Abstract
In this paper the author presents a singular perturbation analysis of the fundamental semiconductor device equations which form a system of three second order elliptic differential equations subject to mixed Neumann-Dirichlet boundary conditions. The system consists of Poisson's equation and the continuity equations and describes potential and carrier distributions in an arbitrary semiconductor device. The singular perturbation parameter is the minimal Debye-length of the device under consideration. Using matched asymptotic expansions they demonstrate the occurrence of internal layers at surfaces across which the impurity distribution which appears as an inhomogeneity of Poisson's equation has a jump discontinuity (these surfaces are called 'junctions') and the occurrence of boundary layers at semiconductor-oxide interfaces. The author derives the layer-equations and the reduced problem (charge-neutral-approximation) and give existence proofs for these problems. They layer solutions which characterize the solution of the singularly perturbed problem close to junctions and interfaces resp. are shown to decay exponentially away from the junctions and interfaces resp. It is shown that, if the device is in thermal equilibrium, then the solution of the semiconductor problem is close to the sum of the reduced solution and the layer solution assuming that the singular perturbation parameter is small. Numerical results for a two-dimensional diode are presented. (Author)