# Structure and Optical Properties of Transparent Cobalt-Doped ZnO Thin Layers
## 3 Results and Discussion
### Optical Measurements
#### 3.2.2 Refractive Index and Thickness
The interference fringes can be used to calculate the optical constants of the layer [49]. The Gaussian distribution can model maxima of the fringes. The width of the peaks increases towards the longer wavelengths (Figure 3b). The calculated dependence of the refractive index as a function of wavelength for the ZnO:Co layer annealed at 400 \({}^{\circ}\)C is shown in Figure 4a. It is clear that the refractive index \(n\) is close to 1.62 in the visible near infrared region and decreases with increasing wavelength. A similar trend is observed in the undoped ZnO layers [50]. This behavior can be explained by an increase in transmission and a decrease in the absorption coefficient with wavelength [51]. The behavior of the refractive index in the UV-VIS region is not uniform with wavelength because of the absorption of electrons that takes place (Figure 4b), where the lowest value of the refractive index is observed at 590 nm. Figure 3: (**a**) Modeling of interference fringes using the Swanepoel method. (**b**) Adjusting the interference fringes of optical transmission with Gauss. In the visible and near-infrared regions, the refractive index decreases with wavelength, indicating normal dispersion. The calculated refractive index at \(\lambda\)= 700 nm for the ZnO:Co layer annealed at 400 \({}^{\circ}\)C is 1.624 (Figure 4b). It is less than the basic value for the stoichiometric ZnO obtained by the sputter deposition method [52]. This can be explained by the low packing density of the layers obtained by the used PLD method. Whereas, [PERSON] et al. [53] showed that the refractive index for undoped ZnO layers for wavelengths above 800 nm was lower than 1.60. An increase in the refractive index with doping can be explained by changing the value of the polarization of the smaller atomic radius of Co [54]. This may be attributed to the small difference between the ionic diameters of the Co+2 (0.69 nm) and Zn+2 (0.74) [55; 56]. A similar effect is seen in Si-doped ZnO [57]. Co+ ions in the crystal structure of ZnO (presented in [58]) substitute the Zn+ ions [55]. The decrease in transmission results from the presence of the absorption band located at \(\lambda\approx 550\) nm, which is caused by energy-to-energy transitions. The absorption arm is believed to be due to an electron transition to the dopant levels, and the increase in the absorption of the doped ZnO layers may be a result of the high reflectance. Moreover, at different concentrations of Co ions, the absorption coefficient changes slightly. Changes in the refractive index \(n\) and the extinction coefficient \(k\) as a function of wavelengths in the range of 400-1000 nm are shown in Figure 4b. In the absorption area, the absorption coefficient of the layer and the extinction coefficient were calculated using the following equation:  
\[\alpha=2.303\frac{A}{d} \tag{9}\]  
\[k=\frac{\alpha\lambda}{4\pi} \tag{10}\]  
where \(A\)--optical absorption constant (absorbance \(ln(I/I_{0})\)); \(d\)--thickness of the layers [59]. The parameters used for the calculation of the refractive index parameter are given in Table 2, and \(\mathrm{T_{max}}-\mathrm{T_{min}}\) and \(\mathrm{T_{max}}\times\mathrm{T_{min}}\) are presented in Figure 4a.