Metal-Insulator phase transition in thin films of vanadium dioxide doped with indium

The electrical conductivity of thin polycrystalline films V$_{(1-x)}$In$_x$O$_2$ has been studied in a wide temperature range covering the regions of existence of both the metallic and insulator phases. It is shown that with increasing indium concentration, the temperature of the metal-insulator phase transition decreases, and the width of the temperature region of phase coexistence monotonically increases. To explain the temperature dependence of the electrical conductivity of the insulator phase V$_{(1-x)}$In$_x$O$_2$, a model of hopping conductivity is applied, taking into account the effect of thermal vibrations of atoms on the resonance integral. Calculated the values of the parameter $\varepsilon$ depend on the degree of doping of VO$_2$.