- Email: [email protected]
oxygen flames used for diamond deposition
Diagnostics and Modeling of Strained Fuel-Rich Acetylene / Oxygen Flames Used for Diamond Deposition N. G. GLUMAC*
and D. G. GOODWIN
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125
flames similar to those used for diamond chemical vapor Low pressure (35 torr) strained acetylene/oxygen deposition are studied using laser-induced fluorescence (LIF) and mass spectrometty. Relative OH concentration and OH rotational temperature profiles are obtained by LIF, while absolute mole fractions of C,H,, CH,, H,, and CO are measured at the substrate by mass spectrometry. The results of the diagnostics are compared with the predictions of a one-dimensional strained flame code. The agreement between model prediction and experiment is generally good and usually within experimental uncertainties.
Recently, several groups have used fuel-rich premixed flat flames for diamond thin film deposition [l-7]. Building on earlier work using torch-stabilized flames [8-101, these recent experiments have demonstrated that flame methods can be used to deposit uniform-thickness diamond films over moderate areas. In experiments at atmospheric pressure, high deposition rates (up to 40 pm/h) have been achieved over small areas (- 2 cm’) [2, 31. In our laboratory, we have used low-pressure 30-50-torr flat flames to achieve large area coverage (19 cm2) at lower growth rates (l-2 pm/h) [5]. This area coverage is competitive with that of current plasma chemical vapor deposition methods, and the flame method is easily scalable to much larger areas, which most plasma methods are not. Diamond growth requires use of fast, hot flames, which are able to deliver a large flux of H to the substrate. This requirement stems from the critical role played by H in the diamond growth mechanism [ll-131. Most studies have employed acetylene/oxygen [5, S-10] or acetylene/hydrogen/oxygen [2, 31 flames. However, diamond has also been grown in ethylene/oxygen [14, 61, MAPP/oxygen [7], and recently propylene/oxygen 1151flames. The fact that these latter fuels are significantly cheaper and easier to handle than acetylene may greatly improve the economics of the flame synthesis process.
*Corresponding author. Present address: Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08855. COMBUSTIONAND FLAME 105: 321-331 Copyright 0 1996 by The Combustion Institute Published by Elsevier Science Inc.
The flat flame geometry of interest for diamond film deposition is shown in simplified form in Fig. 1. Premixed gas emerges from a flat-flame burner a distance L above an isothermal substrate with downward velocity uL and zero radial velocity. The flow between the burner and substrate is axisymmetric, and a constant-thickness boundary layer forms above the substrate. Depending on the gas flow rate, the flame may be stabilized either on the burner [4-7, 151 or in the stagnation-point flow above the substrate [l-3]. To make this technique viable for commercial use, flame conditions need to be found which result simultaneously in moderate growth rates (for most applications, a few microns/hr), high film quality, good uniformity, and large area coverage [16]. Since a large number of experimental variables are involved (for example, fuel type, pressure, flow rate, equivalence ratio, substrate temperature, and burner/substrate configuration), numerical simulations are a valuable aid in narrowing the range of conditions which must be investigated experimentally. Therefore, it is critically important to have available validated, robust numerical models for flames of the type used for diamond growth, which include effects due to the presence of the substrate, such as strain, heat loss, and radical recombination. Several groups have developed models of the flame synthesis process [5, 17-191, but to date there have been few experimental measurements available to assess these models. Axisymmetric strained flames similar to those of interest here have been the subject of many studies [20-24, 26-301, primarily focused on OOlO-2180/96/$15.00 SSDI OOlO-2180(95MO214-6
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N. G. GLUMAC AND D. G. GOODWIN
Flat Flame Burner
Substrate
+D* Fig. 1. The flat flame geometry.
flame speed measurement and extinction behavior. Most studies have dealt with premixed opposed-jet flames, in order to remove the complications of downstream heat loss and surface chemistry (which are central to the diamond deposition problem), although in some studies stagnation-point flames were used [21, 231. These studies dealt almost exclusively with methane/air and propane/air flames, rather than the much faster and hotter flames necessary for diamond growth. Numerical models of strained methane/air or propane/air flames have reproduced in detail their extinction characteristics [24, 301. To date, there has been only one comparison of measured species profiles in a counterflow premixed flame to model predictions [25]; the agreement was generally good, although there was poor agreement for temperature profiles (possibly due to experimental difficulties). For diamond deposition studies, a numerical model must accurately predict the concentrations at the substrate of those species important for deposition of diamond and nondiamond carbon (believed to include CH,, H, OH, O,, 0, C,H,, possibly C, and C, and perhaps heavier species). Therefore, boundary layer and surface effects are an important part of the problem. In contrast, in extinction studies, the extinction limit is insensitive to the boundary layer and surface, since the flame is outside the boundary layer at the extinction limit [26]. Whether current flame mechanisms and models are adequate is not yet clear. Indeed, there is some evidence of problems: superadiabatic flame temperatures are predicted [ 18,311, which, while possible, clearly warrant further investigation. Also, diamond film growth rates are generally overpredicted [18, 311, using a
diamond growth mechanism know to be accurate in other non-flame environments [ll, 321. This latter problem suggests that CH, and/or H at the surface are being overpredicted by the models. In this paper, we report experimental measurements of selected species concentrations and temperatures in flames similar to those used for diamond growth [19], and compare the result to the predictions of a numerical model. We are particularly interested in examining the effects of the cold substrate on the measured profiles. Rotational temperature and relative OH concentration profiles are acquired using laser-induced fluorescence (LIF), and several stable-species mole fractions at the substrate are measured using mass spectrometry. The model is found to reproduce the measurements reasonably well, and clearly shows the effects due to the substrate. EXPERIMENTAL The experimental setup is shown schematically in Fig. 2. The burner and substrate are housed within a water-cooled bell-jar vacuum chamber. Optical access is provided through three fused silica windows. To limit condensation of water vapor on the windows, a flow of nitrogen is directed over the interior window surfaces. A throttle valve under closed loop control in the exhaust line maintains the system pressure to within +0.2 torr of the chosen set point. Electronic mass flow controllers meter the input gas flows to the burner. The burner is mounted in a downflow configuration and was designed especially for work with rich acetylene/oxygen flames. Its face consists of a 6-cm-diameter, 12-mm-thick copper plate drilled with several hundred l-mmdiameter holes 2.5 mm apart in a hexagonal array. The burner surface temperature is measured by an ice-point-corrected thermocouple in one of the burner face holes near the center of the array. The substrate is mounted horizontally, approximately 1 cm below the burner surface. For the LIF experiments, the substrate consisted of a thin (0.5 mm) silicon wafer (10 cm diameter) which was thermally isolated from its holder by narrow ceramic supports. In the presence of the flame, the wafer rose to a
ACETYLENE
+ 1
/ OXYGEN
FLAMES FOR DIAMOND
6cm Burner
1
Laser Beam
To Mass spectrometer Fig. 2. A schematic of the experimental setup.
