Hopping Conduction of Heavily Compensated n-InSb in Magnetic Field

Abstract

Shklovskii derived an expression of the magneto-resistivity of lightly doped semiconductors in the variable range hopping region. According to his result the resistivity takes the form of ρ∝exp {const. [λ 2 a H g (µ) k 0 T ] -1/3 } in strong magnetic field, where a H denotes the field-dependent Bohr radius, λ the magnetic length defined by \(\lambda{=}\sqrt{\hbar c/eH}\) and g (µ) is the density of states at the Fermi level µ. However, the experiments carried out by Gershenzon et al. revealed that ρ of highly compensated n -InSb behaves quite differently from the Shklovskii's prediction. Such discrepancy can be attributed to an assumption of constant density of states on which Shklovskii's result is based. This assumption leads to an erroneous conclusion because in the case of highly compensated samples the density of states is strongly energy-dependent. By extending the percolation theory to the strong magnetic field region and considering the energy-dependent density of states, a qualitative agreement w...