Wigner-Poisson and nonlocal drift-diffusion model equations for semiconductor superlattices
Abstract
A Wigner-Poisson kinetic equation describing charge transport in doped semiconductor superlattices is proposed. Electrons are supposed to occupy the lowest miniband, exchange of lateral momentum is ignored and the electron-electron interaction is treated in the Hartree approximation. There are elastic collisions with impurities and inelastic collisions with phonons, imperfections, etc. The latter are described by a modified BGK (Bhatnagar-Gross-Krook) collision model that allows for energy dissipation while yielding charge continuity. In the hyperbolic limit, nonlocal drift-diffusion equations are derived systematically from the kinetic Wigner-Poisson-BGK system by means of the Chapman-Enskog method. The nonlocality of the original quantum kinetic model equations implies that the derived drift-diffusion equations contain spatial averages over one or more superlattice periods. Numerical solutions of the latter equations show self-sustained oscillations of the current through a voltage biased superlattice, in agreement with known experiments.
Cite
@article{arxiv.cond-mat/0503109,
title = {Wigner-Poisson and nonlocal drift-diffusion model equations for semiconductor superlattices},
author = {L. L. Bonilla and R. Escobedo},
journal= {arXiv preprint arXiv:cond-mat/0503109},
year = {2007}
}
Comments
20 pages, 1 figure, published as M3AS 15, 1253 (2005) with corrections