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On group analysis of a class of energy-transport models of semiconductors in the two dimensional stationary case. (English) Zbl 1065.35019

Monaco, Roberto (ed.) et al., “WASCOM 2003”—Proceedings ot the 12th conference on waves and stability in continuous media, Villasimius, Italy, June 1–7, 2003. River Edge, NJ: World Scientific (ISBN 981-238-748-X/hbk). 434-440 (2004).
The unipolar energy-transport models for charge carriers in semiconductors are given by the balance equations for density and energy density of electrons, coupled to the Poisson equation for the electric potential. The authors perform a group classification of these models in the two dimensional stationary case at the usage of equivalence transformations. Functional forms of the constitutive functions for mobilities, energy relaxation time and doping profile are obtained.
For the entire collection see [Zbl 1057.76003].

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
78A20 Space charge waves
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
82D37 Statistical mechanics of semiconductors
78A35 Motion of charged particles
58J70 Invariance and symmetry properties for PDEs on manifolds
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