AMIGOS: analytical model interface and general object-oriented solver

To accurately simulate modern semiconductor process steps, a simulation tool must include a variety of physical models and numerical methods. Increasingly complex physical formulations are required to account for effects that were not important in simulating previous generations of technology. Thus flexibility in definition of models as well as numerical solving methods is highly desirable. An object-oriented approach has been applied to implementing a dimension independent solver which interface in the manner of Math-Cad, Mathematica, Matlab, etc., but highly optimized for high performance semiconductor modeling. To demonstrate the abilities of AMIGOS a new approach to the local oxidation in three dimensions is presented, based on a parameter dependent smooth transition zone between silicon and silicon-dioxide. The resulting two phase problem is solved by calculating a free diffusive oxygen concentration and its chemical reaction with pure silicon to silicon-dioxide. This effect causes a volume dilatation which leads to mechanical stress concerning the surrounding boundary conditions. By a suitable set of parameters this kind of approach is equivalent to the standard sharp interface model based on the fundamental work of Deal and Grove.