Example: gas-surface reaction Zr(OH)2/s/+ZrCl4->Zr(OH)OZrCl3/s/ + HCl
Atomic layer chemical vapor deposition (ALD) is one of the most promising methods of oxide film growth. At present rather cheap multilevel modeling of the macroscopic ALD process is feasible. An important step of the multilevel modeling of such complicated heterogeneous process is evaluation of the rate constants of elementary gas-surface chemical reactions.
To obtain estimates for the rate constant of the important step of ZrO2 film growth Zr(OH)2/s/ + ZrCl4 -> Zr(OH)OZrCl3/s/ + HCl performing multilevel modeling of ALD of ZrO2 film (M.Deminsky, A. Knizhnik, I.Belov, et al Surface Science, 549, 67 (2004)), the following approach was accepted. Based on the local character of interactions involved in this process ab initio quantum chemical calculations were performed in Kintech for the prototype gas-phase reaction Zr(OH)4 + ZrCl4 -> Zr(OH)3OZrCl3 + HCl in framework of density functional theory with the use of quantum chemical software Gaussian 98. Reaction energy profile obtained is shown in left figure. It is seen that stable intermediate complex Zr(OH)4-ZrCl4 exists. Correspondingly the following model of the gas-surface reaction of interest was accepted. The gas molecule ZrCl4 is adsorbed (rate constant kads) at the surface center Zr(OH)4/s/ forming the precursor Zr(OH)4-ZrCl4/s/. The latter may decay either due to the desorption of ZrCl4 (rate constant kdes) or due to the chemical transformation with the desorption of the product molecule HCl (rate constant kr). The bulk does not modify energy and vibrational characteristics of the model gas phase reaction but induce energy relaxation of the initially vibrationally excited precursor Zr(OH)4-ZrCl4/s/. Evaluated using model “Calculation of rate constant of chemical sorption” are as follows: kads=10–13T0.86exp(110/T) cm3/s, kdes=1013.7exp(–11500/T) 1/s, kr=1010.3T0.5exp(–8150/T)1/s, T is temperature in K.
This example demonstrates that Kintech Lab expertise and software allows to get quantitative information on the rate of the practically important gas-surface reactions, for which both experimental and theoretical data are lacking.