- Email: [email protected]
Microbalance studies of diamond nucleation and growth rates
ELSEVIER
Diamond and Related Materials 5 (1996) 200-205
DJAMOND RE D bdldliw ALS
Microbalance studies of diamond nucleation and growth rates Edward A. Evans, John C. Angus Chemical Engineering Department, Case Western Reserve University, Cleveland, OH 441067217,
USA
Abstract In situ measurements of diamond nucleation and growth rates using a microbalance within a hot-filament reactor were made. Methane, acetylene, ethylene and ethane in hydrogen, with and without the addition of oxygen, were used as source gases. The measured reaction orders strongly support the view that the bulk of the atom addition is by single-carbon species, e.g. CH3. The reaction order shifts to zero at high hydrocarbon concentrations, suggesting that diamond growth is a surface-site-limited process. Diamond nucleation on virgin substrates shows an initial period in which d2M/dt2~0, which is attributed to the incorporation of
carbon into the substrate. Keywords:
Microbalance; Nucleation; Reaction orders; Growth rates
1. Introduction
2. Experimental methods
A better understanding of the growth mechanisms is required to improve the growth rates and quality of diamond grown by chemical vapor deposition. We have made in situ measurements of the growth rates and reaction orders using a microbalance within a hotfilament reactor. Preliminary studies were also completed on the initial stages of diamond nucleation on both carbide-forming and non-carbide-forming substrates. Growth rate data alone cannot unambiguously determine the growth mechanism. However, these data can suggest possible mechanisms of diamond growth, provide a database against which proposed mechanisms can be tested and give insight into the relationship between the growth rate and quality. Some previous microbalance studies of diamond growth have been made [l-6]. Our results are in general agreement with these earlier studies despite differences in the deposition methods. Wang et al. [4,5] have presented a large amount of growth rate data that can be summarized briefly as follows. For a methane feed concentration in hydrogen between 0.3% and l%, there is a first-order relationship between the feed concentration and the diamond growth rate. Above 1% methane, there is a gradual change to zero order. For twocarbon- atom source gases, they observed first-order kinetics below 0.3% feed concentration and approximately half-order kinetics above 0.3%. Wang et al. also reported similar growth rates for all two-carbon-atom source gases.
The microbalance system is a stainless steel bell jar with a Cahn D200 microbalance (practical sensitivity, f0.2 pg) mounted on the top. The reactor has been described in detail elsewhere [4-61. The source gases are introduced through a 0.25 inch stainless steel tube about 15 cm from the filament. The estimated reactor Peclet number, Pe = (VL)/D, is much less than unity, indicating that within the reactor the gases are well mixed. The Grashof number, Gr=(gj3CAT)/v2, is a measure of the momentum flux from thermal convection to that by viscous transport and describes the tendency to form convective roll cells. Estimates of Gr indicate that large roll cells can be expected within the reactor body, which has a diameter of 50 cm, but not within the region defined by the filament, which is approximately 3 cm in horizontal dimension. These predictions are confirmed by modelling [4] and by our observations of the behavior of the reactor. (Here D is the axial dispersion coefficient, V is the convective velocity, L is a characteristic length, g is the acceleration due to gravity, /I is the thermal expansion coefficient, AT is the temperature difference and v is the kinematic viscosity.) The microbalance continuously reports the weight of the substrate during a run. The substrates are small circular discs of molybdenum sheet (0.5 mm thick and 6 mm in diameter), with a total surface area of 64.4 mm2, and are hung with a 10 cm long platinum wire. For these substrates, a growth rate of 1 mg h-l translates into a nominal linear growth rate of 4.4 pm h-l.
0925-9635/96/$15X)00 1996 Elsevier Science S.A. All rights reserved SSDZ 0925-9635(95)00444-O
E.A. Evans, J. C. AngusfDiamond and Related Materials 5 (19%) 200-205
Substrates are suspended from the microbalance so that they hang within a U-shaped tantalum carbide filament. The filament is 10 cm long and the distance between the sides of the U is 3 cm. The filament thickness is 0.5 mm. The filament temperature is monitored with a Williamson two-color pyrometer and, for the data reported here, is in the range 2300-2600°C. We were unable to obtain a direct in situ measurement of the substrate temperature while the mass measurements were being made. A free-standing thermocouple in the vicinity of the substrate is .used to measure the gas phase temperature. From these measurements, we estimate that, for all of our runs, the substrate temperature varies from 900 to 1000 “C. During a single run, however, the substrate temperature varies over a much smaller range. The reported growth rate data are taken at steady state conditions. Each data point reported in the figures is an average of 120 measurements taken over 0.5 h; steady state is usually attained l-2 h after a change is made in the growth conditions. Growth rate data are taken after a continuous diamond film has been deposited. Before a sample is removed from the system, each data point is repeated to ensure the reproducibility of the data. To permit a comparison of the morphology of the films deposited in different conditions, we start with bare molybdenum substrates. The substrates are cleaned with a high strength detergent (Micro) and rinsed with alcohol. For these experiments the substrates are not scratched before deposition, and are referred to as virgin substrates. Each substrate is first treated with 1% methane in hydrogen at a filament temperature of 2100 “C
201
for 0.5 h. After this carburization and nucleation stage, the growth conditions are changed, and deposition is carried out until the mass has increased by approximately 2 mg.
