  A two miniband model for electron transport in semiconductor superlattices
that includes scattering and interminiband tunnelling is proposed. The model is
formulated in terms of Wigner functions in a basis spanned by Pauli matrices,
includes electron-electron scattering in the Hartree approximation and modified
Bhatnagar-Gross-Krook collision tems. For strong applied fields, balance
equations for the electric field and the miniband populations are derived using
a Chapman-Enskog perturbation technique. These equations are then solved
numerically for a dc voltage biased superlattice. Results include
self-sustained current oscillations due to repeated nucleation of electric
field pulses at the injecting contact region and their motion towards the
collector. Numerical reconstruction of the Wigner functions shows that the
miniband with higher energy is empty during most of the oscillation period: it
becomes populated only when the local electric field (corresponding to the
passing pulse) is sufficiently large to trigger resonant tunneling.