temperature which was fairly uniform over at least the innermost 4 cm. The temperature was measured by an ice-pointcorrected thermocouple cemented to the top of the substrate. For the mass spectrometry work, the substrate was l-cm-thick copper plate, 7.5 cm in diameter. A l-mm hole in the center was drilled to allow gas to be sampled from near the surface. The experimental arrangement for the LIF measurements is shown in Fig. 3. To obtain axial profiles of rotational temperature, the experimental protocol established by Rensberger et al. [33] is used. A Nd:YAG laser pumps a dye laser (bandwidth 0.08 cm-’ > using DCM, and the output is frequency doubled and attenuated, yielding 7-8 ns pulses of _ 1 PJ with wavelength in the range from 309.2 to steady-state
Bplittar
DEPOSITION
323
309.7 nm. The beam is focussed into the flame with a 50 cm focal length lens. The laser is scanned over seven P and Q rotational branch lines with N” ranging from 1 to 9 in the (0-O) band of the A2Z --f X211 transition in OH. Fluorescence is collected at right angles to the laser beam using f/5 optics through a l/8 m monochromator to a photomultiplier. The monochromator slits are set with a narrow front slit (0.5 mm) and wide exit slit (3.0 mm) such that it serves as a flat bandpass filter (with bandwidth 20 nm) over the entire rotational manifold of the (0-O) band. The fluorescence signal is sampled using a boxcar integrator with a short (10 ns), prompt detector gate to minimize effects of rotational-level-dependent collisional quenching [331. A small portion of the beam is reflected from a sapphire beam splitter and directed to a photodiode. The photodiode measures laser power on a shot-to-shot basis, and these data are used to normalize the fluorescence signal. The linearity of the fluorescence signal with laser power is assured by operating at low laser energies. This was verified by plotting the fluorescence vs. laser power signal for laser power levels ranging from 0.5 to 1.5 PJ per pulse. The data shown in Fig. 4 concur with the results of other investigators [33, 341, who found linear OH fluorescence signal behavior with laser power under similar conditions. Optical depth effects were measured by a separate absorption experiment, and the maximum uncertainty due to optical depth was calculated.
I
Vacuum Chamber Fig. 3. The experimental setup for the laser-induced fluorescence measurements of OH.
N. G. GLUMAC AND D. G. GOODWIN
324
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2.5 : _
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0
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1’
~~~~‘~~~~‘~~~~‘~~~~‘~~~~ 5
10 Laser
15 Power
20
25
0
T=2055*103K 3 scan average I,,, 500 Rotational
(mV)
III
I
Energy
I
I
I
I
#I
1500
1000 (cm-‘)
Fig. 4. Fluorescence intensity versus laser power. 10 mV of laser power is approximately 1 PJ per pulse.
Fig. 6. The Boltzmann plot for the fluorescence taken 3 mm below the burner surface.
The burner and substrate can be translated relative to the laser beam. In this way, rotational temperature and relative OH concentration measurements were obtained at four locations in the flame. Blockage of the collection optics limits us to measurements further than 1 mm from the burner or substrate. The positional uncertainty is roughly kO.2 mm. Normalized LIF spectra are analyzed by comparing relative areas of fluorescence lines. For most positions, the data are averaged over 2-3 scans. A typical scan is shown in Fig. 5, and the resulting Boltzmann plot in Fig. 6. The experimental arrangement for the mass spectrometry measurements is also shown in Fig. 2. Gas near the surface is sampled through the 1 mm diameter, 0.5 mm deep hole in the substrate by a quartz probe with an orifice opening of 400 pm. The pressure in the probe
is maintained at 0.3 torr. Gas in the region surrounding the quartz probe beneath the substrate is differentially pumped away to insure that gas entering the mass spectrometer originates from the flame. After passing through a short length of quartz tube, the sampled gas is directed to a quadrupole mass spectrometer and analyzed. Absolute mole fractions were determined by calibrating the ionization signal of each species relative to argon, using calibration mixtures of known composition, The mass peaks of 2,15,26,28, and 40 amu were used to monitor relative number densities of H,, CH,, C,H,,’ CO, and Ar, respectively. Argon mole fractions in the flame are then calculated using the flame model, and the mole fractions of the other species are inferred using Ar as a reference. This calibration procedure allows determination of major species mole fractions with a relative uncertainty of f 10%-S%. Background signal levels were subtracted from the measured signal for each mass peak. For CO, Ar, and H,, background signal levels were negligibly small compared to the measured signals. For CH, and C,H,, both present in amounts near or below the system detection limit, background levels were of the same order of magnitude as the measured signals. To ascertain background levels for C,H, and CH,, the flame equivalence ratio was decreased until the measured signal level no longer dropped, and this was chosen as the’ background level, assuming that, for small 4, both C,H, and CH, are below detection limits.
1
Laser Excitation
Wavelength
(nm)
Fig. 5. A typical scan of OH fluorescence intensity versus excitation wavelength, taken 3 mm below the burner surface.
scans
ACETYLENE / OXYGEN FLAMES FOR DIAMOND DEPOSITION NUMERICAL MODEL The numerical model is similar to that of Meeks et al. [351 and Kim and Cappelli [17]. The governing equations for axisymmetric flow admit a similarity solution, which is valid in the limit when the ratio of the burner diameter D to the burner/substrate separation L is large, and when the Mach number is small. In this limit, the axial velocity U, the temperature T, and species mass fractions Yk are all independent of r, while the radial velocity u has the form rV(z) [30]. With these assumed functional forms, the conservation equations reduce to
u dp P dz
Radial Momentum dV pu--& + pv*
d - z
Energy dT pc,‘z
+ $
PC,,,
UY k
dT +M,cj,h,
k dz
Species +
;( pu,y,)
- ‘bkMk = 0;
(4)
Equation of State p = pRT.
