A Simplified Viscoelastic Model for the Thermal Growth of Thin SiO2 Films

Abstract

Recently, thermal dry oxidation of silicon was quantitatively described by the present authors in a model accounting for the relaxation phenomena occurring in the oxide film. Clarity about the underlying physical mechanisms and satisfactory matching with existing data both make the model rather appealing; also, the well-known anomalous behavior encountered in the thin film region appears to be adequately predicted. The resulting numerical problem is rather complex when compared with other existing models. A simplified mathematical formulation of the mentioned model is proposed here. The viscoelastic relaxations occurring in the oxide layer are lumped into a time-dependent effective diffusivity for which an explicit expression was found in terms of the parent model parameters. A deviation of, at most, 2.3% in the oxidation rate was obtained by comparing the results from rigorous and simplified approach. The simplified model proposed requires numerical procedures as simple as for some previously existing models; it has the additional advantage of being written in terms of quantities which all have precise physical meanings and can be measured independently of the oxidation process.

Intrinsic SiO2 film stress measurements on thermally oxidized Si

“…One study (12) uses this stress-diffusion model to predict the shape of the very initial regime. The model proposed by Doremus (11) has no explicit orientation dependence, but is very similar to the other proposed transport models (12,13) …”

“…When the oxide becomes sufficiently thick and the diffusion regime commences, the intrinsic compressive oxide stress alters the oxidation order in favor of the (111) since smaller compressive stress in the oxide reduces the diffusivity least for the (111) surface. This latter idea on the effect of stress on diffusivity has been discussed by several authors (11,12,13). Leroy's calculations require lateral oxidation at steps and is therefore consistent with the Kott step model (17).…”

“…Three recent models (11,12,13) treat the possible effects of stress on the transport of oxidant through an SiO 2 film during oxidation. According to Fargeix et al (12) and Camera Roda et al (13) the conditions that yield the lowest intrinsic stress should also yield the fastest rate, since these authors couple an increased compressive stress with decreased diffusivity.…”

“…The kinetics of the thermal oxidation of Si have been explained using the A number of models have been proposed which consider stress to be influential on either the interface reaction (9,10) or the diffusivity of oxidant species through a strained oxide (11,12,13 (14) observations have included the effects of mechanical properties on the Si-SiO 2 interface and on the early stages of oxidation.…”

“…Other studies (11,12,13) also include the effects of interfacial stresses on oxidation kinetics using the transport limitation of oxidant through a stressed film.…”