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

The paper commented on here [R. M. C. de Almeida, S. Gonçalves, I. J. R. Baumvol, and F. C. Stedile, Phys. Rev. B 61, 12992 (2000)] claims that the Deal and Grove model of oxidation is unable to describe the kinetics in the thin oxide regime due to two main simplifications: (a) the steady-state assumption and (b) the abrupt $\mathrm{Si}∕{\mathrm{SiO}}_2$ interface assumption. Although reasonably good fits are obtained without these simplifications, it will be shown that the values of the kinetic parameters are not reliable and that the solutions given for different partial pressures are erroneous. Finally, it will be shown that the correct solution of their model is unable to predict the oxidation rate enhancement observed in the thin oxide regime and that the predicted width of the interface compatible with the Deal and Grove rate constants is too large.

Figure 1

Arrhenius plot of the diffusivity values obtained from all the experimental curves fitted by AGB (Ref. 2). Only the empty symbols were reported in that paper.

Figure 2

Kinetic curves obtained theoretically for different values of $p_0$. The curves for $p_0={10}^{-3}$ and $2\times {10}^{-6}$ are indistinguishable (curve B). Inset: inverse growth rate vs oxide thickness. The dashed line is the DG law $(\mathrm{slope}=1)$. Note that for thin oxides the predicted oxidation rate is slower than expected.

Figure 3

Concentration profiles calculated for $p_0=1$ and $2\times {10}^{-6}$ (i.e., $P_{{\mathrm{O}}_2}\approx 0.5\times {10}^6$ and $1\mathrm{atm}$, respectively). The thickness of the interface is taken from ${\rho }_{\mathrm{Si}}=0.1$–0.9. Note that, outside the interface, the ${\rho }_{{\mathrm{O}}_2}$ profile is not a straight line for $p_0=1$.