A generalized finite element method for hydrodynamic modeling of short-channel devices

Abstract

A generalized finite element formulation based on the least-squares scheme is developed for hydrodynamic modeling of two-dimensional short-channel semiconductor devices. Although this general-purpose finite element method appears to be more universal to now problems than other finite element approaches and has been applied in recent years to a wide range of problems in fluid dynamics, it is still unfamiliar to the semiconductor device community. The least-squares finite element (LSFE) formulation possesses many advantages. The algebraic system derived in the LSFE method is symmetric and positive definite. It allows adoption of equal-order interpolations for all independent variables, which makes the method simple to formulate and easy to program The LSFE method is also effective for handling convective problems because the method contains an upwind mechanism to stabilize the numerical solution of the equations with the hyperbolic nature. Unlike the mixed Galerkin schemes, the LSFE method contains no adjustable parameter. Transport problems in the LSFE formulation can be handled in a very simple framework. Application ofthe LSFE method to different problems or modification of the physical model amounts to simple subroutine changes in the computer code associated with the coefficient matrices and vectors. The developed LSFE method is applied to modeling of a depletion-mode n-channel MESFET with a gate length of 0.2/spl mu/m at V/sub gs/=0.6V and V/sub ds/=2.0V to examine its stability and effectiveness.