Plasma Chemistry and Plasma Processing, VoL 6, No. 3, 1986 A Model of the Chemical Processes Occurring in CFffO2 Discharges Used in Plasma Etching I. C. Plumb 1 and K. R. Ryan 1 Received September 20, 1985; revised February 17, 1986 A model has been developed in an attempt to explain the chemistry which occurs in plasmas produced in mixtures of CF4 and 02. Emphasis is placed on gas-phase free radical reactions, and the predictions of the model are compared with experi- mental results. Dissociation rates following electron impact are deduced mainly from experimental observations although relative dissociation rates have been calcu- lated. An important assumption of the model is that CF e can be produced as a primary dissociation product following electron impact. Furthermore, this process is favored over that producing CF3 by more than a factor of 2. Experimental evidence is presented to support this assumption. Although the model agrees well with experiment on the total amount of fluorine produced, some discrepancy exists between the predicted and measured values ofF2. It is suggested that the higher concentra- tions detected in the experiments resulted from recombination of F atoms in the sampling region. The agreement for concentrations of COe, CO, and COF 2 is generally better than a factor of 2 over a wide range of experimental conditions. KEY WORDS: Plasma etching; gas-phase reactions; modelling. 1. INTRODUCTION Plasma etching represents an important step in the fabrication of semiconductor devices for the microelectronics industry. Nevertheless the rapid progress which has been evident in this area has been based largely on an empirical approach. This is because the multitude of complex proces- ses which occur in the plasma environment make it very difficult to develop a model which can predict or explain the observed results for a given set of conditions. It is evident that, for further rapid development of etching technology, the fully empirical approach will have to give way to more sophisticated methods based upon at least a partial understanding of the processes involved. Attempts to develop quantitative models must focus on 1 CSIRO Division of Applied Physics, Sydney, Australia 2070. 205 0272-4324/86/0900-0205505.00/0 ~) 1986 Plenum Publishing Corporation
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`206 Plumb and Ryan two complicated aspects of the plasma process, namely processes occurring in the gas phase and those occurring at the gas-solid interface. Clearly these are strongly coupled regions of interaction, but this somewhat arbitrary separation can provide some insight into the possible mechanisms of the overall process. For example, a reasonable model for the gas-phase chemistry will be able to predict the chemical identity of the active species which arrive at the gas-surface interface. With this knowledge, one is then in a better position to begin to consider how these identified species interact with the surface. In the gas phase one is confronted with a particularly complicated set of conditions which can lead to a diverse range of reactions. Furthermore, important parameters such as the electron number density and energy distribution are poorly defined and, even if they were well known, dependent parameters such as the rates and pathways of molecular dissociation result- ing from electron impact are not. One aspect of the gas-phase processes about which there is considerable uncertainty is the free radical chemistry. In particular one needs to know which are the important reactions, how the rates of these reactions vary with gas number density, gas composition and temperature, and what role these variations play in controlling the identity of the species arriving at the surface. Recent publications from this laboratory (1-4) have reported measure- ments of the rate coefficients for gas-phase free radical reactions which are believed to occur in plasma etching. In this study we consider in more detail the implications of some of those measurements for the chemistry of plasmas of mixtures of CF4 with 02. In particular a reaction set is developed using the best available reaction rate coefficients--either estimated or measured-- and the predictions derived from this reaction set are compared with available measurements of the gas-phase composition downstream of the plasma. In an accompanying work (5) the relevant parts of the model are applied to plasmas of pure CF4 and the results again compared with experimental findings. The most detailed experimental information concerning stable products detected downstream of a CFJO2 plasma can be found in the work of Smolinsky and Flamm. (6) In that work, mixtures of CF4/O 2 at a total gas number density of 1.6 x 1016 cm -3 (0.5 tort) flowing in a 1.9 cm i.d. alumina tube were excited by a 49 W 13.56 MHz discharge extending over 5 cm of the tube length. Sampling of the effluent from the discharge was by mass spectrometry with the inlet pinhole located 15 cm downstream from where the discharge commenced. The residence time could be varied by changing the pumping speed, while the pressure was maintained by increasing or decreasing the incoming flow rates. Experimental results were reported for nominal discharge residence times of 7, 20, and 99 ms.
