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On Maxwellian equilibria of insulated semiconductors

Cafarelli, Luis; Dolbeault, Jean; Markowich, Peter; Schmeiser, Christian (2000), On Maxwellian equilibria of insulated semiconductors, Interfaces and free boundaries, 2, 3, p. 331-339. http://dx.doi.org/10.4171/IFB/23

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Type
Article accepté pour publication ou publié
Date
2000
Journal name
Interfaces and free boundaries
Volume
2
Number
3
Publisher
European Mathematical Society
Pages
331-339
Publication identifier
Metadata
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Author(s)
Cafarelli, Luis
Dolbeault, Jean cc
Markowich, Peter
Schmeiser, Christian
Abstract (EN)
A semi-linear elliptic integro-differential equation subject to homogeneous Neumann boundary conditions for the equilibrium potential in an insulated semiconductor device is considered. A variational formulation gives existence and uniqueness. The limit as the scaled Debye length tends to zero is analysed. Two different cases occur. If the number of free electrons and holes is sufficiently high, local charge neutrality prevails throughout the device. Otherwise, depletion regions occur, and the limiting potential is the solution of a free boundary problem.
Subjects / Keywords
Semiconductors; equilibrium; free boundary problems; charge neutrality