Kinetic analysis of the chemical processes in the decomposition of gaseous dielectrics by a non-equilibrium plasma - part 1: CF4 and CF4/O2

Article

Kinetic analysis of the chemical processes in the decomposition of gaseous dielectrics by a non-equilibrium plasma - part 1: CF₄ and CF₄/O₂.

Glauco F. Bauerfeldt and Graciela Arbilla ^*

Departamento de Físico-Química, Instituto de Química, Universidade Federal do Rio de Janeiro, Sala 408, CT Bloco A, Cidade Universitária, 21949-900, Rio de Janeiro - RJ, Brazil

A integração numérica das equações diferenciais ordinárias que descrevem um sistema cinético e a análise de sensibilidade dos resultados aos parâmetros são metodologias cada vez mais utilizadas na cinética química. Neste trabalho, é apresentado um estudo de simulação numérica da decomposição em fases gasosa de CF₄ e de misturas CF₄/O₂ na presença de silício. É analisada a importância relativa dos processos individuais e são calculados os coeficientes de sensibilidade e o efeito da incerteza nos parâmetros. Os resultados são comparados com dados experimentais da literatura para ajustar os parâmetros do modelo. O principal agente de corrosão neste sistema é o flúor atômico. As concentrações das principais espécies (SiF₄, CO, CO₂ e COF₂) dependem da composição da mistura.

Numerical integration of the coupled differential equations which describe a chemical reacting system and sensitivity analysis are becoming increasingly important tools in chemical kinetics. In this work, a numerical modelling analysis of the chemical processes in the gas-phase decomposition of pure CF₄ and CF₄/O₂ mixtures, in the presence of silicon, was performed. The relative importance of individual processes was analysed and the sensitivity coefficients as well as the effect of the parameters uncertainties were determined . The results were compared with experimental data from the literature to adjust the model parameters. The main etching agent in the system is the fluorine atom. The concentrations of the main species (SiF₄, CO, CO₂ and COF₂) depend on the composition of the mixture.

Keywords: sensitivity analysis, rate of production analysis, CF₄ decomposition

Introduction

Models for the plasma chemistry of SF₆/O₂ and CF₄/O₂ mixtures have been extensively investigated by different research groups^1-18. The complexity of the involved processes makes it very difficult to develop and solve a complete model to explain and predict experimental results^19,20.

Such models should consider the homogeneous processes in the gas phase and the heterogeneous processes occurring at the gas-solid interface. Some aspects, such as free radical chemistry, electron impact dissociation rates for molecules and radicals, electron number density in the plasma, energy distribution for electrons and chemical species and also the need of solving the system in spatial and temporal coordinates, require an exact approach beyond the capabilities of current computational resources.

In this work, we used the submodel approach which is also frequently applied in other areas of kinetic and numerical modeling such as atmospheric and combustion chemistry²¹. Our main goal was to obtain a good description of the principal chemical processes in the gaseous phase and to analyse the relative importance of individual reactions and the parameters influence in the model results by estimating the sensitivity coefficients S_ij for the species (i) towards the parameters of the model (l_j ). Thus, we constructed chemical submodels in which the other processes are considered in a parameterised, simplified way. The present submodels use a semi-empirical approach in which phenomenological dissociation rates, calculated from the measured conversions of the feed gases in experimental studies, are incorporated and where the analysis is centered on the description of the neutral gas-phase chemistry which occurs in the plasma as the ionic species analysis did not prove relevant¹⁸.

Formulation of the models

The models of Edelson and Flamm³ and Ryan and Plumb^4,5 were used as a basis for the present kinetic scheme. The complete set was introduced and discussed by Bauerfeldt and Arbilla¹⁸ in a previous work on the plasma etching of silicon. This set of reactions included surface phenomena as physical adsorption and desorption, as well as surface reactions. The plasma was considered a source of ions and electrons which led to CF₄ dissociation and to atomic fluorine production.

Experimental data from Smolinsky and Flamm²², were also used to choose the boundary conditions, the parameters of the model and to test the validity of the model results. In that work, the CF₄/O₂ mixtures at a total gas number density of 1.6 ´ 10¹⁶ cm^-3 (0.5 Torr) flowing in a 5 cm length aluminum tube, were excited by a 49 W, 13.56 MHz discharge. The stable products analysis was performed up to 10 cm downstream from where the discharge started.

