the temperature for ZnSe:Eu\({}^{3+}\) and ZnSe:Eu\({}^{3+}\)/Yb\({}^{3+}\) is shown in Figure 4.  
\begin{table}
\begin{tabular}{c c c} \hline
**Temperature, K** & **Zn:Se:Eu\({}^{3+}\), eV** & **Zn:Se:Eu\({}^{3+}\)/Yb\({}^{3+}\), eV** \\ \hline
15 & 2.225 & 2.562 \\
25 & 2.216 & 2.554 \\
50 & 2.228 & 2.562 \\
75 & 2.250 & 2.551 \\
100 & 2.249 & 2.549 \\
150 & 2.234 & 2.548 \\
200 & 2.211 & 2.515 \\
300 & 2.201 & 2.492 \\ \hline \end{tabular}
\end{table}
Table 1: Values of the direct band gaps of samples at different temperatures by UV–Vis spectrophotometry and Kubelka–Munk theory.  
Figure 3: Energy gap calculation plot for ZnSe:Eu\({}^{3+}\) at 300 K. The circles represents the experimental values and the line is the extrapolation of the linear part.