Dynamics of thermal growth of silicon oxide films on Si

Thermal growth of silicon oxide films on Si in dry ${\mathrm{O}}_2$ is modeled as a dynamical system, assuming that it is basically a reaction-diffusion phenomenon. Relevant findings of the last decade are incorporated, as structure and composition of the oxide/Si interface and ${\mathrm{O}}_2$ transport and reaction at initial stages of growth. The present model departs from the well-established Deal and Grove framework [B. E. Deal and A. S. Grove, J. Appl. Phys. 36, 3770 (1965)] indicating that its basic assumptions, steady-state regime, and reaction between ${\mathrm{O}}_2$ and Si at a sharp oxide/Si interface are only attained asymptotically. Scaling properties of these model equations are explored, and experimental growth kinetics, obtained for a wide range of growth parameters including the small thickness range, are shown to be well described by the model.