(5)
In these equations, u is the axial velocity, V is the radial velocity divided by radius, and p is the density. The quantity n in Eq. 2 is the radial pressure-gradient eigenvalue, defined as A=;;.
u, = Boundary Conditions
-pY,[u(L) (3)
” dY, dz
specific enthalpy, and molar production rate, respectively, for species k. The transport properties (viscosity p, thermal conductivity h, multicomponent diffusion coefficient Dkj, and thermal diffusion coefficient Di) are calculated using the multicomponent formalism with the subroutines of Kee et al. 1361.The diffusion velocities U, are given by
The boundary conditions are as follows. The mass flw rit at the burner is specified, and the mass flux to the substrate is equated to the net mass deposition rate due to surface chemistry, summed over all surface reactions. For the radial velocity, V is set to zero both at the substrate and at the burner surface (no slip). The temperature is specified both at the burner (Ts) and substrate CT,). For the species equations, flux boundary conditions are used. At the burner surface (z = L) we impose
Continuity ;+2V+--=o;
325
1 dP
It may be shown that A is constant throughout the flowheld under conditions for which the similarity solution holds [30]. The quantities X,, Yk, Mk, h,, I%, are the mole fraction, mass fraction, molecular weight,
+ u,(L)]
= kY,,,,
(8)
where Yk I is the specified mass fraction of species k’ in the pure reactants upstream of the burner. At the substrate, the mass flux of each species balances its mass deposition rate pY,[u(O) + u,(O)] = M&,
(9)
where gk is the net molar production rate for species k due to surface chemistry. The governing equations are solved using a hybrid Newton/time integration method on an adaptive mesh. We use the TWOPNT boundary-value-problem solver developed by Grcar [37], which is the same solver used in the Sandia premixed flame code 1381,as well as in the flame models of Meeks et al. [35] and Kim and Cappelli [171. Gas-Phase Chemistry The gas phase chemistry mechanism is taken from Miller and Melius [39]. This mechanism is designed for simulating fuel-rich hydrocar-
N. G. GLUMAC AND D. G. GOODWIN
326
molar production rates at the surface are easily calculated for use in Eq. 9. The assumed diamond growth mechanism is listed in Table 1. Reactions sl-s5 implement a reduced form [12] of the methyl growth mechanism for diamond proposed by Harris [ill. The Harris mechanism accurately reproduces measured diamond growth rates in many different chemical environments [32]. Reactions sl and s2 constitute a mechanism for surface recombination of H to H,. The rate constants used reproduce the measured H recombination coefficient and its temperature dependence (E = 6 kcal/mol) in the temperature range 700-1200 K [42, 431. In addition, k, reproduces the molecular dynamics simulation results of Brenner [44]. The rate constant for s3 is empirical, and is set to give the measured temperature dependence of diamond growth in the temperature range 1000-1200 K (23 kcal/mol) [45]. As pointed out by Harris [46], more detailed mechanisms [32] suggest methyl addition occurs primarily at radical site pairs, which may account for the high (18 kcal/mol) activation energy required to simulate the measured kinetics in this reduced mechanism. Rate constant k, is the same as used by Harris [ll], and k, is set to a large value so that it is not rate-limiting. Reactions s6 and s7 are included to provide a mechanism for loss of OH and 0 on the surface by abstraction of an H atom. The rate constants for these reactions are chosen to be identical to those of the analogous gas-phase reactions:
bon flames, and consists of 50 species and 218 reactions. This same mechanism has been used in previous simulations of diamond-depositing flames [17, 351, and has been used to simulate unstrained, 25torr, rich, nonsooting C,H,/O,/Ar flames with generally good results [40]. The chemical terms in the equations are evaluated with calls to the Chemkin-II [41] subroutine library, and the Chemkin thermodynamic database is employed as well. Surface Chemistry Surface reactions are included which model diamond growth and radical recombination. The surface is assumed to consist of diamond, and several different types of surface species are defined, with which gas-phase species may react. The surface species used include chemisorbed hydrogen (C,H), dangling-bond sites CC,*), chemisorbed methyl groups (C,M), chemisorbed methylene groups (C,M*), and several others. We take the surface species density to be 3 x lo-’ mol/cm*, which is the surface carbon density on the (111) surface of diamond. Rate equations are solved for the surface species to determine their steady-state surface coverages. We only allow reactions between surface- and gas-phase species (not between surface species), and therefore the set of rate equations is linear in the vector of surface coverages. This linear system is easily solved for any specified set of gas-phase concentrations at the surface, so we may regard the surface coverages as functions of the instantaneous gas-phase concentrations at the surface. With the coverages known, the net surface
0 + i-C,H,,
+ OH + i-C,H,
OH + i-C,H,,
(10)
+ H,O + i-C,H,.
(11)
TABLE 1 Surface Mechanism Used in the Simulations.”
(sl) (s2) (s3) (s4) (SS) (~6) (s7)
reaction
A
C,H+H+C,*+H, C,* + H --) C,H C,* + CH, + C,M CdM+H-+CdM*+Hz CdM*+H+CdH+H2 C,H + OH + C,* + H,O C,H+O =C,*+OH
7.8E13 2.2Ell l.OE15 2.8E7 fast 2.47E6 2.14E5
’ Rate constants are of the form k = AT”exp(-E/RT).
n
E
0 0.5 0 2.0
7.3 -2.1 18.0 7.7
2.152 2.5
Units: cm3, mol, s, kcal.
0.3217 0.924
AGO
-31.14 - 19.74
ACETYLENE
/ OXYGEN
FLAMES FOR DIAMOND
DEPOSITION
327
In addition to the reactions in Table 1, we include global reactions which destroy the radicals C, CH, CH,, and CH,(S) on the surface. We assume that these radicals are destroyed with unity probability at the surface through the global reactions 2C + H, + C,H,,
(12)
2CH -+ C,H,,
(13)
2CH, -+ C,H,,
(14)
‘mom 0.20
0.15
and 2CH,(S)
+ C,H,.
(15)
(These reactions are actually implemented as a sequence of first-order reactions, giving a destruction rate at the surface which is first-order in the radical concentration.) The product species are chosen to be major species whose concentrations are not significantly perturbed by the inclusion of these reactions. In practice, the concentrations of these and other radicals at the substrate are very low even without these reactions, and the results of the simulations are insensitive to the inclusion of these reactions. ‘Qpical Results
of the simulation results, a typical flame profile predicted by the model is shown in Figs. 7 and 8. The case shown corresponds to one flame used for the mass spectroscopy measurements. The C,HJO,/Ar ratio is 1:1.25:0.25, corresponding to an equivalence ratio of 2.0. The mass flow rate is 3.1 X 10e3 g/cm2/s, and the substrate temperature is 900 K. The pressure is 35 torr and the burner/substrate separation is 1.5 cm. Under these conditions, the peak strain rate of 220 s-l occurs 0.5 cm above the substrate, which may be taken as the velocity boundary layer thickness. The thermal boundary layer is seen to be somewhat thicker, with the temperature maximum occurring 1 cm from the substrate Most of the major species detected by mass spectrometry have flat profiles at the substrate. The exception is H,,which decreases due to thermal diffusion near the substrate. All radical species other than CH, decrease markedly near the substrate.
