Diamond thin film deposition in low-pressure premixed flames

Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 1817–1824

DIAMOND THIN FILM DEPOSITION IN LOW-PRESSURE PREMIXED FLAMES D. G. GOODWIN, N. G. GLUMAC and H. S. SHIN Division of Engineering and Applied Science California Institute of Technology Pasadena, CA 91125, USA

A study of combustion synthesis of diamond films has been carried out using low-pressure, fuel-rich hydrocarbon/oxygen flames. Diamond growth results are reported for acetylene/oxygen, propylene/oxygen, and propane/oxygen flames. The best results are achieved with acetylene/oxygen flames, in which we have grown uniform, 5-cm-diameter polycrystalline films at up to 2.3 lm/h. The deposition rate in propane/ oxygen is much lower (0.15 lm/h), and the diamond film quality is also lower. The experimental results are compared to the predictions of a numerical model that includes both detailed flame chemistry and simplified diamond surface chemistry. The comparison of the experimental conditions with the simulation results shows that diamond growth occurs for stoichiometries where a small amount of hydrocarbon (,1%) is present at the substrate location, and the H/CH3 ratio is of order 10. These conditions are quite similar to those found in other diamond chemical vapor deposition methods. Both experiment and simulation show that under some conditions oxidation of diamond can occur simultaneously with diamond deposition. However, oxidation is negligible for the best diamond film growth conditions. The model correctly predicts the variation of film growth rate with changes in pressure, substrate temperature, and fuel type. For all flames, the absolute predicted growth rate is somewhat higher than measured, but the agreement is reasonable considering the modeling uncertainties associated with the high peak flame temperatures and incompletely understood diamond surface kinetics.

Introduction Ever since the demonstration by Hirose and Mitsuizumi in 1988 [1] that diamond could be deposited using a simple oxygen-acetylene welding torch, combustion methods for diamond synthesis have attracted great interest. While the original method usually produces small, nonuniform deposits, by using multiple nozzles [2] or substrate-stabilized flat flames [3,4], uniform polycrystalline diamond films a few square centimeters in area may be grown at rates exceeding 20 lm/h at atmospheric pressure. However, these methods require very large flows of acetylene and oxygen and elaborate substrate cooling techniques. An alternative approach to combustion synthesis of diamond films is to use a low-pressure flat flame [5–12]. While this results in a lower growth rate than achieved at atmospheric pressure, large area (;20 cm2 [8]), uniform films are easily grown, and substrate temperature control is greatly simplified. Also, low-pressure flat flames are well-suited to diagnostics and modeling of combustion synthesis of diamond [13]. Some basic requirements of any technique to grow diamond films from the gas phase are the ability to supply the substrate with a large flux of atomic

hydrogen (which plays important roles in the surface chemistry, including suppression of nondiamond sp2 carbon deposition) and to provide a flux of hydrocarbons (particularly CH3) as a carbon source, while maintaining a reducing environment to suppress diamond oxidation. In order to deposit a diamond film, rather than a graphitic or amorphous film, the carbon deposition rate must be small compared to the rate at which H impinges on the surface. In standard diamond chemical vapor deposition (CVD) reactors, which typically employ a dilute hydrocarbon/hydrogen gas mixture, diamond growth requires the H/ CH3 ratio at the substrate to be approximately 10 or greater [14–16]. For a combustion technique, these conditions can be satisfied by using a fuel-rich, presooting flame, which results in a reducing postflame environment with a small level of residual hydrocarbons. Using pure O2 as the oxidizer results in a hot flame (.3000 K), leading to a high H flux at the substrate. However, the gas-phase environment the substrate is exposed to in a flame differs significantly from a conventional diamond CVD environment in several respects. For example, it has been suggested that OH in a flame may play a role similar to H, creating surface radical sites and suppressing sp2

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MATERIALS SYNTHESIS

carbon [17]. The high CO and H2O levels might also conceivably alter the diamond surface chemistry. In the present paper, we present a comparison of experimental diamond growth results we have obtained in several different low-pressure flames [6– 8,10,18,19], with predictions of a numerical model which includes detailed flame chemistry and a surface mechanism known to describe diamond growth kinetics in noncombustion CVD environments. Despite the uncertainties inherent in the simulation, we find that the model is able to account semiquantitatively for the experimental diamond growth observations, and therefore we conclude that diamond growth chemistry in flames is essentially the same as that in other CVD environments. For several of the cases discussed here (A, C, F), we have previously presented SEM images and Raman spectra of the diamond films [6,7,10]. A complete discussion of these experiments, including additional diagnostics and modeling of these flames is given in the reports by Glumac [18] and Shin [19].

