A POSITIVITY-PRESERVING FINITE ELEMENT METHOD FOR QUANTUM DRIFT-DIFFUSION MODEL

作     者：Pengcong Mu Weiying Zheng Pengcong Mu;Weiying Zheng

作者机构：School of Mathematical ScienceUniversity of Chinese Academy of SciencesBeijing 100049China LSECNCMISInstitute of Computational Mathematics and Scientific ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2023年第41卷第5期

页      面：909-932页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by National Key R&D Program of China 2019YFA0709600 and 2019YFA0709602 Weiying Zheng was supported in part by National Key R&D Program of China 2019YFA0709600 and 2019YFA0709602 the National Science Fund for Distinguished Young Scholars 11725106,and the NSFC major grant 11831016 

主　　题：Quantum drift-diffusion model Positivity-preserving finite element method Newton method FinFET device High bias voltage 

摘      要：In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion *** model consists of five nonlinear elliptic equations,and two of them describe quantum corrections for quasi-Fermi *** propose an interpolated-exponential finite element(IEFE)method for solving the two quantum-correction *** IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction ***,we solve the two continuity equations with the edge-averaged finite element(EAFE)method to reduce numerical oscillations of quasi-Fermi *** Poisson equation of electrical potential is solved with standard Lagrangian finite *** 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 *** 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.