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Plasma Chemistry and Plasma Processing, Vol. 13, No. 2, 199.t

Fluid Boundary Layer Effects in Atmospheric-Pressure

Plasma Diamond Film Deposi t ion

S. L. Girshick, t C. Li, ~ B. W. Yu, t and H. Han t

Received July 10, 1992; revised September 7, 1992

Diamond films were deposited in an atmospheric-pressure radio-frequent3' plasma reactor. Hydrogen and methane were injected coaxially into the plasma as a high-velocity jet which impinged on the molybdenum substrate. In some cases argon was added to the reactant jet to increase its momentum, thereby reducing the boundary layer thickness, In most cases argon addition substantially improved diamond growth. A numerical model was developed, which calculated two- dimensional reactor temperature and velocity distributions, and the chemical kinetics in the boundary layer. The calculations indicate that under the experimental conditions argon addition reduced the thickness of the hydrogen nonequilihrium boundary layer from 3.5 to 1.0 mm. In addition, the calculations suggest that monatomic carbon may be a key diamond growth species under thermal plasma conditions,

KEY WORDS: Thermal plasmas; chemical vapor deposition; diamond film; impinging jet; atomic carbon.

1. INTRODUCTION

Thermal plasmas have been used to deposit diamond films at relatively high rates, but little is known about how the fluid mechanics of a hot plasma jet impinging on a cooled substrate affects diamond growth. The freestream of this jet is characterized by a pressure of - 1 atm, a temperature in excess of 5000 K, and hydrogen in a completely dissociated state. This jet impinges on a substrate, usually oriented normal to the flow, which is maintained for diamond growth at a temperature of -1000-1400 K. A fluid boundary layer with a steep temperature gradient exists above the substrate.

The thickness of this boundary layer has considerable significance for the transport to the substrate of chemically active species. For example, although hydrogen may be completely dissociated in the freestream, H

~Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455.

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170 Girshick, Li, Wu, and Han

atoms may recombine before reaching the substrate if the boundary layer is sufficiently thick. Alternatively, depending on species diffusion velocities, on mean free paths between collisions involving chemical reactions, and on the boundary layer thickness, the species responsible for diamond growth may be chemically destroyed in the boundary layer.

An analytical solution is available for constant-property stagnation- point flow, which shows that the boundary layer thickness is inversely correlated with the jet momentum. That is, the boundary layer thickness scales o n ( p V ) t 2, w h e r e p a n d V are the freestream values of mass density and velocity, respectively.' ~' We believe that this correlation explains why higher linear diamond growth rates have in general been reported using dc plasma jets '2 ~'~ than with rf thermal plasmasJ 7 t~ Core velocities in dc plasma jets are typically much higher ( - 5 0 0 m/s) than in rf thermal plasmas ( - l0 m/s), producing a thinner boundary layer and more effective transport to the substrate of diamond growth species. However, the higher velocity in a dc plasma jet comes at the expense of plasma uniformity, and hence of film uniformity. Another advantage of rf plasmas is that, being electrode- less, they do not suffer contamination from electrode erosion, which may be a significant impediment to the use of dc plasma jets in depositing diamond for electronic device applications. In our earlier work, we attempted to combine the advantages ofboth types of plasma by introducing reactants (methane and hydrogen) directly into an rf plasma in the form of a high-velocity je t (V, ..... > 100m/s). The results were promising in that good diamond film uniformity was obtained over 25-ram-diameter substrates at growth rates exceeding 10 ~m/h .

In the present work we investigate the effect of adding argon to the reactant jet. As argon atoms are 20 times as massive as hydrogen molecules, we would expect argon addition to increase the jet momentum substantially, reducing the boundary layer thickness. Presumably this should result in improved or at least modified film deposition. The reduction in boundary layer thickness by adding argon to the central jet is not completely decoupled from other effects--for example, the temperature profile downstream of the injection tube is affected--but within a certain range of conditions we hypothesized that the reduction in boundary layer thickness would be the dominant effect, which would have clear effects on film growth.

2. DESCRIPTION OF EXPERIMENTS

The experimental apparatus is shown schematically in Figure 1, and was the same as for the earlier experiments '~''~°~ except that a small modification was made to the substrate holder, employing a ring clamp rather than a screw-down design.

