A self-consistent solution of the transport equation is presented for semic
onductor superlattices within different approaches: (i) a full quantum tran
sport model based on nonequilibrium Green functions, (ii) the semiclassical
Boltzmann equation for electrons in a miniband, and (iii) Boltzmann equati
on for electrons in Wannier-Stark states. We find good quantitative agreeme
nt of the approximations (ii) and (iii) with (i) in their respective ranges
of validity. (C) 1999 Elsevier Science B.V. All rights reserved.