c © 2002 Kluwer Academic Publishers. Manufactured in The Netherlands. A Space Dependent Wigner Equation Including Phonon Interaction

Abstract. We present a kinetic equation which is obtained after a hierarchy of approximations from the generalized Wigner function equation which accounts for interaction with phonons. The equation treats the coherent part of the transport imposed by the nanostructure potential at a rigorous quantum level. It is general enough to account for the quantum effects in the dissipative part of the transport due to the electron-phonon interaction. Numerical experiments demonstrate the effects of collisional broadening, retardation and the intra-collisional field effect. The obtained equation can be regarded as a generalization of the Levinson equation for space dependence. An analysis shows that the equation is nonlocal in the real space. This quantum effect is due to the correlation between the interaction process and the space component of the Wigner path