On Maxwellian equilibria of insulated semiconductors | Zendy

Luis Caffarelli | Zendy; Jean Dolbeault | Zendy; Peter A. Markowich | Zendy; Christian Schmeiser | Zendy

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On Maxwellian equilibria of insulated semiconductors

Author(s) -

Luis Caffarelli,

Jean Dolbeault,

Peter A. Markowich,

Christian Schmeiser

Publication year - 2000

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/23

Subject(s) - uniqueness , limit (mathematics) , semiconductor , neumann boundary condition , boundary (topology) , boundary value problem , limiting , homogeneous , mathematical analysis , electron , physics , charge (physics) , free boundary problem , debye , mathematics , condensed matter physics , quantum mechanics , thermodynamics , mechanical engineering , engineering

A semilinear elliptic integro-differential equation subject to ho- mogeneous 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 analyzed. 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.

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