Experimental The experiments were carried out using a flatflame burner contained in a water-cooled bell-jar vacuum chamber. The burner faces downward above a horizontal substrate [13], which consisted of a molybdenum plate or disk in most cases, although silicon wafers were also used. The burner is designed for work with hot, premixed, fuel-rich hydrocarbon/oxygen flames, and is based loosely on the design of Bittner [20]. Most of the results discussed here were obtained with a water-cooled burner constructed from a 6-cm-diameter tellurium copper rod, with an 4-cm-diameter array of 1-mm-diameter holes spaced 2.5 mm apart in one end, through which the fuel/oxygen mixture flows. The earliest experiments (case A) were carried out in a different burner, which was limited to low flow rates by cooling limitations. For some experiments (case F), the flame area had to be reduced to 2 cm in diameter due to limitations of our mass flow controllers. This was done by attaching to the burner a faceplate with a smaller drilled area. Electronic mass flow controllers meter the input gas flows to the burner, and the pressure is regulated with a feedback-controlled throttle valve in the exhaust line. Depending on flame conditions, the substrate is either heated or cooled to maintain the desired temperature. Heating is accomplished by passing current through the silicon wafer substrate or by using a resistively heated nichrome coil in the substrate holder. Cooling is provided by a helium flow in a narrow gap (;1 mm) between the back of the substrate and a water-cooled copper cooling block. The gap between the substrate and the cooling block can be varied during a run, and this ca-

pability was used to maintain a constant temperature in the initial period of film growth, as the substrate emissivity changed due to the diamond film deposition. The substrate temperature was measured using a two-color pyrometer. Calibration against a thermocouple indicated a temperature uncertainty of approximately 5358C. In all experiments below 60 torr, the flame appeared visually flat, and little if any structure due to the individual holes in the burner face was obvious. However, in some of the higher-pressure runs (particularly at 180 torr) the flame appeared convoluted and the burner hole pattern was apparent in the film deposited on the substrate, indicating the presence of distinct jets impinging on the substrate. The burner was designed primarily for the lower pressure range; a more suitable burner for the higher pressures would require more tightly spaced, smaller holes. Typically, each run lasted 5 h or longer. The diamond growth rate was estimated as the film thickness divided by the run duration, which may underestimate the true growth rate somewhat since it does not account for the time required for nucleation. The carbon film deposited was characterized by scanning electron microscopy and by Raman spectroscopy. A sharp line at 1332 cm11 in the Raman spectrum is a clear signature of the presence of diamond in the sample. Numerical Model The numerical model we have developed is described in more detail elsewhere [13]. The model solves the continuity, radial momentum, energy, and species equations for axisymmetric flow in the gap between the burner and substrate for the limiting case of large D/L, where D is the burner (and substrate) diameter and L the burner/substrate separation. In this limit, a similarity solution holds for low Mach number, such that the temperature, axial velocity, and species profiles are functions only of axial distance [21,22]. This limit is approximately valid for our experiments, for which D/L is of order 4–6. The conservation equations are solved in similarity form by first finite-differencing them, and then solving the resulting set of algebraic equations using the Sandia hybrid Newton/time-integration boundaryvalue-problem solver (TWOPNT [23]), refining the grid as necessary. The solution is found in a manner very similar to the Sandia premixed flame code [24]. All chemical and thermodynamic terms in the equations are evaluated using the Chemkin subroutine library [25], and all transport properties are evaluated using the package of Kee et al. [26] in the multicomponent formulation. Thermal diffusion is included, and is found to be important in the boundary layer above the substrate.

