# Electron Transport in \(n\)-Type InSe van der Waals Crystals with Co Impurities
## 3 Results and Discussion
### Electrical Conductivity Anisotropy  
Physical properties of van der Waals materials are highly anisotropic due to the nature of their layered crystal structure [35; 36; 37]. Thus, in this work we investigated the variation of electrical conductivity in different crystallographic directions. For all the samples under investigation the transversal electrical conductivity is significantly lower than the longitudinal one and its variation with temperature exhibit semiconductor behavior (Figure 7, Table 3). In case of the Co-intercalated crystals, the electrical conductivity is lower than for the pristine one and is the lowest for the doped samples. The electrical conductivity anisotropy (ratio of longitudinal and transversal components) is the highest for the pristine \(n\)-type InSe and equals \(\sim\) 3.3 \(\times\) 10\({}^{3}\) at \(T\) = 80 K (Figure 8). Meanwhile, it decreases significantly with increasing temperature, namely by a factor of-270 in the temperature range from \(T\) = 80 K to 300 K. The intercalation of cobalt decreases both the anisotropy ratio and the range of its variation in this temperature range. The lowest \(\sigma_{\perp\text{C}}\)/\(\sigma_{\parallel\text{C}}\) values are found for the doped samples, namely, at \(T\) = 80 K the conductivity anisotropy decreased by more than a factor of 150 with respect to the pristine sample. It should be noted that to a large degree such low anisotropy values are due to the decrease in the longitudinal component but not to the increase in the transversal one. Figure 7: The out-of-plane electrical conductivity (i.e., across the van der Waals layers) versus temperature for as-grown pristine (1), Co-intercalated (2), and Co-doped (3) crystals of \(n\)-type InSe. It was shown in [38] that the energy bands, which form the fundamental absorption edge of indium selenide are created with strong contribution of \(p_{z}\)-orbitals of selenium and have a 3D character, and even the component of longitudinal effective mass is higher than the transversal one (\(m_{\perp C}^{*}=0.13m_{0}\), \(m_{\parallel C}^{*}=0.08m_{0}\)). As a result, the apparent high anisotropy values should be related to defects. In layered materials, weak van der Waals bonding between neighboring layers promotes the formation of planar stacking faults between various structural polytypes. Such disordered ranges are places for aggregation of impurities and a reason for the appearance of energy barriers \(\Delta E_{b}\) between the layers which can explain activation dependence of the transversal conductivity:  
\[\sigma_{\parallel C}=en\mu_{\parallel C}exp(-\Delta E_{b}/kT), \tag{5}\]  
and high values of the conductivity ratio  
\[\sigma_{\perp C}/\sigma_{\parallel C}=Aexp(-\Delta E_{b}/kT) \tag{6}\]  
The determined energy barrier value for the pristine crystal is the highest and equals \(\sim\) 42 meV. For the samples intercalated and doped with Co the energy barrier decreases more than twice. The values of the preexponential factor \(A\) are evidently higher than the effective mass ratio \(\left(m_{\parallel C}^{*}/m_{\perp C}^{*}=0.615\right)\). It can be related to the high density of 2D electrons in all of the samples, which in contrast to three-dimensional (3D) carriers do not contribute to the charge carrier transfer across the InSe layers [39]. In this model, apart  
Figure 8: The electrical conductivity anisotropy versus temperature for as-grown pristine (1), Co-intercalated (2) and Co-doped (3) crystals of \(n\)-type InSe.