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 k_ads) 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 k_des) or due to the chemical transformation with the desorption of the product molecule HCl (rate constant k_r).  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: k_ads=10^–13T^0.86exp(110/T) cm³/s, k_des=10^13.7exp(–11500/T) 1/s, k_r=10^10.3T^0.5exp(–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.