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Gas phase and surface kinetic schemes for metal organic chemical vapor deposition processes: a theoretical perspective
Materials Chemistry and Physics 66 (2000) 197–200
Gas phase and surface kinetic schemes for metal organic chemical vapor deposition processes: a theoretical perspective Carlo Cavallotti, Maurizio Masi∗ , Sergio Carrà Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, via Mancinelli 7, 20131 Milan, Italy
Abstract In this work we propose a systematic procedure of realization of detailed kinetic schemes for gas phase and surface systems. The fundamental step in this process is the evaluation of the kinetic constants for the considered elementary reaction. Here we propose to evaluate the kinetic constants through statistical thermodynamic methods such as transition state theory using quantum chemistry calculated energies and vibrational frequencies. Different cases where that approach was followed are presented. In particular, we discuss the realization of microscopically reversible kinetic schemes for the chemical vapor deposition of zinc sulfide and cadmium telluride from metal-organic precursors. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Gas phase; Surface system; Quantum chemistry
1. Introduction The realization of detailed kinetic schemes of gas phase and surface processes is a fundamental step in the modeling of many systems of interest for chemical engineers and material scientists. Some examples of situations, where a detailed gas phase kinetic scheme is required are the combustion of hydrocarbons, plasma systems adopted for the deposition of advanced materials, the description of the reactivity of gases affecting the stratospheric ozone. The availability of a detailed surface reaction scheme is of great importance in all those systems where a chemical interaction between gas phase and surface occurs, such as chemical vapor deposition systems and catalytic reactors. A generic procedure of realization of a detailed kinetic scheme requires as first step the identification of all the chemical species (i.e., neutral species, radicals or ions) that are likely to be present in the gas or on the surface. Successively all the elementary reactions that can occur among these species must be considered and a kinetic constant for each reactive event must be determined. At this stage physical intuition is of great importance in order to cancel from the hypothesized events all those reactions that are unlikely to occur (e.g., a reactive event between two neutral species in a gas is possible only at very high temperatures because of the stability of the reagents). The next step is the determination of the kinetic constants for all the selected ∗ Corresponding author. E-mail address: [email protected] (M. Masi).
reactions. Many kinetic constant values for gas phase reactions are readily available from the literature [1] or can be found in kinetic data bases accessible from Internet (e.g., www.ca.sandia.gov/crf/research/applied/thermokindata/). However, when a system different from those already studied is considered the kinetic constants for many possible processes are often not known. In these cases the kinetic constant value can be either calculated or experimentally determined. The experimental evaluation of a kinetic constant is usually a time consuming process and can be hampered by many problems in the realization of a reliable experimental set-up. Moreover, it is not known ‘a priori’ if the considered reaction will have a relevant impact on the reactivity of the overall system or not. It is therefore a better approach to evaluate the kinetic constants of all the considered processes from a ‘priori method’ and then to identify the key reactions in the developed kinetic scheme from a sensitivity analysis and evaluate experimentally the kinetic constants of these processes. The generic procedure we propose for the realization of a kinetic scheme is summarized in Fig. 1. In this work we focused our analysis on the evaluation of values of kinetic constants for gas phase and surface kinetic processes from first principles. 2. Evaluation of kinetic constants of gas phase reactions The progress in the theory of evaluation of kinetic constants of gas phase reactions from first principles has been such that reliable theoretical estimation of rate coefficients for many processes can now be carried out. For example,
0254-0584/00/$ – see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 0 ) 0 0 3 2 0 - 5
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C. Cavallotti et al. / Materials Chemistry and Physics 66 (2000) 197–200
Fig. 1. Generic procedure proposed for the realization of a kinetic scheme.
