WignerPoisson and nonlocal driftdiffusion model equations for semiconductor superlattices
Abstract
A WignerPoisson 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 electronelectron 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 (BhatnagarGrossKrook) collision model that allows for energy dissipation while yielding charge continuity. In the hyperbolic limit, nonlocal driftdiffusion equations are derived systematically from the kinetic WignerPoissonBGK system by means of the ChapmanEnskog method. The nonlocality of the original quantum kinetic model equations implies that the derived driftdiffusion equations contain spatial averages over one or more superlattice periods. Numerical solutions of the latter equations show selfsustained oscillations of the current through a voltage biased superlattice, in agreement with known experiments.
 Publication:

arXiv eprints
 Pub Date:
 March 2005
 arXiv:
 arXiv:condmat/0503109
 Bibcode:
 2005cond.mat..3109B
 Keywords:

 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect
 EPrint:
 20 pages, 1 figure, published as M3AS 15, 1253 (2005) with corrections