The hopping variable range conduction in amorphous InAs thin films

This paper studies the influence of temperature on electrical resistivity in ${\alpha}-InAs$ thin films between 30 K-2K based on the analysis of Mott VRH model and ES VRH model. The effect of the interactions between electrons at lower temperature must be considered, therefore, ES VRH conduction will dominate mechanism, and the crossover from Mott to ES VRH conduction is observed about 7 K. Based on available experiment data and VRH conduction model, the parameters of VRH conduction are determined. And the calculated values of $T_C$ are consistent with the experimental results. In addition, $R_M/{\xi}$, ${\Delta}_M/kT$, $R_{ES}/{\xi}$ and ${\Delta}_{ES}/kT$ are satisfied with the validity of Mott and ES models. Furthermore, the temperature dependence of resistivity at low temperature obeys a universal scaling law, which well describes the overall temperature range of VRH conduction. However, the values of $T^{\prime}_M$ from the universal function are two order of magnitudes lower than $T_M$ deduced from fitting experiment.