Correlated Variable Range Hopping in Doped GaAs, CdTe, Ge and Si

Abstract

A comparison is reported between the variable-range hopping resistivity (vrh) of chemically (CdTe : Cl, Si : (As), P, B) or neutron transmutation doped (NTD) (GaAs : Ge, Se; Ge : As, Ga) crystals which is: ϱ(T) = ϱ0 exp (T0/T)1/2 with the one-electron expression of Efros and Shklovskii: ϱ(T) = ϱ0 exp (TES/T)1/2. In the dilute limit of small doping concentrations N ≪ Nc (Nc is the critical doping concentration of the metal–insulator transition) and low or medium compensation K, the experimentally found values of T0 are much smaller than TES. This can be due to many-particle excitations which reduce the Coulomb gap width. In isotopically engineered (IE) NTD-p-Ge at very high K = 0.9, where a large scale potential relief exists, a good agreement was found: T0 ≅ TES = 2.8 e2/kBaB4πε0κ0 (aB is the localization length and ϰ the dielectric constant). The one-electron theory seems to be a good approximation in this case.