Asymptotic boundary conditions for an oxide region in a semiconductor device

Abstract

We study how the equations of the potential of a semiconductor device, as described by Markowich (1986) and Selberherr (1984), behave when the width and the permittivity of the oxide region go to zero. According to their ratio, the problems converge to different asymptotic limits. This provides the correct boundary value approximation to the full problem avoiding costly computations (see, as an example, the discussion in Chapter 5 of (Selberherr, 1984), about the boundary conditions).