Plasma Deposition of Diamond Film 171

Sheath ~Ias Ar

I Water Out

-.,ll---------

© gv 0 Coil

© © ©

Substrate ~

Stainless Steel Plate

Substrate Holder

Reactant Gas CH4+H2+Ar

0 0 0 0 0

Quartz Tube

Water In T Water Out

Fig. I. Reactor schematic.

Water In

Table I. Operating Conditions in Common ['or the 16 Cases

Total pressure 1 atm Generator plate power 12-14 kW Frequency 2.9 MHz ('oil current 80-

85 A (rms) Main plasma gas (argon) flow rate 40slpm


Operating conditions are summarized in Table I. The plasma operated at atmospheric pressure and was driven by inductive coupling to a nominally 20-kW radio-frequency power generator. Our calculations indicate that typically - 4 - 6 kW of power was actually coupled to the plasma, and the measured frequency through the five-turn induction coil was 2.9 MHz. The plasma tube was made of water-cooled quartz, with an inner diameter of 44 mm. The main plasma gas, argon, was introduced at the top of the torch at a flow rate of 40 slpm. It entered the torch through injection tubes oriented at 45 ° with respect to the plasma tube axis, so as to impart swirl, which stabilizes the plasma.

A water-cooled stainless steel injection probe, with an inner diameter of 1.8 mm, was inserted coaxially directly into the plasma, terminating at the level of the midplane of the induction coil. Hydrogen, methane, and in some cases additional argon were injected through this tube into the plasma. For each experiment the separate flow rates of these three gases were maintained at either a "low" or a "high" value: for hydrogen, either 4 or 8 slpm; for methane, either 1 or 2% of the hydrogen flow rate; and for argon, either 0 or 4 slpm.

Table I1. Cond i t i ons of the 16 Cases Tes ted"

Case Ar (s lpm) H 2 (s lpm) C H 4 / H 2 (%) T.s (°C) number

1 0 4 1 890

2 0 4 1 1014

3 0 4 2 901 4 0 4 2 1039

Fig. 2

5 0 8 1 900 6 0 8 1 1070

7 0 8 2 845 8 1) 8 2 959

Fig. 3

9 4 4 1 906

10 4 4 1 1027 11 4 4 2 884 12 4 4 2 1047

Fig. 4

13 4 8 1 874 14 4 8 1 951

15 4 8 2 830 16 4 8 2 1005

Fig. 6

"The argon flow rate refers to the flow rate through the central in ject ion tube,

not the main p lasma gas.


The reactant jet impinged on a molybdenum substrate which was mounted to a cooling assembly. Referring to Fig. 1, the distances y and z were respectively 25 mm and 45 mm, giving a total distance from the injection tube exit to the substrate surface of 70 mm. The total diameter of this assembly was 27.4 mm; accounting for the 5-mm molybdenum ring which fastened the substrate, the actual deposition area of the substrate was 17.4 mm in diameter. (Typically diamond was also deposited on the ring.) The substrate surface temperature was controlled by inserting stainless steel disks of various thicknesses d between the substrate and a water-cooled stainless cylinder; d could range from 1 to 10 mm. Surface temperatures as measured by a two-color optical pyrometer (Ircon Modline Series R) ranged from 830-1070°C. For each set of conditions we ran one case with a surface temperature which was relatively low within this range, and another case with a relatively high temperature.

We tested all 16 possible combinations of these four parameters (the three central jet flow rates and the surface temperature), with all other conditions held the same, as listed in Table I1. In each case we ran the deposition for 4 hours. The internal consistency of the results, together with several repeated runs, indicated a high degree of reproducibility.

