Model of DC Tunneling Conductivity via Hydrogen‐Like Impurities in Heavily Doped Compensated Semiconductors

Herein, a theoretical model is proposed for the weakly temperature‐dependent electrical conductivity of compensated crystalline semiconductors with hydrogen‐like impurities near the insulator–metal concentration phase transition (Mott transition). The model uses a simple non‐stoichiometric cubic “impurity lattice” formed by the doping and compensating impurities in crystal matrix. A shift of the c‐band bottom (v‐band top) into the bandgap due to overlap of the excited states of neighboring impurities is considered. The distribution of electron (and hole) density of states in the band of ground (unexcited) states of impurities is assumed to be Gaussian. Tunneling transitions of electrons between nearest donors in the charge states ( 0 ) and ( + 1 ), and tunneling transitions of holes between acceptors in the charge states ( 0 ) and ( − 1 ) are considered. It is shown that, at low temperatures, transitions of electrons (holes) near the Fermi level in the impurity band lead to electrical conductivity that weakly depends on temperature (in the form of a characteristic plateau). The results of calculating electrical resistivity in the zero‐temperature limit for the plateau region agree with the known experimental data for moderately compensated n‐ and p‐type Ge, Dia, Si, ZnSe, GaAs, InSb, and InP crystals. A model is proposed for the plateau in temperature dependence of the stationary electrical resistivity (red line) in moderately compensated and heavily doped crystalline semiconductors near the concentration insulator–metal phase transition (Mott transition). The modeling results agree with experimental data on n‐ and p‐type Ge, Dia, Si, ZnSe, GaAs, InSb, and InP crystals, which were previously beyond quantitative description.