Uniform convergence to equilibrium for a family of drift–diffusion models with trap‐assisted recombination and self‐consistent potential

Klemens Fellner; Michael Kniely

doi:10.1002/mma.7604

journal article Open Access Jul 06, 2021

Uniform convergence to equilibrium for a family of drift–diffusion models with trap‐assisted recombination and self‐consistent potential

Klemens Fellner

Michael Kniely

Mathematical Methods in the Applied Sciences Vol. 44 No. 17 pp. 13040-13059 · Wiley

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Abstract

We investigate a recombination–drift–diffusion model coupled to Poisson's equation modelling the transport of charge within certain types of semiconductors. In more detail, we study a two‐level system for electrons and holes endowed with an intermediate energy level for electrons occupying trapped states. As our main result, we establish an explicit functional inequality between relative entropy and entropy production, which leads to exponential convergence to equilibrium. We stress that our approach is applied uniformly in the lifetime of electrons on the trap level assuming that this lifetime is sufficiently small.

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References

23

[1]

Statistics of the Recombinations of Holes and Electrons

W. Shockley, W. T. Read

Physical Review 10.1103/physrev.87.835

[2]

10.1103/physrev.87.387

[3]

10.1007/978-3-7091-6961-2

[4]

On the Shockley–Read–Hall Model: Generation-Recombination in Semiconductors

Thierry Goudon, Vera Miljanović, Christian Schmeiser

SIAM Journal on Applied Mathematics 10.1137/060650751

[5]

On the entropy method and exponential convergence to equilibrium for a recombination–drift–diffusion system with self-consistent potential

Klemens Fellner, Michael Kniely

Applied Mathematics Letters 10.1016/j.aml.2017.12.017

[6]

10.1007/s41808-020-00068-8

[7]

10.1080/00411450008205893

[8]

10.1137/16m1073935

[9]

10.1016/j.na.2017.02.007

[10]

10.1007/s00033-018-0948-3

[11]

10.1007/s10884-014-9394-x

[12]

10.1016/j.jmaa.2005.07.003

[13]

10.4171/rmi/541

[14]

Desvillettes L "Exponential convergence to equilibrium for a nonlinear reaction–diffusion system arising in reversible chemistry" Syst Modell Optim IFIP AICT (2014)

[15]

10.1080/00036819608840428

[16]

10.1002/zamm.19970771105

[17]

10.1007/978-3-0348-8428-0

[18]

10.1098/rspa.2008.0214

[19]

Mikhaı̆lov VP (1978)

[20]

10.1090/gsm/112

[21]

10.1002/zamm.19960760502

[22]

Willett D "A linear generalization of Gronwall's inequality" Proc Amer Math Soc (1965)

[23]

Beesack PR (1975)

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Citations

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References

Details

Published: Jul 06, 2021
Vol/Issue: 44(17)
Pages: 13040-13059
License: View

Authors

K

Klemens Fellner

Institute of Mathematics and Scientific Computing University of Graz Graz Austria

M

Michael Kniely

Faculty of Mathematics TU Dortmund University Dortmund Germany

Cite This Article

Klemens Fellner, Michael Kniely (2021). Uniform convergence to equilibrium for a family of drift–diffusion models with trap‐assisted recombination and self‐consistent potential. Mathematical Methods in the Applied Sciences, 44(17), 13040-13059. https://doi.org/10.1002/mma.7604

Uniform convergence to equilibrium for a family of drift–diffusion models with trap‐assisted recombination and self‐consistent potential

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