WIGNER-POISSON AND NONLOCAL DRIFT-DIFFUSION MODEL EQUATIONS FOR SEMICONDUCTOR SUPERLATTICES

@article{Bonilla2005WIGNERPOISSONAN,
  title={WIGNER-POISSON AND NONLOCAL DRIFT-DIFFUSION MODEL EQUATIONS FOR SEMICONDUCTOR SUPERLATTICES},
  author={L. Bonilla and R. Escobedo},
  journal={Mathematical Models and Methods in Applied Sciences},
  year={2005},
  volume={15},
  pages={1253-1272}
}
A Wigner–Poisson kinetic equation describing charge transport in doped semiconductor superlattices is proposed. Electrons are assumed 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… Expand

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References

SHOWING 1-10 OF 40 REFERENCES
Generalized drift-diffusion model for miniband superlattices
A drift-diffusion model of miniband transport in strongly coupled superlattices is derived from the single-miniband Boltzmann-Poisson transport equation with a Bhatnagar-Gross-Krook collision term.Expand
TOPICAL REVIEW: Theory of nonlinear charge transport, wave propagation, and self-oscillations in semiconductor superlattices
Nonlinear charge transport in semiconductor superlattices under strong electric fields parallel to the growth direction results in rich dynamical behaviour including the formation of electric fieldExpand
A Drift-Collision Balance for a Boltzmann--Poisson System in Bounded Domains
TLDR
A low density approximation to a Boltzmann--Poisson system for electrons in a semiconductor in regimes where strong forcing balances the collision terms is considered, yielding a velocity saturated mobility. Expand
The Quantum Hydrodynamic Model for Semiconductor Devices
  • C. Gardner
  • Physics, Computer Science
  • SIAM J. Appl. Math.
  • 1994
TLDR
The full three-dimensional quantum hydrodynamic (QHD) model is derived for the first time by a moment expansion of the Wigner–Boltzmann equation. Expand
Semiclassical limit for the Schrödinger‐Poisson equation in a crystal
We give a mathematically rigorous theory for the limit from a weakly nonlinear Schrodinger equation with both periodic and nonperiodic potential to the semiclassical version of the Vlasov equation.Expand
Semiconductor superlattices: a model system for nonlinear transport
Abstract Electric transport in semiconductor superlattices is dominated by pronounced negative differential conductivity. In this report, the standard transport theories for superlattices, i.e.Expand
Distribution function of a drifting electron gas for general energy-band structures.
  • Huang, Wu
  • Physics, Medicine
  • Physical review. B, Condensed matter
  • 1994
TLDR
It is demonstrated that this difficulty can be overcome by introducing a distribution function for a drifting electron gas by maximizing the entropy subject to a prescribed average drift velocity. Expand
Quantum Kinetics in Transport and Optics of Semiconductors
to Kinetics and Many-Body Theory.- Boltzmann Equation.- Numerical Solutions of the Boltzmann Equation.- Equilibrium Green Function Theory.- Nonequilibrium Many-Body Theory.- Contour-Ordered GreenExpand
Effect of elastic scattering on miniband transport in semiconductor superlattices.
  • Gerhardts
  • Physics, Medicine
  • Physical review. B, Condensed matter
  • 1993
TLDR
Within the quasiclassical Boltzmann-Bloch approach to nonlinear miniband transport in superlattices, elastic scattering is included in a relaxation-time approximation and leads in the regime of negative differential conductance to results that are qualitatively different from those of the quasi-one-dimensional models considered previously. Expand
Solitary waves in semiconductors with finite geometry and the Gunn effect
An asymptotic analysis of the Gunn effect (oscillations of the current through a semiconductor under constant voltage bias) is given. The electric field inside the one-dimensional semiconductor isExpand
...
1
2
3
4
...