Inelastic quantum transport in superlattices: Success and failure of the Boltzmann equation

Electrical transport in semiconductor superlattices is studied within a ful ly self-consistent quantum transport model based on nonequilibrium Green fu nctions, including phonon and impurity scattering. We compute both the drif t-velocity-held relation and the momentum distribution function covering th e whole held range from linear response to negative differential conductivi ty. The quantum results are compared with the respective results obtained f rom a Monte Carlo solution of the Boltzmann equation. Our analysis thus set s the limits of validity for the semiclassical theory in a nonlinear transp ort situation in the presence of inelastic scattering.