## 3 Results & Discussions
### Optical Studies of Cr Doped NiO Thin Film  
Figure 4 depicts the optical transmittance of Cr-NiO over a wavelength range of 300 to 1000 nm. Within the visible range, transmittance gradually decreases with increasing doping time of Cr. The optical transmittance of the undoped NiO is nearly 84.92% within the visible region but gradually decreases to \(\sim\)68% as the doping time increased from 0 s to 80 s. This finding may be a result of the increase in the Cr content in the NiO thin film. Light scattering is expected to be noticeable due to the presence of numerous grain boundaries and point defects that reflect incident light.  
Figure 4: Spectral transmittance of the Cr-doped NiO.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Doping Time (s)** & \begin{tabular}{c} **Carrier Concentration** \\ **(cm\({}^{-3}\))** \\ \end{tabular} & \begin{tabular}{c} **Carrier Mobility** \\ **(cm\({}^{2}\)/V\(\cdot\)s)** \\ \end{tabular} & \
\begin{tabular}{c} **Resistivity** \\ **(\(\Omega\cdot\)cm)** \\ \end{tabular} &
\begin{tabular}{c} **Conductivity** \\ **(Scm\({}^{-1}\))** \\ \end{tabular} \\ \hline Undoped & \(2.85\times 10^{14}\) & 10.20 & 2150 & \(4.65\times 10^{-4}\) \\
20 & \(6.47\times 10^{14}\) & 20.90 & 462 & \(2.16\times 10^{-3}\) \\
40 & \(2.35\times 10^{15}\) & 33.60 & 79.1 & \(1.26\times 10^{-2}\) \\
60 & \(5.52\times 10^{15}\) & 31.6 & 35.9 & \(2.79\times 10^{-2}\) \\
80 & \(2.17\times 10^{16}\) & 25.1 & 11.5 & \(8.73\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Hall parameters of the Cr-doped NiO thin films.  
Optical bandgap is tabulated from the transmission spectrum of the Cr doped NiO thin films by using the well-known Tauc plot relation as follows [26]:  
\[(\alpha\mathrm{h}\upsilon)^{2}=A(\mathrm{h}\upsilon-\mathrm{E}_{\mathrm{g}}) \tag{6}\]  
where A is the constant, \(\mathrm{E}_{\mathrm{g}}\) is the optical bandgap, \(\alpha\) is the absorption coefficient, \(\upsilon\) is the incident photon frequency, and h is [PERSON]'s constant.  
The direct bandgap of Cr-NiO reduces from 3.43 eV to 3.28 eV with increasing doping time from 0 s (undoped) to 80 s. This change in bandgap value may be attributed to the presence of Cr or the valance defect in the NiO thin film that helps form an intraband state within the bandgap and decreases the bandgap. Narrowing of the energy band-gap in the presence of dopants is ordinary and rather detrimental but the presence of Cr dopant led to enhance the electrical properties of NiO thin film.  
The exponential region between the absorption coefficient curve and the optical band edge is called Urbach tail. Because of their localized states, this tail appears in structurally disordered, poor crystalline, or amorphous materials. When plotting \(\mathrm{In}(\alpha)\) against the incident photon energy, the Urbach energy can be calculated by inverting the slope of the straight line, as shown in Figure 5a. The Urbach energy of the Cr-NiO films increases from 181 meV to 458 meV as the doping time increases from 0 to 80 s. At a doping time of 80 s, the highest Urbach energy is observed. This result indicates that as temperature rises, crystallinity deteriorates since the degree of defect increases. Figure 5b shows the variation in the bandgap and Urbach energy at different doping times. Urbach energy increases with doping time, but the bandgap trend is opposite to that of the Urbach energy.