Kinetics of thermal growth of thin silicon oxide films

Abstract

The thermal growth of dry SiO 2 layers is usually described by the so-called linear parabolic equation, based on the assumption that oxygen diffusion takes place in the oxide layer according to Fick's law with constant diffusivity, and that the oxidation occurs at the Si-SiO 2 interface with a first-order reaction rate. The predictions of this model are obeyed at temperatures higher than 980°C. For lower temperatures, vice versa, the observed behaviour deviates significantly from the above classical model; this is particularly true for very thin oxide layers. In the present work a theoretical model is analysed in which the diffusion process is not described by Fick's law but by a constitutive equation which allows for the relaxation process in the SiO 2 layer. This relaxation was recognized to take place by several authors. The resulting formulation gives a satisfactory interpretation for the kinetics of the growth of the oxide layer, also for very thin oxide films.