12.5.1 The Heterogeneous Deposition Model

This deposition model consists of the two reaction steps

$$\textsc{teos}\xspace _{\mathrm{(g)}} + 2S \overset{k_a}{\rightleftarrows} 2I$$

$$I \overset{k_d}{\rightarrow} \textrm{SiO$_2$}\xspace _{\mathrm{(s)}} + S + 2 \textrm{H$_2$O}\xspace _{\mathrm{(g)}} + 4\mathrm{C_2H_4}_{\mathrm{(g)}},$$

where $S$ represents a surface site and $I$ an unspecified surface intermediate. $\mathrm{(g)}$ and $\mathrm{(s)}$ denote gas phase resp. solid phase.

Using the Langmuir adsorption model and assuming that the decomposition of the surface intermediate $I$ determines the rate, the SiO$_2$ deposition rate is given by

$$R_1 = { k_d \sqrt{k_a P_\textsc{teos}\xspace } \over 1 + \sqrt{k_a P_\textsc{teos}\xspace }},$$

where $P_\textsc{teos}\xspace$ is the local partial pressure of TEOS.

A variant of this reaction scheme is the following: If it is assumed that TEOS adsorbs molecularly and that uni-molecular heterogeneous decomposition of adsorbed TEOS determines the rate, then the deposition rate is

$$R_2 = { k_d k_a P_\textsc{teos}\xspace \over 1 + k_a P_\textsc{teos}\xspace }.$$