3. Growth rate results We used the source gases methane, acetylene, ethylene and ethane in hydrogen, with and without the addition of oxygen. The growth rate data are shown in Figs. l-6. There is a linear, i.e. first-order, relationship between the methane concentration in the source gas and the growth rate up to about 1% methane in hydrogen. Above 1% methane, the reaction order gradually shifts to approximately zero, i.e. there is no increase in the growth rate with an increase in the methane concentration (Fig. 1). Growth rate data for the two-carbon-atom source gases, ethane, ethylene and acetylene, are shown in Fig. 2. In Fig. 2, the growth rate is plotted vs. the square root of the source gas concentration. The data fall on a straight line up to approximately [C2HJo.’ =0.8, i.e. a concentration of [C,H,] =0.64%. The growth rate is therefore approximately half order in the source gas concentration up to 0.64%. We also find, in agreement with the earlier work of Wang et al. [4,5], that the growth rates from all three two-carbon-atom source gases are very similar (Fig. 2). This similarity probably arises from the rapid conversion of C,H, and C2H, to C,H, in the substrate-filament region [6].
0.9
T 0.8 ) 0.7 q
t
53 = 0.8 -5
0.5 --
z c
0.4 --
r g
0.3 --
i
q
0
0.2 0.1
cl f
0 : 0
0.2
0.4
I
1
t
0.8
0.8
1
1.2
1.4
1.8
I
4
1.8
2
Percent Methane Fig. 1. Growth rate (mg h-‘) vs. methane concentration in hydrogen in the source gas (1 mg h-’ corresponds to a nominal linear growth rate of 4.4 pm h-l). Open square symbols indicate data from a single run.
E. A. Evans, J. C. Angus/Diamond and Related Materials 5 (1996) 200-205
202 0.6 -
0.5 -’
s =
0.4 --
.z 8 0.3 -CT
g 8
0.2
0’ /’
0.1
/’ l
I 0 0
I
I I
0.1
0.2
I
I
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Square Root of Percent Hydrocarbon in Feed Fig. 2. Growth rate (mg h-r) vs. square root of the hydrocarbon growth rate of 4.4 urn h-r).
concentration
When oxygen is added to the source gas, a decrease in the growth rate is observed for all source gases studied (see Figs. 3 and 4). Fig. 5 shows the growth rate data for various mixtures of methane, oxygen and hydrogen presented on a ternary C-H-O diagram. An increase in 0.80
1
0.80
Methane Concentration - -. 2% _-_ L
1% ’ 0.5 % l
i
o.oo.g 0.40 0.80 1.20 Percent Avallable Carbon (CO)/(C+O+HplOO
0.00
Fig. 3. Growth rate (mg h-r) vs. available carbon expressed as the atomic per cent of carbon less the atomic per cent of oxygen (1 mg h-r corresponds to a nominal linear growth rate of 4.4 urn h-l).
in the source gas (1 mg h-r corresponds to a nominal linear
growth rate is observed as the composition of the source gas moves away from the HZ-CO tie line. No detectable change in the growth rate is observed when CO is added to the source gas. These results imply that, once a carbon atom reacts to form CO, it is no longer available for diamond growth in a hot-filament system. We therefore define the concentration of available carbon as the difference between the total number of atoms of carbon and oxygen (C - 0) divided by the total number of atoms (C + 0 + H). For example, a source gas of 1% CH, and 0.25% O2 in Hz has Xc-o = (C - O)/(C + 0 + H) of 2.463 x 10m3. The results for all of the source gases (Figs. l-5) show that the growth rate approaches zero order as 100 x [(C - O)/(C + 0 + H)] increases above 0.5%. A maximum in the growth rate with pressure is observed around 30 Torr for a feed composition of 1% CH, and 0.125% O2 in hydrogen at a filament temperature of 2550 “C. This result agrees with that of Harris and Weiner [ 71 who also found a growth rate maximum at 30 Torr. Virgin substrates were used to compare the characteristics of the deposited films as the growth conditions were changed. Scanning electron microscopy (SEM) was carried out on a number of these samples to analyze how the morphology changed with the growth conditions. SEM photographs show that faceting is predominantly {111). At values of 100 x [(C - O)/(C + 0 + H)] greater than 0.5, secondary nucleation and “cauliflowerlike” deposits increase. As the growth rate increases, an
E. A. Evans, J. C. Angus/Diamond and Related Materials 5 (1996) 200-205
203
0.9 A
0.8 -0.7 --
A A
S=
0.8 --
3
0.5 --
, A A
3 r
0.4 --
2 6
0.3 -0.2 --
A Etharm (1%, 750 Watts) m
[ m Ethylene (0.75%, 420
m
Watts) 1
n
0.1 --
O0.00
1
0.20
0.10
0.30
I
I
0.40
0.50
1
0.80
I
0.70
0.80
I
1
0.90
1.00
{(GO)l(C+O+H))‘lOO Fig. 4. Growth rate (mg h-‘) vs. available carbon expressed as the atomic per cent of carbon less the atomic per cent of oxygen (1 mg h-’ corresponds to a nominal linear growth rate of 4.4 pm h-l).
