Discretization of the Steady State Semiconductor Device Equations
Abstract
The continuity equations of the drift-diffusion semiconductor device model are hard to discretize because of the severe variations of variables. The Scherfetter - Gummel scheme applies harmonic averages to the conductance function, and usually produces acceptable solutions despite the sharp parameter changes. Some authors attribute the success of this scheme to the relative smoothness of the currents, as compared with carrier concentrations. In this report it is shown that current smoothness cannot be derived from the differential equations, but is related to the specific boundary condition configuration. The success of the Scherfetter-Gummel method is hence easy to justify for nearly 1-D devices, but is harder to justify for some other geometries. A stream function formulation related to the scheme is shown to overcome cases where the continuity equations are ill-conditioned. (AW)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1989
- Accession Number
- ADA215807
Entities
People
- I. Efrat
Organizations
- Yale University