ABSTRACT
This chapter describes the differential equations and physics implemented in commercial device simulators, as well as the practical aspects of using the simulators for device analysis and optimization. Analytical transistor analysis inevitably involves approximations and assumptions in order to obtain closed-form solutions. Numerical analysis based on the fundamental differential equations governing semiconductors has become necessary in integrated circuit technology development, and is often referred to as “device simulation.” The electrical characteristics of a transistor can be simulated by solving the fundamental semiconductor transport equations. Nonphysical boundaries not only lead to inaccurate simulation results, but also cause convergence problems during the numerical solution process. The choice of the bandgap narrowing model must be made consistently, together with the choice of the mobility models and carrier statistics. The continuous functions in the semiconductor equations are discretized on a user-defined simulation mesh. The discretized nonlinear equations are solved iteratively using Newton’s method.
