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Stationary energy models for semiconductor devices with incompletely ionized impurities
Author(s) -
Glitzky A.,
Hünlich R.
Publication year - 2005
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200510230
Subject(s) - nonlinear system , semiconductor , boundary value problem , neighbourhood (mathematics) , boundary (topology) , thermodynamic equilibrium , impurity , function (biology) , heterojunction , semiconductor device , ionization , stationary solution , physics , mathematics , mathematical analysis , thermodynamics , chemistry , quantum mechanics , organic chemistry , layer (electronics) , evolutionary biology , biology , ion
Dedicated to Professor Herbert Gajewski on his 65th birthday The paper deals with two‐dimensional stationary energy models for semiconductor devices, which contain incompletely ionized impurities. We reduce the problem to a strongly coupled nonlinear system of four equations, which is elliptic in nondegenerated states. Heterostructures as well as mixed boundary conditions have to be taken into account. For boundary data which are compatible with thermodynamic equilibrium there exists a thermodynamic equilibrium. Using regularity results for systems of strongly coupled linear elliptic differential equations with mixed boundary conditions and nonsmooth data and applying the Implicit Function Theorem we prove that in a suitable neighbourhood of such a thermodynamic equilibrium there exists a unique stationary solution, too.