Abstract
Resolvent super-operator techniques are used to establish a formal expression for the exact nonlinear response of nondegenerate semiconductor electrons to an arbitrary high d.c. electric field in the presence of arbitrary phonon and impurity scattering. The theory is based on the Liouville equation and is exact in the thermodynamic limit. Infinite-order perturbation expansions of the field-dependent resolvent lead to a simple kinetic equation for the one-electron density matrix. The steady-state Boltzmann high-field transport equation is derived exactly under the assumptions of weak scattering and point collisions, that is for zero collision broadening and neglecting the influence of the field within the collisions. Collision broadening corrections are derived for arbitrary scattering processes.