## 3 Results and Discussions
### Optical Properties
#### 3.3.2 Ellipsometric Measurements  
For determination of the refractive index (\(n\)), extinction coefficient (\(k\)) and film thickness (\(d\)), we used ellipsometric measurements and consequent modelling using DeltaPsi2 commercial software, version 2.6 (UVISEL 2, Horiba Jobin Yvon, Longjumeau, France). The measured parameters were the ellipsometric angles \(\Psi\) and \(\Delta\), defined by Equations (1) and (2):  
\[\tan(\Psi)=\frac{\left|r_{\mathrm{p}}\right|}{\left|r_{\mathrm{s}}\right|},\;0^ {\mathrm{o}}\leq\Psi\leq 90^{\mathrm{o}} \tag{1}\]  
\[\Delta=\delta_{\mathrm{p}}-\delta_{\mathrm{s}},\;0^{\mathrm{o}}\leq\Delta \leq 360^{\mathrm{o}} \tag{2}\]  
where \(r_{\mathrm{p}}\), \(r_{\mathrm{s}}\) and \(\delta_{\mathrm{p}}\), \(\delta_{\mathrm{s}}\) are the amplitudes and phases of reflection coefficients for p- and s-polarized light, respectively, and are functions of the unknown parameters \(n\), \(k\) and \(d\). The last were determined by nonlinear minimization of the difference between the measured and calculated ellipsometric angles \(\Psi\) and \(\Delta\). The Forouhi and Bloomer dispersion equations [38] were applied to express \(n\) and \(k\) as a function of wavelength, and a three-layered model was implemented for matching the real film. The model comprises a thin (3 nm) native oxide on the silicon substrate, film with unknown parameters (\(n\), \(k\) and \(d\)) and a top layer with unknown thickness \(d_{\mathrm{top}}\) consisting of a 50% volume fraction of voids and a 50% volume fraction of a medium with the unknown parameters \(n\) and \(k\). The idea behind the top effective layer is to model the surface roughness of the studied films.  
The calculated dispersion curves of the refractive index and extinction coefficient are shown in Figure 6a,b, respectively. The refractive index of all studied films obeys normal dispersion in the visible spectra range, i.e., \(n\) decreases with wavelength. This is expected because all films are transparent in this spectral range. It can be seen from Figure 6b that the extinction coefficient is zero for wavelengths longer than 450 nm. The refractive index increases with doping: \(n\) for pure ZnO at a wavelength of 600 nm is 1.86 (Table 2), increasing to 2.00 and 1.94 for CZO and AZO films, respectively. For Co/Al-co-doped films, \(n\) is 1.97, between the values for CZO and AZO films, as would be expected.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Sample** & **rms Roughness (nm)** & \(n\) **@ 600 nm** & \(E_{\mathrm{g}}\) (eV)** & \(E_{\mathrm{U}}\) (meV)** \\ \hline ZnO & 26 & 1.86 & 3.29 & 119 \\ AZO & 34 & 1.94 & 3.35 & 110 \\ CZO & 31 & 2.00 & 3.35 & 236 \\ CAZO & 35 & 1.97 & 3.33 & 138 \\ \hline \end{tabular}
\end{table}
Table 2: Surface roughness in nm, refractive index \(n\) at wavelength of 600 nm, direct optical band gap \(E_{\mathrm{g}}\) in eV and Urbach energy \(E_{\mathrm{U}}\) in meV.  
Figure 6: Refractive index (**a**) and extinction coefficient (**b**) of pure ZnO (black line) and ZnO doped with Al (AZO) (red line), Co (CZO) (blue line) and Co/Al (CAZO) (magenta line) measured ellipsometrically.  
All films have high absorption in the spectral range shorter than 350 nm and strong abnormal dispersion (\(n\) increases with wavelength), typical for spectral ranges with high absorption. The fundamental absorption edges of the films are in the spectral range 330-430 nm, and a distinct blue-shift for AZO films compared to pure ZnO is observed. Therefore, an increase in optical band gap for AZO films can be expected. The shift of the absorption edge for CZO and CAZO films is not so clearly distinguished, but there is a very clear change in the slope of the fundamental edge, which is typical for materials with defects and levels in the forbidden band.