A Note on the Energy-Transport Limit of the Semiconductor Boltzmann Equation

Degond, Pierre; Levermore, C. David; Schmeiser, Christian

doi:10.1007/978-1-4613-0017-5_8

Cited by 12 publications

(13 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…according to the dominant scattering mechanisms, Q. We refer to [1,2,6,7,8,13,19,12,24] for the rigorous derivation of macroscopic models from kinetic equations. We consider here the collision operator for a Boltzmann statistics in the linear BGK approximation given by:…”

Section: Introductionmentioning

confidence: 99%

Diffusion models for spin transport derived from the spinor Boltzmann equation

Hajj

2014

Communications in Mathematical Sciences

View full text Add to dashboard Cite

Abstract. The aim of this paper is to derive and analyse diffusion models for semiconductor spintronics. We begin by presenting and studying the so called "spinor" Boltzmann equation. Starting then from a rescaled version of linear Boltzmann equation with different spin-flip and non spin-flip collision operators, different continuum (drift-diffusion) models are derived. By comparing the strength of the spin-orbit scattering with the scaled mean free paths, we explain how some models existing in the literature (like the two-component models) can be obtained from the spinor Boltzmann equation. A new spin-vector drift-diffusion model keeping spin relaxation and spin precession effects due to the spin-orbit coupling in semiconductor structures is derived and some of its mathematical properties are checked.

show abstract

Section: Introductionmentioning

confidence: 99%

Diffusion models for spin transport derived from the spinor Boltzmann equation

Hajj

2014

Communications in Mathematical Sciences

View full text Add to dashboard Cite

show abstract

“…However, it is much delicate to estimate the electron-electron collision frequency as it depends on the distribution function itself. Following the discussion in [10], we assign this term O(α). That is, the electron-electron interactions are not as strong as elastic collisions, yet their density is not small enough to be safely neglected.…”

Section: Elastic Approximation Of the Electron-phonon Interactionsmentioning

confidence: 99%

An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit

Wang

2015

Journal of Computational Physics

View full text Add to dashboard Cite

We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and energy as mean free path goes to zero. As opposed to the classical drift-diffusion limit where the stiff collisions are all in one scale, new difficulties arise in the two-scale stiff collision terms because the simple BGK penalization [15] fails to drive the solution to the correct limit. We propose to set up a spatially dependent threshold on the penalization of the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level. Formal asymptotic analysis and numerical results confirm the efficiency and accuracy of our scheme.

show abstract

“…An efficient AP scheme in the high field regime was developed in [25]. The authors in [16] further study the semiconductor Boltzmann equation with a two-scale stiff collision operators, by taking into account different effects including the interactions between electrons and the lattice defects caused by ionized impurities [3]; they design and demonstrate the efficiency and accuracy of an asymptoticpreserving scheme that leads to an energy-transport system as mean free path goes to zero at a discretized level.…”

Section: Introductionmentioning

confidence: 99%

A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalings

Liu

2019

Journal of Computational Physics

View full text Add to dashboard Cite

In this paper, we study the bipolar Boltzmann-Poisson model, both for the deterministic system and the system with uncertainties, with asymptotic behavior leading to the drift diffusion-Poisson system as the Knudsen number goes to zero. The random inputs can arise from collision kernels, doping profile and initial data. We adopt a generalized polynomial chaos approach based stochastic Galerkin (gPC-SG) method. Sensitivity analysis is conducted using hypocoercivity theory for both the analytical solution and the gPC solution for a simpler model that ignores the electric field, and it gives their convergence toward the global Maxwellian exponentially in time. A formal proof of the stochastic asymptotic-preserving (s-AP) property and a uniform spectral convergence with error exponentially decaying in time in the random space of the scheme is given. Numerical experiments are conducted to validate the accuracy, efficiency and asymptotic properties of the proposed method.

show abstract

A Note on the Energy-Transport Limit of the Semiconductor Boltzmann Equation

Cited by 12 publications

References 28 publications

Diffusion models for spin transport derived from the spinor Boltzmann equation

Diffusion models for spin transport derived from the spinor Boltzmann equation

An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit

A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalings

Contact Info

Product

Resources

About