Challenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies (Paper title: Nonlinear diffusion, boundary layers and nonsmoothness: Analysis of challenges in drift-diffusion semiconductor simulations)
- Farrell, Patricio
- Peschka, Dirk
2010 Mathematics Subject Classification
- 35Q99 82D37 65M08 65M06 65M60
- Finite volume method, finite element method, finite difference method, comparison, benchmark, flux discretization, Scharfetter-Gummel scheme, semiconductors, van Roosbroeck system, device simulation, nonlinear diffusion, diffusion enhancement
We analyze and benchmark the error and the convergence order of finite difference, finite-element as well as Voronoi finite-volume discretization schemes for the drift-diffusion equations describing charge transport in bulk semiconductor devices. Three common challenges, that can corrupt the precision of numerical solutions, will be discussed: boundary layers at Ohmic contacts, discontinuties in the doping profile, and corner singularities in L-shaped domains. The influence on the order of convergence is assessed for each computational challenge and the different discretization schemes. Additionally, we provide an analysis of the inner boundary layer asymptotics near Ohmic contacts to support our observations.
- Comput. Math. Appl., 78 (2019), pp. 3731--3747, DOI 10.1016/j.camwa.2019.06.007 .