Gilbert and Smith [2] asserted that the kinetic constant for unimolecular reactions involving hydrocarbons can be calculated with an uncertainty factor of 3, which is acceptable in many practical cases. The main problem in the ‘a priori’ evaluation of a kinetic constant is that the most accurate theories require as input a great amount of data. In particular the expression of the kinetic constant for a generic reactive event given by classical transition state theory is kb T Q6= −Ea exp (1) kcin = sf h Qreag RT where kb and h are the Boltzmann and Planck constants, respectively, Q6= and Qreag are the partition functions of transition state and reagents, respectively, Ea is the activation energy of the process and sf the statistical factor accounting for the reaction path degeneracy. The partition function Qi is the product of the translational, rotational, vibrational and electronic partition functions of the considered specie: Qi = Qtrans Qrot Qvib Qel
(2)
with Qtrans =
2π mkb T h2
3/2
1/2 2 1/2 8π 2 Ia kb T 8π Ib kb T h2 h2 2 1/2 8π Ic kb T × h2
(3)
Qrot = π 1/2
Qvib =
s Y i=1
1 1 − exp(−hcυi /kb T )
(4)
(5)
Qel =
X −Ei gi exp kb T
(6)
i
where m is the mass of the molecule, Ia , Ib and Ic are the moments of inertia of the molecule around the principle axes, ν i the vibrational frequencies and Ei and gi the energies and degeneracies above the lowest level of the system. Rarely electronic states above the ground state have to be considered, while for reactions involving doublet or triplet species the degeneracy of the ground state is equal to that of the spin (i.e., two and three, respectively). Summarizing, the data required to evaluate the partition functions are the vibrational frequencies and moments of inertia of reagents and of transition state. All the information required can be obtained from a priori quantum chemistry calculations with a precision depending on the chosen method of calculation and on the system under consideration. Computational quantum chemistry (QC) is a field of research that has made much progress in the last few years and the awarding of the Nobel prize in 1998 to two pioneers of QC viz. W. Kohn and J.A. Pople is an acknowledgement of this trend. The steps that must be followed to obtain the data required by transition state theory are reported at the bottom of Fig. 1. To perform the calculations a software package can be adopted (e.g., g98, alchemy, mopac, qchem, cerius, etc.). All the calculations reported here were performed adopting the g98 suite of programs [3]. The procedure described above was applied to evaluate the kinetic constant of the gas phase reaction H+(CH3 )2 Zn⇒CH4 +CH3 Zn. From experimental results it was hypothesized that this reaction might have an impact on the process of deposition of zinc sulfide (ZnS) from gas phase precursors. However, the kinetic constant of the process is not known and in order to investigate the feasibility
C. Cavallotti et al. / Materials Chemistry and Physics 66 (2000) 197–200
199
Fig. 2. Structures of reagents, products and transition state and calculated parameters for the reaction (CH3 )2 Zn+H⇒(CH3 )Zn+CH4 .
of the hypothesis, a QC research of transition state structure, energy and vibrational frequencies was performed. A sketch of the structures of reagents and transition state together with some of the calculated data are presented in Fig. 2. A good agreement between calculated (−36±4 kcal mol−1 ) and experimental (−34.6 kcal mol−1 ) enthalpy of reaction was found. The calculations were conducted using the density functional theory method to solve the Shroedinger equation with the three parameters of Becke exchange and the Perdew–Wang correlation functionals (i.e., B3PW91) [4–6]. The triple zeta 6-311+G** basis set with added polarization and diffusion functions was adopted for the calculations.
3. Evaluation of kinetic constants of surface reactions The evaluation of kinetic constants for reactions involving surface species is a more difficult task than the study of gas phase reactions. The main problem consists in the individualisation of the structure of the surface site to be considered as representative of the entire surface. Successively this site can be considered as a reacting chemical species and the surface reaction kinetics can be investigated with the methods similar to those adopted for the gas phase. Since quantum chemistry calculations require an amount of computer time that scales from the square to the seventh/eighth power of the problem size, the dimension of the considered surface cluster must be limited. This limitation can be a major source of error because it excludes the possibility to account for the long range effects that are typical of surface networks. To illustrate a possible approach to the study of surface kinetics, we report here the process we followed to evaluate
the kinetic constant for the desorption of adsorbed species from a (1 0 0) CdTe surface. In Fig. 3 the structure of the site adopted to investigate the kinetics of adsorption of Cd(CH3 )2 on the CdTe (1 0 0) surface is presented [7]. In this case the calculations were performed adopting the B3LYP method and the 3-21G** basis set. The film surface was assumed to have the same structure as that of the solid network (i.e., zinc-blend), so that each metal atom can be bonded only to the other metal atom (i.e., Cd to Te and vice versa) and the bond angles are tetrahedral. Four hydrogen atoms are added at the sides of the surface cluster to avoid the presence of unpaired electrons, which would affect the results of the calculations. The evaluation of the kinetic constants for the processes of desorption is a more difficult task than the study of gas phase processes because of the lack of experimental data on surface reactivity. Moreover
Fig. 3. Structures of Cd(CH3 )2 adsorbed over a CdTe (1 0 0) surface site. The calculated adsorption energy was 31.4 kJ mol−1 .
