Analysis of the thin-oxide growth kinetic equation

Detailed understanding of the atomic-level mechanisms of oxidation is required to achieve control of ultrathin oxide growth processes. Published models support the widely accepted empirical description of Massoud et al (Massoud H Z, Plummer J D and Irene E A 1985 J. Electrochem. Soc. 132 2685), in which the growth rate is the sum of two terms, a 'Deal-Grove' term that produces linear-parabolic behaviour and an exponential term that enhances the growth rate for thin oxides. We give accurate although approximate analytical solutions for the Massoud kinetic equation. These solutions reduce to the Deal-Grove form for large thickness, give a value for the otherwise ad hoc initial time parameter in that model, become exact for small oxide thickness and have known error bounds as a function of growth thickness and temperature. The solutions should be useful for design calculations and general presentation of an enhanced Deal-Grove growth model.