DIAMOND DEPOSITION PREMIXED FLAMES

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TABLE 1 Gas-phase reactions used in the propane and propylene simulations in addition to the 218 reactions of Miller and Melius [27]a

(219) (220) (221) (222) (223) (224) (225) (226) (227) (228) (229) (230) (231) (232) (233) (234)

aRate

Reaction

A

n

E

Reference

C2H5 ` CH3 s C3H8 H ` C3H8 s H2 ` n-C3H7 H ` C3H8 s H2 ` i-C3H7 O ` C3H8 s OH ` n-C3H7 O ` C3H8 s OH ` i-C3H7 OH ` C3H8 s H2O ` n-C3H7 OH ` C3H8 s H2O ` i-C3H7 C2H4 ` CH3 s n-C3H7 C3H6 ` H sn-C3H7 C3H6 ` H s i-C3H7 C3H6 ` O s CH3 ` CH3CO C3H6 ` OH s CH3 ` CH3CHO H ` CH3CHO s H2 ` CH3CO O ` CH3CHO s OH ` CH3CO OH ` CH3CHO s H2O ` CH3CO CH3CO(`M) s CH3 ` CO(`M) High pressure limit Low pressure limit

2.83 E 13 1.33 E 6 1.3 E 6 1.93 E 5 4.77 E 4 3.16 E 7 7.08 E 6 2.11 E 11 1.3 E 13 1.3 E 13 5.0 E 12 7.0 E 12 4.0 E 13 5.0 E 12 3.37 E 12

0.0 2.54 2.4 2.68 2.71 1.8 1.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 6756.0 4471.0 3716.0 2106.0 934.0 1159.0 7353.0 3261.0 1560.0 597.0 0.0 4207.0 1792.0 1616.0

34 35 35 35 35 36 36 34 37 37 28 28 38 38 39

2.5 E 13 3.95 E 16

0.0 0.0

16382.0 13753.0

40 40

constants are of the form k 4 ATn exp(1E/RT). Units: cm3, mol, s, cal.

The gas-phase mechanism must be capable of simulating fuel-rich, presooting flames (f ' 2). For the acetylene/oxygen simulations, we use the rich flame mechanism of Miller and Melius [27] (218 reactions). For the propylene and propane flames, we add 16 reactions, listed in Table 1, to describe the oxidation of C3H8 and C3H6. These reactions are taken from Warnatz [28] but we use updated rate constants. Surface chemistry is included in the model to simulate diamond film growth and oxidation, and is listed in Table 2. Reactions s1–5 are a reduced mechanism for diamond growth, which we have described elsewhere [13]. This reduced mechanism is a simplification of a CH3 growth mechanism [29,30] which is known to reproduce experimental growth rates to within a factor of 2 over a range of two orders of magnitude. Abstraction of surface H by OH is accounted for by reaction s6, with a rate constant estimated from that for the analogous gas-phase reaction [31] OH ` i-C4H10 → H2O ` t-C4H9. Reactions s7 and s8 are global reactions that implement the oxidation rate of CVD diamond measured by Sun and Alam [32]. The oxidation rate expression they report is proportional to [O2]0.6. We include this nonintegral

reaction order for this reaction only. Their data extend to 1073 K, requiring an extrapolation to higher temperatures. We estimate an uncertainty in the calculated oxidation rate of at least a factor of 2. We do not include oxidation of the diamond film by OH or other species, since no rate data exists. We will return to this question later. Results and Discussion Diamond Growth Diamond was successfully deposited for a variety of different flame conditions, summarized in Table 3. Case A is similar to the flame conditions of Cooper and Yarbrough [5], who first deposited isolated diamond particles in a low-pressure flame. Cases B–E are much hotter, higher-flow-rate acetylene/oxygen flames. Cases F and G have conditions that deposit diamond in propylene and propane flames, respectively. Case A Under the low-flow-rate conditions of case A, only isolated diamond particles could be grown [6]. The

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MATERIALS SYNTHESIS TABLE 2 Reduced diamond surface mechanisma

(s1) (s2) (s3) (s4) (s5)c (s6) (s7)d (s8)d

Reactionb

A

n

E

CdH ` H → C*d ` H2 C*d ` H → CdH C*d ` CH3 → CdM CdM ` H → CdM* ` H2 CdM* ` H → CdH ` H2 CdH ` OH → C*d ` H2O CdH ` O2 → CO2 ` CdH C*d ` O2 → CO2 ` C*d

