Stationary energy models for semiconductor devices with incompletely ionized impurities

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 no...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Mechanik 2005-11, Vol.85 (11), p.778-792
Main Authors: Glitzky, A., Hünlich, R.
Format: Article
Language:English
Subjects:
Analytical and numerical techniques
and energy transport in heterostructures
charge
energy models
Exact sciences and technology
existence
Fundamental areas of phenomenology (including applications)
Heat transfer
Implicit Function Theorem
mass
Mathematical analysis
Mathematics
mixed boundary conditions
Partial differential equations
Physics
regularity
Sciences and techniques of general use
strongly coupled elliptic systems
uniqueness
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Summary: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.
ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.200510230