On a Variational Inequality and Its Approximation, in the Theory of Semiconductors

Abstract

The determination of the space charge layer in p–n junction semiconductors leads to a boundary value problem with unknown interfaces. The solution $u(x,y)$ which is the potential at $(x,y)$ satisfies in the domains separated by the interface either the Poisson equation or the Laplace equation. We show that this problem reduces to a variational inequality, giving existence and uniqueness of the interfaces and at the same time discuss a direct computational technique based on the finite element method.