7.8E13 2.2E11 1.0E15 2.8E7 1.E17 5.73E10 2.1E16 2.1E16

0 0.5 0 2.0 0 0.51 0 0

7.3 12.1 18.0 7.7 0 0.064 54.7 54.7

aThe surface site density is assumed to be 3 2 1019 moles/cm2. Rate constants are of the form k 4 ATn exp(1E/RT). Units: cm3, mol, s, kcal. bC H denotes a chemisorbed surface hydrogen, C* an open surface radical site, C M a surface methyl group, and d d d CdM* a surface methylene group. cRate chosen to be large enough that (s4) is rate limiting. d0.6 reaction order in O [32]. 2

TABLE 3 Experimental conditions for which diamond deposition was observeda

Case

Fuel

P (torr)

Vu (m/s)

L (cm)

Ts (8C)

Fuel/oxygen

Growth rate (lm/h)

A B C D E F G

C2H2 C2H2 C2H2 C2H2 C2H2 C3H6 C3H8

40 52 52 30 30 180 90

2.2 4.6 4.6 8.3 8.3 2.6 1.6

0.8 1.0 1.0 1.0 1.0 0.425 1.05

965 850 800 800 870 800 700

0.71–0.77 0.86 0.86 0.84 0.84 0.47 0.42

0.3 1.0 0.6 1.5 2.3 0.9 0.15

aV

u is the unburned bIsolated particles

Notes b c c c c d e

gas velocity, L is the substrate/burner separation, and Ts is the substrate temperature.

cHigh

quality continuous film film eLow quality continuous film dNonuniform

deposits were similar to those reported by Cooper and Yarbrough [5], except that we were able to achieve a uniform nucleation density due to the stagnation flow geometry. Diamond deposition required bringing the substrate very close to the edge of the luminous flame, 7–9 mm from the burner. Moving the substrate to 6 mm resulted in flame extinction, and moving it further away led only to nondiamond carbon deposition. Faceted diamond was deposited only in a narrow stoichiometry window that depended on burner/ substrate distance [18]. The diamond particles deposited exhibit etch pits characteristic of diamond that has been partially oxidized. For slightly leaner flame conditions (C2H2/O2 4 0.71, f 4 1.78), no

deposition occurred, and the silicon substrates appeared oxidized after the run. For slightly richer conditions (C2H2/O2 4 0.83, f 4 2.1), a carbon film was deposited, but it had no diamond content detectable by Raman spectroscopy. These results suggest that oxidation is occurring simultaneously with carbon deposition under these diamond deposition conditions. Attempts were made to allow the isolated diamond particles to grow together in long-duration runs. However, the diamond quality inevitably degraded as the film became continuous. We interpret this as due to depletion of atomic hydrogen, since the recombination coefficient of H on diamond is higher than that on silicon or silicon dioxide.

DIAMOND DEPOSITION PREMIXED FLAMES

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film. The crystallites, approximately 0.5–1.0 lm in size, are less sharply defined than expected for highquality diamond. The diamond peak in the Raman spectrum is weak, but distinctly observable above the amorphous carbon background [19]. The polycrystalline morphology indicates this film is primarily sp3 diamond, but sp2 carbon is present as well. Simulation Results

Fig. 1. Model predictions for growth rate and H/CH3 ratio compared to experiment for cases A, C, and D. Calculations are done both using full surface mechanism (solid curves) and neglecting diamond oxidation (dashed curves). Filled circles, experimental growth rates for cases C and D; shaded region, stoichiometry range for diamond particle deposition for case A.

