Wavelet Adaptivity for 3-D Device Simulation

A new technique has been implemented with the aim of providing an adaptive tool for the generation of computational meshes for 3-D semiconductor device simulation. The core of the proposed wavelet-based adaptive method (WAM) is a refinement algorithm based on the wavelet transform, which gives an estimation of solution regularity and progressively adapts the grid by increasing the resolution only in regions where the important physical phenomena take place. WAM is inserted into a validation tool that provides the interfacing filters with both the solver and a meshing engine. Additional features assure the quality of the generated meshes by increasing the selectivity properties of the refinement tool, preventing numerical instabilities or artifacts, such as abrupt variations of I-V curves between successive bias points during quasi-stationary simulations. Simulation results are provided, which show the effectiveness of the proposed approach as a means to guide the automatic refinement of the discretization grid, preserving accuracy with negligible computational overhead and no skilled control from the user.