Adaptive mesh refinement for multilayer process simulation using the finite element method

An adaptive mesh refinement technique is proposed for a two-dimensional finite-element multilayer process simulator. Mesh refinement is based on the dopant concentration ratio inside each element, together with a prediction technique, minimizing the interpolation errors. A significant reduction in CPU time is obtained by automatic grid refresh. Several methods were tested. The mesh adequacy is evaluated with bipolar test structures using analytical punch-through voltage calculations. Applications of these methods are presented in two ways. First, an advanced trench-isolated polysilicon bipolar transistor was simulated to show the general possibilities of the techniques, and second, a coupled process and device simulation approach allows the evaluation of the scheme on real structures in relation to experimental measurements