4. Nucleation remits
Ii
OTie Line
I-
H
99.5
99
99.5
0
Fig. 5. Growth rate data displa:yed on a ternary C-H-O diagram. The diameter of the filled circle is proportional to the growth rate. The axes of the diagram are the atomic per cent of hydrogen in the source gas.
increase in the appearance of sp’ structures, as indicated by Raman spectroscopy, is also observed. This is in general agreement with models which suggest that more sp2 structures are incorporated into diamond at higher growth rates [8-lo]. As the amount of oxygen is increased, however, second.ary nucleation decreases.
We have also studied diamond nucleation using tde microbalance reactor. A plot of mass vs. time for a virg$ molybdenum substrate is shown in Fig. 6. The initial apparent drop in substrate weight is due to the drag force from the convective flow as the power to the filament is turned on. After this apparent decrease in mass, the mass vs. time plot shows two distinct growth periods. The first period, in which the second derivative, d2M/dtZ, is negative, corresponds to carburization. During the carburization period, carbon diffuses into the substrate, forming either a carbide in the case of a carbide-forming substrate or a solid solution of carbon for a non-carbide former. During this period, the rate of mass increase dM/dt decreases with time. The second period, in which d2M/dt2 is positive, is believed to correspond to the onset of the formation of diamond nuclei. At long times, steady state growth is observed, i.e. the second derivative is zero. Scanning electron micrographs taken at the end of the first stage and the beginning of the second stage show an increasing number of nuclei with time. The same trends are observed for slow carbide-forming substrates, i.e. rhenium, and noncarbide-forming substrates, i.e. platinum. In all cases, the total amount of carbon deposited during the initial stages is well below the solubility limits of the substrate. Diffusion coefficients can be estimated from these data
204
E. A. Evans, J. C. Angus/Diamond and Related Materials 5 (1996) 200-205
, / I I
, I
,
/
I
-
- Diamond Coated Substrete
-Virgin
Carburizetion
II 0.5
Substrate
Nucleation
I I 1
II 1.5
I 2
Time (hrs) Fig. 6. Relative mass changes during initial stages of diamond nucleation. M* is the sample mass M divided by the initial sample mass Me. During the carburization time period, dZM/dtZ < 0; during the nucleation period, d’M/dt’> 0. The substrate was molybdenum. Conditions for the run on the virgin substrate were 0.3% CH4 and a filament temperature of 2100 “C.
using the slope, dM/dt, just after the initial apparent decrease in mass. Diffusion coefficients were estimated for carbon diffusion in titanium, tantalum and molybdenum. The diffusion coefficients were also calculated from tabulated values [ 11,121 of the frequency factors and activation energies assuming a substrate temperature between 900 and 1000 “C. The results are shown in Table 1. The measured coefficients show the same qualitative behavior as the reported coefficients: the diffusion coefficient for carbon in titanium is at least an order of magnitude higher than in tantalum and molybdenum. The reported and measured values of the diffusion coefficient for carbon in titanium are very similar. The coefficients measured for tantalum and molybdenum, however, are significantly higher than the
reported values. The data suggest that, in addition to the diffusion of carbon into the substrate, nucleation of solid carbon is occurring on the tantalum and molybdenum surfaces starting at the very initial stages of the run. We did not observe diamond nucleation on titanium for deposition times up to 1 h. Therefore, in this case, the initial increase in mass reflects only carbon diffusion into the substrate. When a substrate that has been coated with diamond is subjected to similar conditions, the carburization and nucleation stages are not observed; steady state growth is achieved more quickly when a diamond-coated substrate is used (broken line in Fig. 6). These trends agree with the work of Joffreau et al. [13] who described carbon diffusion into substra)es prior to diamond nucleation.