5 ._ r, G
0.10
S P 0.05
0
0.2
0.4
0.6
0.6
1.0
1.2
1.4
Distance from Burner (cm) Fig. 7. Predicted major species profiles in a typical flame. The flame conditions are: C#J = 2.0, 10% Ar dilution, mass flow rate per unit area = 3.1 X 10e3 g/cm*/s, substrate temperature = 900 K, pressure = 35 torr, burner to substrate separation = 1.5 cm.
As an example
0
0.2
0.4 Distance
0.6
0.6
1.0
1.2
1.4
from Burner (cm)
Fig. 8. Prediced minor species profiles in a typical flame. The flame conditions are the same as in Fig. 7.
328
N. G. GLUMAC
RESULTS Fluorescence
The OH fluorescence measurements were carried out for a single flame with P = 34 torr, 4 = 1.67, total flow rate = 4 slm, TB = 993 K, T, = 1068 K, burner to substrate distance L = 0.92 cm. The flow rate corresponds to a cold gas velocity of 2.2 m/s. The maximum strain rate calculated from the flame model is 340 s-’. This flame is similar to (but slightly leaner than) a flame used for diamond deposition [19]. Temperatures measured at four different locations in the flame are shown in Fig. 9 along with the predictions of the flame code. The error bars show the statistical uncertainties in the linear fit to Boltzmann data, using 2u uncertainties in the peak areas. Absorption of the laser beam by the flame was below our detection limits, which is about 4%. From calculations assuming 4% absorption of the strongest line, we calculate a maximum temperature correction of -35 K. That is, the reported temperature is at most 35 K larger than the actual temperature. The uncertainty varies from f 100 to f 175 K. Within this level of uncertainty, the agreement of experiment and theory is good. Figure 9 also shows the calculated temperature for a flame with the same input flame parameters and no substrate. It can be seen that the predicted peak temperature of the flame with a
2500
1
0
0.2
x
I
I
0.4
0.6
’
I
0.5
Distance from Burner (cm)
Fig. 9. Comparison of OH rotational temperature data with predictions of the model. The solid curve shows the predicted flame temperature with the substrate in place, and the dashed curve shows the predicted temperature with no substrate.
AND D. G. GOODWIN
substrate present is lower than that of the flame with no substrate, and our measurements support this prediction as well. The agreement in the temperature profile between prediction and measurement is slightly better than that observed in many unstrained burner-stabilized flames. There are at least two possible reasons for this. First, in unstrained flames, the temperature overprediction is usually largest in the postflame zone where heat losses due to radial conduction and radiation have accumulated enough to be appreciable. The predicted temperature profile in the reaction zone of the flame is often much closer to the measured profile. In the strained flames at 34 torr, the reaction zone covers a substantial portion of the gap width, and there is only few mm of the gap which can be considered a postflame region. Thus, because of the lack of a large postflame zone, better agreement between predicted and measured temperatures is anticipated. Second, in the region of the flame past the reaction zone, the primary heat loss mechanism is axial conduction downstream towards the relatively cool substrate. This gas-phase conduction is included in the model. It is possible that the heat loss to the substrate dominates any heat losses by radiation in these strained flames. In that case, better agreement in such flames is expected because the dominant heat loss mechanisms in the postflame gases are accounted for, whereas in the unstrained flames the heat loss mechanisms in the postflame gases typically are neglected. Relative OH concentrations were obtained by measuring the relative area of the Qr(6) line at each location and correcting for the variation in Boltzmann fraction. The realtive concentrations are shown in Fig. 10, normalized to theory at x = 3 mm. Again, agreement with theory is good. The predicted effect of the substrate, in this case, is to reduce the OH concentration to 5% of its maximum value at x = 8 mm. This is compared to the case of a flame without the substrate in which the OH concentration at 8 mm is 95% of its maximum value. Our measurements are in agreement with the 5% prediction. The measured relative OH profile is insensitive to surface chemistry, however. If the mea-
ACETYLENE
/ OXYGEN
FLAMES FOR DIAMOND
DEPOSITION
329
0.6 -
A j
0.4 -
A
A
A
IL s P
_
5.0 -
_______--------
0.2 -
-
2.5 -
0.2
0.4
0.6
0.6
Distance from Burner (cm)
Fig. 10. Comparison of OH number density profiles with the predictions of the model. The measured values are normalized to the theoretical predictions at x = 0.3 cm. The curves are predictions of the model as follows: solid line, surface chemistry included; dotted line, no surface chemistry; dashed line, no substrate.
sured values are normalized to the predicted OH concentration profile obtained by neglecting surface chemistry, the experimental data fit equally well. Thus, though there are significant predicted differences in the absolute OH concentration when the surface chemistry mechanism is altered, our data cannot be used to evaluate the accuracy of the surface mechanism. However, the data clearly show the decrease in OH near the substrate due to the lower gas temperature.
Mass Spectrometry
Absolute surface mole fractions for C,H,, CH,, H,, and CO were obtained at several equivalence ratios ranging from 1.67 to 2.25. For these measurements, the experimental parameters are as follows: P = 35 torr, total flow rate = 3.91 slm, T, = 900 K, T, = - 840 K, L = 15 mm, Ar dilution = 10%. The results of these measurements are shown in Figs. 11-13. For H, and CO, the results match the predictions of the model to within the lo%-15% experimental uncertainty, although for CO the agreement is only slightly within experimental uncertainty. The gas mixture used to calibrate the relative sensitivity factors for Ar and CO was a 2.1% CO in Ar mixture, which has an At-/CO ratio significantly different than that in the flame. For this reason, the uncertainty in
Fig. 11. Comparison of measured H, and CO surface mole fractions with the predictions of the model. The symbols represent experimental data, and the curves are predictions of the flame model with a substrate present (solid line), and with no substrate (dashed line).
the CO mole fraction measurement may be slightly larger than for the other species. Since the mass peak of 15 amu was used for the detection of CH,, there may be substantial contributions to the measured signal from CH, and other hydrocarbon radicals that recombine with other radicals to produce methane in the probe. Additionally, some signal contribution may be obtained from larger hydrocarbons which fragment into methyl radicals in the mass spectrometer. Thus, it is anticipated that in using the measured signal at the mass peak of 15 amu, the methane concentration is overestimated. Indeed, the measured methane con-
0.06
(
I
I
1.6
1.6
I
I
I
2.0
2.2
2.4
e
Fig. 12. Comparison of measured C,H, surface mole fractions with the predictions of the model. The symbols represent experimental data, and the curves are predictions of the flame model with a substrate present (solid line), and with no substrate (dashed line).