3. RESULTS

The different cases produced significant differences in whether or not diamond was produced and in the film morphology. Morphologies were consistently uniform over the substrate surface. Cases with continuous diamond films had film thicknesses ranging from 20 to 70 ~m, indicating time-averaged linear growth rates of 5-18 ~m/h , which is about the same as has been reported for a dc plasma torch operating at atmospheric pressure/~-~

Figure 2 shows scanning electron microscope (SEM) photographs of the films produced in Cases 1-4, in which the hydrogen flow rate was 4 slpm and no argon was added to the central jet. Under these conditions the jet velocity and momentum were at a minimum, and the micrographs indicate that in all four cases nondiamond carbon was produced. In both of the high-temperature cases (Cases 2 and 4) one observes ball-like structures that are coated with what appear to be graphite fibers, the effect being particularly pronounced in Case 4, for which the methane/hydrogen ratio was higher.

In Fig. 3 SEM photographs are shown for Cases 5-8, in which the hydrogen flow rate was increased to 8 slpm, still without argon added to the central jet. These conditions were similar to those of our previously reported experiments, '~'m~ and the results were the same. Clear diamond


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faceting was observed for the cases with a 1% methane/hydrogen ratio but not for the 2% cases, both of which produced ball-like structures. A comparison of Cases 5 and 6 shows a strong temperature effect. In Case 5, with a surface temperature T,. = 900°C, one sees a fairly uniform array of vertically oriented cubo-octahedrons, all terminating in (100) faces, with crystal dimensions of 1-2/~m at the top face. In Case 6, with all other conditions the same except for Ts = 1070°C, one finds layer-type growth of isolated columns having much larger characteristic dimensions.

Among Cases 1-8, which comprise all the cases without argon addition, the most noteworthy comparison is that between Cases 1 and 5, both of which had 1% methane, and which were at virtually identical temperatures of -895°C. Both cases produced a fine-grained, dense film, but the film in Case 1, with 4 stpm hydrogen, is graphite whereas Case 5, with 8 slpm H2,

produced diamond. SEM photographs of Cases 9-12 are shown in Fig. 4. Each case shown

in Fig. 4 corresponds to the case shown in the same position in Fig. 2, except that the cases in Fig. 4 had 4s lpm argon added to the central jet. The effect of argon addition was dramatic: in each case, argon addition changed the result from nondiamond carbon to well-faceted diamond. Two of these pairings particularly stand out: Cases 1 and 9, and Cases 4 and 12.

Cases 1 and 9 were both run with 1% methane and with Ts~900°C. Both resulted in dense, relatively fine-grained films. But the film in Case 1 appears graphitic, while Case 9 shows a well-faceted, continuous diamond film characterized by (111) faces.

Cases 4 and 12 were both obtained with 2% methane and with Ts 1040°C. Case 4, without argon addition, resulted in fibrous, graphitic balls. Case 12, with argon addition, is shown under lower magnification in Fig. 5. We find a homogeneous, continuous diamond film with exceptionally large (100) faces, the crystallite edges being 40-50/zm long. Figure 5 also shows a case where we repeated the conditions of Case 12, except that the temperature was slightly lower, 1013°C.

A comparison of the two low-temperature cases in Fig. 4 (Cases 9 and 11) with the corresponding high-temperature cases (10 and 12) shows a temperature effect observed by numerous investigators: (111) faces dominate at lower temperature, (100) at high temperature.

Figure 6 shows the results for Cases 13-16, which are the counterparts with argon addition of the results shown in Fig. 3. Compar ing Figs. 3 and 6 again shows the significant effect of argon addition, which in each case produced a continuous diamond film. Case 13 produced clean (111) faces with edges exceeding 10 ,am. A comparison of Cases 15 and 16 again shows the temperature effect regarding (111) vs. (100) morphology. The latter case is a remarkable example of randomly oriented layer-type growth.

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4. NUMERICAL M O D E L

We developed a numerical model which included a two-dimensional (axisymmetric) model of the plasma reactor and a one-dimensional model of the chemical kinetics in the boundary layer above the substrate.

The plasma model was the same as discussed previously.' r"' It solved the conservation equations for laminar flow, namely the continuity equation, all three components of the momentum equation (the tangential component being included because of the swirl injection of the main plasma gas), and the energy equation, coupled to the Maxwell 's equations for the electromag- netic field based on a two-dimensional vector potential ~ ~ and to diffusion equations for H2, H, and Ar. The latter included convection, ordinary diffusion, thermal diffusion, and finite-rate dissociat ion/recombination via three-body reactions with neutral species. The computational domain corresponded to the geometry of the experiments, and boundary conditions corresponded to the experimental values of argon and hydrogen flow rates and of measured induction coil current and frequency, c'4~ It was assumed that the injection of methane at the experimental level of only 1 or 2% of the hydrogen flow rate (thus much less than 1% of the total flow rate) would not significantly affect temperature and velocity profiles in the reactor.

