QUASINEUTRAL LIMIT OF THE DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS WITH GENERAL INITIAL DATA

The limit for vanishing Debye length (charge neutral limit) in a bipolar drift-diffusion model for semiconductors with general initial data allowing the presence of an initial layer is studied. The quasineutral limit (zero-Debye-length limit) is performed rigorously by using two different entropy functionals which yield appropriate uniform estimates. This investigation extends the results of Refs. 7 and 8 for charge neutral initial data where no initial layer occurs.

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Quasi-neutral limit and the initial layer problem of the drift-diffusion model

Acta Mathematica Scientia ◽

10.1007/s10473-020-0419-8 ◽

2020 ◽

Vol 40 (4) ◽

pp. 1152-1170

Author(s):

Shu Wang ◽

Limin Jiang

Keyword(s):

Diffusion Model ◽

Drift Diffusion Model ◽

Drift Diffusion ◽

Initial Layer ◽

Layer Problem

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QUASINEUTRAL LIMIT OF THE MULTI-DIMENSIONAL DRIFT-DIFFUSION-POISSON MODELS FOR SEMICONDUCTORS WITH PN-JUNCTIONS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s021820250600125x ◽

2006 ◽

Vol 16 (04) ◽

pp. 537-557 ◽

Cited By ~ 12

Author(s):

SHU WANG

Keyword(s):

Debye Length ◽

Functional Method ◽

Time Dependent ◽

Drift Diffusion ◽

Uniform Estimates ◽

Poisson Models ◽

Entropy Functional ◽

Quasineutral Limit ◽

Background Charge ◽

Doping Profiles

In this paper the vanishing Debye length limit (space charge neutral limit) of bipolar time-dependent drift-diffusion models for semiconductors with p-n-junctions (i.e. with a fixed bipolar background charge) is studied in the multi-dimensional case. For generally smooth sign-changing doping profiles with good boundary conditions, the quasineutral limit (zero-Debye-length limit) is justified rigorously in the Sobolev's norm uniformly in time. The proof is based on the elaborate energy method and the relative entropy functional method which yields the uniform estimates with respect to the scaled Debye length.

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The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model

European Journal of Applied Mathematics ◽

10.1017/s0956792501004533 ◽

2001 ◽

Vol 12 (4) ◽

pp. 497-512 ◽

Cited By ~ 46

Author(s):

INGENUIN GASSER ◽

C. DAVID LEVERMORE ◽

PETER A. MARKOWICH ◽

CHRISTIAN SCHMEISER

Keyword(s):

Singular Perturbation ◽

Diffusion Model ◽

Time Scale ◽

Initial Time ◽

Mathematical Tool ◽

Drift Diffusion Model ◽

Drift Diffusion ◽

Time Layer ◽

Quasineutral Limit ◽

Layer Problem

The classical time-dependent drift-diffusion model for semiconductors is considered for small scaled Debye length (which is a singular perturbation parameter). The corresponding limit is carried out on both the dielectric relaxation time scale and the diffusion time scale. The latter is a quasineutral limit, and the former can be interpreted as an initial time layer problem. The main mathematical tool for the analytically rigorous singular perturbation theory of this paper is the (physical) entropy of the system.

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The Small Debye Length Limit in the Drift-Diffusion Model for Semiconductors

Equadiff 99 ◽

10.1142/9789812792617_0248 ◽

2000 ◽

pp. 1322-1324

Author(s):

Ingenuin Gasser

Keyword(s):

Diffusion Model ◽

Debye Length ◽

Drift Diffusion Model ◽

Drift Diffusion

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QUASI-NEUTRAL LIMIT OF THE MULTIDIMENSIONAL DRIFT-DIFFUSION MODELS FOR SEMICONDUCTORS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s021820251000474x ◽

2010 ◽

Vol 20 (09) ◽

pp. 1649-1679 ◽

Cited By ~ 1

Author(s):

QIANGCHANG JU ◽

SHU WANG

Keyword(s):

Approximate Solution ◽

Debye Length ◽

Functional Method ◽

Diffusion Models ◽

Multidimensional Space ◽

Drift Diffusion ◽

Uniform Estimates ◽

General Initial Data ◽

Entropy Functional ◽

Doping Profiles

This paper is devoted to the rigorous justification of the quasi-neutral limit of bipolar transient drift-diffusion models for semiconductors with p–n junctions in the multidimensional space. The general initial data and smooth sign-changing doping profiles with good boundary conditions are considered. The limit is performed rigorously by using multiple scaling asymptotic analysis, in which one main point is the construction of a more accurate approximate solution involving the effect of initial layer. The uniform estimates with respect to the scaled Debye length are obtained through the elaborate energy method and the relative entropy functional method.

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