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`Chemistry of CFJO 2 Discharges 207 Perhaps the most notable feature of the results at each of these residence times was the dependence of COF2 and CO2 on the mole percent of 02 in the feed gas. In all cases COF2 was much higher than CO2 at low mole percent O2 while for high mole percent 02, CO2 became the dominant product. In a recent publication (3) we have speculated that reactions of COF may provide a partial explanation for these observations. It was proposed that, under conditions of low O, COF would be converted mainly to COF2 whereas at higher O, COF would be converted mainly to CO2. The mechanisms controlling the production of COF2 and CO2 in these plasmas must clearly be an important part of any model developed to explain the chemistry. In the next section details of the development and structure of the model are given. This is followed in Section 3 by a detailed comparison of the predictions of this model with experimental results obtained by Smolinsky and Flamm. 2. DEVELOPMENT OF THE MODEL Apart from the free radical chemistry the most uncertain aspects in the formulation of the model are: (a) the electron impact dissociation rates for molecules and radicals in the plasma, (b) the branching ratios for these dissociations, particularly for CF4, and (c) the influence of walls on the chemistry by providing a significant sink for radicals. Each of these aspects will be considered in turn. 2.1. Dissociation Rates In principle these can be derived by estimating the electron number density and the electron energy distribution and combining these estimates with what is known of the electron impact dissociation cross-sections of the species concerned. We have made such estimates for CF4, 02, and CO: and the results of our calculations are given in Appendix 1. Because of the number of approximations employed in these calculations we would not expect them to be accurate to better than an order of magnitude. An alternati*e approach for the estimation of dissociation rates is suggested by the results of Fig. 7 of Smolinsky and Flamm. The percent conversions of both CF4 and 02 are plotted as functions of both composition and discharge residence time. At the longest residence time, 99 ms (equivalent to a flow rate of 5 seem), it is seen that for 80% 02, the CF4 is 82% converted to products. At this particular 02 it would be expected that reactions between O and CF4 dissociation products (CF 3 and CF2) would dominate and that reactions between CF3 or CF2 and F to reform
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`208 Plumb and Ryan CF4 would be unimportant. From the reported percent conversion it can be concluded that the phenomenological rate coefficient for dissociation is of the order of 20 s -1. One can arrive at an estimate of the dissociation rate coefficient for 02 using arguments similar to those outlined above for CF4. Thus in Fig. 7 of Smolinsky and Flamm it can be seen that for a gas composition of 18% 02, 76% of the 02 is converted to products. If it is assumed that the O is kept so low by reaction with radicals derived from CF4 that combination to reform 02 downstream may be ignored, then these figures again result in a value of about 20 s -1 for the first-order dissociation rate coefficient for 02. From these observations we make the simplifying assumption that the dissociation rate for all species is 20 s -1 throughout the entire range of conditions considered in this study unless more quantitative information is available. 2.2. Branching Ratio for CF4 Dissociation No quantitative experimental evidence exists from which the break- down pathways for CF4, following electron impact, can be deduced. Obviously CF3 formed by electron impact on CF4 can dissociate further following subsequent electron impact. However, because CF3 reacts rapidly with neutral species under the conditions discussed here, electron impact of CF3 is a negligible source of CF2. However, CF2 can be produced rapidly following the initial electron impact on CF 4. This can occur through the production of CF3 in an excited state which then undergoes a rapid dissoci- ation to produce CF 2. In this regard we note that Flamm (31~ postulated a short-lived state of CF3 which dissociates, after a transition to a repulsive state, into CF2+F. These observations were made in a radiofrequency discharge and support the suggestion that CF2 can be looked upon as a direct product of electron impact of CF4 on the time scale appropriate to collisions in the plasma etching environment. The branching ratio forms an important component of any model designed to describe these plasma processes. Earlier studies from this laboratory demonstrate that, in O atom rich environments, CF3 reacts to produce COF2 while CF2 produces CO2 and CO. (1'3) This information may be used to obtain an estimate of the relative rates for dissociation of CF4 to produce CF3 and CF2 from the results in Fig. 8 of the work of Smolinsky and Flamm. In part c of that diagram the results obtained at high mole % 02 and short discharge residence times indicate that COF2 , CO2, and CO are all roughly equal. Assuming that under these conditions COF 2 arises predominantly from CF3 while CO2 and CO are derived from CF2, the results imply that the primary dissociation of CF4 favors the production of CF2 by about a factor of 2.