Typical calculated results for the flow streamlines are shown in Fig. 7, The injection tube protrudes past the characteristic recirculation vortex caused by Lorentz forces. The impinging jet forms a stagnation-point flow boundary layer over the substrate.

Figure 8 show typical results for the temperature distribution. The peak temperature, located downstream of the injector exit and off the flow axis, exceeds 10,000 K. A relatively cold central channel exists along the axis, caused by the introduction of cold gas through the injector; consequently the peak temperature along the centerline is limited to about 5000 K. It

INACTION SUBST~TE TUBE HOLDER

\ co Ls / 0 0 0 0 0 /

0.0 5 .0 10.0 15.0 20 .0 2510 Z (cm)

Fig. 7. Calculated streamlines, conditions of case 8.

Plasma Deposition of Diamond Film t81

INJECTION SUBSTRATE TUBE HOLDER

0 0 0 0 0

.

o - ~ ~ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ~

I I l I l 0.0 5.0 10.0 15.0 20.0 25.0

Z (cm)

Fig. 8. Calculated isotherms (kK), conditions of Case 8.

should be noted, however, that hydrogen diffuses freely into the hottest plasma regions and is not confined to the narrow central channel.

We modeled the gas phase chemistry in the boundary layer as follows. Following the approach of Goodwin,"~ '" ' the conservation equations for stagnation-point flow were transformed to ordinary differential equations under a similarity transformation, allowing the chemical rate equations to be expressed in one-dimensional form. Goodwin initiated his calculations at the edge of a hypothetical boundary layer which by definition has zero temperature gradient. In our case, however, with reference to Fig. 8, this would require us to initiate our kinetics calculation at a temperature exceeding 10,000 K. This seems neither warranted nor sensible, because the hydrocarbon chemistry of interest occurs at much lower temperature, and in any case reaction rates at such high temperatures are so fast that chemical equilibrium is a good assumption. We arbitrarily adopted the location of the 4000 K isotherm as the point at which to begin our calculation, and assumed that chemical equilibrium prevailed at that point. This temperature was chosen as being roughly the temperature which satisfies two criteria: (1) above this temperature, chemical equilibrium is a reasonable assumption; (2) below this temperature, chemical rate constants are available for most reactions of interest, albeit with considerable uncertainty at the high- temperature end.

For cases with zero argon addition through the central injector our plasma model indicated that the 4000 K isotherm was located - 5 mm above the substrate, while for the cases with 4slpm argon added this isotherm was located - 2 mm above the substrate. We used these locations to define the computational domains for the kinetics calculations, and also used the temperature profiles determined by the plasma calculations as input. (That is, the energy equation was not resolved.)


We then solved rate equations for the C - H - A r system, including 23 species and 60 chemical reactions, using the Chemkin database and software package.' .7~ Rate constants were obtained from the literature.' 's -'~" The full set of reactions considered and rate constants are given in Table III. For boundary conditions at the surface, we assumed: (1) the same temperature as measured in the experiments; (2) all H atoms recombined to H2 at the surface; (3) the carbon species C and C~ "stuck" at the surface; and (4) all other species did not react at the surface. The last condition is not expected to be accurate, but was taken in view of the lack of rate constants for heterogeneous surface chemistry in this system. We adopted a unity sticking coefficient for the carbon vapor species as these would be highly supersaturated with respect to the cold substrate. These boundary conditions affect the species concentration profiles close to the substrate, and the results for these should be treated with caution.