The most uncertain aspects in the formulation of this submodel are the electron impact dissociation rate for CF₄, the rate constants for gas-phase free radical reactions and the heterogeneous processes. Electron impact dissociation rates can be calculated from estimated electron number density, electron energy distribution and electron impact dissociation cross-section of the interest species. Plumb and Ryan⁴ have made such estimates which are expected to be accurate within one order of magnitude. From measured results^22,23 the dissociation coefficients for CF₄ and O₂ can be estimated in the experimental conditions. In our model, these values were adjusted as parameters in order to fit the experimental dissociation rates.

For the boundary conditions of our work, a plug flow in a cylindrical tube was assumed. The plasma region of the reactor corresponds to a gas mixture residence time of 2.25 ´ 10^-2 s. The space beyond the plasma region, called afterglow, was also included in the calculations, what leads to a total residence time in the reactor of 4.45 ´ 10^-2 s. The adsorption of gas phase species on the reactor wall and further reaction or desorption to return to the gas phase were considered in a simplified way.

The numerical method

The set of differential equations were solved using the fourth order Runge-Kutta-Semi-Implicit Method²⁴ as implemented in the package KINAL²⁵. The relative relevance of each reaction was first evaluated by calculating the contribution of each step to the total rate of concentration change for each species. Then, in order to evaluate the effect of parameters uncertainties on the predicted concentrations, the sensitivity coefficients²⁶ were calculated by the Direct Decomposed Method²⁷. In addition to the relevance and sensitivity analysis, another test was done by changing some of the parameters within their range of uncertainties. This calculation was necessary as some of the parameters and constants are quite hard to evaluate, such as electron number density, branching ratios and heterogeneous reaction rate coefficients.

Results and Discussion

As described above, the reaction set used for the sensitivity calculations was previously employed to describe the plasma etching of silicon by pure CF₄ and CF₄/O₂ mixtures, and can be found in our previous paper¹⁸. This reaction set was proposed to fit experimental data from Smolinsky and Flamm²². Initial conditions for the simulation are listed in Table 1 and are the same as used in reference 18.

Pure CF₄

There is no direct experimental evidence about the branching ratio for CF₄ decomposition. Some indirect information may be obtained from CF₄/O₂ results, as will be discussed below. Clearly, this ratio is an important parameter of the model. In this work we explored the effect of a wide range of values. Following electron impact, CF₄ may dissociate to CF₃ and CF₂ radicals. In fact these are probably non direct processes. The direct dissociation of CF₄ through the reaction:

(1)

proceeds only at high electron energies (12.5 eV threshold)²⁸. More recent data²⁹ show that the alternative reaction:

(2)

is relatively fasterand proceeds at lower energies, 5 - 6 eV. This reaction is followed by the rapid detachment reaction:

(3)

This sequence being equivalent to reaction 1.

In a similar way, it was proposed³⁰ that CF₂ is produced through the rapid dissociation of an excited state of CF₃ radical which in turn is formed from CF₄ decomposition. In the time scale of the experiments, the CF₂ production may be considered a direct process after electron impact of CF₄ :

(4)

Branching ratios k_{CF4 ® CF2} / k_{CF4 ® CF3}, k_j being the rate constant for the reaction j, from 14 to zero were tested. The best results, when compared with experimental data, are obtained when the primary dissociation of CF₄ favours the formation of CF₂ by a factor 2.3. Because of that a ratio of 2.4, as estimated by Plumb and Ryan⁴, was used.

Table 2 shows the relative importance of individual reactions, based on a rate of production analysis, for the main gaseous species. The production of CF₂ by electron impact of CF₃ is a negligible path of reaction for CF₃ radicals. Reactions of CF₃ with neutral species F and F₂ are the main path of consumption of the radical. Also, at the early stages of reaction, when F and F₂ concentrations are still low, the recombination to C₂F₆ appears an important path.

Our simulations show that the rate of the recombination processes is at least 10³ times faster than the electron impact dissociation, not included in the final model. Also, since CF₄ concentration is 10² - 10³ times greater than CF₃ concentration, the direct electron dissociation of CF₃ radical is a negligible source of CF₂ when compared with CF₄ dissociation to produce CF₂ + 2 F. A similar situation arises for CF₂ radicals. The electron impact dissociation, to give CF + F, is at least 30 times slower than the recombination reaction of CF₂ with F atoms. Also, CF₂ dissociation is a negligible source of F atoms when compared with the primary CF₄ dissociation to produce CF₂ + 2 F.