Table 1 Reported and measured diffusion coefficients for carbon in different substrates Substrate
Titanium Tantalum Molybdenum
Reported [11,12] diffusion coefficient for substrate temperature of 900-1000 “C (cm' s-r)
Measured diffusion coefficient from initial growth rate data (cm’ s-r)
1 x lo-‘-5.3 x lo-’ 3.7 x 10-10-1.44 x 10Wg 4.7 x lo-‘O-l.86 x 10s9
2.5 x 1O-7 1.5 x 10-s 1 x lo-*
5. Discussion
The half-order kinetics observed with the two-carbonatom gases strongly support the view that, during diamond growth, the bulk of the atom addition is by singlecarbon-atom species, e.g. CH,. Half-order kinetics have also been observed for two-carbon-atom gases by Wang et al. [4,5] and by Chauhan et al. [l]. Half-order
E. A. Evans, J. C. AngusJDiamond and Related Materials 5 (1996) 200-205
kinetics typically arise from the dissociation of a twocarbon-atom species into two single-carbon-atom species. Simple models indicate that the concentration at which zero-order behavior becomes evident depends on the relative fluxes of atomic hydrogen and the carboncontaining growth species [9,10]. These models show that the diamond growth rate, dM/dt, is expected to be of the general form dM
-= dt
ACCKI 1+ JWH,IICH I)
where A and B are collections of rate constants which depend on temperature aad [CH,] and [H] are the concentrations of the growth precursor and atomic hydrogen. At very high fila.ment temperatures, where the generation of atomic hydrogen will be greater, the shift to zero order will be observed at higher hydrocarbon concentrations [ 141. The reaction order shift to zero observed at high hydrocarbon concentrations is characteristic of surfacesite-limited processes and can be described by Langmuir-Hinshelwood kinetics [ 15,161. The growth rate does not continue to increase at high carbon concentrations because the surface becomes saturated with surface-adsorbed species. This surface-adsorbed species may be an intermediate which participates in the subsequent formation of diamond, or may simply be a poison that blocks active surface sites. We have previously postulated that the surface-adsorbed species is an sp’ (graphite-like) structure that is subsequently converted to diamond by the action of atomic hydrogen [9,10]. A shift towards zero-order behavior at high hydrocarbon concentrations has also been reported by Wang et al. [4,5] in a similar hot-filament reactor, by Kobashi [17] in a microwave reactor and by Windischmann [ 181 in a d.c. arc jet reactor.
205
Acknowledgements The support of the National (USA) is gratefully acknowledged.
Science Foundation
References J. Appl. Phys., 47 (1976) 4746. PI D.V. Fedoseev and B.V. Deryagin, Zh. Fiz. Khim., 53 (1979) 252. c31 S.J. Harris and A.M. Weiner, J. Appl. Phys., 70 (1991) 1385. c41 Y. Wang, E. Evans, L. Zeatoun and J.C. Angus, Proc. Third IUMRS Co@ on Advanced Materials, Nikkan Kogyo Shimbum Ltd., Tokyo, 1993. c51 Y. Wang and J.C. Angus, in J.P. Dismukes and K.V. Ravi (eds.), Vol. 93-17, Proc. 3rd Symp. on Diamond Materials, Electrochemical Society, Pennington, NJ, 1993, p. 249. 161E.A. Evans, MS. Thesis, Case Western Reserve University, 1994. c71 S.J. Harris and A.M. Weiner, J. Appl. Phys., 75 (1994) 5026. ca D.G. Goodwin, J. Appl. Phys., 74 (1993) 6888. 191J.C. Angus and E.A. Evans, Mater. Res. Sot. Symp. Proc., 348
VI S.P. Chauhan, J.C. Angus and NC. Gardner,
(1994) 385.
J.C. Angus, E.A. Evans and Y. Wang, Advances in New Diamond Science and Technology, Fourth International Conference on New Diamond Science and Technology, MYU, Tokyo, 1994, p. 141. Cl11 J.F. Shackelford and W. Alexander (eds.), The CRC Materials Science and Engineering Handbook, CRC Press, Boca Raton, FL, 1992, pp. 392-400. Cl21 C.J. Smithells (ed.), Metals Reference Book, Plenum, New York, 1967, p. 664. [I31 P.O. Joffreau, R. Haubner and B. Lux, J. Ref. Hard Met., 7 (4)
WI
(1988) 186.
Cl41 D.M. Li, T. Mantyla, R. Hernberg and J. Levoska, Diamond Relat. Mater., 5 (1996) 350.
Cl51 G. Schwab, H.S. Taylor and R. Spence, Catalysis, Van Nostrand, New York, 1937. Cl61 P.G. Ashmore, Catalysis and Inhibition of Chemical Reactions, Butterworths, London, 1963. Cl71 K. Kobashi, K. Nishimura, Y. Kowate and T. Horiuchi, Phys. Rev. B, 38 (1988) 4067. Cl81 H. Windischmann, personal communication, 1994.