Cases B–E The high-flow-rate acetylene/oxygen flames (cases B–E) proved much better suited to diamond film growth, and large-area continuous films could be routinely grown [7,8]. The mass flow rate for all of these cases was close to 0.02 g/cm2/s, only a factor of 2–3 below the mass flow rate calculated for an adiabatic, freely propagating flame. For the runs at 52 torr, diamond films were deposited on molybdenum substrates that were essentially the same diameter as the flame (4 cm). At 30 torr, the deposition was done on 5-cm-diameter disks and the diamond film completely covered the top of the disk, extending somewhat beyond the burner diameter. In all cases where large-area films were grown, the film thickness was very uniform, typically 53%, due to the stagnation flow geometry. No evidence of diamond oxidation was observed on any of the films deposited under these conditions. Cases F and G For case F at 180 torr, the flame was convoluted, as already discussed. The best diamond was generally deposited directly below the burner holes. This may be due to the flame front being closest to the substrate at these points. High-quality, continuous diamond films were deposited in small regions on the molybdenum substrate [10]. The propane/oxygen conditions (case G) resulted in a large-area, continuous, uniform polycrystalline

Cases A–E The model predictions for the diamond growth rate and H/CH3 ratio at the substrate are shown in Fig. 1 for the conditions of cases A, C, and D, except that the acetylene/oxygen ratio is allowed to vary from 0.6 to 1.0 (f 4 1.5 to 2.5). The simulations were done with both the full surface mechanism (solid curves) and neglecting diamond oxidation (dashed curves). Since the growth rate is assumed to be first order in CH3, for a given substrate temperature the growth rate neglecting oxidation is simply proportional to the methyl concentration at the surface. Considering first cases C and D (both at 8008C), the results show that the experimental diamond growth conditions correspond to conditions where hydrocarbons just barely survive to the substrate. For case C, the calculated acetylene mole fraction (the predominant hydrocarbon) at C2H2/O2 4 0.86 is 0.25%, while for case D it is 0.37%. These results are very reasonable in light of the standard gas composition of , 1% hydrocarbon in H2 for diamond CVD in other environments. For both cases C and D, the predicted H/CH3 ratio is of order 10 at the experimental growth conditions, and the oxidation rate is insignificant. Both the simulation and experiment show that the 30-torr flame produces a higher growth rate than the 52-torr flame. This results since both have essentially the same mass flow rate, leading to a higher velocity and flame temperature (3892 K for case D vs. 3420 for case C) for the lower pressure case. This in turn results in more H delivered to the substrate (2.86 2 1019 mol/cm3 for case D; 1.75 2 1019 mol/cm3 for case C) despite the lower pressure. The absolute calculated growth rate is higher than that measured, but considering the uncertainties in diamond surface kinetics, the predicted CH3 concentration, and the experimental induction time, the agreement is reasonable. The simulations indicate that the chemical environment the substrate is exposed to under these conditions is very similar to conventional plasma or hot-filament diamond chemical vapor deposition conditions. Diamond film growth in these flames can therefore be accounted for in terms of the standard picture of diamond CVD. For richer flame conditions, the calculated growth

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MATERIALS SYNTHESIS

Fig. 2. Model predictions for growth rate and H/CH3 ratio compared to experiment for cases F and G. Calculations are done both using full surface mechanism (solid curves) and neglecting diamond oxidation (dashed curves). Filled circles, experimental growth rates.

rate saturates as the methyl concentration levels off and heavier hydrocarbons are formed. The H/CH3 ratio falls to a level of 2–3, insufficient to suppress sp2 carbon deposition required to maintain diamond growth. The simulations thus predict that richer flames will result in nondiamond carbon films, in agreement with experiment. If chemical equilibrium existed in the postflame gas at the substrate, no hydrocarbons would be present for acetylene/oxygen ratios below 1.0. The appearance of hydrocarbons at the substrate for the C/D conditions at C2H2/O2 ' 0.8 is therefore due to kinetics, and the agreement between model and experiment is an indication that the model is at least semi-quantitatively-correct. Cases B and E differ from C and D, respectively, only in substrate temperature. The calculated growth rate ratio at 52 torr GB/GC 4 1.5 is essentially identical to the measured ratio of 1.7. For cases D and E at 30 torr, the calculated ratio GE/GD 4 1.9, while the measured ratio is 1.5. The simulations for case A show, not surprisingly, that this flame is significantly different than the flames of cases B–E. The case A flame is highly burner stabilized, with a mass flow rate 13 times lower than the calculated value for an adiabatic freely propagating flame (0.046 g/cm2/s). The calculated peak flame temperature is 2076 K, which agrees well with temperature profile measurements we have recently reported using OH LIF in a flame very similar to this one [13]. In this much cooler flame, oxidation kinetics are slower and some hydrocarbons survive to the substrate position even at C2H2/O2 4 0.7 (f 4 1.75).

