Charge Transport Systems with Fermi-Dirac Statistics for Memristors

被引：0
作者：
Herda, Maxime [1 ]
Juengel, Ansgar [2 ]
Portisch, Stefan [2 ]
机构：
[1] Univ Lille, Inria, CNRS, UMR 8524,Lab Paul Painleve, F-59000 Lille, France
[2] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria
来源：
JOURNAL OF NONLINEAR SCIENCE | 2025年 / 35卷 / 02期
基金：
欧洲研究理事会; 奥地利科学基金会;
关键词：
Drift-diffusion equations; Fermi-Dirac statistics; Blakemore statistics; Global existence; Bounded weak solutions; Memristors; Semiconductors; Neuromorphic computing; SEMICONDUCTOR EQUATIONS; GLOBAL EXISTENCE; DIFFUSION;
D O I：
10.1007/s00332-025-10140-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An instationary drift-diffusion system for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The electron and hole densities are governed by Fermi-Dirac statistics, while the oxygen vacancy density is governed by Blakemore statistics. The equations model the charge carrier dynamics in memristive devices used in semiconductor technology. The global existence of weak solutions is proved in up to three space dimensions. The proof is based on the free energy inequality, an iteration argument to improve the integrability of the densities, and estimations of the Fermi-Dirac integral. Under a physically realistic elliptic regularity condition, it is proved that the densities are bounded.
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页数：37
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