330
N. G. GLUMAC AND D. G. GOODWIN
1.5,
g E
4
2m
I
I
I
1
I
l.O-
0.5 -
s
0 -”
1
.,..
I
I
1.6
I
1.6
2.0
I
I
2.2
2.4
0
Fig. 13. Comparison of measured CH, surface mole fractions with the predictions of the model. The symbols represent experimental data, and the curves are predictions of the flame model for Xcu4 (solid line), and Xcu, + xCH 3 (dashed line).
centration shows better agreement with the sum of predicted surface CH, and CH, concentrations (as shown in Fig. 131, which would be expected if a substantial fraction of CH, radicals recombine to form CH, in the probe. For C,H, and CH, there is larger statistical uncertainty in the measurements, especially at low values of equivalence ratio, due to the fact that both hydrocarbons are only present in amounts near or below our detection limit (- lop4 mole fraction). Even with the larger uncertainty, the predicted rise in both C,H, and CH, mole fractions with increasing 4 is similar to the rise observed in the experiments, although the measured onset of significant residual hydrocarbons at the substrate occurs at a lower 4 than predicted by the model. The model shows that the effect of the substrate is to shift the onset to lower equivalence ratio, due to the lower flame temperature. The experimental results may indicate that the oxidation of acetylene in the low-temperature boundary layer region near the substrate is not well-modeled by the present mechanism. This is potentially an important deficiency of the model, since diamond film quality is sensitively dependent on the hydrocarbon to atomic hydrogen ratio at the substrate [12, 131. CONCLUSIONS Experimental temperature,
observations of OH rotational OH axial profiles, and stable
species surface concentrations have reproduced many of the flame features predicted by our stagnation-point flame model. The OH rotational temperature measurements suggest that the model-predicted temperature is good at least to within 175 K throughout the gap region. The predicted OH relative concentration profile shows excellent agreement with the LIF measurements. The mass spectrometry data also indicates that the model is capable of predicting some major species (e.g., CO and H,) to within experimental uncertainties. The dependence of C,H, and CH, at the substrate on equivalence ratio is predicted reasonably well, although the measurements show the onset of residual hydrocarbons at the substrate occurring at a lower equivalence ratio than predicted. No conclusions can be drawn about the accuracy of the surface chemistry mechanism, although the model predictions indicate that an absolute measurement of OH concentration a few mm above the substrate may be sensitive to changes in OH surface chemistry. Such a measurement might be useful in refining surface reaction rates for OH. The authors would like to thank Dr. Jay Jeffries for several helpful discussions on rotational temperature measurements. i%12 work was supported in part by grants from the National Science Foundation and Norton Corporation. REFERENCES Murayama, M., Kojima, S., and U&da, Phys. 69:7924-7926
Murayama, 91:239-245
K., J. Appf.
(1991).
M., and U&da,
K., Cornbust.
Flame
(1992).
McCarty, K. F., Meeks, E., Kee, R. J., and Lutz, A. E., Appl. Phys. Lett. 63:1498-1500 (1993). Cooper, J. A., Jr., and Yarbrough, W. A., Diamond Optics III @PIE Proceedings Vol. 1325), (A. Feldman and S. Holly, Eds.), SPIE, Bellingham, Washington, 1990, pp. 41-54. Glumac, N. G. and Goodwin, D. G., Mater. Lett. l&119-122 (1993). Kim, J. S. and Cappelh, M. A., Appl. Phys. Lett. 65:2786-2788
(1994).
Harris, S. J., Shin, H. S., and Goodwin, D. G, Appl. Phys. L&t. 66:891-893 (1995). Hirose, Y., and Mitsuizumi, M., New Diamond 4:34 (1988).
ACETYLENE / OXYGEN FLAMES FOR DIAMOND DEPOSITION 9.
Hirose, Y., Amanuma, S., and Komaki, K., J. Appl. Phys. 68:6401-6405
(1990).
10. Hanssen, L. M., Carrington, W. A., Butler, J. E., and Snail, K. A., Mater. Lett. 71289-292. 11. Harris, S. J., Appl. Phys. Lett. 56:2298-2300 (1990). 12. Goodwin, D. G., J. Appl. Phys. 74:6888-6894 (1993). 13. Butler, J. E., and Woodin, R. L., Philos. Trans. R. Sot. Lond. 342:209-224
(1993).
14. Carrington, W. A., Hanssen, L. M., Snail, K. A., Oakes, D. B., and Butler, J. E., h4etulltag. Trans. A 20x&1282-1284
(1989).
15. Shin, H. S., and Goodwin, D. G., Appl. Phys. Lett. (in press). 16. Dismukes, J. P., Busch, J. V., Nallicheri, N. V., and Walton, K. R., Applications of Diamond Films and Related Materials (Y. Tzeng, M. Yoshikawa, M. Murakawa, and A. Feldman, Eds.), Elsevier, Amsterdam, 1991, pp. 635-644. 17. Kim, J. S., and Cappelli, M. A., J. Appl. Phys. 72:5461-5466
Kee, R. J., Miller, J. A., Evans, G. H., and DixonLewis, G., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 147991494. 31. Glumac, N. G., Shin, H. S., and Goodwin, D. G., Spring Western States Meeting, The Combustion Institute, 1994. 32. Harris, S. J., and Goodwin, D. G., J. Phys. Chem. 30.
97:23-28
33.
34. 35.
36.
(1992).
