12.5.2 The Homogeneous Intermediate-Mediated Deposition Model

In the homogeneous intermediate-mediated deposition model TEOS partially decomposes in the gas phase and the reaction steps are

$$\textsc{teos}\xspace _{\mathrm{(g)}} \overset{k_g}{\rightleftarrows} I_{\mathrm{(g)}} + R_{\mathrm{(g)}}$$

$$I_{\mathrm{(g)}} + S \overset{k_I}{\rightleftarrows} I$$

$$I \overset{k_d}{\rightarrow} \textrm{SiO$_2$}\xspace _{\mathrm{(s)}} + S + \mathrm{byproducts}_{\mathrm{(g)}},$$

where $R$ is an unspecified byproduct of the homogeneous partial dissociation step and $I_{\mathrm{(g)}}$ is an unspecified gas phase derivative of TEOS. Again $S$ is a surface site and $I$ is an unspecified surface intermediate.

Assuming that the surface decomposition step is rate limiting and that the preceding steps are in equilibrium, the deposition rate is

$$R_3 = { k_d k_I P_I \over 1 + k_I P_I } = { k_d k_I \sqrt{k_g P_\textsc{teos}\xspace } \over 1 + k_I \sqrt{k_g P_\textsc{teos}\xspace } }.$$