Mixing finite elements and finite differences for the analysis of silicon on sapphire

The analysis of electron devices involves the solution of the Poisson equation, made nonlinear as a result of the charge cloud density being a function of the unknown potential. Because of the nonlinear term, the finite-element scheme becomes time consuming. However, the finite difference method, which is shown to model the term Δ² more accurately, cannot handle line charge densities and the rapid variation in the source term near such charge accumulations. It is shown that there is much to be gained by mixing the two methods in analyzing electron devices, and the method is demonstrated for a silicon-on-sapphire device