18. Meeks, E., Kee, R. J., Dandy, D. S., and Coltrin, M. E., Combust. Flame 92:144-160 (1993). 19. Glumac, N. G., and Goodwin, D. G., Thin Solid Films 212:122-126 (1992). 20. Ishizuka, S., and Law, C. K., Nineteenth Symposium Untemational) on Combustion, The Combustion Institute, Pittsburgh, 1982, pp. 327-335. 21. Sato, J., Nineteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1982, pp. 1541-1547. 22. Yamaoka, I., and Tsuji, H., Twenty-Second Symposium Untemational) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 1565-1572. 23. Law, C. K., Ishizuka, S., and Mizomot, M., Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1981, pp. 1791-1795. 24. Zhu, D. L., Egolfopoulos, F. N., and Law, C. K., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988,
pp. 1537-1545. Smooke, M. D., Crump, J., Seshadri, K., and Giovangigli, V., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 463-478. 26. Law, C.K., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 1381-1402. 27. Dixon-Lewis, G., Twenty-Third Symposium (Intemational) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 305-324. 28. Giovangigili, V., and Smooke, M. D., Combust. Sci. 25.
Technol. 53:23-49
(1987).
37. 38.
39.
(1993).
Rensberger, K. J., Jeffries, J. B., Copeland, R. A., Kohse-Hoeinghaus, K., Wise, M. L., and Crosley, D. R., Appl. Opt. 28:3556-3566 (1989). Fleming, J. W., Burton, K A., and Ladouceur, H. D., Chem. Phys. Lett. 175:395-400 (1990). Meeks, E., Kee, R. J., Coltrin, M. E., and Dandy, D. S., Western States Section, The Combustion Institute, 1992 Spring Meeting. Kee, R. J., Dixon-Lewis, G., Wamatz, J., Coltrin, M. E., and Miller, J. A., Technical Report SAND868246, Sandia National Laboratories, 1986. Grcar, J. F., Technical Report SAND91-8230, Sandia National Laboratories, 1992. Kee, R. J., Grcar, J. F., Smooke, M. D., and Miller, J. A., Technical Report SAND85-8240, Sandia National Laboratories, 1985. Miller, J. A., and Melius, C. F., Combust. Flume 91:21 (1992).
40.
Miller, J. A., Volpone, J. V., Durant, J. L. Jr., Goldsmith, J. E. M., Fisk, G. A., and Kee, R. J., TwentyThird Symposium (International) on Combustion, The
Combustion Institute, Pittsburgh, 1990, pp. 187-194. 41. Kee, R. J., Rupley, F. M., and Miller, J. A., Technical Report SAND89-8009, Sandia National Laboratories, 1989. 42. Harris, S. J., and Weiner, A. M., J. Appl. Phys. 74:1022-1026
(1993).
43.
Krasnoperov, L. N., Kahnvoski, I. J., Chu, H. N., and Gutman, D. J. Phys. Chem. 97~11787-11796 (1993). 44. Bremier, D. W., Robertson, D. H., Carty, R. J., Srivastava, D., and Garrison, B. J., Computational Methods in Materials Science, J. E. Mark, M. E. Glicksman, and S. P. Marsh, Eds.), Materials Research Society, Pittsburgh, 1992, pp. 255-260. 45. Kondoh, E., Ohta, T., Mitomo, T., and Ohtsuka, K.,
46. 47.
Appl. Phys. Lett. 59488-498 S. J. Harris and Weiner, 75:5026-5036 (1994).
(1991).
A. M., J. Appl. Phys.
Mallard, W. G., Westley, F., Herron, J. T., Hampson, R. F., and Frizzell, D. H., NIST Chemical Kinetics Database: Version 5.0, National Institute of Standards and Technology, Gaithersburg, MD, 1993.
29. Darabiha, N., Candel, S. M., Giovangigli, V., and Smooke, M. D., Combust. Sci. Technol. 60:267-285 (1988).
Received 6 April 1995; revised 19 September 1995
and D. G. GOODWIN
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125
flames similar to those used for diamond chemical vapor Low pressure (35 torr) strained acetylene/oxygen deposition are studied using laser-induced fluorescence (LIF) and mass spectrometty. Relative OH concentration and OH rotational temperature profiles are obtained by LIF, while absolute mole fractions of C,H,, CH,, H,, and CO are measured at the substrate by mass spectrometry. The results of the diagnostics are compared with the predictions of a one-dimensional strained flame code. The agreement between model prediction and experiment is generally good and usually within experimental uncertainties.
Recently, several groups have used fuel-rich premixed flat flames for diamond thin film deposition [l-7]. Building on earlier work using torch-stabilized flames [8-101, these recent experiments have demonstrated that flame methods can be used to deposit uniform-thickness diamond films over moderate areas. In experiments at atmospheric pressure, high deposition rates (up to 40 pm/h) have been achieved over small areas (- 2 cm’) [2, 31. In our laboratory, we have used low-pressure 30-50-torr flat flames to achieve large area coverage (19 cm2) at lower growth rates (l-2 pm/h) [5]. This area coverage is competitive with that of current plasma chemical vapor deposition methods, and the flame method is easily scalable to much larger areas, which most plasma methods are not. Diamond growth requires use of fast, hot flames, which are able to deliver a large flux of H to the substrate. This requirement stems from the critical role played by H in the diamond growth mechanism [ll-131. Most studies have employed acetylene/oxygen [5, S-10] or acetylene/hydrogen/oxygen [2, 31 flames. However, diamond has also been grown in ethylene/oxygen [14, 61, MAPP/oxygen [7], and recently propylene/oxygen 1151flames. The fact that these latter fuels are significantly cheaper and easier to handle than acetylene may greatly improve the economics of the flame synthesis process.
*Corresponding author. Present address: Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08855. COMBUSTIONAND FLAME 105: 321-331 Copyright 0 1996 by The Combustion Institute Published by Elsevier Science Inc.