Typical results for species profiles are shown in Fig. 9. These were obtained for the conditions of Case 12. However, all cases showed the same interesting feature, namely the abundance of monatomic carbon vapor. Similar results for the monatomic carbon abundance in kinetic models of thermal plasmas have been reported by Raiche et al. '27~ and by Goodwin ~'~'' in their studies of a dc arcjet and by Owano et al. '2s' in rf thermal plasma diamond deposition. This feature may indicate a significant difference between the diamond growth mechanism in thermal plasma CVD compared to other techniques. For example, in hot-filament and combustion systems the peak temperatures are too low to generate carbon vapor at the significant levels found in a thermal plasma. In contrast, under our conditions at 4000 K an equilibrium calculation shows over 90% of the carbon atoms to be in the form of monatomic carbon vapor.

Monatomic carbon itself is thus a viable candidate as the major "growth species" in thermal plasma diamond CVD. If the flux of H atoms to the surface were as great as suggested by Fig. 9, one can postulate a simple overall growth mechanism:

C(g) + H(g) + H(surface) ---, C(surface) + H2(g)

Recent semi-empirical quantum chemical calculations by Huang and Frenk- lach ~2~' indicate that diamond growth by addition of C atoms on a (100) diamond plane is energetically quite favorable.

To investigate this phenomenon further, we calculated the growth rates which would be obtained if the entire carbon vapor flux deposited on the surface. As was noted above in Section 3, two experimental pairings particularly stand out: Cases 1 and 9, and Cases 4 and 12. Figure 10 shows the calculated results for the carbon fluxes in these four cases. In the experiments, Cases 1 and 4 produced nondiamond carbon, while Cases 9

Plasma Deposition of Diamond Film

Table III. Reaction Mechanisms for the Kinetics Calculations"

183

React ion A b E References

1. 2CH)+M,~-C2H~,+M 9 . 0 3 E + 1 6 -1 .2 654.0 21

E n h a n c e d th i rd -body efficiency: H, = 2.0 2. C H 3 + H + M ~ . ~ - C H 4 + M 6 . 0 0 E + 1 6 -1 .3 0.0 21

E n h a n c e d th i rd -body efficiency: H, = 2.0 3. C H 4 + H ~,-~- C H ~ + H~ 2.20E + 0 4 3.0 8750.0 21 4. CHs + H ~..-~- C H ~ + H, 9 .00E + 13 0.0 15100.0 21

5. C H 2 + H . ~ - - C H + C H ~ 1 . 0 0 E + 1 8 - 1 . 6 0.0 21 6. C + H2 ~,.~- C H + H 4.00E + 14 0.0 23400.0 25

7. CH + C2H_, ~,-~- C3H2 + H 1 . 0 0 E + 14 0.0 0.0 21 8. CH + C H 2 ~ C,~Hz+ H 4.00E + 13 0.0 0.0 21

9. C H + C H 3 ~ C e H 3 + H 3.00E + 13 0.0 0.0 21

10. CH + CH.~ ~ CeH.~+ H 6.00E + 13 0.0 o.o 21 I I . C + C H 3 ~.~- C2H2+ H 5.00E + 13 0.0 0.0 21 12. C+CH2,~-- C 2 H + H 5.00E + 13 0.0 0.0 21

13. C2H~+CH3.~--C2Hs+CHa 5.50E - 01 4.0 8300.0 21

14. C2H,~+ H ~.-~- C2Hs + H~ 5.40E + 02 3.5 5200.0 21 15. C2H4+ H ~,~- C2H3 + H2 1 . 1 0 E + 14 0.0 8500.0 21

16. CH2+CH3~-C2H4+H 3.00E + 13 0.0 0.0 21 17. H+C2Ha+M~C2Hs+M 2 . 2 1 E + 13 0.0 2066.0 21

Enhanced th i rd -body efficiency: H, = 2.0 18. C e l l s + H ~.~- 2CHx 1.00E + 14 0.0 0.0 21

19. H2+C2H~-C2H2+H 4.09E +05 2.4 864.0 21 20. H2+C2H2+M~C2H3+M 5.54E + 12 0.0 2410.0 21

E n h a n c e d th i rd -body efficiency: H2 = 2.0

21. C2H3+H~C2H2+H2 4.00E + 13 0.0 0.0 21 22. C~Hx+CH2,~C2H2+CHx 3.00E + 13 0.0 0.0 21

23. C2H3+C2H~2C2H2 3.00E + 13 0.0 0.0 21 24. C2H3+CH~C2H2+CH2 5.00E + 13 0.0 0.0 21

25. C2H2+C2H~-C4H2+H 3.00E + 13 0.0 0.0 21 26. ~ C H 2 + M ~,~- C H , + M 1.00E + 13 0.0 0.0 21

E n h a n c e d th i rd -body efficiency: H 2 = 0.0 27. ICH2 + CH4 ~,-~ 2CHa 4.00E + 13 0.0 0.0 21

