Chapter 10, Problem 10.15P

Titanium dioxide is a wide-bandgap semiconductor that is showing promise as an insulating dielectric in VLSI capacitors and for use in solar cells. Thin films of TiO₂ are to be prepared by chemical vapor deposition from gaseous titanium tetraisopropoxide (TTIP). The overall reaction is

$\text{Ti}{({\text{OC}}_3{\text{H}}_7)}_4\to {\text{TiO}}_2+4{\text{C}}_3{\text{H}}_6+2{\text{H}}_2\text{O}$

The reaction mechanism in a CVD reactor is believed to be [K. L. Siefering and G. L. Griffin, J. Electrochem. Soc., 137, 814 (1990)]

$\begin{array}{l}\text{TTIP}(\text{g})+\text{TTIP}(\text{g})\rightleftarrows \text{I}+{\text{P}}_1\\ \text{I}+\text{S}\rightleftarrows \text{I}\cdot \text{S}\\ \text{I}\cdot \text{S}\to {\text{TiO}}_2+{\text{P}}_2\end{array}$

where I is an active intermediate and P₁ is one set of reaction products (e.g., H₂O, C₃H₆), and P₂ is another set. Assuming the homogeneous gas-phase reaction for TTIP is in equilibrium, derive a rate law for the deposition of TiO₂. The experimental results show that at 200°C the reaction is second order at low partial pressures of TTIP and zero order at high partial pressures, while at 300°C the reaction is second order in TTIP over the entire pressure range. Discuss these results in light of the rate law you derived.

³³Scheffe, J.R., J. Li, and A. W. Weimer, “A Spinel Ferrite/Hercynite Water-Splitting Redox Cycle,” International Journal of Hydrogen Energy, 35, 3333–3340 (2010).