Under these conditions, there is still enough oxygen present (1014 mole fraction at C2H2/O2 4 0.75) to result in significant diamond oxidation. The H/CH3 ratio is well below 10 throughout the range where isolated diamond particle deposition is observed. However, the simulation assumes a diamond surface, in contrast to the experimental situation of isolated particles on a silicon substrate. The level of H at the diamond particle surface may have been greater than that calculated, due both to the lower recombination rate on silicon, and to the enhanced diffusive transport of H to the small diamond nuclei. It is also possible that oxygen is playing an enabling role under these conditions, assisting H in suppressing sp2 carbon deposition. The simulation predicts a lean boundary for diamond growth under case A conditions of C2H2/O2 4 0.68. The experimental boundary is closer to 0.72, but the uncertainties in both the oxidation and diamond growth kinetics could easily account for this difference. Cases F and G The simulation results for cases F and G are shown in Fig. 2. The comparison to experiment can be made only qualitatively, since for case F the flame and diamond film are nonuniform, while for case G the film quality is low. For case F, the simulations suggest that H/CH3 4 10 occurs at a C3H6/O2 ratio of 0.45, at which point the growth rate should be ;2 lm/h. The experimental C3H6/O2 ratio for diamond growth was 0.47. The qualitative trend is the same as for the acetylene/oxygen cases: diamond film deposition occurs when residual hydrocarbons are present in dilute amounts at the substrate, adequate H is present, and the oxygen concentration is low enough that film oxidation is negligible. The simulations predict that H/CH3 is only 2–3 under the case G experimental conditions. This is consistent with the low film quality observed. By moving to a slightly leaner flame (C3H8/O2 4 0.38), it appears possible to achieve an H/CH3 ratio adequate for high-quality diamond growth. However, the growth rate would be expected to fall by a factor of 3–4 from the already low experimental value of 0.15 lm/h. It is likely that this could be increased somewhat by using a substrate temperature closer to 8008C, but it still appears unlikely that propane/oxygen flames will be an attractive environment for diamond film deposition. Effects of OH Although we include the possibility of OH contributing to surface radical site production, in practice, the OH concentration at the surface is too low for this to be important. For example, for case D, which had one of the highest OH mole fractions at

DIAMOND DEPOSITION PREMIXED FLAMES

the surface other than case A, the radical surface site coverage with reaction s6 is 0.1175, while without this reaction it is 0.1157. We conclude that OH does not appreciably contribute to surface activation for these conditions. While we do not include diamond oxidation by OH, we can estimate an upper bound on the rate. For case D, the OH mole fraction at the surface is 5.6 2 1015, and no evidence of oxidation is apparent in the film morphology. If we assume that the OH oxidation rate is at most one-tenth the measured growth rate, then the number of carbons removed per incident OH is at most 2 2 1013. Superadiabatic flame temperatures For all of the flames except cases A and G, the peak flame temperature is predicted to be greater than the adiabatic flame temperature. For cases C, D, and F, the peak calculated temperatures are 3420, 3892, and 2986 K, compared to their respective adiabatic flame temperatures of 3012, 2941, and 2739 K. These temperature overshoots result from the high level of thermal dissociation (particularly the high atomic hydrogen level) at the final equilibrium state. Since slow, pressure-dependent reactions such as H2 ` M → H ` H ` M (1) are required to achieve this equilibrium dissociation level in the postflame region, the temperature overshoots the equilibrium value and then decays as H is produced beyond the flame. Similar (but smaller) temperature overshoots have been predicted [22] and verified experimentally [33] in atmosphericpressure, substrate-stabilized acetylene/oxygen flames. Summary and Conclusions A study of diamond film deposition in low-pressure hydrocarbon/oxygen flames has been presented. Comparison of experimental results with a detailed model clearly shows the flame conditions needed for diamond deposition. Good diamond films may be grown for conditions where the H/CH3 ratio is of order 10 at the substrate, which in turn requires a low residual hydrocarbon level (,1%). Under conditions well-suited to high-quality diamond deposition, no effects of oxidation are observed or predicted, although for cases where diamond growth is otherwise marginal, oxygen may play an enabling role. In general, these results are in good agreement with standard ideas and growth mechanisms for diamond CVD in other environments. Acknowledgments Financial support from the National Science Foundation and the Naval Research Laboratory is gratefully acknowledged.

