Oxidation-induced stresses in the isolation oxidation of silicon

The two-dimensional isolation oxidation of silicon is studied in the reacti on-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 wh ich analytical progress can be made in the whole oxide region. Slowly-varyi ng or long-wave approximations can be used to derive equations that govern the growth of the oxide interfaces (which form two moving boundaries) and t he oxidation-induced stresses in the oxide. Here, these equations are solve d numerically, by use of a Keller-Box discretisation scheme, complementing previously obtained asymptotic results. The numerical scheme is used to inv estigate the effects of the nitride-cap rigidity and the initial oxide thic kness 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 qua ntitative comparisons can be made with experimental results.