THE OXIDATION PROCESS OF SILICON - MODELING AND MATHEMATICAL TREATMENT

In this paper we develop a mathematical model describing the oxidation process of silicon. At first we introduce a model with a sharp reacti on front between the silicon and the oxide layer. From this we turn ov er to a phase field model where the reaction front is replaced by an e xtended reaction zone. The silicon dioxide and the silicon are regarde d as components of a reacting mixture, and the oxygen is assumed to be dissolved in it. We formulate a local existence result of that second model in three space dimensions assuming some simplifications concern ing the boundary conditions and solve the complete free boundary value problem numerically. For this, it has been implemented into the proce ss simulator DIOS which allows two-dimensional computations.