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`Chemistry of CF4/O2 Discharges 209 In view of the importance of this branching ratio and the uncertainty in the estimate given above, it was decided to make a more direct determina- tion which was again based upon product analysis in an oxygen-rich environment. Such a determination will be accurate provided that: (i) the degree of dissociation of products by electron impact is negli- gible, (ii) O >> IF, CF2, or CF3 so that CF2 and CF3 react only with oxygen atoms, and (iii) sufficient time is allowed downstream of the discharge so that CF2 and CF3 are consumed completely. Experiments were performed using the gas flow reactor described previously. (1-4) Mixtures of CF4 with 02 in helium were passed through a microwave discharge. Typically the 02 was 1.6 x 1015 cm -3 and the CF4 1013 cm -3. The residence time in the discharge was 1 ms, which resulted in 5% dissociation of 02 and 7% dissociation of CF4, although the amount of dissociation depended on the discharge power employed. The O was > 1014 cm -3 and typically >200 times the combined initial concentrations of CF3 and CF2. Given the rate coefficients for reactions of CF3 and CF2 with O atoms, the pseudo-first-order loss rates for CF3 and CF2 with O would be >3.1 x 10 3 and 1.8 x 103 s -1 respectively. Assuming that the first- order dissociation rates for CF3 and CF2 are comparable to those for CF4 and 02, then, under these experimental conditions, a negligible fraction of the radicals produced in the primary dissociation step is subjected to further electron impact dissociation. The sensitivity of the instrument for CO and for CO2 was determined using known flows of the pure gases while that for COF2 was obtained by allowing CF3 produced by reaction of F atoms with CF3H to react with excess O atoms. The COF2 produced was equated with the measured change in O. These experiments resulted in a value of (2.5 + 1.0) for the ratio of the primary dissociation rate for CF2 production relative to that for CF3 production. In subsequent treatment of the dissociation of CF4 by electron impact it has been assumed that (CF 3 + F) and (CF2 + 2F) are the dissociation routes. The processes producing CF2 are viewed as consecutive unimolecular dissociations of CFa and CF3 rather than a direct process which yields CF2 + F2. This view is taken mainly because, in experiments using the flow reactor, the F2 detected was <1% of the F. It is important to note that the experiments of Smolinsky and Flamm were carried out in a radiofrequency discharge whereas those described here used a microwave discharge to produce the free radicals. Clearly, one would expect that the electron energy distribution would be quite different in these two cases but, nevertheless, both provide strong evidence for the production of CF2 by very fast processes following electron impact on CF4.
