Hybrid coupling of a one-dimensional energy-transport Schrodinger system

被引：0

作者：

Jourdana, Clement ^{[1
]}

Pietra, Paola ^{[2
]}

Vauchelet, Nicolas ^{[3
,4
]}

机构：

[1] Univ Grenoble Alpes, Lab Jean Kuntzmann, F-38000 Grenoble, France

[2] CNR, Ist Matemat Applicata & Tecnol Informat E Magenes, Via Ferrata 1, I-27100 Pavia, Italy

[3] UPMC Univ Paris 06, Lab Jacques Louis Lions, CNRS, UMR 7598, F-75005 Paris, France

[4] INRIA Paris Rocquencourt, EPI MAMBA, F-75005 Paris, France

来源：

MONATSHEFTE FUR MATHEMATIK | 2017年 / 184卷 / 04期

关键词：

Schrodinger equation; Boltzmann equation; Energy-transport system; Spherical harmonic expansion system; Semiconductors; Interface conditions; Mixed finite elements; DRIFT-DIFFUSION MODEL; PARTIALLY QUANTIZED PARTICLES; MAXIMUM-ENTROPY PRINCIPLE; MACROSCOPIC MODELS; SUBBAND MODEL; SEMICONDUCTORS; APPROXIMATION; SIMULATIONS; EQUATIONS; COMPUTATION;

D O I：

10.1007/s00605-016-1008-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider one dimensional coupled classical-quantum models for quantum semiconductor device simulations. The coupling occurs in the space variable: the domain of the device is divided into a region with strong quantum effects (quantum zone) and a region where quantum effects are negligible (classical zone). In the classical zone, transport in diffusive approximation is modeled through diffusive limits of the Boltzmann transport equation. It can lead to an energy-transport model, obtained using a Spherical Harmonic Expansion model as intermediate step. The quantum transport is described by the Schrodinger equation. The aim of this work is to focus on the derivation of boundary conditions at the interface between the classical and quantum regions. Numerical simulations are provided for a resonant tunneling diode with the energy-transport model.

引用

页码：563 / 596

页数：34

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