A Wigner-function approach to interband transitions based on the multiband-envelope-function model

The Wigner-function approach is used to describe an interband transition of electrons between the conduction and the valence band in a semiconductor under the action of an electric field in the uniform field approximation. The quantum dynamics is governed by the k·p Hamiltonian; an approximate closed-form solution is obtained by an iterative procedure that exploits the different time scales on which the intraband and interband dynamical variables evolve. The results of this approximation are compared with a numerical solution, showing an excellent agreement, which paves the way for its use in more realistic situations where the numerical solution is much harder to obtain.