CF₃ and CF₂ dissociation processes may be included in a more comprehensive reaction set, in order to obtain a better description of the system. Nevertheless, it would not lead to important changes in the results of the model mainly due to the uncertainties in primary dissociation rates and heterogeneous reactions of atoms.

The plasma chemistry is highly influenced by the dissociation and recombination processes of CF₂ and CF₃ . Clearly, the main recombination reaction of CF₃ is with F atom. This fast reaction controls the CF₃ concentration and restricts the amount of CF₄ consumed to very low values. At the end of the discharge region (5 cm) 96% of the initial CF₄ remains. In the afterglow region, where electron dissociation ceases, the reforming of CF₄, through reactions

(5)

(6)

continues and, because of that, a net consumption of 2 % is found at 10 cm.

Figures 1 and 2 show the first-order local concentration sensitivity coefficients S_ij for the main species towards the parameters of the model. As usual, these coefficients, elements of the local concentration sensitivity matrix, are defined as

were Y_i are the concentrations of the chemical species and l_jare the parameters of the model. The sensitivity matrix, S, represents a linear approximation of the dependence of the solutions on parameters changes. The change of a parameter belonging to reaction j causes a direct concentration change in those species which are reactants or products in that reaction. Also, the direct concentration changes cause further differences in the concentration of other species. The latter, indirect, effects are non-linear and can not be predicted by screening analysis^25b. This non-linear effects can be revealed by sensitivity analysis. The information taken from these coefficients is rather different from that taken from the so-called brute force method, where a parameter (for example the electron density) is changed. The S_ij values are local, since they belong to a time interval defined by the time of the perturbation t₁ and the time of the observation t₂ and, also, they represent the perturbation on a species i , while all the others are kept constant. On the other hand, the previous analysis showed the effect of a substantial change on one of the parameters, during the total time of observation t₂^25b. The information taken from all the analysis done here is complementary and should be considered as a whole in order to assess the relevance and interconnection of parameters and variables and to decide whether a reaction or a chemical species may be eliminated from the model, or not.

The high level of CF₂ concentration relative to CF₃ is due to two factors: as shown in Figures 1 and 2, CF₂ formation through the reaction e^- + CF₄® CF₂ + 2F + e^- is faster than CF₃ production reactions1 and

(7)

by a factor of about 1.5. Also, the rate of consumption of CF₃ by reaction 5 is about 1.2 times greater than that for CF₂ recombination reaction 7.

In the plasma region stable C₂F₆ grows steadily. CF₃ recombination reaction to produce the vibrationally excited species C₂F₆^* :

(8)

takes account of about 15.5% of the total lost of CF₃ radicals. The model considers the C₂F₆ electron dissociation:

(9)

The dissociation coefficient used by Edelson and Flamm³ leads to a considerable reduction of C₂F₆ concentration, since the rate of C₂F₆ electron dissociation is about 0.5 times the rate of C₂F₆ production by CF₃ radical recombination. If the rate coefficient of Ryan and Plumb^4,5, 20 times smaller, is used, the contribution of C₂F₆ electron dissociation reaction drops to virtually zero and C₂F₆ concentration increases by a factor of 2. Nevertheless, CF₃ concentration does not alter significantly since that electron dissociation contributes in about 6% to its formation.

In the post-discharge region CF₃ concentration drops drastically and very little C₂F₆ is further formed. In this region, the main recombination reactions are with F and F₂. Also, in this region a considerable fall of CF₂ concentration occurs, mainly because the production of CF₂ by CF₄ electron dissociation stops and the rapid recombination reaction with F atoms continues downstream.

The silicon etching process was modelled as a sequence of single F atom reactions which forms SiF₄ on the surface (SiF₄/Si) that subsequently desorbs to the gas phase. The choice of atomic fluorine as the active etching is supported in previous experimental and simulated data^1-20. As in the previous works^3,5 the first F atom reaction was chosen as the limiting step in order to emulate experimental results³¹. Silicon was assumed to be uniformly distributed in the reactor. In the presence of Si, the F atom concentration is reduced in about 10-15% for a silicon number density of 1 ´ 10¹⁴ particles cm^-3 and in about 25% for a silicon number density of 1.6 ´ 10¹⁶ particles cm^-3 . The value of the rate coefficient for:

(10)

is certainly one of the most uncertain aspects in the formulation of the model. In this work we used the value of Edelson and Flamm³ and also the value of Ryan and Plumb⁵, which is smaller by a factor of 4.6. The results for SiF₄, CF₃, CF₂ and F differ in less than 25% which is not a significant figure when considering the other uncertainties of the model.