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C. Cavallotti et al. / Materials Chemistry and Physics 66 (2000) 197–200
the theoretical aspects of the kinetics of surface reactions have not yet been investigated as much as those of gas phase reactions [8]. Here we adopted transition state theory to determine desorption kinetic constants, but care must be placed in the interpretation of these results because of the above mentioned consideration and for the many approximations that had to be devised to account for missing data. Transition state theory requires the knowledge of the partition function of the molecule in the transition state and of the reactants according to the following equation: rot Qvib −Ea kb T 6= Q6= exp (7) k= rot h Qvib RT ads.spec. Qads.spec. vib rot rot where Qvib 6= , Q6= , Qads.spec. , and Qads.spec. are the vibrational and rotational partition functions for transition state and adsorbed species, respectively. With respect to Eq. (1) the translational and electronic partition functions for reactants and transition state were considered equal to 1. This was done to account for the fact that adsorbed surface species have no translational degrees of freedom. Eq. (7) can be further simplified observing that adsorbed species do not rotate and therefore Qrot ads.spec. = 1. Finally, it was assumed that the transition state structure is similar to that of the products. That is a direct consequence of the Hammond postulate, according to which in an endothermic process the structure of the transition state is near that of the products, and vice versa for an exothermic process. The desorption kinetic constant for adsorbed Cd(CH3 )2 was determined observing that, because of the little bond energy between Cd(CH3 )2 and the surface, the vibrational frevib quency of the bond is small and therefore Qvib 6= /Qads.spec. ≈ 1. Moreover because of the proximity of Cd(CH3 )2 to the growing surface it was assumed that no rotational degrees of freedom are active and therefore Qrot 6= ≈ 1. The pre-exponential factor calculated from Eq. (4) is about 6×1012 for the desorption process and the calculated activation energy for this reaction is 31 kJ mol−1 . The desorption of methyl from adsorbed Cd(CH3 )2 was assumed to have a pre-exponential factor of 1016 , in the range of those experimentally found for unimolecular gas phase reactions, and an activation energy of 135 kJ mol−1 , therefore increasing slightly the value calculated for the abstraction of the first methyl radical from adsorbed Cd(CH3 )2 (≈100 kJ mol−1 ).
4. Results and discussion The approach described above was applied to the study of the metal organic chemical vapor deposition of cadmium telluride (CdTe). The proposed kinetic scheme consisted of gas phase and surface reactions. In particular a feasible surface reaction scheme was identified linking information obtained at the atomic scale through quantum chemical methods with simulations and experimental observations
Fig. 4. Calculated (line) and experimental (points [9]) deposition rate as a function of the inverse of the substrate temperature. The deposition precursors Cd(CH3 )2 and Te(CH3 )2 with mole fractions of 1×10−3 and 2×10−3 , respectively, are fed to the reactor in a hydrogen carrier gas of 1.1×10−2 mol min−1 .
performed at the reactor scale. Embedding the kinetic scheme in a fluid-dynamic model of the reactor the growth rate of the film could be predicted for different operating conditions. A comparison between the predictions of the model and the experimental data is presented in Fig. 4. 5. Conclusions The possibility to follow a systematic procedure in order to realize kinetics schemes of gas phase and surface kinetic processes was investigated. The proposed approach consists of the adoption of quantum chemistry to generate the reaction parameters (e.g., transition state structure and energy) required by statistical thermodynamics theories in order to evaluate the kinetic constants for each investigated reaction. It was found that this approach can lead to good results if adopted together with physical and chemical intuition, which are helpful in order to reduce the total number of investigated reactions and to identify the surface species that can be considered representative of the whole surface structure. References [1] W. Tsang, R.F. Hampson, J. Phys. Chem. Ref. Data 15 (1987) 887. [2] R.G. Gilbert, S.C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell Scientific Publications, Oxford, 1990. [3] M.J. Frisch, et al., Gaussian 98, Gaussian Inc., Pittsburgh, PA, 1998. [4] W. Kohn, L.J. Sham, Phys Rev. 140 (1965) A1133. [5] A.D. Becke, J. Chem. Phys. 90 (1989) 5622. [6] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [7] C. Cavallotti, M. Masi, S. Carrà, J. Electrochem. Soc. 146 (9) (1999) 3264–3270. [8] D.G. Truhlar, B.C. Garret, S.J. Klippenstein, J. Phys. Chem. 100 (1996) 12771. [9] A.H. McDaniel, B. Liu, R.F. Hicks, J. Crystal Growth 124 (1992) 676.