Diamond and Related Materials 5 (1996) 200-205
DJAMOND RE D bdldliw ALS
Microbalance studies of diamond nucleation and growth rates Edward A. Evans, John C. Angus Chemical Engineering Department, Case Western Reserve University, Cleveland, OH 441067217,
USA
Abstract In situ measurements of diamond nucleation and growth rates using a microbalance within a hot-filament reactor were made. Methane, acetylene, ethylene and ethane in hydrogen, with and without the addition of oxygen, were used as source gases. The measured reaction orders strongly support the view that the bulk of the atom addition is by single-carbon species, e.g. CH3. The reaction order shifts to zero at high hydrocarbon concentrations, suggesting that diamond growth is a surface-site-limited process. Diamond nucleation on virgin substrates shows an initial period in which d2M/dt2~0, which is attributed to the incorporation of
carbon into the substrate. Keywords:
Microbalance; Nucleation; Reaction orders; Growth rates
1. Introduction
2. Experimental methods
A better understanding of the growth mechanisms is required to improve the growth rates and quality of diamond grown by chemical vapor deposition. We have made in situ measurements of the growth rates and reaction orders using a microbalance within a hotfilament reactor. Preliminary studies were also completed on the initial stages of diamond nucleation on both carbide-forming and non-carbide-forming substrates. Growth rate data alone cannot unambiguously determine the growth mechanism. However, these data can suggest possible mechanisms of diamond growth, provide a database against which proposed mechanisms can be tested and give insight into the relationship between the growth rate and quality. Some previous microbalance studies of diamond growth have been made [l-6]. Our results are in general agreement with these earlier studies despite differences in the deposition methods. Wang et al. [4,5] have presented a large amount of growth rate data that can be summarized briefly as follows. For a methane feed concentration in hydrogen between 0.3% and l%, there is a first-order relationship between the feed concentration and the diamond growth rate. Above 1% methane, there is a gradual change to zero order. For twocarbon- atom source gases, they observed first-order kinetics below 0.3% feed concentration and approximately half-order kinetics above 0.3%. Wang et al. also reported similar growth rates for all two-carbon-atom source gases.
The microbalance system is a stainless steel bell jar with a Cahn D200 microbalance (practical sensitivity, f0.2 pg) mounted on the top. The reactor has been described in detail elsewhere [4-61. The source gases are introduced through a 0.25 inch stainless steel tube about 15 cm from the filament. The estimated reactor Peclet number, Pe = (VL)/D, is much less than unity, indicating that within the reactor the gases are well mixed. The Grashof number, Gr=(gj3CAT)/v2, is a measure of the momentum flux from thermal convection to that by viscous transport and describes the tendency to form convective roll cells. Estimates of Gr indicate that large roll cells can be expected within the reactor body, which has a diameter of 50 cm, but not within the region defined by the filament, which is approximately 3 cm in horizontal dimension. These predictions are confirmed by modelling [4] and by our observations of the behavior of the reactor. (Here D is the axial dispersion coefficient, V is the convective velocity, L is a characteristic length, g is the acceleration due to gravity, /I is the thermal expansion coefficient, AT is the temperature difference and v is the kinematic viscosity.) The microbalance continuously reports the weight of the substrate during a run. The substrates are small circular discs of molybdenum sheet (0.5 mm thick and 6 mm in diameter), with a total surface area of 64.4 mm2, and are hung with a 10 cm long platinum wire. For these substrates, a growth rate of 1 mg h-l translates into a nominal linear growth rate of 4.4 pm h-l.
0925-9635/96/$15X)00 1996 Elsevier Science S.A. All rights reserved SSDZ 0925-9635(95)00444-O
E.A. Evans, J. C. AngusfDiamond and Related Materials 5 (19%) 200-205
Substrates are suspended from the microbalance so that they hang within a U-shaped tantalum carbide filament. The filament is 10 cm long and the distance between the sides of the U is 3 cm. The filament thickness is 0.5 mm. The filament temperature is monitored with a Williamson two-color pyrometer and, for the data reported here, is in the range 2300-2600°C. We were unable to obtain a direct in situ measurement of the substrate temperature while the mass measurements were being made. A free-standing thermocouple in the vicinity of the substrate is .used to measure the gas phase temperature. From these measurements, we estimate that, for all of our runs, the substrate temperature varies from 900 to 1000 “C. During a single run, however, the substrate temperature varies over a much smaller range. The reported growth rate data are taken at steady state conditions. Each data point reported in the figures is an average of 120 measurements taken over 0.5 h; steady state is usually attained l-2 h after a change is made in the growth conditions. Growth rate data are taken after a continuous diamond film has been deposited. Before a sample is removed from the system, each data point is repeated to ensure the reproducibility of the data. To permit a comparison of the morphology of the films deposited in different conditions, we start with bare molybdenum substrates. The substrates are cleaned with a high strength detergent (Micro) and rinsed with alcohol. For these experiments the substrates are not scratched before deposition, and are referred to as virgin substrates. Each substrate is first treated with 1% methane in hydrogen at a filament temperature of 2100 “C
201
for 0.5 h. After this carburization and nucleation stage, the growth conditions are changed, and deposition is carried out until the mass has increased by approximately 2 mg.
