Asymptotic Analysis of the Current-Voltage Curve of a pnpn Semiconductor Device

Abstract

We consider the one-dimensional steady-state semiconductor device equations modelling a pnpn device. There are two relevant scalings of the equations corresponding to small and large applied voltages. In both scalings, the semiconductor equations can be considered as singularly perturbed. It turns out that the small-voltage scaling breaks down for current values between two saturation currents. In that interval, the large-voltage scaling has to be employed. For both scalings, we derive the first-order terms of an asymptotic expansion and show that the reduced problem has a solution. An example verifies that the current-voltage curves obtained have the expected qualitative structure.