# 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={Luis 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…

## Figures from this paper

## 15 Citations

Numerical Methods for a Quantum Drift–diffusion Equation in Semiconductor Physics

- Physics
- 2006

We present the numerical methods and simulations used to solve a charge transport problem in semiconductor physics. The problem is described by a Wigner–Poisson kinetic system we have recently…

Transport in semiconductor nanowire superlattices described by coupled quantum mechanical and kinetic models.

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2013

The kinetic model uses the dispersion relation obtained by the generalized Kronig-Penney method, and allows us to estimate radii of quantum wire superlattices that have the same miniband widths as in experiments, and to determine more accurately the time-dependent characteristics of superLattices, in particular their current density.

Two miniband model for self-sustained oscillations of the current through resonant-tunneling semiconductor superlattices

- Physics
- 2010

A two miniband model for electron transport in semiconductor superlattices that includes scattering and interminiband tunnelling is proposed. The model is formulated in terms of Wigner functions in a…

Nonequilibrium free energy, H theorem and self-sustained oscillations for Boltzmann–BGK descriptions of semiconductor superlattices

- Physics
- 2011

Semiconductor superlattices (SL) may be described by a Boltzmann–Poisson kinetic equation with a Bhatnagar–Gross–Krook (BGK) collision term which preserves charge, but not momentum or energy. Under…

Nonlinear Electron and Spin Transport in Semiconductor Superlattices

- PhysicsSIAM J. Appl. Math.
- 2008

Numerical solutions show stable self-sustained oscillations of the current and the spin polarization through a voltage biased lateral superlattice thereby providing an example of superlATTice spin oscillator.

Theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices

- Physics
- 2011

In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that nonlinearities may compensate it and Bloch oscillations persist even in…

Charge transport in a superlattice: a numerical study using moment methods

- Physics
- 2012

A semiclassical model of charge transport in a semiconductor superlattice is solved, using moments in the wavenumber direction and finite elements in the spatial direction (first order). The…

Rigorous drift-diffusion asymptotics of a high-field quantum transport equation

- Mathematics
- 2006

The asymptotic analysis of a linear high-field Wigner-BGK equation is developped by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number…

An Optimal Transport Approach to Nonlinear Evolution Equations

- Mathematics
- 2012

An Optimal Transport Approach to Nonlinear Evolution Equations Ehsan Kamalinejad Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2012 Gradient flows of energy…

## References

SHOWING 1-10 OF 40 REFERENCES

Theory of nonlinear charge transport, wave propagation, and self-oscillations in semiconductor superlattices

- Physics
- 2002

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 field…

Generalized drift-diffusion model for miniband superlattices

- Physics
- 2003

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.…

TOPICAL REVIEW: Theory of nonlinear charge transport, wave propagation, and self-oscillations in semiconductor superlattices

- Physics
- 2001

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 field…

A Drift-Collision Balance for a Boltzmann--Poisson System in Bounded Domains

- PhysicsSIAM J. Appl. Math.
- 2001

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.

Distribution function of a drifting electron gas for general energy-band structures.

- PhysicsPhysical review. B, Condensed matter
- 1994

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.

Quantum Kinetics in Transport and Optics of Semiconductors

- Physics
- 2004

to Kinetics and Many-Body Theory.- Boltzmann Equation.- Numerical Solutions of the Boltzmann Equation.- Equilibrium Green Function Theory.- Nonequilibrium Many-Body Theory.- Contour-Ordered Green…

Effect of elastic scattering on miniband transport in semiconductor superlattices.

- PhysicsPhysical review. B, Condensed matter
- 1993

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.

Solitary waves in semiconductors with finite geometry and the Gunn effect

- Physics
- 1991

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 is…

High-field limit of the Vlasov-Poisson-Fokker-Planck system: A comparison of different perturbation methods

- Mathematics, Physics
- 2000

A reduced drift-diffusion (Smoluchowski–Poisson) equation is found for the electric charge in the high-field limit of the Vlasov–Poisson–Fokker–Planck system, both in one and three dimensions. The…