# Structure and Optical Properties of Transparent Cobalt-Doped ZnO Thin Layers
## 3 Results and Discussion
### Optical Measurements
#### 3.2.4 Calculations of the Shape of the Urbach Absorption Edge  
As already mentioned, the values of \(E_{g}\) for the ZnO:Co layers were calculated. As can be seen in Figure 5b, for example, nanostructured ZnO:Co layers (annealed at 400 \({}^{\circ}\)C) have a shift in the position of the optical band gap from 3.37 to 3.15 eV, relating to pure ZnO [66; 67; 68]. This shift can be explained by the development of the resonance structure in the density of states, and the splitting of the band by introducing deep states into the region of the band gap. Thus, it can be used to extend the optoelectronic and photoelectric \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**No.** & \(\mathbf{1_{max}}\) & \(\mathbf{1_{min}}\) & \(\mathbf{1_{av}}\) & \(\mathbf{T_{max}}\) & \(\mathbf{T_{min}}\) & \(\mathbf{T_{max}-T_{min}}\) & \(\mathbf{T_{max}\times T_{min}}\) & **n** \\ \hline
1 & 1059.89 & 967.83 & 1013.86 & 52.57 & 48.39 & 4.17 & 2544.43 & 1.6231 \\
2 & 894.94 & 827.73 & 861.33 & 50.62 & 46.44 & 4.17 & 2351.49 & 1.6235 \\
3 & 781.11 & 728.80 & 754.95 & 48.39 & 44.41 & 3.98 & 2149.39 & 1.6237 \\
4 & 698.51 & 649.22 & 673.87 & 45.93 & 41.97 & 3.96 & 1928.15 & 1.6244 \\
5 & 625.55 & 593.07 & 608.67 & 42.58 & 39.72 & 2.86 & 1700.42 & 1.6232 \\
6 & 571.77 & 541.86 & 556.82 & 40.23 & 37.17 & 3.05 & 1495.88 & 1.6243 \\
7 & 523.14 & 498.19 & 510.67 & 36.77 & 34.12 & 2.65 & 1254.98 & 1.6246 \\ \hline \end{tabular}
\end{table} 
Table 2: Data for calculation of the refractive index from the transmission spectrum. Figure 5: (**a**) Optical transmission spectra (dashed line) and layer absorption coefficient (solid line) at different annealing temperatures; (**b**) The Tauc plot of layers at different annealing temperature. applications of these layers. The Urbach energy \(E_{U}\) is related to the width of the exponential edge of the absorption (tail) and can be calculated using the following equation:  
\[E_{U}=\alpha_{0}\cdot exp\left(\frac{h\
u}{E_{U}}\right)^{-1}\Rightarrow E_{U}= \left[\frac{d(\ln(\alpha))}{d(h\
u)}\right]^{-1} \tag{12}\]  
where \(\alpha_{0}\)--the parameter of the tail range that can be found in the dependencies:  
\[\alpha_{0}=\sqrt{\frac{2\sigma_{0}\left(\frac{4\pi}{c}\right)}{\Delta E}} \tag{13}\]  
where \(\sigma_{\sigma}\)--the electrical conductivity at a temperature of absolute zero; \(c\)--the speed of light; \(\Delta E\)--the tail width of the localized band gap states [69]. \(E_{U}\) values were obtained from the slopes of the linear part of the curve \(\ln\left(\alpha\right)\) with respect to \(h\
u\) (Figure 6). The E\({}_{\rm U}\) value, for the annealed layers, increases with annealing temperature from 200 meV (at a temperature of 300 \({}^{\circ}\)C) to 250 meV (at a temperature of 400 \({}^{\circ}\)C). This corresponds to the transition from the morphology of the hexagonal nanodisks to nanowires against the hexagonal morphology of the nanodisks. The increase in the value of the \(E_{U}\) can be explained by a violation of the structure of the material, which leads to the formation of a tail in the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ref. ** & **Concentration of Co,\%** & **Energy Band Gap, eV** & \begin{tabular}{c} **Annealed** \\ **Temperature, \({}^{\circ}\)C** \\ \end{tabular}  \\ \hline
[61] & 1 & 3.17 & as grown \\
[62] & 1 & 3.23 & as grown \\
[63] & 2 & 3.36 & 350 \\
[61] & 3 & 2.99 & as grown \\
[61] & 5 & 3.05 & as grown \\
[64] & 5  
valence and conductivity zones. These results are confirmed by XRD measurements, in which the crystallite planes of the ZnO:Co layers show the lowest preferred orientation along the \(\alpha\)-axis direction (100) compared to other ZnO layers. Experimental results concerning the change of the optical gap of the thin layer and disturbances (Urbach energy given for each sample) depending on the annealing are presented in Figure 6. The presence of high concentrations of states located in thin layers causes the reduction of the optical width of the band gap.