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Nonlinear diffusion, boundary layers and nonsmoothness: Analysis of challenges in drift–diffusion semiconductor simulations
Publikationstyp
Journal Article
Date Issued
2019-12-15
Sprache
English
Author(s)
Institut
Volume
78
Issue
12
Start Page
3731
End Page
3747
Citation
Computers and Mathematics with Applications 78 (12): 3731-3747 (2019-12-15)
Publisher DOI
Scopus ID
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.
Subjects
Convergence order
Finite element method
Finite volume method
Nonlinear diffusion and diffusion enhancement
Scharfetter–Gummel scheme
Van Roosbroeck system for semiconductors