  In this work we include electron-electron interaction beyond Hartree-Fock
level in our non-equilibrium Green's function approach by a crude form of GW
through the Single Plasmon Pole Approximation. This is achieved by treating all
conduction band electrons as a single effective band screening the Coulomb
potential. We describe the corresponding self-energies in this scheme for a
multi-subband system. In order to apply the formalism to heterostructures we
discuss the screening and plasmon dispersion in both 2D and 3D systems. Results
are shown for a four well quantum cascade laser with different doping
concentration where comparisons to experimental findings can be made.