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`210 Plumb and Ryan 2.3. Wall Effects If radical loss at the walls is severe, this Can have a controlling influence on the overall chemistry. However, the results of Smolinsky and Flamm were obtained in an alumina tube. It has been our experience, at least outside of the discharge zone, that if a suitable conditioning time is allowed this material will present an inert surface to gas-phase species and we would expect wall loss to be a very minor route. Therefore we neglect radical loss at the walls. 2.4. Details of The Model Given estimates for the overall dissociation rates for CF4 and 02 as well as a value for the branching ratio for CF4 decomposition, it should be possible to compare the predictions of the model with the results of Smolinsky and Flamm. Table I lists the complete reaction set used in the Table I. Reaction Set Used for the Calculations Reaction Reaction Rate Notes References number coefficient at 0.5 torr a *1 CFa-% CF3+F 6 b,~ *2 CF4 -% CF2 + 2F 14 b,~ 3 CF3 -% CF2+ F 20 b,a 4 CF2-% CF+F 20 b,a 5 CF 3 + CF 3 M C2F6 8 X 10 -12 e *6 CF3 + F ~ CF 4 1.3 x 10 -it e 7 CF2+ CF2-* C2F 4 5 x 10 -14 f 18, 19 *8 CF2+ F M--* CF 3 4.2X 10 -13 9 CF+F ~--* CF2 5x10 -15 10 CEF 6 .-%. CF3-1- CF 3 20 b,d 11 C2Fa -% cg2+ CF 2 20 b,d 12 F+ C2F4--°" CF3 + CF2 4x10 -n 20 13 CF2+CF3 M C2Fs 8.8 X 10-13 e 14 C2F5 + F--'," CF3 + CF 3 lxl0 -11 g 15 CF+ CF2-* C2F s 1 x 10 -12 h 16 C2Fs + F --~ C2F 4 1 x 10 -12 h "17 O2 ~'~ O'q- O 6.5 b.i 18 02 ..% O+OOD) 7.5 b,i 19 O2-% O-+O 6 b,~ 20 O(1D)+O2-* O+O2 4x10 -n 21 21 O(ID) + CF4-*" O+ CF4 1.8×10 -13 22 22 O(1D) +COF2-* O+COF/ 5.3x 10 -tl 23 23 O(1D) + COF2 "-~ g2+ CO2 2.1x 10 -it 23 24 O(1D) ,,¢~11 ~ O 2 x 103 J 25 O-+O --', O2(+e) 3 x 10 -~° 24
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`Chemistry of CF4O 2 Discharges 211 Table I. Continued Reaction Reaction Rate Notes number coefficient at 0.5 torr a References 26 O- -%" O(+e) 5 × 103 b,i *27 CF3 +O---* COF2+ F 3.1 x 10 -11 *28 CF2+O---* COF+ F 1.4× 10 -it *29 CF2+ O---* CO+2F 4× 10 -14 *30 COF+O---* CO2+ F 9.3× 10 -11 "31 COF+ F ~-~ COFu 8)<10-13 e 32 CF3 + O2 M--* CF302 3.9 X 10-t3 e 33 CF302+ O--* COF2+F+O 2 1 × 10 -11 k 34 CF302 -% CF 3 + 02 20 b,d 35 F2-% F+F 20 b,d *36 COF2 -~ COF+ F 20 b,d *37 CO 2 -% CO + O 40 b,i *38 F+ CO ~ COF 1.3 × 10 -15 e 39 F+ 02 ~ FO 2 1.8 × 10 -16 e 40 F+ FO2---~ F2-~O 2 5 x 10-11 k 41 O+ FO2---~ FO+O2 5110 -11 42 O+ FO--* O2+ F 5110 -11 43 COF+ CF2 --, CF3 + CO 3 X 10-13 l 44 COF+ CF2 ~ COF2+CF 3 X 10 -13 ! 45 COF+CF 3 -* CF4+CO 1 x 10 -11 k 46 COF+ CF3 --* COF2 + CF 2 lxl0 -11 k 47 COF+ COF--* COF2+CO 1 x 10 -11 k 48 C2F5 + O --* CF3COF+ F 3110 -11 " 49 CF+O-* CO+F 2110 -11 25 21 21 a Units of s -1 (for first-order reaction)or cm 3 s -1 (for second-order reaction). b Rate quoted is for discharge region; reduced to a negligible value for z > 5 cm. c The overall rate of reactions (1 +2) is based on the measured % conversion of CF4 at long residence time and large dilution by 0 2 by Smolinsky and Flamm (see Section 2(a) and Appendix 1). d Set equal to (k 1 + k2). e Reaction in fall-off region. See Table II for parameters used to calculate the rate. f Mean of values quoted in Refs. 18 and 19. Rate assumed to be independent of pressure over the range of the simulations. g RRKM calculations show that the reaction proceeds as shown for the pressures of interest in these studies. The estimate of the rate was made using a crude Gorin model calculation (Ref. 28). hEstimate. Rate assumed to be independent of pressure over the range of the simulations. i See Appendix 1. J Deactivation on walls, assuming y ~ 0.05 (estimate). k Estimate. l Based on a preliminary measurement of the combined rate of reactions (43) and (44) from this laboratory. m Set'equal to k(CF3+O). " Set equal to k(CF2+O ).
