Inelastic Quantum Transport in Superlattices: Success and Failure of the Boltzmann Equation

Electrical transport in semiconductor superlattices is studied within a fully self-consistent quantum transport model based on nonequilibrium Green functions, including phonon and impurity scattering. We compute both the drift-velocity-field relation and the momentum distribution function covering the whole field range from linear response to negative differential conductivity. The quantum results are compared with the respective results obtained from a Monte Carlo solution of the Boltzmann equation. Our analysis thus sets the limits of validity for the semiclassical theory in a nonlinear transport situation in the presence of inelastic scattering.