Gas phase and surface kinetic schemes for metal organic chemical vapor deposition processes: a theoretical perspective Carlo Cavallotti, Maurizio Masi∗ , Sergio Carrà Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, via Mancinelli 7, 20131 Milan, Italy
Abstract In this work we propose a systematic procedure of realization of detailed kinetic schemes for gas phase and surface systems. The fundamental step in this process is the evaluation of the kinetic constants for the considered elementary reaction. Here we propose to evaluate the kinetic constants through statistical thermodynamic methods such as transition state theory using quantum chemistry calculated energies and vibrational frequencies. Different cases where that approach was followed are presented. In particular, we discuss the realization of microscopically reversible kinetic schemes for the chemical vapor deposition of zinc sulfide and cadmium telluride from metal-organic precursors. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Gas phase; Surface system; Quantum chemistry
1. Introduction The realization of detailed kinetic schemes of gas phase and surface processes is a fundamental step in the modeling of many systems of interest for chemical engineers and material scientists. Some examples of situations, where a detailed gas phase kinetic scheme is required are the combustion of hydrocarbons, plasma systems adopted for the deposition of advanced materials, the description of the reactivity of gases affecting the stratospheric ozone. The availability of a detailed surface reaction scheme is of great importance in all those systems where a chemical interaction between gas phase and surface occurs, such as chemical vapor deposition systems and catalytic reactors. A generic procedure of realization of a detailed kinetic scheme requires as first step the identification of all the chemical species (i.e., neutral species, radicals or ions) that are likely to be present in the gas or on the surface. Successively all the elementary reactions that can occur among these species must be considered and a kinetic constant for each reactive event must be determined. At this stage physical intuition is of great importance in order to cancel from the hypothesized events all those reactions that are unlikely to occur (e.g., a reactive event between two neutral species in a gas is possible only at very high temperatures because of the stability of the reagents). The next step is the determination of the kinetic constants for all the selected ∗ Corresponding author. E-mail address: [email protected] (M. Masi).
reactions. Many kinetic constant values for gas phase reactions are readily available from the literature [1] or can be found in kinetic data bases accessible from Internet (e.g., www.ca.sandia.gov/crf/research/applied/thermokindata/). However, when a system different from those already studied is considered the kinetic constants for many possible processes are often not known. In these cases the kinetic constant value can be either calculated or experimentally determined. The experimental evaluation of a kinetic constant is usually a time consuming process and can be hampered by many problems in the realization of a reliable experimental set-up. Moreover, it is not known ‘a priori’ if the considered reaction will have a relevant impact on the reactivity of the overall system or not. It is therefore a better approach to evaluate the kinetic constants of all the considered processes from a ‘priori method’ and then to identify the key reactions in the developed kinetic scheme from a sensitivity analysis and evaluate experimentally the kinetic constants of these processes. The generic procedure we propose for the realization of a kinetic scheme is summarized in Fig. 1. In this work we focused our analysis on the evaluation of values of kinetic constants for gas phase and surface kinetic processes from first principles. 2. Evaluation of kinetic constants of gas phase reactions The progress in the theory of evaluation of kinetic constants of gas phase reactions from first principles has been such that reliable theoretical estimation of rate coefficients for many processes can now be carried out. For example,
0254-0584/00/$ – see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 0 ) 0 0 3 2 0 - 5
198
C. Cavallotti et al. / Materials Chemistry and Physics 66 (2000) 197–200
Fig. 1. Generic procedure proposed for the realization of a kinetic scheme.
