Self-sustained current oscillations in the kinetic theory of semiconductor superlattices

Journal Article · Sun Nov 01 00:00:00 EDT 2009 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2009.07.008· OSTI ID:21308119

Cebrian, E. ^[1]; Bonilla, L.L. ^[2]; Carpio, A. ^[3]

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1. Departamento de Matematicas y Computacion, Universidad de Burgos, 09001 Burgos (Spain), E-mail: [e-mail]
2. G. Millan Institute of Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganes (Spain), E-mail: [e-mail]
3. Departamento de Matematica Aplicada, Fac. Matematicas, Universidad Complutense de Madrid, 28040 Madrid (Spain), E-mail: [e-mail]

We present the first numerical solutions of a kinetic theory description of self-sustained current oscillations in n-doped semiconductor superlattices. The governing equation is a single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. Appropriate boundary conditions for the distribution function describe electron injection in the contact regions. These conditions seamlessly become Ohm's law at the injecting contact and the zero charge boundary condition at the receiving contact when integrated over the wave vector. The time-dependent model is numerically solved for the distribution function by using the deterministic Weighted Particle Method. Numerical simulations are used to ascertain the convergence of the method. The numerical results confirm the validity of the Chapman-Enskog perturbation method used previously to derive generalized drift-diffusion equations for high electric fields because they agree very well with numerical solutions thereof.

• OSTI ID: 21308119
• Journal Information: Journal of Computational Physics, Vol. 228, Issue 20; Other Information: DOI: 10.1016/j.jcp.2009.07.008; PII: S0021-9991(09)00388-X; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BERNSTEIN MODE
BOUNDARY CONDITIONS
COMPUTERIZED SIMULATION
CONVERGENCE
DIFFUSION EQUATIONS
DISTRIBUTION FUNCTIONS
DOPED MATERIALS
ELECTRIC FIELDS
ELECTRON BEAM INJECTION
KINETIC EQUATIONS
NUMERICAL SOLUTION
PERTURBATION THEORY
PLASMA WAVES
SEMICONDUCTOR MATERIALS
SUPERLATTICES
TIME DEPENDENCE
TRANSPORT THEORY