Calculation of the activation energy of electrical ε2-conductivity of weakly compensated semiconductors

Abstract

A model of tunneling (jumping) migration of charge carriers near their mobility edge in the upper band of neutral states of majority hydrogen-like impurities is pro-posed to calculate the energy of thermal activation of electrical ε2-conductivity of weakly compensated semiconductors. The difference from the known Hubbard model consists in the scheme of interimpurity transitions of charge carriers and in the method of calculating the position of their tunnel mobility edge. The drift mobility edge of free charge carriers corresponds to the thermal ionization energy of majority impurities ε1 > ε2, which is located near the c-band bottom or the v-band top in n- and p-type semiconductors, respectively, and is due to the overlap of excited states of electrically neutral majority impurities. The position of the tunnel mobility edge for ε2-conductivity is determined by taking into account the Coulomb interaction of the majority impurities in the charge states (−1) and (+1). It is assumed that doping and compensating impurities form a single simple nonstoichiometric cubic lattice in a crystal matrix. The calculations of the activation energy ε2 on the insulator side of the insulator–metal concentration phase transition for weakly compensated p-Si:B, n-Si:P, and n-Ge:Sb crystals quantitatively agree with known experimental data.