Gilbert and Smith [2] asserted that the kinetic constant for unimolecular reactions involving hydrocarbons can be calculated with an uncertainty factor of 3, which is acceptable in many practical cases. The main problem in the ‘a priori’ evaluation of a kinetic constant is that the most accurate theories require as input a great amount of data. In particular the expression of the kinetic constant for a generic reactive event given by classical transition state theory is kb T Q6= −Ea exp (1) kcin = sf h Qreag RT where kb and h are the Boltzmann and Planck constants, respectively, Q6= and Qreag are the partition functions of transition state and reagents, respectively, Ea is the activation energy of the process and sf the statistical factor accounting for the reaction path degeneracy. The partition function Qi is the product of the translational, rotational, vibrational and electronic partition functions of the considered specie: Qi = Qtrans Qrot Qvib Qel
(2)
with Qtrans =
2π mkb T h2
3/2
1/2 2 1/2 8π 2 Ia kb T 8π Ib kb T h2 h2 2 1/2 8π Ic kb T × h2
(3)
Qrot = π 1/2
Qvib =
s Y i=1
1 1 − exp(−hcυi /kb T )
(4)
(5)
Qel =
X −Ei gi exp kb T
(6)
i
where m is the mass of the molecule, Ia , Ib and Ic are the moments of inertia of the molecule around the principle axes, ν i the vibrational frequencies and Ei and gi the energies and degeneracies above the lowest level of the system. Rarely electronic states above the ground state have to be considered, while for reactions involving doublet or triplet species the degeneracy of the ground state is equal to that of the spin (i.e., two and three, respectively). Summarizing, the data required to evaluate the partition functions are the vibrational frequencies and moments of inertia of reagents and of transition state. All the information required can be obtained from a priori quantum chemistry calculations with a precision depending on the chosen method of calculation and on the system under consideration. Computational quantum chemistry (QC) is a field of research that has made much progress in the last few years and the awarding of the Nobel prize in 1998 to two pioneers of QC viz. W. Kohn and J.A. Pople is an acknowledgement of this trend. The steps that must be followed to obtain the data required by transition state theory are reported at the bottom of Fig. 1. To perform the calculations a software package can be adopted (e.g., g98, alchemy, mopac, qchem, cerius, etc.). All the calculations reported here were performed adopting the g98 suite of programs [3]. The procedure described above was applied to evaluate the kinetic constant of the gas phase reaction H+(CH3 )2 Zn⇒CH4 +CH3 Zn. From experimental results it was hypothesized that this reaction might have an impact on the process of deposition of zinc sulfide (ZnS) from gas phase precursors. However, the kinetic constant of the process is not known and in order to investigate the feasibility
C. Cavallotti et al. / Materials Chemistry and Physics 66 (2000) 197–200
199
Fig. 2. Structures of reagents, products and transition state and calculated parameters for the reaction (CH3 )2 Zn+H⇒(CH3 )Zn+CH4 .
of the hypothesis, a QC research of transition state structure, energy and vibrational frequencies was performed. A sketch of the structures of reagents and transition state together with some of the calculated data are presented in Fig. 2. A good agreement between calculated (−36±4 kcal mol−1 ) and experimental (−34.6 kcal mol−1 ) enthalpy of reaction was found. The calculations were conducted using the density functional theory method to solve the Shroedinger equation with the three parameters of Becke exchange and the Perdew–Wang correlation functionals (i.e., B3PW91) [4–6]. The triple zeta 6-311+G** basis set with added polarization and diffusion functions was adopted for the calculations.
3. Evaluation of kinetic constants of surface reactions The evaluation of kinetic constants for reactions involving surface species is a more difficult task than the study of gas phase reactions. The main problem consists in the individualisation of the structure of the surface site to be considered as representative of the entire surface. Successively this site can be considered as a reacting chemical species and the surface reaction kinetics can be investigated with the methods similar to those adopted for the gas phase. Since quantum chemistry calculations require an amount of computer time that scales from the square to the seventh/eighth power of the problem size, the dimension of the considered surface cluster must be limited. This limitation can be a major source of error because it excludes the possibility to account for the long range effects that are typical of surface networks. To illustrate a possible approach to the study of surface kinetics, we report here the process we followed to evaluate
the kinetic constant for the desorption of adsorbed species from a (1 0 0) CdTe surface. In Fig. 3 the structure of the site adopted to investigate the kinetics of adsorption of Cd(CH3 )2 on the CdTe (1 0 0) surface is presented [7]. In this case the calculations were performed adopting the B3LYP method and the 3-21G** basis set. The film surface was assumed to have the same structure as that of the solid network (i.e., zinc-blend), so that each metal atom can be bonded only to the other metal atom (i.e., Cd to Te and vice versa) and the bond angles are tetrahedral. Four hydrogen atoms are added at the sides of the surface cluster to avoid the presence of unpaired electrons, which would affect the results of the calculations. The evaluation of the kinetic constants for the processes of desorption is a more difficult task than the study of gas phase processes because of the lack of experimental data on surface reactivity. Moreover
Fig. 3. Structures of Cd(CH3 )2 adsorbed over a CdTe (1 0 0) surface site. The calculated adsorption energy was 31.4 kJ mol−1 .
