On maxwellian equilibria of insulated semiconductors

Luis Caffarelli, Jean Dolbeault, Peter A. Markowich, Christian Schmeiser

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)331-339
Number of pages9
JournalInterfaces and Free Boundaries
Issue number3
StatePublished - 2000
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Oxford University Press 2000.


  • Charge neutrality
  • Equilibrium
  • Free boundary problems
  • Semiconductors

ASJC Scopus subject areas

  • Applied Mathematics


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