Oxidation-induced stresses in the isolation oxidation of silicon

The two-dimensional isolation oxidation of silicon is studied in the reaction-controlled limit, which corresponds to the case of initially thin oxides. This limit is both of physical relevance and one of the few regimes in which analytical progress can be made in the whole oxide region. Slowly-varying or long-wave approximations can be used to derive equations that govern the growth of the oxide interfaces (which form two moving boundaries) and the oxidation-induced stresses in the oxide. Here, these equations are solved numerically, by use of a Keller-Box discretisation scheme, complementing previously obtained asymptotic results. The numerical scheme is used to investigate the effects of the nitride-cap rigidity and the initial oxide thickness on both the lateral extent of oxidation (the so-called 'bird's beak' length) and the stresses that occur on the silicon/silicon-oxide interface. The results from the model are interpreted in dimensional form so that quantitative comparisons can be made with experimental results.