12.5.3 The Heterogeneous Deposition with Byproduct Inhibition Model

The third model assumes heterogeneous decomposition of adsorbed TEOS and that gaseous byproducts released by the net deposition reaction readsorb on the growing film surface inhibiting deposition. This leads to the reaction steps

$$\textsc{teos}\xspace _{\mathrm{(g)}} + * \overset{k_T}{\rightleftarrows} \textsc{teos}\xspace *$$

$$\textsc{teos}\xspace * \overset{k_d}{\rightarrow} I^* + R_{\mathrm{(g)}}$$

$$I* \overset{\textrm{fast}}{\rightarrow} \textrm{SiO$_2$}\xspace _{\mathrm{(s)}} + * + (\nu-1) R_{\mathrm{(g)}} + \mathrm{byproducts}_{\mathrm{(g)}}$$

$$R_{\mathrm{(g)}} + * \overset{k_R}{\rightleftarrows} R^*,$$

where $\nu$ is the stoichiometric coefficient of the inhibiting byproduct in the net deposition reaction.

Assuming that the initial heterogeneous deposition step is rate limiting and that both adsorption processes are in equilibrium, the deposition rate is

$$R_4 = { k_d k_T P_\textsc{teos}\xspace \over 1 + k_T P_\textsc{teos}\xspace + k_R P_R}.$$