3. Growth rate results We used the source gases methane, acetylene, ethylene and ethane in hydrogen, with and without the addition of oxygen. The growth rate data are shown in Figs. l-6. There is a linear, i.e. first-order, relationship between the methane concentration in the source gas and the growth rate up to about 1% methane in hydrogen. Above 1% methane, the reaction order gradually shifts to approximately zero, i.e. there is no increase in the growth rate with an increase in the methane concentration (Fig. 1). Growth rate data for the two-carbon-atom source gases, ethane, ethylene and acetylene, are shown in Fig. 2. In Fig. 2, the growth rate is plotted vs. the square root of the source gas concentration. The data fall on a straight line up to approximately [C2HJo.’ =0.8, i.e. a concentration of [C,H,] =0.64%. The growth rate is therefore approximately half order in the source gas concentration up to 0.64%. We also find, in agreement with the earlier work of Wang et al. [4,5], that the growth rates from all three two-carbon-atom source gases are very similar (Fig. 2). This similarity probably arises from the rapid conversion of C,H, and C2H, to C,H, in the substrate-filament region [6].
0.9
T 0.8 ) 0.7 q
t
53 = 0.8 -5
0.5 --
z c
0.4 --
r g
0.3 --
i
q
0
0.2 0.1
cl f
0 : 0
0.2
0.4
I
1
t
0.8
0.8
1
1.2
1.4
1.8
I
4
1.8
2
Percent Methane Fig. 1. Growth rate (mg h-‘) vs. methane concentration in hydrogen in the source gas (1 mg h-’ corresponds to a nominal linear growth rate of 4.4 pm h-l). Open square symbols indicate data from a single run.
E. A. Evans, J. C. Angus/Diamond and Related Materials 5 (1996) 200-205
202 0.6 -
0.5 -’
s =
0.4 --
.z 8 0.3 -CT
g 8
0.2
0’ /’
0.1
/’ l
I 0 0
I
I I
0.1
0.2
I
I
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Square Root of Percent Hydrocarbon in Feed Fig. 2. Growth rate (mg h-r) vs. square root of the hydrocarbon growth rate of 4.4 urn h-r).
concentration
When oxygen is added to the source gas, a decrease in the growth rate is observed for all source gases studied (see Figs. 3 and 4). Fig. 5 shows the growth rate data for various mixtures of methane, oxygen and hydrogen presented on a ternary C-H-O diagram. An increase in 0.80
1
0.80
Methane Concentration - -. 2% _-_ L
1% ’ 0.5 % l
i
o.oo.g 0.40 0.80 1.20 Percent Avallable Carbon (CO)/(C+O+HplOO
0.00
Fig. 3. Growth rate (mg h-r) vs. available carbon expressed as the atomic per cent of carbon less the atomic per cent of oxygen (1 mg h-r corresponds to a nominal linear growth rate of 4.4 urn h-l).
in the source gas (1 mg h-r corresponds to a nominal linear
growth rate is observed as the composition of the source gas moves away from the HZ-CO tie line. No detectable change in the growth rate is observed when CO is added to the source gas. These results imply that, once a carbon atom reacts to form CO, it is no longer available for diamond growth in a hot-filament system. We therefore define the concentration of available carbon as the difference between the total number of atoms of carbon and oxygen (C - 0) divided by the total number of atoms (C + 0 + H). For example, a source gas of 1% CH, and 0.25% O2 in Hz has Xc-o = (C - O)/(C + 0 + H) of 2.463 x 10m3. The results for all of the source gases (Figs. l-5) show that the growth rate approaches zero order as 100 x [(C - O)/(C + 0 + H)] increases above 0.5%. A maximum in the growth rate with pressure is observed around 30 Torr for a feed composition of 1% CH, and 0.125% O2 in hydrogen at a filament temperature of 2550 “C. This result agrees with that of Harris and Weiner [ 71 who also found a growth rate maximum at 30 Torr. Virgin substrates were used to compare the characteristics of the deposited films as the growth conditions were changed. Scanning electron microscopy (SEM) was carried out on a number of these samples to analyze how the morphology changed with the growth conditions. SEM photographs show that faceting is predominantly {111). At values of 100 x [(C - O)/(C + 0 + H)] greater than 0.5, secondary nucleation and “cauliflowerlike” deposits increase. As the growth rate increases, an
E. A. Evans, J. C. Angus/Diamond and Related Materials 5 (1996) 200-205
203
0.9 A
0.8 -0.7 --
A A
S=
0.8 --
3
0.5 --
, A A
3 r
0.4 --
2 6
0.3 -0.2 --
A Etharm (1%, 750 Watts) m
[ m Ethylene (0.75%, 420
m
Watts) 1
n
0.1 --
O0.00
1
0.20
0.10
0.30
I
I
0.40
0.50
1
0.80
I
0.70
0.80
I
1
0.90
1.00
{(GO)l(C+O+H))‘lOO Fig. 4. Growth rate (mg h-‘) vs. available carbon expressed as the atomic per cent of carbon less the atomic per cent of oxygen (1 mg h-’ corresponds to a nominal linear growth rate of 4.4 pm h-l).
