MOVING ADAPTIVE UNSTRUCTURED 3-D MESHES IN SEMICONDUCTOR PROCESS MODELING APPLICATIONS

The next generation of semiconductor process and device modeling codes will require 3-D mesh capabilities including moving volume and surfac e grids, adaptive mesh refinement and adaptive mesh smoothing. To illu strate the value of these techniques, a time dependent process simulat ion model was constructed using analytic functions to return time depe ndent dopant concentration and time dependent SiO2 volume and surface velocities. Adaptive mesh refinement and adaptive mesh smoothing techn iques were used to resolve the moving boron dopant diffusion front in the Si substrate. The adaptive mesh smoothing technique involves minim izing the L-2 norm of the gradient of the error between the true dopan t concentration and the piecewise linear approximation over the tetrah edral mesh thus assuring that the mesh is optimal for representing evo lving solution gradients. Also implemented is constrained boundary smo othing, wherein the moving SiO2/Si interface is represented by moving nodes that correctly track the interface motion, and which use their r emaining degrees of freedom to minimize the aforementioned error norm. Thus, optimal tetrahedral shape and alignment is obtained even in the neighborhood of a moving boundary. If desired, a topological ''reconn ection'' step maintains a Delaunay mesh at all times. The combination of adaptive refinement, adaptive smoothing, and mesh reconnection give s excellent front tracking, feature resolution, and grid quality for f inite volume/finite element computation.