Quantum mechanical treatment of polar optical mode mobility and application to InSb

Abstract

Abstract A manifestly quantum mechanical calculation of the electrical conductivity for polar optical mode lattice scattering of carriers has been carried out by application of a Kubo formula. Frohlich's interaction Hamiltonian has been used in an S matrix approximation scheme. The resulting conductivity is then found to lie above the corresponding classical expression when the temperature is below the characteristic temperature, as expected. However, for temperatures above the characteristic temperature the conductivity lies below the classical expression and is contrary to expectation. When both calculations are compared to mobility data for heavy holes in InSb, the quantum calculation gives a better fit to the data. Experimentally it is found that the dominant lattice scattering for heavy holes is the polar mechanism for T ⩽ 300°K; above 300°K a second mechanism contributes to the scattering and is tentatively identified as non-polar optical mode scattering. The identification is complicated by the fact that the carrier-optical mode coupling constant and the optical mode characteristic temperature are both unknown.