4. Nucleation remits
Ii
OTie Line
I-
H
99.5
99
99.5
0
Fig. 5. Growth rate data displa:yed on a ternary C-H-O diagram. The diameter of the filled circle is proportional to the growth rate. The axes of the diagram are the atomic per cent of hydrogen in the source gas.
increase in the appearance of sp’ structures, as indicated by Raman spectroscopy, is also observed. This is in general agreement with models which suggest that more sp2 structures are incorporated into diamond at higher growth rates [8-lo]. As the amount of oxygen is increased, however, second.ary nucleation decreases.
We have also studied diamond nucleation using tde microbalance reactor. A plot of mass vs. time for a virg$ molybdenum substrate is shown in Fig. 6. The initial apparent drop in substrate weight is due to the drag force from the convective flow as the power to the filament is turned on. After this apparent decrease in mass, the mass vs. time plot shows two distinct growth periods. The first period, in which the second derivative, d2M/dtZ, is negative, corresponds to carburization. During the carburization period, carbon diffuses into the substrate, forming either a carbide in the case of a carbide-forming substrate or a solid solution of carbon for a non-carbide former. During this period, the rate of mass increase dM/dt decreases with time. The second period, in which d2M/dt2 is positive, is believed to correspond to the onset of the formation of diamond nuclei. At long times, steady state growth is observed, i.e. the second derivative is zero. Scanning electron micrographs taken at the end of the first stage and the beginning of the second stage show an increasing number of nuclei with time. The same trends are observed for slow carbide-forming substrates, i.e. rhenium, and noncarbide-forming substrates, i.e. platinum. In all cases, the total amount of carbon deposited during the initial stages is well below the solubility limits of the substrate. Diffusion coefficients can be estimated from these data
204
E. A. Evans, J. C. Angus/Diamond and Related Materials 5 (1996) 200-205
, / I I
, I
,
/
I
-
- Diamond Coated Substrete
-Virgin
Carburizetion
II 0.5
Substrate
Nucleation
I I 1
II 1.5
I 2
Time (hrs) Fig. 6. Relative mass changes during initial stages of diamond nucleation. M* is the sample mass M divided by the initial sample mass Me. During the carburization time period, dZM/dtZ < 0; during the nucleation period, d’M/dt’> 0. The substrate was molybdenum. Conditions for the run on the virgin substrate were 0.3% CH4 and a filament temperature of 2100 “C.
using the slope, dM/dt, just after the initial apparent decrease in mass. Diffusion coefficients were estimated for carbon diffusion in titanium, tantalum and molybdenum. The diffusion coefficients were also calculated from tabulated values [ 11,121 of the frequency factors and activation energies assuming a substrate temperature between 900 and 1000 “C. The results are shown in Table 1. The measured coefficients show the same qualitative behavior as the reported coefficients: the diffusion coefficient for carbon in titanium is at least an order of magnitude higher than in tantalum and molybdenum. The reported and measured values of the diffusion coefficient for carbon in titanium are very similar. The coefficients measured for tantalum and molybdenum, however, are significantly higher than the
reported values. The data suggest that, in addition to the diffusion of carbon into the substrate, nucleation of solid carbon is occurring on the tantalum and molybdenum surfaces starting at the very initial stages of the run. We did not observe diamond nucleation on titanium for deposition times up to 1 h. Therefore, in this case, the initial increase in mass reflects only carbon diffusion into the substrate. When a substrate that has been coated with diamond is subjected to similar conditions, the carburization and nucleation stages are not observed; steady state growth is achieved more quickly when a diamond-coated substrate is used (broken line in Fig. 6). These trends agree with the work of Joffreau et al. [13] who described carbon diffusion into substra)es prior to diamond nucleation.
