Comparison of Discretization Methods for Device Simulation

The characteristics of semiconductor devices are modeled by three coupled nonlinear partial differential equations consisting of the electron continuity, hole continuity, and Poisson equations. A variety of discretization approaches can be used to solve these equations. This paper compares finite volume Scharfetter-Gummel and finite element quasi-Fermi discretization schemes for a variety of devices and mesh element types. The simulation results show that a quasi-Fermi approach may be preferable to the more common finite volume Scharfetter-Gummel method for certain device simulation applications.