Nonlinear diffusion, boundary layers and nonsmoothness: Analysis of challenges in drift–diffusion semiconductor simulations. (15th December 2019)

• Record Type: Journal Article
• Authors: Farrell, Patricio; Peschka, Dirk
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 12(2019)
• Page Start: 3731
• Page End: 3747
• Publication Date: 2019-12-15
• Subjects: Finite volume method -- Finite element method -- Nonlinear diffusion and diffusion enhancement -- Scharfetter–Gummel scheme -- Van Roosbroeck system for semiconductors -- Convergence order; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.06.007
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We study different discretizations of the van Roosbroeck system for charge transport in bulk semiconductor devices that can handle nonlinear diffusion. Three common challenges corrupting the precision of numerical solutions will be discussed: boundary layers, discontinuities in the doping profile, and corner singularities in L -shaped domains. We analyze and benchmark the error and the convergence order of finite difference, finite-element as well as advanced Scharfetter–Gummel type finite-volume discretization schemes. The most problematic of these challenges are boundary layers in the quasi-Fermi potentials near ohmic contacts, which can have a drastic impact on the convergence order. Using a novel formal asymptotic expansion, our theoretical analysis reveals that these boundary layers are logarithmic and significantly shorter than the Debye length.