Abstract
A unified theory of electron transport in a phonon bath using the Wigner formalism is presented. The resulting quantum kinetic equation not only lends itself to a phase space description of the electron transport, but also includes higher-order effects such as degeneracy, collisional broadening, and intracollisional field effect. The equation provides a rigorous theoretical foundation for Monte Carlo simulation of high-field electron transport in submicron and quasi-two-dimensional device structures.