A Singularly Perturbed Boundary Value Problem Modelling a Semiconductor Device.

This paper is concerned with the static, one-dimensional modelling of a semiconductor device (namely the $pn$-junction) when a bias is applied. The governing equations are the well-known equations describing carrier transport in a semiconductor which consist of a system of ordinary differential equations subject to boundary conditions imposed at the contacts. Because of the different orders of magnitude of the solution components at the boundaries, we scale the components individually and obtain a singular perturbation problem.We analyse the equilibrium case (zero bias applied) and set up approximate models, posed as singularly perturbed second order equations, by neglecting the hole and electron current densities. This makes sense for small forward bias and for moderate reverse bias.For the full problem we prove an a priori estimate on the number of electron-hole carrier pairs and derive asymptotic expansions (as the perturbation parameter tends to zero) by setting up the reduced system and the boundary ...