A Singularly Perturbed Boundary Value Problem Modelling a Semiconductor Device.
Abstract
This paper is concerned with the static, one-dimensional modelling of a semiconductor device (namely the pn-junction) when a bias is appled. The governing equations are the well known equations describing carrier transport in a semiconductor which consist of a system of five 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 reverse bias. For the full problems 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 layer system. We prove existence theorems for both systems and use the asymptotic expansion to solve the model equations numerically and analyse the dependence of the solutions on the applied bias. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1982
- Accession Number
- ADA116213
Entities
People
- Chr. A. Ringhofer
- Erasmus Langer
- Peter A. Markowich
- Siegfried Selberherr
Organizations
- University of Wisconsin–Madison