Least-squares finite element formulation for hydrodynamic modeling of semiconductor devices Original Research Article

A least-squares finite element formulation is presented for the hydrodynamic modeling of semiconductor devices. The formulation results in a symmetric and positive definite algebraic system. Its capability of adopting equal-order interpolations for all unknown variables makes it simple to formulate and easy to program. The semiconductor hydrodynamic equations coupled with the Poisson equation are formulated as one unified equation system in this least-squares finite element scheme. The developed method is examined on 1-D and 2-D deep-submicron semiconductor device structures to demonstrate its capability of handling the large gradients of variables and highly nonlinear source terms in the semiconductor hydrodynamic equations.