Reply to “Comment on ‘Dynamics of thermal growth of silicon oxide films on Si’ ”

In a Comment on “Dynamics of thermal growth of silicon oxide films on Si” [Phys. Rev. B 61, 12992 (2000)], Roura and Farjas argue that the values of the kinetics parameters obtained from the model proposed in that paper are not reliable and that the solutions given for different partial pressures are erroneous. Moreover, that the solution from such model is unable to predict the oxidation rate experimentally observed in the thin oxide regime neither the width of the interface. Resorting to experimental results, and old and new results obtained from our model, we show in this Reply that none of the criticisms are solid and that the results of the original paper represent indeed an improvement over the Deal-Grove model. Finally, motivated by one of the issues raised by Roura and Farjas, we present here new fittings of experimental data using our model together with experimental estimates for the interface width between the oxide layer and the silicon substrate. This turned a two parameter fitting problem into a much simpler one parameter procedure.

Figure 1

(Color online) Symbols: growth kinetics by Ganem et al. (Ref. 8) with rescaled time using ${\mathrm{O}}_2$ partial pressure. Lines: fits using different values for the interface width (see text).

Figure 2

(Color online) (a) Growth kinetics and (b) ${\mathrm{O}}_2$ and Si profiles at $t=200∕p_0$ time steps for different values of $p_0$. In (b), ${\mathrm{O}}_2$ profiles have been multiplied by $1∕p_0$. $D$ and $k$ are the same for all numerical solutions, and all quantities are given in natural units.

Figure 3

(Color online) Numerical solutions $\chi \left(\tau \right)$ and the reciprocal of its time derivative obtained using finite time steps $\Delta \tau$. For all curves $p_0=1$. All quantities are given in natural units. Zoomed plots in the right column.

Figure 4

(Color online) $d\tau ∕d\chi$ derivative vs $\chi$ obtained using finite space steps $\Delta u$. For all curves, $p_0=0.1$. All quantities are given in natural units.