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`212 Plumb and Ryan model. Table II explains how rate coefficients for association reactions in the fall-off region were calculated. Rate coefficients used in Table I are based on measurements made at 295 K whereas Smolinsky and Flamm measured a gas temperature of 313 K. We would not expect the rate coefficients for reactions to vary significantly over this small temperature range. In developing the reaction set for Table I positive and negative ion chemistry has not been considered. This is not to imply that such processes are unimportant, but rather to determine to what extent free radical chemistry alone can describe current experimental observations. It should be emphasized that many of the reactions listed in Table I are added for completeness and that only about 13 reactions have important effects in these mixtures. This point is discussed further in Section 3. Table II. a Parameters for the Calculation of Rates of Association Reactions in the Fall-off Region Reaction k0 koo F¢ number Value References, Value References, Value References (cm 6 s -l) notes (cm 3 s -t) notes notes 5 2.8 X 10 -23 b 8.3 × 10 -12 28 0.32 b 6 7.7x10 -27 c 2×10-11 c 0.63 8 3.0 X 10 -29 c 1.3 × 10 -11 c 0.73 c 9 3.2x 10 -31 b lx10-11 d 0.72 b 13 2.3 × 10 -26 b 1 × 10 -12 e 0.39 b 31 6.5 X 10 -29 b 1.4 × 10 -11 f 0.68 b 32 3.5 × 10 -29 g 8 X 10 -12 g 0.49 ~: 38 8.1 × 10 -32 h 9.4 × 10 -n f 0.73 b 39 1.6 X 10 -32 21 3 x 10 -tl 21 0.70 b Values quoted for ko and Fc are based on CF4 as a third body, but are expected to apply to apply quite well to CF4/O 2 mixtures. For total gas number density M, the two-body rate coefficient is calculated from (Ref. 26) k k°M F (l+l°8'okoM/kJ2)-I 1 + koM/k~o b Calculated by methods given in Ref. 26, assuming a collision efficiency of 0.5, with ther- mochemical data from Ref. 27. c Based on measurements reported in Ref. 29, with adjustments to /co, and F c for relative collision efficiencies and Lennard-Jones collision frequencies for CF4 and He as third bodies. d Set approximately equal to k~(CF2 + F). e Value based on preliminary measurements from this laboratory. f Calculated using modified Gorin model (Refi 28). g Based on measurements reported in Ref. 1, with adjustments to k o and Fc for relative collision ettleiencies and Lennard-Jones collision frequencies for CF4 and He as third bodies. h Based on measurements reported in Ref. 30 with adjustments for relative collision efficiencies and Lennard-Jones collision frequencies for CF4 and He as third bodies.
