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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2005
- DOI:
- 10.48550/arXiv.cond-mat/0503109
- arXiv:
- arXiv:cond-mat/0503109
- Bibcode:
- 2005cond.mat..3109B
- Keywords:
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- Condensed Matter - Mesoscopic Systems and Quantum Hall Effect
- E-Print:
- 20 pages, 1 figure, published as M3AS 15, 1253 (2005) with corrections