Another uncertain parameter of the model is the electron number density in the plasma. The main sources of F atoms are reaction 1 and 4 which depend on electron number density. The values of Edelson and Flamm³ (1 ´ 10¹⁰ cm^-3) and Ryan and Plumb⁵ (6 ´ 10¹⁰ cm^-3) were both tested. The best agreement with experimental results²² is obtained for an electron number density of 1.0 ´ 10¹⁰cm^-3 , a silicon number density of 1.0 ´ 10¹⁴cm^-3 and with a rate constant of 4.61 ´ 10^-13 molec^-1 cm³ s^-1 for reaction 9.

The results stress our previous conclusions: the shape of the sensitivity curves follows the general shape of the individual rate curves¹⁸ and the ratio between the S_ijvalues is closely related to the contribution of each reaction (Table 2). For example, S_{F, CF4}®CF2³² values are twice the S_{F, CF4}®CF3 values and are nearly constant within the plasma region (Figure 1a). The S_{F, j} values for the atomic fluorine association reactions with CF₂ and Si (Figure 1b) show that for small residence times, the changes in F + Si association rate constant will affect F concentrations more than the changes in F + CF₂ association rate constant. The inverse holds for longer residence times. That is a direct consequence of the contribution of F + Si association, on the silicon surface, being more important at the reactor entrance or for short times and the contribution of F + CF₂ association being more important as the CF₂ concentration grows up. Also, the S_F,j coefficients (Figures 1b and 1c) show that the more relevant reactions for atomic fluorine are the production reactions CF₃ + F and CF₂ + F and the recombination to form F₂.

Similar results were obtained for CF₂ and CF₃ sensitivity coefficients. The values for S_{CF3, CF3 + F + M} ®CF4 + M /[M] and S_{CF3, F + CF2}®CF3 are similar, except in the post discharge region, where changes in F + CF₂ association rate constant should affect more the CF₃ concentration (Figure 2a). For CF₂ radicals, Figure 2b, the system is more sensitive to changes in F + CF₂ association rate constant. Because of the non linearity of the system, a perturbation in CF₄ electron dissociation rate to give CF₂ + 2F leads to a rather small change in [CF₂] , which recombines, further, with fluorine atoms. In other words, since CF₂ production from CF₄ and consumption by association with atomic fluorine reactions are coupled, small changes in the former hardly affect the radical concentration.

CF₄ / O₂ Mixtures

In our previous work on the plasma etching of silicon by CF₄/O₂ mixtures, F, CF₃ and CF₂ concentrations dependence on the oxygen concentration was suggested, both in the plasma region and in the afterglow region¹⁸.

In the presence of oxygen, the O atoms, which are mainly formed through electron impact dissociation of the molecule:

(11)

and

(12)

compete with F atom for CF₃ and CF₂ radicals through reactions:

(13)

(14)

(15)

The rate constant of CF₂ + O(³P) reaction is one order of magnitude higher than the rate constant for the F + CF₂ recombination. For the set of rate constants used in this model, the reverse situation holds for CF₃ .

Thus, in the presence of O₂ , new intermediates and new products (COF, COF₂, CO and CO₂ ) appear¹⁸ and also the concentration of F, CF₂ and CF₃ are controlled by the coupled association and recombination reactions of CF₂ and CF₃ with either F or O(³P). The relative relevance of reactions with F and O atoms changes with the composition of the mixture. For low concentrations of O₂, the reactions of CF₂ and CF₃ with F atoms become relevant and a significant fraction of COF is converted to COF₂. At high concentrations of O₂, COF is almost completely oxidised to CO₂ . The ratio (3.5) between the O(³P) reaction with CF₃ and CF₂ rate constants is slightly higher than the ratio (2.5) between CO₂ and CO concentrations, showing that part of COF is still reacting with F.

Table 2 compares the rate of sink reactions for F, CF₂ and CF₃. The entries of the table show some of the significant differences between the results for pure and oxygenated mixtures. With low concentrations of molecular oxygen, a very significant fraction of CF₂ is still converted to CF₃ through association with atomic fluorine. The COF which is formed by reaction of O atoms with CF₂ , reacts further with atomic fluorine to produce COF₂ . Only a minor part of COF reacts with oxygen producing CO₂ .