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REFERENCES 1. Hirose, Y. and Mitsuizumi, M., New Diamond 4:34 (1988). 2. Ravi, K. V., Koch, C. A., and Olson, D., Proc. 2nd Int. Conf. Appl. Diamond Films and Related Materials, MYU, Tokyo, 1993, p. 491. 3. Murayama, M. and Uchida, K., Combust. Flame 91:239 (1992). 4. McCarty, K. F., Meeks, E., Kee, R. J., and Lutz, A. E., Appl. Phys. Lett. 63:1498 (1993). 5. Cooper, J. A., Jr. and Yarbrough, W. A., Diamond Optics III, SPIE Proceedings, SPIE, Bellingham, Washington, 1990, Vol. 1325, p. 41. 6. Glumac, N. G. and D. G. Goodwin, Thin Solid Films 212:122 (1992). 7. Glumac, N. G. and Goodwin, D. G., Mater. Lett. 18:119 (1993). 8. Shin, H. S., Glumac, N. G., and Goodwin, D. G., Proc. 4th Intl. Conf. New Diamond Science and Technology, Materials Research Society, Pittsburgh, 1995, p. 27. 9. Harris, S. J., Shin, H. S., and Goodwin, D. G., Appl. Phys. Lett. 66:891 (1995). 10. Shin, H. S. and Goodwin, D. G., Appl. Phys. Lett. 66:2909 (1995). 11. Kim, J. S. and Cappelli, M. A., Appl. Phys. Lett. 65:2786 (1994). 12. Kim, J. S. and Cappelli, M. A., J. Mater. Res. 10:149 (1995). 13. Glumac, N. G. and Goodwin, D. G., Combust. Flame 105:321 (1996). 14. Hsu, W. L., Appl. Phys. Lett. 59:1427 (1991). 15. Hsu, W. L., J. Appl. Phys. 72:3102 (1992). 16. Harris, S. J. and Weiner, A. M., J. Appl. Phys. 75:5026 (1994). 17. Hiroso, Y., Amanuma, S., and Komaki, K., J. Appl. Phys. 68:6401 (1990). 18. Glumac, N. G., Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 1994. 19. Shin, H. S., Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 1995. 20. Bittner, J. D., Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1981. 21. Kee, R. J., Miller, J. A., Evans, G. H., and DixonLewis, G., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, p. 1479. 22. Meeks, E., Kee, R. J., Dandy, D. S., and Coltrin, M. E., Combust. Flame 92:144 (1993). 23. Grcar, J. F., Report No. SAND91-8230, Sandia National Laboratories, 1985. 24. Kee, R. J., Grcar, J. F., Smooke, M. D., and Miller, J. A., Report No. SAND85-8240, Sandia National Laboratories, 1985. 25. Kee, R. J., Rupley, F. M., and Miller, J. A., Report No. SAND89-8009, Sandia National Laboratories, 1989. 26. Kee, R. J., Dixon-Lewis, G., Warnatz, J., Coltrin, M. E., and Miller, J. A., Report No. SAND86-8246, Sandia National Laboratories, 1986.

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27. Miller, J. A. and Melius, C. F., Combust. Flame 91:21 (1992). 28. Warnatz, J., Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1981, p. 369. 29. Harris, S. J., Appl. Phys. Lett. 56:2298 (1990). 30. Harris, S. J. and Goodwin, D. G., J. Phys. Chem. 97:23 (1993). 31. Tsang, W., J. Phys. Chem. Ref. Data 19:1 (1990). 32. Sun, Q. and Alam, M., J. Electrochem. Soc. 139:933 (1992). 33. Bertagnolli, K. E. and Lucht, R. P., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, p. 1825–1833.

