Crossover from Mott to Efros-Shklovskii variable-range-hopping conductivity inInxOyfilms

Crossover from Mott variable-range-hopping conductivity to the Coulomb-gap Efros-Shklovskii (ES) variable-range-hopping conductivity has been observed in amorphous indium oxide films. The hopping exponent x≃0.56 in the activated Coulomb-gap regime is greater than the x=0.50 value predicted by Efros and Shklovskii. The experimental value of x≃0.56 is in excellent agreement with the computational calculations of Mobius and Richter, who suggest that x=0.55. The experimental ratios for ${\mathit{T}}_{\mathrm{Mott}}$/${\mathit{T}}_{\mathrm{ES}}$≃54 are in close agreement with the prediction of Castner that ${\mathit{T}}_{\mathrm{Mott}}$/${\mathit{T}}_{\mathrm{ES}}$=81. Experimental values for the crossover temperatures, which separate the two hopping regimes, are consistent with predicted values. The Coulomb-gap energy ${\mathrm{\Delta }}_{\mathrm{CG}}$ is estimated to range from a few tenths of a meV for films close to the metal-insulator transition to several meV’s for films quite deep in the insulating regime.