  The transport and gain properties of quantum cascade (QC) structures are
investigated using a nonequilibrium Green's function (NGF) theory which
includes quantum effects beyond a Boltzmann transport description. In the NGF
theory, we include interface roughness, impurity, and electron-phonon
scattering processes within a self-consistent Born approximation, and
electron-electron scattering in a mean-field approximation. With this theory we
obtain a description of the nonequilibrium stationary state of QC structures
under an applied bias, and hence we determine transport properties, such as the
current-voltage characteristic of these structures. We define two contributions
to the current, one contribution driven by the scattering-free part of the
Hamiltonian, and the other driven by the scattering Hamiltonian. We find that
the dominant part of the current in these structures, in contrast to simple
superlattice structures, is governed mainly by the scattering Hamiltonian. In
addition, by considering the linear response of the stationary state of the
structure to an applied optical field, we determine the linear susceptibility,
and hence the gain or absorption spectra of the structure. A comparison of the
spectra obtained from the more rigorous NGF theory with simpler models shows
that the spectra tend to be offset to higher values in the simpler theories.
