Diffusion-reaction modeling of silicon oxide interlayer growth during thermal annealing of high dielectric constant materials on silicon

Abstract

We present the quantitative physicochemical modeling of the thermal annealing of high dielectric constant $(k)$ thin films on silicon in oxygen and/or inert ambient. In particular, we study the kinetics of the ${\text{SiO}}_{2}$ interfacial layer growth at the high-$k$ material structure/Si interface. Upon annealing, the transport of oxygen species in the high-$k$ film to the silicon interface is quantitatively evaluated. One-dimensional unsteady-state diffusion-reaction equations are used to model the time evolution of the interfacial ${\text{SiO}}_{2}$ layer thickness. Because of the continuously increasing interfacial ${\text{SiO}}_{2}$ layer, the proposed model incorporates the moving interface that alters the diffusion length of the oxygen species. The numerical solution of the resulting modeling equations is based on the finite volume analysis method and it results in ${\text{SiO}}_{2}$ thickness profiles that comprise of an early fast growth stage followed by pseudosaturation into a self-limited regime. Our model predictions are found to satisfactorily agree with published experimental results. We also study the use of alumina as a potential oxygen diffusion barrier. Alumina is predicted to be an efficient barrier to oxygen diffusion, which is in agreement with published experimental data.