Nonlinear conductivity in polar semiconductors: Alternative derivation of the Thornber-Feynman theory

Abstract

The nonlinear response of continuum polarons to a static electric field is investigated. The Thornber-Feynman expression for the nonlinear conductivity (in the case of the Feynman model) is rederived in the framework of the Heisenberg equations of motion. Following the prescription of Thornber, the electron velocity distribution function corresponding to the Thornber-Feynman theory is calculated explicitly for every value of the electron-phonon coupling constant, temperature, and electric field strength. It turns out to be a drifted Maxwellian with an effective electron temperature which is only a function of the lattice temperature and the effective electron-phonon interaction (which is given by the parameters of Feynman's polaron model). For small electron-phonon coupling this conclusion is discussed in the context of solutions of the Boltzmann equation for the distribution function.