Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model

K. Fellner, M. Kniely, Journal of Elliptic and Parabolic Equations (2020).


Journal Article | Epub ahead of print | English

Scopus indexed
Author
Fellner, Klemens; Kniely, MichaelIST Austria
Department
Abstract
In this paper, we establish convergence to equilibrium for a drift–diffusion–recombination system modelling the charge transport within certain semiconductor devices. More precisely, we consider a two-level system for electrons and holes which is augmented by an intermediate energy level for electrons in so-called trapped states. The recombination dynamics use the mass action principle by taking into account this additional trap level. The main part of the paper is concerned with the derivation of an entropy–entropy production inequality, which entails exponential convergence to the equilibrium via the so-called entropy method. The novelty of our approach lies in the fact that the entropy method is applied uniformly in a fast-reaction parameter which governs the lifetime of electrons on the trap level. Thus, the resulting decay estimate for the densities of electrons and holes extends to the corresponding quasi-steady-state approximation.
Publishing Year
Date Published
2020-05-07
Journal Title
Journal of Elliptic and Parabolic Equations
ISSN
eISSN
IST-REx-ID

Cite this

Fellner K, Kniely M. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. 2020. doi:10.1007/s41808-020-00068-8
Fellner, K., & Kniely, M. (2020). Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. https://doi.org/10.1007/s41808-020-00068-8
Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations, 2020. https://doi.org/10.1007/s41808-020-00068-8.
K. Fellner and M. Kniely, “Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model,” Journal of Elliptic and Parabolic Equations, 2020.
Fellner K, Kniely M. 2020. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations.
Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations, Springer Nature, 2020, doi:10.1007/s41808-020-00068-8.
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