At high relative concentrations of molecular oxygen in the feed gas, the CF₂ produced in the primary dissociation step reacts exclusively with O atoms forming CO and COF which are rapidly converted to CO₂. In the same way, the CF₃ is converted rapidly to COF₂, which may dissociate to COF and ultimately CO₂ and CO.

Some of the sensitivity coefficients are presented in Figures 3 and 4. The sensitivity coefficients for the formation reactions (Figures 3a, 3b and 3c) follow the relative importance of individual reactions, that is S_F,CF4®CF2 + 2F > S_F,CF4®CF3 + F /[M] > S_F,F2®2F /[M] . Also, these S_F,j values are higher than values for reactions 13 – 15 (Figure 3c). The S_F,j coefficients calculated for the main sink reactions (Figures 3a, 3b and 3c), in the presence of O₂, show that in that environment the main atomic fluorine reaction is the self recombination to form F₂, as confirmed by Table 2.

The S_F,j coefficients calculated for reactions

(16)

and

(17)

follow the same trend, the ratio between them being approximately the [M] value (Figure 3d). For the 75% CF₄ / 25% O₂ mixture, the S_F,COF+O(3P)®CO2+F value is about 15 times the S_F,COF+F®COF2 /[M] since the COF , which is formed by reaction of O atoms with CF₂, reacts with O to produce CO₂, rather than with F, to produce COF₂. For these plasmas where the CF₄/O₂ ratio in the feed gas is higher, the S_F,COF+FàCOF2 /[M] becomes relatively higher.

The sensitivity coefficients for COF₂ (Figure 4a) and COF (Figure 4b) confirm that the main path of formation of COF₂ is the reaction between CF₃ and O(³P) atoms, which is about 27 times faster than reaction 17 (COF + F + M à COF₂ + M). Finally, in the plasma region, reaction between CF₂ and O(³P) to form COF:

(18)

is about 16 times faster than the further reaction of COF with atomic fluorine (reaction 16). This result is also shown by the comparison of the sensitivity coefficients S_COF,COF+FàCOF2 /[M] and S_{COF,CF2+O(3P)}àCOF+F (Figure 4b). Downstream of the discharge region, atomic oxygen concentration dramatically drops through reactions with CF₂ and COF and the formation of the final product COF₂ predominates.

In Figure 5 the rate of formation of gaseous SiF₄ as function of the distance from the origin and the mole percent of O₂ in the feed is displayed. Since in this model atomic fluorine is the active etching agent and the primary etching reaction was considered rate controlling, the surface in Figure 5 closely reproduces the change in atomic fluorine concentration with distance from the origin and the mole percent of O₂ in the feed¹⁸.

Conclusions

The main goal of this work was to analyse the chemical processes in the plasma decomposition of CF₄ and CF₄/O₂ mixtures in the presence of silicon. The rate of production and sensitivity analysis, as well as the computed concentrations, show that the major features of plasma etching of silicon are explained in terms of gas-phase reactions. For this system, positive and negative ionic species were also considered, and incorporated to the model using literature experimental rate coefficients. The results showed that reactions involving these species are not important in determining the gas phase chemistry.

The model reproduces the experimental conclusion that atomic fluorine is the active etching agent. The fact that the primary etching reaction appears to be the most significant process and the sequential fluorination reactions have no significant sensitivities, is due to the fact that their rates were purposely chosen not to be rate-controlling.

For a complex system with significant uncertainties, such as this, the more important contribution of modelling is to demonstrate, through the rate of production and the sensitivity analysis, which reactions require further experimental or theoretical investigation.

The importance analysis shows that many key processes are poorly known and need a better determination. The major uncertainties in the gas phase chemistry are the branching ratios for the primary dissociation processes, the cross sections for electron impact dissociation and the electron number densities.

The extension of these chemical sub-models to more complete models will involve a better determination of the surface chemistry and the transport of radicals and ions, which were crudely parameterised in this work. The formulation of a complete model must also involve the consideration of the energy distribution of particles and temperature gradients. These results may be considered as an extension of previous chemical models and provide forward insight into the chemical processes details.

Acknowledgements

The authors thank partial financial support from CNPq and FAPERJ. They also thank Prof. T. Turányi (Central Research Institute of Chemistry, Budapest, Hungary) for a free copy of KINAL package and Prof. Gerardo Gerson B. de Souza (DFQ/IQ/UFRJ) for his interest in this project.