The flat flame geometry of interest for diamond film deposition is shown in simplified form in Fig. 1. Premixed gas emerges from a flat-flame burner a distance L above an isothermal substrate with downward velocity uL and zero radial velocity. The flow between the burner and substrate is axisymmetric, and a constant-thickness boundary layer forms above the substrate. Depending on the gas flow rate, the flame may be stabilized either on the burner [4-7, 151 or in the stagnation-point flow above the substrate [l-3]. To make this technique viable for commercial use, flame conditions need to be found which result simultaneously in moderate growth rates (for most applications, a few microns/hr), high film quality, good uniformity, and large area coverage [16]. Since a large number of experimental variables are involved (for example, fuel type, pressure, flow rate, equivalence ratio, substrate temperature, and burner/substrate configuration), numerical simulations are a valuable aid in narrowing the range of conditions which must be investigated experimentally. Therefore, it is critically important to have available validated, robust numerical models for flames of the type used for diamond growth, which include effects due to the presence of the substrate, such as strain, heat loss, and radical recombination. Several groups have developed models of the flame synthesis process [5, 17-191, but to date there have been few experimental measurements available to assess these models. Axisymmetric strained flames similar to those of interest here have been the subject of many studies [20-24, 26-301, primarily focused on OOlO-2180/96/$15.00 SSDI OOlO-2180(95MO214-6
322
N. G. GLUMAC AND D. G. GOODWIN
Flat Flame Burner
Substrate
+D* Fig. 1. The flat flame geometry.
flame speed measurement and extinction behavior. Most studies have dealt with premixed opposed-jet flames, in order to remove the complications of downstream heat loss and surface chemistry (which are central to the diamond deposition problem), although in some studies stagnation-point flames were used [21, 231. These studies dealt almost exclusively with methane/air and propane/air flames, rather than the much faster and hotter flames necessary for diamond growth. Numerical models of strained methane/air or propane/air flames have reproduced in detail their extinction characteristics [24, 301. To date, there has been only one comparison of measured species profiles in a counterflow premixed flame to model predictions [25]; the agreement was generally good, although there was poor agreement for temperature profiles (possibly due to experimental difficulties). For diamond deposition studies, a numerical model must accurately predict the concentrations at the substrate of those species important for deposition of diamond and nondiamond carbon (believed to include CH,, H, OH, O,, 0, C,H,, possibly C, and C, and perhaps heavier species). Therefore, boundary layer and surface effects are an important part of the problem. In contrast, in extinction studies, the extinction limit is insensitive to the boundary layer and surface, since the flame is outside the boundary layer at the extinction limit [26]. Whether current flame mechanisms and models are adequate is not yet clear. Indeed, there is some evidence of problems: superadiabatic flame temperatures are predicted [ 18,311, which, while possible, clearly warrant further investigation. Also, diamond film growth rates are generally overpredicted [18, 311, using a
diamond growth mechanism know to be accurate in other non-flame environments [ll, 321. This latter problem suggests that CH, and/or H at the surface are being overpredicted by the models. In this paper, we report experimental measurements of selected species concentrations and temperatures in flames similar to those used for diamond growth [19], and compare the result to the predictions of a numerical model. We are particularly interested in examining the effects of the cold substrate on the measured profiles. Rotational temperature and relative OH concentration profiles are acquired using laser-induced fluorescence (LIF), and several stable-species mole fractions at the substrate are measured using mass spectrometry. The model is found to reproduce the measurements reasonably well, and clearly shows the effects due to the substrate. EXPERIMENTAL The experimental setup is shown schematically in Fig. 2. The burner and substrate are housed within a water-cooled bell-jar vacuum chamber. Optical access is provided through three fused silica windows. To limit condensation of water vapor on the windows, a flow of nitrogen is directed over the interior window surfaces. A throttle valve under closed loop control in the exhaust line maintains the system pressure to within +0.2 torr of the chosen set point. Electronic mass flow controllers meter the input gas flows to the burner. The burner is mounted in a downflow configuration and was designed especially for work with rich acetylene/oxygen flames. Its face consists of a 6-cm-diameter, 12-mm-thick copper plate drilled with several hundred l-mmdiameter holes 2.5 mm apart in a hexagonal array. The burner surface temperature is measured by an ice-point-corrected thermocouple in one of the burner face holes near the center of the array. The substrate is mounted horizontally, approximately 1 cm below the burner surface. For the LIF experiments, the substrate consisted of a thin (0.5 mm) silicon wafer (10 cm diameter) which was thermally isolated from its holder by narrow ceramic supports. In the presence of the flame, the wafer rose to a
ACETYLENE
+ 1
/ OXYGEN
FLAMES FOR DIAMOND
6cm Burner
1
Laser Beam
To Mass spectrometer Fig. 2. A schematic of the experimental setup.
temperature which was fairly uniform over at least the innermost 4 cm. The temperature was measured by an ice-pointcorrected thermocouple cemented to the top of the substrate. For the mass spectrometry work, the substrate was l-cm-thick copper plate, 7.5 cm in diameter. A l-mm hole in the center was drilled to allow gas to be sampled from near the surface. The experimental arrangement for the LIF measurements is shown in Fig. 3. To obtain axial profiles of rotational temperature, the experimental protocol established by Rensberger et al. [33] is used. A Nd:YAG laser pumps a dye laser (bandwidth 0.08 cm-’ > using DCM, and the output is frequency doubled and attenuated, yielding 7-8 ns pulses of _ 1 PJ with wavelength in the range from 309.2 to steady-state
Bplittar
DEPOSITION
323
309.7 nm. The beam is focussed into the flame with a 50 cm focal length lens. The laser is scanned over seven P and Q rotational branch lines with N” ranging from 1 to 9 in the (0-O) band of the A2Z --f X211 transition in OH. Fluorescence is collected at right angles to the laser beam using f/5 optics through a l/8 m monochromator to a photomultiplier. The monochromator slits are set with a narrow front slit (0.5 mm) and wide exit slit (3.0 mm) such that it serves as a flat bandpass filter (with bandwidth 20 nm) over the entire rotational manifold of the (0-O) band. The fluorescence signal is sampled using a boxcar integrator with a short (10 ns), prompt detector gate to minimize effects of rotational-level-dependent collisional quenching [331. A small portion of the beam is reflected from a sapphire beam splitter and directed to a photodiode. The photodiode measures laser power on a shot-to-shot basis, and these data are used to normalize the fluorescence signal. The linearity of the fluorescence signal with laser power is assured by operating at low laser energies. This was verified by plotting the fluorescence vs. laser power signal for laser power levels ranging from 0.5 to 1.5 PJ per pulse. The data shown in Fig. 4 concur with the results of other investigators [33, 341, who found linear OH fluorescence signal behavior with laser power under similar conditions. Optical depth effects were measured by a separate absorption experiment, and the maximum uncertainty due to optical depth was calculated.
I
Vacuum Chamber Fig. 3. The experimental setup for the laser-induced fluorescence measurements of OH.
N. G. GLUMAC AND D. G. GOODWIN
324
I”“I”“I”’ 4.25 5 !z.
