Non-isothermal Scharfetter–Gummel Scheme for Electro-Thermal Transport Simulation in Degenerate Semiconductors

DOI10.1007/978-3-030-43651-3_14zbMath1471.65175arXiv2002.10133OpenAlexW3007834591MaRDI QIDQ5117435

Markus Kantner, Thomas Koprucki

Publication date: 25 August 2020

Published in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.10133

zbMATH Keywords

Scharfetter-Gummel schemeFermi-Dirac statisticsself-heatingSeebeck effectelectro-thermal transportnon-isothermal drift-diffusion system

Mathematics Subject Classification ID

Heat equation (35K05) Statistical mechanics of semiconductors (82D37) Irreversible thermodynamics, including Onsager-Machlup theory (82B35) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Heat kernel (35K08) PDEs in connection with statistical mechanics (35Q82) Finite volume methods applied to problems in thermodynamics and heat transfer (80M12) Finite volume methods for boundary value problems involving PDEs (65N08) Fermionic systems in quantum theory (81V74)

Cites Work

• A finite volume scheme for convection-diffusion equations with nonlinear diffusion derived from the Scharfetter-Gummel scheme
• Generalized Scharfetter-Gummel schemes for electro-thermal transport in degenerate semiconductors using the Kelvin formula for the Seebeck coefficient
• H-Convergence and Numerical Schemes for Elliptic Problems
• Thermodynamic design of energy models of semiconductor devices

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