Numerical Simulation of Carrier Transport at Cryogenic Temperatures

Part of the Springer Theses book series (Springer Theses)


This chapter provides an introduction to the finite volume Scharfetter–Gummel method for the multi-dimensional numerical simulation of the van Roosbroeck system. The scope of this thesis is the numerical simulation of charge transport in quantum light sources based on InGaAs-QDs, which are typically operated at cryogenic temperatures. This requires an extension of the standard discretization scheme towards an accurate consideration of Fermi–Dirac statistics, to properly describe the strong degeneration effects that arise in the electron-hole gas at extremely low temperatures. In the recent years, several generalizations of the classical Scharfetter–Gummel discretization scheme for Fermi–Dirac statistics have been proposed, which are compared and assessed. At cryogenic temperatures, the discrete van Roosbroeck system is subject to serious convergence issues and numerical underflow using the standard continuation scheme. The problem is investigated in detail and is traced back to an ill-conditioned Jacobian matrix. This observation leads to the revision of the standard continuation routine towards a new temperature-embedding method.


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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Weierstrass Institute for Applied Analysis and Stochastics (WIAS)Leibniz Institute in Forschungsverbund Berlin e. V.BerlinGermany

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