28. CH2 + C H 4 ~,-~- 2CH3 1.00E + 13 0.0 0.0 21

29. ICH,+C2H6,-.~-CH~+C2Hs 1.20E + 14 0.0 0.0 21 30. ~CH_, + H2 ~..-~ CHs + H 7.00E + 13 0.0 0.0 21 31. ~CH2+ H ~.,~- C H 2 + H 2.00E + 14 0.0 0.0 21

32. 2CHe ,~- C e l l 2 + H2 4.00E + 13 0.0 0.0 21 33. C2H2+ M -,~- C 2 H + H + M 4.20E + 16 0.0 107000.0 21

34. C e H 4 + M ~ C 2 H 2 + H 2 + M 1.50E + 15 0.0 55800.0 21 35. C2Ha+ M ~--~- C2H3 + H + M 1.40E + 16 0.0 82360.0 21 36. 2 H + M ~ , ~ - H e + M 1 . 0 0 E + 1 8 - 1 . 0 0.0 21

Enhanced th i rd -body efficiencies: H2=

0.0, Ar = 0.0 37. 2 H + H 2 ~ - ~ 2 H 2 9 . 2 0 E + 1 6 -0 .3 0.0 21

38. 2 H + A r , ~ H 2 + A r 6 . 4 0 E + 1 7 -1 .3 0.0 18 39. C + C H 4 , ~ - C H s + C H 5.00E + 13 0.0 24000.0 19 40. C 2 + M ~,~-2C+ M 3 . 7 2 E + I1 0.0 138557.0 26


Table !11. Continued.

Reaction A b E References

41. C , + H 2 + M ~ C 2 H 2 + M 1 . 8 1 E + I 0 0.0 0.0 26 42. C H + M ~ C + H + M 1.00E + 16 0.0 82000.0 24

43. C 2 H + M ~ C 2 + H + M 3.60E + 15 0.0 143000.0 24 44. C,H + H ~.~- C : + H: 3.60E + 13 0.0 28260.0 24

45. C3H4+ H ~ C H 3 + C 2 H z 2.00E + 13 0.0 2411.0 20

46. C4H6 ~ C2H3+CH 3 1.00E + 18 0.0 74000.0 20

47. CeH3+CH3 ~- C:H2+CH4 7.90E + 11 0.0 0.0 22

48. C2H4+CH3,.~-CH4+C2H3 4.20E + 11 0.0 11200,0 22 49. C2Hs+CH3 ~ CeH4+CH4 7.90E + 11 0.0 0.0 22 50. CH3+ M ~,~- CH2+ H + M 1.00E + 16 0.0 90600.0 22

51. CH3 +CH3 --~-~ C2Ha + H2 1.00E + 16 0.0 31792.0 20

52. C2Hs+C2H3 ~-- C4H s 8.90E + 12 0.0 0.0 20 53. C.~H~,+ H ~,~ C2H4 + C2H3 5.00E + I1 0.0 0.0 20

54. C4H6+C2H3.~-C2H.~+C2H2+C2H3 6.30E + 13 0.0 14500.0 20

55. C2H3+C2H3,~-C4H~, 8.90E + 12 0.0 0.0 20 56. C4Hz+ M ~,~ C4H + H + M 3.50E + 17 0.0 80000.0 20

57. C3H4 + ~CH2 -,~-~ C4H6 2.00E + 13 0.0 0.0 23 58. C.,H + H2 ,~-~ C4H2 + H 8.00E + 12 0.0 2626.0 23

59. ~CH2+ H ~,-~- CH + H 2 3.00E + 13 0.0 0.0 23 60. ~CH~ + CH3 ,~ C2H4 + H 1.80E + 13 0.0 0.0 23

"Forward rate constants are in the form k~ = AT t' e x p ( - E / R T ) , where R is the universal gas

constant. Units are cm ~, moles, seconds, Kelvins, and calories/mole. ~CH, = singlet state of

CH~.

