# Electron Transport in \(n\)-Type InSe van der Waals Crystals with Co Impurities
## 3 Results and Discussion
### Electrical Properties along InSe Layers
Thus, by expressing the total mobility as \(\mu^{-1}=\mu_{\rm FS}{}^{-1}+\mu_{\rm BH}{}^{-1}\) and presuming that in the Brooks-Herring relationship for impurity scattering the effective density of screening charge carriers equals to the density of the free electrons, we have obtained the following values \(N_{\rm i}\) = 4.37 \(\times\) 10\({}^{15}\) cm\({}^{-3}\), \(N_{\rm d}\) = 2.76 \(\times\) 10\({}^{15}\) cm\({}^{-3}\) and \(N_{\rm a}\) = 1.61 \(\times\) 10\({}^{15}\) cm\({}^{-3}\) for the pristine sample at \(T\) = 80 K. Here \(N_{\rm i}\), \(N_{\rm d}\) and \(N_{\rm a}\) are the densities of ions, donors \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Sample No**} & \multirow{2}{*}{**Type of Sample**} & \multicolumn{2}{c}{\(\sigma_{\perp C}\)**Ohm\({}^{-1}\).cm\({}^{-1}\)**} & \multicolumn{2}{c}{\(n_{s}\)**cm\({}^{-3}\)**} & \multicolumn{2}{c}{\(\mu_{\perp C}\)**cm\({}^{2}\).V\({}^{-1}\).s\({}^{-1}\)**} \\ \cline{3-7}  & & **80 K** & **300 K** & **80 K** & **300 K** & **80 K** & **300 K** \\ \hline
1 & Undoped & 2.243 & 0.298 & \(1.15\times 10^{15}\) & 1.74 \(\times 10^{15}\) & 12,180 & 1070 \\
2 & Co-intercalated & \(3.17\times 10^{-2}\) & \(4.82\times 10^{-2}\) & \(5.09\times 10^{13}\) & \(5.16\times 10^{14}\) & 3890 & 584 \\
3 & Co-doped & \(1.38\times 10^{-3}\) & \(9.92\times 10^{-3}\) & \(1.09\times 10^{13}\) & \(1.77\times 10^{14}\) & 794 & 350 \\ \hline \end{tabular}
\end{table} 
Table 2: In-plane electrical properties of various \(n\)-type InSe samples. Figure 6: The in-plane mobility versus temperature for as-grown pristine (1), Co-intercalated (2), and Co-doped (3) \(n\)-type InSe crystals; calculated curves: 4–\(\mu_{\rm FS}(T)\), 5–\(\mu_{\rm SCR}(T)\) and 6–total mobility. and acceptors, respectively. This indicates that the as-grown pristine InSe crystal is not a heavily compensated semiconductor material. Doping and intercalation of \(n\)-type InSe with Co also affects the \(n(T)\) dependence leading to a decrease in the free electron density. This effect is more pronounced in the low-temperature range. At \(T\) = 80 K the value of \(n\) is two and nearly twenty orders of magnitude smaller for the doped and intercalated samples, respectively, than for the pristine one. At the highest temperatures, the values of all the Hall coefficients are quite close. For both samples with Co impurities the \(\sigma_{\perp\text{C}}\) variation over the whole temperature range exhibits semiconductor behavior with substantially lower values. Adding Co impurities also leads to a significant decrease in the in-plane electron Hall mobility (i.e., along the layers) and the emergence of non-monotonous high-temperature peculiarities in its variation. For the pristine samples, in the low-temperature range the mobility decreases with increasing temperature, i.e., there is no tendency to create a maximum. It means that even at liquid nitrogen temperature the transition to dominant scattering with charged impurities is not observed. The apparent \(\mu_{\perp\text{C}}(T)\) temperature dependence for the intercalated and doped samples at high temperatures indicates that it is important to take into account an additional scattering mechanism for electrons in this range. As an important mechanism for InSe, we can consider scattering with space-charge regions (SCR) [32,33]. When the SCR radius is less than the free path of electrons these ranges act as scattering centers. Assuming that free carriers cannot penetrate into them, the expression for mobility has the following form [34]:  
\[\mu_{SCR}=\frac{e}{\left(2m^{*}kT\right)^{1/2}N_{SCR}\cdot S} \tag{2}\]  
Here \(N_{SCR}\) defines the density of space-charge regions and \(S\) is the corresponding effective cross-section.