Activation energy of DC hopping conductivity of lightly doped weakly compensated crystalline semiconductors

Abstract

A model is proposed for calculating the thermal activation energy ε3 of direct current hopping conductivity via nearest neighbors in lightly doped and weakly compensated crystalline semiconductors with hydrogen-like impurities. The temperature region is considered in which hops of single holes occur only between acceptors randomly distributed over the crystal (or hops of single electrons only between donors). The model is based on the idea of the Coulomb blockade of charge carriers by the field of compensating impurities (trap impurities). The hopping length of a hole between acceptors (or an electron between donors) is assumed to be equal to the critical (percolation) radius of the spherical region per a majority (doping) impurity atom. At a critical radius, an infinite cluster connecting ohmic contacts is formed in the crystal, along which charge carriers move in a hopping manner via majority impurities. The value of ε3 is defined as average work on overcoming the electrostatic Coulomb blockade by a charge carrier and its hopping via the electrically conducting cluster to “infinity”. The results of calculating ε3 by the proposed model of the Coulomb blockade for the most well-studied bulk germanium and silicon p- and n-type crystals are consistent with known experimental data.