Investigation of the asymptotic properties of a boundary value problem concerning the doping and oxidation of silicon

The mathematical modeling of manufacturing operations involving the production of submicron-size VLSI elements is examined. Physical-chemical processes occurring in submicron MOS transistors during the manufacturing operations are analyzed; and this analysis is used to formulate a generalized boundary value problem concerning oxidation and diffusion of impurities in silicon under nonequilibrium conditions with allowance for the interaction between impurity atoms and silicon defects. A package of applications programs has been developed which is used to analyze the asymptotic properties of the boundary value problem.