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`Chemistry of CF4/O 2 Discharges 213 2.5. Method of Computation Computations were performed using the program sock (Simulation of Chemical Kinetics) developed by Davies and Smith. ~32) A set of differen- tial equations is constructed from the description of the problem and solved using Gear's method. In one of its forms the program provides for a calculation at constant gas number density. This variant is particularly applicable to calculations for flow experiments, such as in the present case, where an increase in the number of molecules produced in a reaction gives rise to an increase in the flow velocity rather than an increase in the pressure as would be the case for an experiment performed at constant volume. Because of the increased flow velocities, residence times in the discharge can be significantly less than the nominal values reported by Smolinsky and Flamm. The effect of change in flow velocity on residence time was accounted for in the following manner. A notional unreactive species X was added to the reaction scheme with some nominal initial concentration. Computed concentrations of this species were then used to deduce the flow velocity at subsequent times through the relationship voXo = vtX,. From the known discharge length, numerical integrations were performed to compute the actual residence time in the discharge for each gas mixture and nominal residence time. Similar computations were performed to deter- mine the flow time between the discharge and the sampling pinhole. In all calculations simple plug flow was assumed and thus the effects on concentrations brought about by diffusion have been ignored. The effects of diffusion are unlikely to be important at the higher flow velocities but will certainly affect the concentration profiles for the longest reactor resi- dence time. Nevertheless it is expected that the general conclusions from the calculations would be unaltered by the inclusion of effects due to diffusion. 3. RESULTS AND DISCUSSION 3.1. Simplified Description of the Predictions of the Model Figure 1 summarizes the major features of the model and indicates how the observed stable product distribution comes about. At high relative concentrations of molecular oxygen in the feed gas the CF2 produced in the primary dissociation step reacts exclusively with O atoms. At this stage, because of the high rate coefficient for reaction (30) and the abundance of O atoms, the COF is converted rapidly to CO2. For long discharge residence times some of the CO/will dissociate into CO. The CO will be controlled by reactions with F to produce COF which is recycled to CO2. Downstream
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`214 Plumb and Ryan of the discharge, because dissociation of CO2 ceases, CO falls and CO2 increases. In the oxygen-rich environment the CF 3 produced in the primary dissociation step is converted rapidly to COF 2. Dissociation of this species produces COF and ultimately CO2 and CO. Thus given sufficient time in the discharge all of the COF 2 would undergo this conversion. On the other hand, for those plasmas where the CF,/O2 ratio in the feed gas is high, the model depicted in Fig. 1 predicts quite different behavior. Under these conditions a very significant fraction of CF 2 produced in the primary dissociation step will be converted to CF 3 through reaction (8). Much of the CF 3 in turn will be reconverted to CF4. The COF which is formed by reaction of O atoms with CF2 will now react with F to produce COF2 rather than with O to produce CO2. At long reaction times the F+ COF reaction converts the COF which is formed by dissociation of COF2 back into COFz, thereby stopping the production of CO2 which is the fate of COF at high O. Thus at low molecular oxygen feed gas concentrations both the CF3 and the CF 2 radicals which react to form products generate predominantly COF 2. This is in sharp contrast to the case of high O2 in the feed gas where CO2 is the dominant product. 3.2. Detailed Analysis of Calculations for Specific Conditions Results of some of the calculations using the reaction set given in Table 1 are shown in Figs. 2-5 where concentrations of various species are plotted as functions of both distance and reaction time. The total reaction time includes that spent both in the discharge and the post-discharge regions. OF 4 .e I e CF 3 ", F CF 2 0 ''e 0 2 eI'O' ,. CO COF 2 ~ :- COF o F CO 2 e ,,. CO Fig. 1. Principal features of the reaction scheme of Table I showing paths to the formation of stable products CO, CO2, and COF 2.