Table 1 Reported and measured diffusion coefficients for carbon in different substrates Substrate
Titanium Tantalum Molybdenum
Reported [11,12] diffusion coefficient for substrate temperature of 900-1000 “C (cm' s-r)
Measured diffusion coefficient from initial growth rate data (cm’ s-r)
1 x lo-‘-5.3 x lo-’ 3.7 x 10-10-1.44 x 10Wg 4.7 x lo-‘O-l.86 x 10s9
2.5 x 1O-7 1.5 x 10-s 1 x lo-*
5. Discussion
The half-order kinetics observed with the two-carbonatom gases strongly support the view that, during diamond growth, the bulk of the atom addition is by singlecarbon-atom species, e.g. CH,. Half-order kinetics have also been observed for two-carbon-atom gases by Wang et al. [4,5] and by Chauhan et al. [l]. Half-order
E. A. Evans, J. C. AngusJDiamond and Related Materials 5 (1996) 200-205
kinetics typically arise from the dissociation of a twocarbon-atom species into two single-carbon-atom species. Simple models indicate that the concentration at which zero-order behavior becomes evident depends on the relative fluxes of atomic hydrogen and the carboncontaining growth species [9,10]. These models show that the diamond growth rate, dM/dt, is expected to be of the general form dM
-= dt
ACCKI 1+ JWH,IICH I)
where A and B are collections of rate constants which depend on temperature aad [CH,] and [H] are the concentrations of the growth precursor and atomic hydrogen. At very high fila.ment temperatures, where the generation of atomic hydrogen will be greater, the shift to zero order will be observed at higher hydrocarbon concentrations [ 141. The reaction order shift to zero observed at high hydrocarbon concentrations is characteristic of surfacesite-limited processes and can be described by Langmuir-Hinshelwood kinetics [ 15,161. The growth rate does not continue to increase at high carbon concentrations because the surface becomes saturated with surface-adsorbed species. This surface-adsorbed species may be an intermediate which participates in the subsequent formation of diamond, or may simply be a poison that blocks active surface sites. We have previously postulated that the surface-adsorbed species is an sp’ (graphite-like) structure that is subsequently converted to diamond by the action of atomic hydrogen [9,10]. A shift towards zero-order behavior at high hydrocarbon concentrations has also been reported by Wang et al. [4,5] in a similar hot-filament reactor, by Kobashi [17] in a microwave reactor and by Windischmann [ 181 in a d.c. arc jet reactor.
205
Acknowledgements The support of the National (USA) is gratefully acknowledged.
Science Foundation
References J. Appl. Phys., 47 (1976) 4746. PI D.V. Fedoseev and B.V. Deryagin, Zh. Fiz. Khim., 53 (1979) 252. c31 S.J. Harris and A.M. Weiner, J. Appl. Phys., 70 (1991) 1385. c41 Y. Wang, E. Evans, L. Zeatoun and J.C. Angus, Proc. Third IUMRS Co@ on Advanced Materials, Nikkan Kogyo Shimbum Ltd., Tokyo, 1993. c51 Y. Wang and J.C. Angus, in J.P. Dismukes and K.V. Ravi (eds.), Vol. 93-17, Proc. 3rd Symp. on Diamond Materials, Electrochemical Society, Pennington, NJ, 1993, p. 249. 161E.A. Evans, MS. Thesis, Case Western Reserve University, 1994. c71 S.J. Harris and A.M. Weiner, J. Appl. Phys., 75 (1994) 5026. ca D.G. Goodwin, J. Appl. Phys., 74 (1993) 6888. 191J.C. Angus and E.A. Evans, Mater. Res. Sot. Symp. Proc., 348
VI S.P. Chauhan, J.C. Angus and NC. Gardner,
(1994) 385.
J.C. Angus, E.A. Evans and Y. Wang, Advances in New Diamond Science and Technology, Fourth International Conference on New Diamond Science and Technology, MYU, Tokyo, 1994, p. 141. Cl11 J.F. Shackelford and W. Alexander (eds.), The CRC Materials Science and Engineering Handbook, CRC Press, Boca Raton, FL, 1992, pp. 392-400. Cl21 C.J. Smithells (ed.), Metals Reference Book, Plenum, New York, 1967, p. 664. [I31 P.O. Joffreau, R. Haubner and B. Lux, J. Ref. Hard Met., 7 (4)
WI
(1988) 186.
Cl41 D.M. Li, T. Mantyla, R. Hernberg and J. Levoska, Diamond Relat. Mater., 5 (1996) 350.
Cl51 G. Schwab, H.S. Taylor and R. Spence, Catalysis, Van Nostrand, New York, 1937. Cl61 P.G. Ashmore, Catalysis and Inhibition of Chemical Reactions, Butterworths, London, 1963. Cl71 K. Kobashi, K. Nishimura, Y. Kowate and T. Horiuchi, Phys. Rev. B, 38 (1988) 4067. Cl81 H. Windischmann, personal communication, 1994.