Geodesic
On Maxwellian equilibria of insulated semiconductors
Luis A. Caffarelli1 ; Jean Dolbeault2 orcid ; Peter A. Markowich3 orcid ; Christian Schmeiser4 orcid
1University of Texas at Austin, USA
2Université de Paris Dauphine, France
3Universität Wien, Austria
4TU Wien, Austria
Interfaces and free boundaries, Tome 2 (2000) no. 3, pp. 331-339

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DOI

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.
DOI : 10.4171/ifb/23
Classification : 46-XX, 60-XX
Mots-clés : Semiconductors, equilibrium, free boundary problems, charge neutrality

Luis A. Caffarelli  1   ; Jean Dolbeault  2   ; Peter A. Markowich  3   ; Christian Schmeiser  4

1 University of Texas at Austin, USA
2 Université de Paris Dauphine, France
3 Universität Wien, Austria
4 TU Wien, Austria 
Luis A. Caffarelli; Jean Dolbeault; Peter A. Markowich; Christian Schmeiser. On Maxwellian equilibria of insulated semiconductors. Interfaces and free boundaries, Tome 2 (2000) no. 3, pp. 331-339. doi: 10.4171/ifb/23
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     title = {On {Maxwellian} equilibria of insulated semiconductors},
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     pages = {331--339},
     year = {2000},
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     doi = {10.4171/ifb/23},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/23/}
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