34. Baulch, D. L., Cobos, C. J., Cox, R. A., Esser, C., Frank, P., Just, Th., Kerr, J. A., Pilling, M. J., and Troe, J., J. Phys. Chem. Ref. Data 21:411 (1992). 35. Tsang, W., J. Phys. Chem. Ref. Data 17:887 (1988). 36. Cohen, N., Int. J. Chem. Kinet. 23:397 (1991). 37. Tsang, W., Ind. Eng. Chem. 31:3 (1992). 38. Warnatz, J., Combustion Chemistry, Springer-Verlag, New York, 1984, p. 197. 39. Atkinson, R., Baulch, D. L., Cox, R. A., Hampson, R. F., Jr., Kerr, J. A., and Troe, J., J. Phys. Chem. Ref. Data 21:1125 (1992). 40. Benosura, A., Knyazev, V. D., Slagle, I. R., Gutman, D., and Tsang, W., Ber. Bunsenges. Phys. Chem. 96:1338 (1992).

COMMENTS Jerry Finlinson, NAWL, USA. In these experiments you quote a substrate surface temperature near 1100 K. How is it measured and what is the accuracy of the measurement? Does the temperature change significantly when diamond is coating the surface? Is it possible to measure temperature on surface of diamond film after formation begins? Author’s Reply. The temperature was measured using a two-color pyrometer; we estimate an uncertainty of `/1 35 K. If no cooling is provided, the substrate temperature initially overshoots the final steady-state value, since the initial substrate emissivity is much lower than that obtained once a diamond film is present. We varied the helium-jet cooling in real time to minimize the temperature overshoot. Techniques exist to measure the diamond film temperature directly, such as Stokes/Anti-Stokes Raman Scattering. However, this is far from a straightforward measurement and may have experimental uncertainties at least as large as pyrometry. For deposition on massive substrates (e.g. thick molybdenum disks) perhaps the most accurate technique would be simply to instrument the substrate with multiple embedded thermocouples, from which the surface temperature and substrate heat flux could be inferred.

mm of the substrate. Further away (out to 2 mm from the substrate), the decay in OH is closely coupled to the decay of H, primarily through OH ` H2 s H ` H2O, which is close to partial equilibrium. ● Katharina Kohse-Ho¨inghaus, Universitat Bielefeld, Germany. What is the role of nucleation in your system? Do you have experimental evidence for this phase of growth? How does the model account for nucleation? Do you grow basically on diamond for that? Author’s Reply. Our substrates are pretreated by polishing them with diamond grit to provide nuclei and allow film growth without a significant induction time. We do not explicitly account for nucleation, which, as stated in the paper, introduces some small uncertainty in the experimental diamond growth rate. The model assumes the existence of a flat, continuous diamond surface. While this is an oversimplification, we feel that it is adequate considering the uncertainties associated with the calculated species concentrations at the surface and the diamond growth kinetics, both of which are uncertain by a factor of at least 2 or 3.

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Jay Jeffries, SRI International, USA. What produces the rapid drop of OH concentration near the surface? Does surface chemistry of OH play an important role or does the OH concentration simply follow the rapid drop of atomic hydrogen in an attempt to maintain a steady state?

Bernhard Ruf, University Heidelberg IWR, Germany. What reactions are involved in the surface oxidation mechanism and do oxygen atoms play a role in that mechanism?

Author’s Reply. Both gas-phase and surface chemistry contribute to the drop in OH near the substrate. For example, for the Case D experimental conditions, if surface reaction (s6) is neglected, the predicted OH mole fraction at the surface is a factor of 5 higher than the value obtained when this reaction is included (5.6 2 1015). However, the OH profile is affected by surface chemistry only within 0.5

Author’s Reply. The surface oxidation mechanism is a global one, which only seeks to implement the experimental oxidation rate measured in Ref. 32. Since the oxidation rate was measured in heated O2, the atomic oxygen level was presumably negligible. In environments with higher O levels, such as a flame, the oxidation rate may be higher. However, there is no experimental data on oxidation of diamond by O (or OH) and this was therefore not included in the model.