Reaction-diffusion model for thermal growth of silicon nitride films on Si

Thermal growth of ultrathin silicon nitride films on Si in ${\mathrm{NH}}_3$ is modeled as a dynamic system governed by reaction-diffusion equations. Solution of the model yields profiles of the involved species consistent with experimental observations of a stoichiometric silicon nitride layer in the near-surface region and a subnitride layer of comparable thickness in the near-interface region. Self-limited growth kinetics are also obtained from the model equations in good agreement with experimental results, owing to a diffusion barrier layer to the nitridant species formed in the near-surface region by stoichiometric silicon nitride.