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`Chemistry of CF4/O 2 Discharges 215 t (ms) 4 8 12 16 I f i I i I I I CFJ L_ ~ 10~5 I~////f1"~'~'~" .............................. / -" ~i CO 2 COF2 ! _ ~l ~'~ 1014 .~//~~ ..- 10,2 ; /~\\ \\ 5 10 15 z (cm) Fig. 2. Computed concentrations for a 75% CF4/25% O 2 plasma as functions of the distance z and elapsed time t from the entry of gas into the plasma. Total gas number density = 1.6 x 101~ cm -3 (p = 0.5 torr), flow rate = 70 sccm. The discontinuity which occurs as the gas leaves the discharge and dissoci- ation mechanisms cease is the result of neglecting the effects of diffusion. In fact the transition will be smooth and not discontinuous. Figures 2-5 are chosen to cover a range of initial gas compositions and flow rates in order that certain aspects of the model may be recognized more readily. Figures 2 and 3 both give results of calculations for a flow rate of 70 sccm which corresponds to a nominal discharge residence time of 7 ms. In Fig. 2 calculations are for a mix of 25 mole % O2 while those in Fig. 3 are for 75 mol% 02. Figure 2 illustrates a number of important aspects of the chemistry of these plasmas. First of all, under these conditions, the CF2 is about 20 times the ECF3. This is a direct consequence of the fact that the rate coefficient for reaction between F and CF3 is about 30 times the rate coefficient for the reaction between F and CF2. At the relatively low O generated under these conditions the rate of reaction between F and CF 3 is more than 10 times higher than that for reaction between O and CF 3.
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`216 Plumb and Ryan Thus the important feature emerges that the fast reaction between F and CF3 controls the CF3 and restricts severely the amount of CF4 consumed. On the other hand, because the reaction of CF2 with F has a much lower rate coefficient, not only does CF2 greatly exceed CF3 but a significant fraction of the CF2 reacts with O atoms. The way in which F+CF 3 and F+ CF2 reactions influence the plasma can also be seen in the results for O. The sharp decline in concentration which is apparent early in the reaction time is arrested due to the rapid buildup of the IF and the consequent increase in importance of reactions (6) and (8). At these short residence times little consumption of the parent molecules occurs and, furthermore, there is relatively little dissociation of the product species. In the post-discharge region CF2 is removed mainly by reaction with F while the observed increase in F2 results mainly from reactions (39) and (40). The concentrations of the stable species and the F atoms remain practically unchanged after the gas leaves the discharge. t (ms) 4 8 12 16 I I I I I I I I I 10~6 .................................................. o; CF4 F I 10 ~ 5 /:~;~.:::- :~ .... Of .............................. .~, 8' jr,-" COFa 1014 /' ~" Y i/" . f / ..." CO o i i - 10 ~ 3 E!~.~\ CF 2 . ....... )i" ~" \I" ....... F, .." \\ /-"" ~'\C 0 F",,,,</" ~,,~',C F ~,,,'" "-, 5 10 15 z (cm) Fig. 3. Computed concentrations for a 25% CF4/75% 02 plasma as functions of the distance z and elapsed time t from the entry of gas into the plasma. Total gas number density = 1.6 x 1016 cm -3 ( p = 0.5 torr), flow rate = 70 sccm.
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`Chemistry of CF4/Oz Discharges 217 Figure 3 shows the results of the calculations for 75 mole % O2, again with a flow rate of 70 sccm. There are several significant differences between these results and those shown in Fig. 2. The most obvious of these is that the O has increased by about two orders of magnitude and has virtually the same value as the IF throughout the entire time scale for these calcula- tions. This dramatic increase in O has the effect that reactions between radicals and O atoms now dominate over all other reactions. This leads to a marked fall in the concentrations of radicals over those shown in Fig. 2. Once again the only significant change in stable product concentration that occurs downstream of the discharge is for F2 whose concentration both there and in the discharge is very similar to that shown in Fig. 2. Another notable difference between the results in Figs. 2 and 3 is the relative concentrations of CO2, CO, and COF2. At 75 mole % O2 virtually all of the CF2 produced in the primary dissociation step reacts with O atoms and is converted ultimately to CO2 and CO in the ratio of the rate coefficients for reactions (28) and (29). Some of the CO2 is dissociated by electron t (ms) 40 80 120 160 I I i I i I i I I I lO~e F~, ! 2~/" ,_ t", 02 CF4 ,,-,~ c -i "-.. ~. CO .-.~.~ 2 _ ~ ~ lo~ ......:-'-<.. "__":::.-..,.-_ -'~ ...... ._ .................. = ,' ,,. CF= "... ,0 / ".J '-./ 10 ~3 i.~Cf30, \ ;, I \ co, 5 10 15 z (cm) Fig. 4. Computed concentrations for a 75% CF4/25% 02 plasma as functions of the distance z and elapsed time t from the entry of gas into the plasma. Total gas number density = 1,6 × 0 z6 cm -3 (p = 0.5 torr), flow rate = 5 sccm.
