The CGU Mathematics Clinic has been conducting clinics for ISI in the area of semiconductor transistor modeling for a number of years. The aim is to simplify the descriptions inserted in the circuit simulator software package SPICE which describe current/voltage characteristics of each transistor. Current flow is governed by a set of nonlinear partial differential equations, and so obtaining simple, accurate formulae is not easy. The Clinic approach has been to use asymptotic analysis.
The current project concerns the source and drain regions on a MOSFET, which have three-dimensional character and are often non-uniformly doped. The problem is to assess their equivalent capacitance features in this complicated geometry.