References

1. Mogab, C. J.; Adams, A. C.; Flamm, D. L. J. Appl. Phys. 1976, 49 , 3796.

2. Kushner, M. J. J. Appl. Phys. 1982, 53 , 2923.

3. Edelson, D.; Flamm, D. L. J. Appl. Phys. 1984, 56, 1522.

4. Plumb, I. C.; Ryan, K. R. Plasma Chem. Plasma Process. 1986, 6 , 205.

5. Ryan, K. R.; Plumb, I. C. Plasma Chem. Plasma Process. 1986, 6 , 233.

6. Plumb, I. C.; Ryan, K. R. Plasma Chem. Plasma Process. 1986, 6 , 247.

7. Kline, L.E. IEEE Trans. Plasma Sci. 1986, PS-14 , 145.

8. Anderson, H. M.; Merson, J. A.; Light, R. W. IEEE Trans. Plasma Sci. 1986, PS-14, 156.

9. Venkatesan, S. P.; Trachtenberg, I.; Edgard, T. F. J. Electrochem. Soc. 1987, 134 , 3194.

10. Ryan, K. R. Plasma Chem. Plasma Process. 1989, 9, 483.

11. Economou, D. J.; Park, S. K.; Williams, G. J. Electro-chem. Soc. 1987, 134 , 3194.

12. Venkatesan, S. P.; Edgard, T. F.; Trachtenberg, I. J. Electrochem. Soc. 1989, 136 , 536.

13. Ryan, K. R.; Plumb, I. C. Plasma Chem. Plasma Process. 1990, 10 , 207.

14. Lii, Y. J.; Jorné, J.; Cadien, K. C.; Schoenholtz Jr., J. E. J. Electrochem. Soc. 1990 , 137 , 3633.

15. Park, S. K.; Economou, D. J. J. Electrochem. Soc. 1991, 138 , 1499.

16. Kopalidis, P. M.; Jorné, J. J. Electrochem. Soc. 1993, 140 , 3037.

17. Khairallah, Y.; Khonsari-Arefi, F.; Amouroux, J. Pure Appl. Chem. 1994, 66 , 1353.

18. Bauerfeldt, G. F.; Arbilla, G. Quím. Nova 1998, 21, 25.

19. Manos, D. M.; Flamm, D. L. Plasma Etching: An Introduction; Academic Press; San Diego, CA , 1989.

20. Ryan, K.R.; Plumb, I.C.; Crit. Rev. Solid State Mater. Sci. 1988, 15 , 153.

21. Finlayson-Pitts, B. J.; Pitts Jr., J. S. Atmospheric Chemistry: Fundamentals and Experimental Techniques; John Willey & Sons ; New York, 1986.

22. Smolinsky, G.; Flamm, D. L. J. Appl. Phys. 1979, 50, 4982.

23. d'Agostino, R.; Flamm, D. L. J. Appl. Phys. 1981, 52, 162.

24. Kaps, P.; Rentrop, P. Numer. Math. 1979 , 33, 55.

25. (a) Turányi, T. Comput. Chem. 1990, 14, 3, 253. (b) Turányi, T. J. Math. Chem. 1990, 5, 203.

26. (a) Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and Dynamics; Prentice Hall, Englewood Cliffs; New Jersey, 1989. (b) Pilling, M. J.; Smith, I. W. M. Modern Gas Kinetics. Theory, Experiment and Application Blackwell Scientific Publications; Oxford, 1987. (c) Hirst, D. M. A Computational Aproach to Chemistry; Blackwell Scientific Publications; Oxford, 1990.

27. Valkó, P.; Vajda, S. Comput. Chem. 1984, 8, 255.

28. Winters, H. F.; Inokuti, M. Phys. Rev. 1982, A25, 1420.

29. Hunter, S. R.; Christophorou, L. G. J. Chem. Phys. 1984, 80 , 6150.

30. Flamm, D. L. J. Appl. Phys. 1980, 51, 5688.

31. Flamm, D. L. Donnelly, V. M. Plasma Chem. Plasma Process. 1981, 1, 317.

32. In this work, the symbol S_{F,CF4 ® CF2} is used to indicate the sensitivity coefficient of species i = F towards the rate constant for reaction e- + CF₄® CF₂ + 2F + e-. A similar nomenclature is used for the other S_ij coefficients.

Received: September 22,1998

Publication Dates

• Publication in this collection
  03 Apr 2001
• Date of issue
  Apr 2000

History

• Received
  22 Sept 1998