On Maxwellian equilibria of insulated semiconductors
type: Item
instance of: scholarly article
title: On Maxwellian equilibria of insulated semiconductors
zbMATH Open document ID: 0961.35158
DOI: 10.4171/IFB/23
author: Jean Dolbeault
author: Christian Schmeiser
author: Luis Caffarelli
author: Peter Alexander Markowich
published in: Interfaces and Free Boundaries
publication date: 2001-01-17T00:00:00Z
review text: Summary: A semilinear elliptic integrodifferential 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 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.
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 78A35
zbMATH DE Number: 1525471
zbMATH Keywords: semilinear elliptic integrodifferential equation
zbMATH Keywords: homogeneous Neumann boundary conditions
zbMATH Keywords: equilibrium
zbMATH Keywords: semiconductor
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: charge neutrality
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1525471