1 0 ° I I I

c~ 10"3

LL

10.6

1 0 - 9 1 = ¢ 0.0

Distance from substrate (mm)

Fig. 9. Calculated chemical species profiles, conditions of Case 12.

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sticking probability = 1.01

Case 1 Case 4

122

Case 9 Case 12

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and 12 produced diamond with growth rates of respectively 8 and 17 #m/h . The results for these latter two cases are consistent with a sticking probability for C atoms of about 0.1. It can be argued that in Cases 1 and 4 the resulting diamond growth rates were too slow, and competing growth mechanisms for nondiamond carbon dominated.

In contrast, we found that the calculated surface concentrations of CH, and C2H2, the two species most discussed in the literature as possible diamond growth species, were actually reduced in the cases with central argon addition compared to the cases without it. This may be viewed as a consequence of the fact that a thicker boundary layer allows more of both of these species to be produced, or equivalently as a result of more carbon being tied up in monatomic carbon vapor in the thinner boundary layer cases. Indeed it has been pointed out that excessive fluxes of hydrocarbon species, including methyl and acetylene, can degrade film quality. '~"~

It should also be noted that the cases with thinner boundary layers had greater fluxes to the surface of H atoms--which itself would be expected to promote diamond growth--and that the C atom concentrations are related to H atom concentrations. We calculate that under our conditions the typical characteristic diffusion length (average distance for diffusion before chemical destruction) for H atoms is about 1.0 mm. One measure of boundary layer thickness for diamond CVD is a "'hydrogen nonequilibrium boundary layer," which we arbitrarily define as the region above the surface over which the hydrogen concentration deviates by more than 1% from its equilibrium value for the same thermochemical conditions. Our calculations indicate that the cases without argon addition had an H-nonequilibrium


boundary layer thickness of 3.5 mm, while the cases with argon addition had a corresponding boundary layer thickness of 1.0 ram. Thus, in the cases with argon addition the H-atom concentration was essentially frozen at its freestream value until close to the substrate, where surface recombination causes a decline in the H-atom profile. In contrast the thicker boundary layer in the cases without argon addition allowed a greater degree of hydrogen recombination in the gas phase.

The characteristic diffusion length for C atoms in this system is much smaller than for H atoms--only about 0.05 mm over most of the boundary layer. However, the reaction

C H + H = C + H e

is found to be in nearly perfect partial equilibrium until very close to the substrate. Thus, the great abundance of H atoms, especially in the thinner boundary layer cases, acts to maintain the high concentration of C atoms in this system.

5. SUMMARY

Diamond films were deposited in an atmospheric-pressure radio- frequency plasma reactor. Hydrogen and methane were coaxially injected into the center of the argon plasma, forming an impinging .jet over the substrate. Argon was sometimes added to the reactants to increase the jet momentum, thereby reducing the boundary layer thickness.

Of the eight cases tested without argon addition, only Case 5 produced a continuous diamond film, and six of the eight cases resulted in nondiamond carbon deposits. In contrast, the eight cases with argon added to the central jet all produced diamond, seven of these being continuous films. While Case 5 indicates that a diamond film could be grown without argon addition, Cases 9-16 demonstrate that argon addition significantly expands the window of conditions over which good quality diamond could be deposited. Within this window various morphologies and crystallite dimensions can be produced, depending on the flow rates of hydrogen and methane and on the surface temperature.

A numerical model was developed to predict the reactor temperature and velocity profiles and to simulate the boundary layer chemistry. The results of this model indicate that under our conditions argon addition reduced the thickness of the "hydrogen nonequilibrium boundary layer" from 3.5 to 1.0 mm. The results also suggest that monatomic carbon vapor may be a major diamond growth species in this type of system.

ACKNOWLEDGMENTS

The authors gratefully acknowledge support for this work by the National Science Foundation, by the Engineering Research Center for


Plasma-Aided Manufacturing, and by the Minnesota Supercomputer Institute.

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