Method of temporary coordinate domains for moving boundary value problems (semiconductor processing simulation)

Abstract

An approach to the numerical solution of moving boundary value problems that is based on the idea of temporary coordinate domains is presented. The method generalizes the concept of coordinate transformations in two respects. First, the physical structure itself at some moment is chosen as the coordinate domain. Thus, the coordinate domain is no longer determined a priori and without regard to the actual physical structure. Second, the coordinate domain is adapted to the geometrical evolution of the structure by redefining it at appropriate time points. In this way the geometrical restrictions of conventional coordinate transformation methods are eliminated. The method is used to simulate thermal processing. It is assumed that the geometry and the material flow are handled by a separate module for simulations of oxide growth. The redistribution of dopants, including segregation at material interfaces, is modeled by diffusion equations and interface conditions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>