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

DOI10.1002/MMA.7604zbMATH Open1479.35859arXiv2101.11927OpenAlexW3179493672MaRDI QIDQ5015789

Michael Kniely, Klemens Fellner

Publication date: 9 December 2021

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/2101.11927

zbMATH Keywords

entropy methodreaction-diffusion equationsexponential convergence to equilibriumself-consistent potentialtrapped statesPDEs in connection with semiconductor devices

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Motion of charged particles (78A35) PDEs in connection with semiconductor devices (35Q81)

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