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

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 boun...

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Bibliographic Details
Published in:Journal of computational physics 2009-11, Vol.228 (20), p.7689-7705
Main Authors: Cebrián, E., Bonilla, L.L., Carpio, A.
Format: Article
Language:English
Subjects:
BERNSTEIN MODE
Boltzmann–BGK–Poisson kinetic equation
BOUNDARY CONDITIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computational techniques
COMPUTERIZED SIMULATION
Contact boundary conditions
CONVERGENCE
DIFFUSION EQUATIONS
DISTRIBUTION FUNCTIONS
DOPED MATERIALS
ELECTRIC FIELDS
ELECTRON BEAM INJECTION
Exact sciences and technology
KINETIC EQUATIONS
Mathematical methods in physics
NUMERICAL SOLUTION
Particle methods
PERTURBATION THEORY
Physics
PLASMA WAVES
Self-sustained current oscillations
SEMICONDUCTOR MATERIALS
Semiconductor superlattice
SUPERLATTICES
TIME DEPENDENCE
TRANSPORT THEORY
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Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2009.07.008