Year: 2023
Author: Pengcong Mu, Weiying Zheng
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 5 : pp. 909–932
Abstract
In this paper, we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion model. The model consists of five nonlinear elliptic equations, and two of them describe quantum corrections for quasi-Fermi levels. We propose an interpolated-exponential finite element (IEFE) method for solving the two quantum-correction equations. The IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction equations. Moreover, we solve the two continuity equations with the edge-averaged finite element (EAFE) method to reduce numerical oscillations of quasi-Fermi levels. The Poisson equation of electrical potential is solved with standard Lagrangian finite elements. We prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional. A Newton method is proposed to solve the nonlinear discrete problem. Numerical experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2206-m2021-0353
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 5 : pp. 909–932
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Quantum drift-diffusion model Positivity-preserving finite element method Newton method FinFET device High bias voltage.
Author Details
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https://doi.org/10.1142/S0218202525500186 [Citations: 0]