200
C. Cavallotti et al. / Materials Chemistry and Physics 66 (2000) 197–200
the theoretical aspects of the kinetics of surface reactions have not yet been investigated as much as those of gas phase reactions [8]. Here we adopted transition state theory to determine desorption kinetic constants, but care must be placed in the interpretation of these results because of the above mentioned consideration and for the many approximations that had to be devised to account for missing data. Transition state theory requires the knowledge of the partition function of the molecule in the transition state and of the reactants according to the following equation: rot Qvib −Ea kb T 6= Q6= exp (7) k= rot h Qvib RT ads.spec. Qads.spec. vib rot rot where Qvib 6= , Q6= , Qads.spec. , and Qads.spec. are the vibrational and rotational partition functions for transition state and adsorbed species, respectively. With respect to Eq. (1) the translational and electronic partition functions for reactants and transition state were considered equal to 1. This was done to account for the fact that adsorbed surface species have no translational degrees of freedom. Eq. (7) can be further simplified observing that adsorbed species do not rotate and therefore Qrot ads.spec. = 1. Finally, it was assumed that the transition state structure is similar to that of the products. That is a direct consequence of the Hammond postulate, according to which in an endothermic process the structure of the transition state is near that of the products, and vice versa for an exothermic process. The desorption kinetic constant for adsorbed Cd(CH3 )2 was determined observing that, because of the little bond energy between Cd(CH3 )2 and the surface, the vibrational frevib quency of the bond is small and therefore Qvib 6= /Qads.spec. ≈ 1. Moreover because of the proximity of Cd(CH3 )2 to the growing surface it was assumed that no rotational degrees of freedom are active and therefore Qrot 6= ≈ 1. The pre-exponential factor calculated from Eq. (4) is about 6×1012 for the desorption process and the calculated activation energy for this reaction is 31 kJ mol−1 . The desorption of methyl from adsorbed Cd(CH3 )2 was assumed to have a pre-exponential factor of 1016 , in the range of those experimentally found for unimolecular gas phase reactions, and an activation energy of 135 kJ mol−1 , therefore increasing slightly the value calculated for the abstraction of the first methyl radical from adsorbed Cd(CH3 )2 (≈100 kJ mol−1 ).
4. Results and discussion The approach described above was applied to the study of the metal organic chemical vapor deposition of cadmium telluride (CdTe). The proposed kinetic scheme consisted of gas phase and surface reactions. In particular a feasible surface reaction scheme was identified linking information obtained at the atomic scale through quantum chemical methods with simulations and experimental observations
Fig. 4. Calculated (line) and experimental (points [9]) deposition rate as a function of the inverse of the substrate temperature. The deposition precursors Cd(CH3 )2 and Te(CH3 )2 with mole fractions of 1×10−3 and 2×10−3 , respectively, are fed to the reactor in a hydrogen carrier gas of 1.1×10−2 mol min−1 .
performed at the reactor scale. Embedding the kinetic scheme in a fluid-dynamic model of the reactor the growth rate of the film could be predicted for different operating conditions. A comparison between the predictions of the model and the experimental data is presented in Fig. 4. 5. Conclusions The possibility to follow a systematic procedure in order to realize kinetics schemes of gas phase and surface kinetic processes was investigated. The proposed approach consists of the adoption of quantum chemistry to generate the reaction parameters (e.g., transition state structure and energy) required by statistical thermodynamics theories in order to evaluate the kinetic constants for each investigated reaction. It was found that this approach can lead to good results if adopted together with physical and chemical intuition, which are helpful in order to reduce the total number of investigated reactions and to identify the surface species that can be considered representative of the whole surface structure. References [1] W. Tsang, R.F. Hampson, J. Phys. Chem. Ref. Data 15 (1987) 887. [2] R.G. Gilbert, S.C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell Scientific Publications, Oxford, 1990. [3] M.J. Frisch, et al., Gaussian 98, Gaussian Inc., Pittsburgh, PA, 1998. [4] W. Kohn, L.J. Sham, Phys Rev. 140 (1965) A1133. [5] A.D. Becke, J. Chem. Phys. 90 (1989) 5622. [6] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [7] C. Cavallotti, M. Masi, S. Carrà, J. Electrochem. Soc. 146 (9) (1999) 3264–3270. [8] D.G. Truhlar, B.C. Garret, S.J. Klippenstein, J. Phys. Chem. 100 (1996) 12771. [9] A.H. McDaniel, B. Liu, R.F. Hicks, J. Crystal Growth 124 (1992) 676.