Dynamics of thermal growth of silicon oxide films on Si

Abstract

Thermal growth of silicon oxide films on Si in dry 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 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 ͑1965͔͒ indicating that its basic assumptions, steady-state regime, and reaction between 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.

Thermal growth of silicon oxynitride films on Si: A reaction-diffusion approach

“…Figure 2 shows the model kinetics curves for incorporated O and N for the three routes as obtained by integration of the corresponding normalized densities. 8 Bare Si in NO presents a plateau in the kinetics for incorporated O and N, which leads to a very slow, almost self-limited growth, up to 40 time units, when both species have been incorporated in comparable quantities. The kinetics curve asymptotically approaches a straight line after presenting dumped oscillations ͑see inset of Fig.…”

“…The latter assume abrupt interfaces and stationary NO diffusion through the silicon oxide film. 7 Thermal growth of silicon oxynitride films on Si has many complicating features in comparison to the oxide film case: 8 ͑i͒ There are various diffusing species, like NO, O 2 , N, and O; 9 ͑ii͒ several different chemical reactions take place in the bulk, surface, and interface of the growing SiO x N y films; 10 ͑iii͒ N incorporation creates a diffusion barrier to all diffusing species, the barrier efficiency increasing with N concentration, 11 such that N concentration dependent diffusivities must be taken into account; and ͑iv͒ further aspects are faster growth kinetics in N 2 O as compared to NO, and the fact that incorporated N piles up in the SiO x N y /Si near-interface region. 4 This article investigates the growth kinetics and N depth distribution in silicon oxynitride films thermally grown on Si in the three routes mentioned above.…”

“…9 Oxynitride film thickness can be estimated from O and N areal densities using the nominal mass densities of SiO 2 These reactions also imply that some silicon is rendered mobile and we emphasize that precise stoichiometric coefficients must still be appropriately determined. Reactiondiffusion equations 8,14 can then be written. Boundary conditions at the surface (xϭ0), considering O 2 and NO partial pressures as, respectively, P O 2 and P NO , together with dissociation and the consequent O and N production are written as:…”

Comment on “Dynamics of thermal growth of silicon oxide films on Si”

“…1͒ ͑DG͒ to describe the oxidation kinetics of silicon represents a milestone in the field and has established the basis for the study of this important technological process until today. It is usually written in the form 2 …”

Si Nanocrystal Arrays Created in SiO2 Matrix by High-Energy Ion Bombardment

“…First of all, it should be noted that the diffusivity of silicon in SiO 2 at temperatures 1110-1400°C is rather low, 10 -21 -10 -17 cm 2 ·s -1 (Mathiot et al, 2003;Tsoukalas et al, 2001;Takahashi et al, 2003). According to the data of (De Almeida et al, 2000;Aleksandrov et al, 2008), oxygen possesses a much higher diffusivity in SiO 2 amounting to 10 -9 -10 -7 cm 2 ·s -1 . That is why the formation processes of Si nanocrystals in Si-rich oxide layers are usually described with consideration given to the fact that those processes should involve migration of oxygen atoms from the region of the growing silicon nanoparticle (see, for instance, Khomenkova et al, 2007).…”