---
_id: '7866'
abstract:
- lang: eng
  text: 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.
acknowledgement: Open access funding provided by Austrian Science Fund (FWF). The
  second author has been supported by the International Research Training Group IGDK
  1754 “Optimization and Numerical Analysis for Partial Differential Equations with
  Nonsmooth Structures”, funded by the German Research Council (DFG) and the Austrian
  Science Fund (FWF) under grant number [W 1244-N18].
article_processing_charge: No
article_type: original
author:
- first_name: Klemens
  full_name: Fellner, Klemens
  last_name: Fellner
- first_name: Michael
  full_name: Kniely, Michael
  id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
  last_name: Kniely
  orcid: 0000-0001-5645-4333
citation:
  ama: 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.
    <i>Journal of Elliptic and Parabolic Equations</i>. 2020;6:529-598. doi:<a href="https://doi.org/10.1007/s41808-020-00068-8">10.1007/s41808-020-00068-8</a>
  apa: Fellner, K., &#38; 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. <i>Journal of Elliptic and Parabolic Equations</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s41808-020-00068-8">https://doi.org/10.1007/s41808-020-00068-8</a>
  chicago: 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.” <i>Journal of Elliptic and Parabolic Equations</i>.
    Springer Nature, 2020. <a href="https://doi.org/10.1007/s41808-020-00068-8">https://doi.org/10.1007/s41808-020-00068-8</a>.
  ieee: 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,” <i>Journal of Elliptic and Parabolic Equations</i>, vol. 6. Springer Nature,
    pp. 529–598, 2020.
  ista: 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. 6, 529–598.
  mla: 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.” <i>Journal of Elliptic and Parabolic Equations</i>,
    vol. 6, Springer Nature, 2020, pp. 529–98, doi:<a href="https://doi.org/10.1007/s41808-020-00068-8">10.1007/s41808-020-00068-8</a>.
  short: K. Fellner, M. Kniely, Journal of Elliptic and Parabolic Equations 6 (2020)
    529–598.
date_created: 2020-05-17T22:00:45Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2021-01-12T08:15:47Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s41808-020-00068-8
file:
- access_level: open_access
  checksum: 6bc6832caacddceee1471291e93dcf1d
  content_type: application/pdf
  creator: dernst
  date_created: 2020-11-25T08:59:59Z
  date_updated: 2020-11-25T08:59:59Z
  file_id: '8802'
  file_name: 2020_JourEllipticParabEquat_Fellner.pdf
  file_size: 8408694
  relation: main_file
  success: 1
file_date_updated: 2020-11-25T08:59:59Z
has_accepted_license: '1'
intvolume: '         6'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 529-598
project:
- _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1
  call_identifier: FWF
  name: FWF Open Access Fund
publication: Journal of Elliptic and Parabolic Equations
publication_identifier:
  eissn:
  - '22969039'
  issn:
  - '22969020'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Uniform convergence to equilibrium for a family of drift–diffusion models with
  trap-assisted recombination and the limiting Shockley–Read–Hall model
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 6
year: '2020'
...