# 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
Therefore, the addition of Co ions increases the concentration of states, which reduces the band gap. Although the Tauc method is based on the application of a linear approximation to the major absorption edge in the band-gap width, the effect of lower energy states on defect absorption may affect the accuracy of the band-gap determination [70,71]. This deviation from linearity in the low-energy field is often referred to as the Urbach tail. The oscillator model [72] is based on a certain dependence of the refractive index dispersion below the interband absorption limit: the dispersion energy. It is an indicator of the intensity of the interband optical transition. In the Urbach-Martienssen model, the Urbach energy \(E_{U}\) is the main parameter that determines the photon capture efficiency of a semiconductor layer. Point-defective binary semiconductor compounds have a special optical absorption edge profile. The absorption coefficient increases exponentially with the energy of the photons near the band gap [73]. The layer is formed by the plasma deposition from the target [74,75]. The obtained material contains various types of impurities that cause disturbances in the crystal structure. The crystal lattice limiting the pure \(E_{V}\) and \(E_{C}\) zones may disappear. When the perturbation becomes too high (for example, due to the appearance of impurities in the material), the tails may overlap. To define this disorder, we use the Urbach parameter \(E_{U}\). After examining the changes in the absorption coefficient, it is possible to estimate the existing disturbance in the layers. The exponential dependence of the photon energy \(h\
u\) on the absorption coefficient \(\alpha\) at the edge of the band for noncrystalline materials corresponds to the Urbach ratio Equation (12). The Urbach curve shows the change in the logarithm of the absorption coefficient as a function of the photon energy for the layer [76]. The value of Urbach energy (\(E_{U}\)) is usually calculated taking into account the inverse value of the slope of the linear portion in the lower photon energy region of these curves. The calculated Urbach energy  
Figure 6: Calculations of Urbach energies for the ZnO:Co layer. values for the annealed ZnO:Co layer are about 200 meV. The Urbach energy value is derived from the plot (In\(\alpha\)) as a function of \(h\
u\). Urbach's energy depends on soaking in. Increasing the annealing temperature of the ZnO:Co layer increases the \(E_{C}\) from 200 to 250 meV. This result shows the difference in the type of incorporation of growth defects in the ZnO matrix. Moreover, there is a strong correlation with the Urbach energy when the difference in the ion radii between the zinc and alloying elements and the difference in the degree of oxidation. This confirms the inclusion of these absorbing defects in the ZnO matrix, which introduces certain perturbations in the energy zones [77]. The result is also confirmed by the structural studies described above. The Urbach tail in the optical absorption of doped ZnO thin layers may occur because of the expansion of defect levels due to their spatial overlap in the conductivity band and nonuniform defect distribution.