Two-dimensional analysis of semiconductor devices using general-purpose interactive PDE software

Analyzing currents and fields in VLSI devices requires solving three coupled nonlinear elliptic partial differential equations in two dimensions. Historically, these equations have been solved using a special-purpose program and batch runs on a large fast computer. We use a general-purpose program and interactive runs on a large minicomputer. We discuss the physical formulation of the semiconductor equations and give three example solutions: a short-channel MOSFET near punchthrough, a DMOS power transistor in the ON state, and a beveled p-n junction. These examples demonstrate that solutions to a very general class of semiconductor-device problems can be obtained using these methods.