Abstract
The system of the van Roosbroeck’s equations, often used to describe the electrical behaviour of semiconductors, is used in a simplified version and without recombination to demonstrate restrictions on discretizations arising from the coupling of the equations: the Jacobi matrix of the discrete current continuity equation with respect to the electrostatic potential should be a definite matrix. It is shown that the Scharfetter-Gummel discretization with common restrictions on the geometry of the grid fulfills this requirement in any space dimension. An example with multiple solutions from the literature has a unique solution if the Scharfetter-Gummel discretization is used.
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References
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© 1994 Springer Basel AG
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Gärtner, K. (1994). On Restrictions for Discretizations of the Simplified Linearized Van Roosbroeck’s Equations. In: Bank, R.E., Gajewski, H., Bulirsch, R., Merten, K. (eds) Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices. ISNM International Series of Numerical Mathematics, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8528-7_15
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DOI: https://doi.org/10.1007/978-3-0348-8528-7_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9665-8
Online ISBN: 978-3-0348-8528-7
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