Quantum transport theory for high electric fields

A central difficulty in high-field transport theory is that the electric field prevents an efficient gradient-expansion formalism and distorts the spectral function from a simple Lorentzian shape. A rescaling of all relevant functions by the electron spectral density (in the presence of an electric field) leads to a simple integral equation for the distribution function. This equation, the integral equivalent of the Boltzmann equation and valid in an arbitrary electric field, is derived in the limit of weak impurity and/or weak electron-phonon scattering. It is shown that the effect of finite collision duration is to broaden the energy-conserving {δ} function in a scattering process. An explicit expression is obtained for the broadened scattering function for a constant field and parabolic bands.