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`218 Plumb and Ryan impact to produce CO, thus decreasing this ratio. Most of the CF 3 is converted to COF2 and, therefore, the ratio of COF2 to the sum of CO and CO2 represents the primary dissociation into CF 3 and CF 2. The sequence of events for 25 mole % 02 is quite different since a significant fraction of COF is then converted to COF2 by reaction (31) which raises the ratio of COF 2 to CO2. Calculations for feed gas flow rates of 5 sccm are shown in Figs. 4 and 5. Two mixtures are considered, 25 mole % 02 in Fig. 4 and 75 mole % O2 in Fig. 5. The large increase in residence times over those for Figs. 2 and 3 means that dissociation of products by electron impact in the discharge as well as reactions in the post-discharge region are now both important aspects of the chemistry in these systems. Figure 4 shows results for a gas composition of 25 mole % 02 flowing at 5 sccm. As in Fig. 2 the CF2 is again much higher than CF3 throughout the discharge zone. The long reaction time and the effect of reactions (6) and (8), however, lead to important differences. Because IF is now greater t (ms) 40 80 120 160 I I I I I I lo,° ~,,., E .......................... & ...... I( ~/ co o~ 10 ~a i g : CF2 Z 10~ ; ~'~ -cFa I i 5 10 15 z (cm) Fig. 5. Computed concentrations for a 25% CF4/75% 02 plasma as functions of the distance z and elapsed time t from the entry of gas into the plasma. Total gas number density = 1.6 x 1016 cm -3 (p = 0.5 torr), flow rate = 5 sccm.
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`Chemistry of CF4/O 2 Discharges 219 than 1015 cm -3 for almost the entire discharge period, the CF3 and CF2 , after reaching peaks at short distances into the discharge, are forced to very low values for the bulk of the residence time in the discharge. This is in contrast to the results in Fig. 2 where both CF3 and CF2 are relatively constant throughout the discharge zone. Thus, even for the long reaction times represented in Fig. 4, the amount of CF4 that can be consumed is still limited by the combination reactions of CF 3 and CF2 with F. The COF2 continues to rise throughout the discharge zone, indicating that loss due to dissociation, while an important process, is more than compensated for by the production of CF3 through reactions (1) and (8) which lead to COF2 by reaction (27). Because of the relatively low O a significant fraction of the COF produced by reaction (28) will form COF2 by reaction (31). CO2 approaches a steady state value after about 30 ms because the rate of dissociation to form CO is then equal to the rate of production of CO2 via reaction (30). Downstream of the discharge significant changes in concentrations occur. O drops rapidly to an insignificant value through reaction with CF2 and COF. However, because the O at the discharge exit point is already quite low, the post-discharge reactions of O atoms do not have a significant effect on the concentrations of any of the stable products. Because of the high F a substantial quantity of CO is consumed to produce initially COF and ultimately COF2. Thus the fall in CO is compensated for by a rise in COF2. The rapid rise in F2 is caused by reactions (39) and (40). The model thus predicts that F2 is a very strong function of the distance between the discharge and the sampling pinhole. The slight rises in the concentrations of 02, CO2, and CF4 occur because, as reactions proceed downstream, the flow velocity falls and thus species which are neither produced nor consumed under these conditions will increase in con- centration. Figure 5 shows the results of calculations for a mixture containing 75 mole % 02 with the same flow rate as in Fig. 4. Significa