2.5 : _
$
2.0 -
I
4.00 -
.cn I rn _ $ 1.5c 0 $
s 8 s
/
1.01 -
3.75
-
3.50
-
/ E
0.5 I 0
0
/
/’
3.25 _ -
1’
~~~~‘~~~~‘~~~~‘~~~~‘~~~~ 5
10 Laser
15 Power
20
25
0
T=2055*103K 3 scan average I,,, 500 Rotational
(mV)
III
I
Energy
I
I
I
I
#I
1500
1000 (cm-‘)
Fig. 4. Fluorescence intensity versus laser power. 10 mV of laser power is approximately 1 PJ per pulse.
Fig. 6. The Boltzmann plot for the fluorescence taken 3 mm below the burner surface.
The burner and substrate can be translated relative to the laser beam. In this way, rotational temperature and relative OH concentration measurements were obtained at four locations in the flame. Blockage of the collection optics limits us to measurements further than 1 mm from the burner or substrate. The positional uncertainty is roughly kO.2 mm. Normalized LIF spectra are analyzed by comparing relative areas of fluorescence lines. For most positions, the data are averaged over 2-3 scans. A typical scan is shown in Fig. 5, and the resulting Boltzmann plot in Fig. 6. The experimental arrangement for the mass spectrometry measurements is also shown in Fig. 2. Gas near the surface is sampled through the 1 mm diameter, 0.5 mm deep hole in the substrate by a quartz probe with an orifice opening of 400 pm. The pressure in the probe
is maintained at 0.3 torr. Gas in the region surrounding the quartz probe beneath the substrate is differentially pumped away to insure that gas entering the mass spectrometer originates from the flame. After passing through a short length of quartz tube, the sampled gas is directed to a quadrupole mass spectrometer and analyzed. Absolute mole fractions were determined by calibrating the ionization signal of each species relative to argon, using calibration mixtures of known composition, The mass peaks of 2,15,26,28, and 40 amu were used to monitor relative number densities of H,, CH,, C,H,,’ CO, and Ar, respectively. Argon mole fractions in the flame are then calculated using the flame model, and the mole fractions of the other species are inferred using Ar as a reference. This calibration procedure allows determination of major species mole fractions with a relative uncertainty of f 10%-S%. Background signal levels were subtracted from the measured signal for each mass peak. For CO, Ar, and H,, background signal levels were negligibly small compared to the measured signals. For CH, and C,H,, both present in amounts near or below the system detection limit, background levels were of the same order of magnitude as the measured signals. To ascertain background levels for C,H, and CH,, the flame equivalence ratio was decreased until the measured signal level no longer dropped, and this was chosen as the’ background level, assuming that, for small 4, both C,H, and CH, are below detection limits.
1
Laser Excitation
Wavelength
(nm)
Fig. 5. A typical scan of OH fluorescence intensity versus excitation wavelength, taken 3 mm below the burner surface.
scans
ACETYLENE / OXYGEN FLAMES FOR DIAMOND DEPOSITION NUMERICAL MODEL The numerical model is similar to that of Meeks et al. [351 and Kim and Cappelli [17]. The governing equations for axisymmetric flow admit a similarity solution, which is valid in the limit when the ratio of the burner diameter D to the burner/substrate separation L is large, and when the Mach number is small. In this limit, the axial velocity U, the temperature T, and species mass fractions Yk are all independent of r, while the radial velocity u has the form rV(z) [30]. With these assumed functional forms, the conservation equations reduce to
u dp P dz
Radial Momentum dV pu--& + pv*
d - z
Energy dT pc,‘z
+ $
PC,,,
UY k
dT +M,cj,h,
k dz
Species +
;( pu,y,)
- ‘bkMk = 0;
(4)
Equation of State p = pRT.
(5)
In these equations, u is the axial velocity, V is the radial velocity divided by radius, and p is the density. The quantity n in Eq. 2 is the radial pressure-gradient eigenvalue, defined as A=;;.
u, = Boundary Conditions
-pY,[u(L) (3)
” dY, dz
specific enthalpy, and molar production rate, respectively, for species k. The transport properties (viscosity p, thermal conductivity h, multicomponent diffusion coefficient Dkj, and thermal diffusion coefficient Di) are calculated using the multicomponent formalism with the subroutines of Kee et al. 1361.The diffusion velocities U, are given by
The boundary conditions are as follows. The mass flw rit at the burner is specified, and the mass flux to the substrate is equated to the net mass deposition rate due to surface chemistry, summed over all surface reactions. For the radial velocity, V is set to zero both at the substrate and at the burner surface (no slip). The temperature is specified both at the burner (Ts) and substrate CT,). For the species equations, flux boundary conditions are used. At the burner surface (z = L) we impose
Continuity ;+2V+--=o;
325
1 dP
It may be shown that A is constant throughout the flowheld under conditions for which the similarity solution holds [30]. The quantities X,, Yk, Mk, h,, I%, are the mole fraction, mass fraction, molecular weight,
+ u,(L)]
= kY,,,,
(8)
where Yk I is the specified mass fraction of species k’ in the pure reactants upstream of the burner. At the substrate, the mass flux of each species balances its mass deposition rate pY,[u(O) + u,(O)] = M&,
(9)
where gk is the net molar production rate for species k due to surface chemistry. The governing equations are solved using a hybrid Newton/time integration method on an adaptive mesh. We use the TWOPNT boundary-value-problem solver developed by Grcar [37], which is the same solver used in the Sandia premixed flame code 1381,as well as in the flame models of Meeks et al. [35] and Kim and Cappelli [171. Gas-Phase Chemistry The gas phase chemistry mechanism is taken from Miller and Melius [39]. This mechanism is designed for simulating fuel-rich hydrocar-
N. G. GLUMAC AND D. G. GOODWIN
326
molar production rates at the surface are easily calculated for use in Eq. 9. The assumed diamond growth mechanism is listed in Table 1. Reactions sl-s5 implement a reduced form [12] of the methyl growth mechanism for diamond proposed by Harris [ill. The Harris mechanism accurately reproduces measured diamond growth rates in many different chemical environments [32]. Reactions sl and s2 constitute a mechanism for surface recombination of H to H,. The rate constants used reproduce the measured H recombination coefficient and its temperature dependence (E = 6 kcal/mol) in the temperature range 700-1200 K [42, 431. In addition, k, reproduces the molecular dynamics simulation results of Brenner [44]. The rate constant for s3 is empirical, and is set to give the measured temperature dependence of diamond growth in the temperature range 1000-1200 K (23 kcal/mol) [45]. As pointed out by Harris [46], more detailed mechanisms [32] suggest methyl addition occurs primarily at radical site pairs, which may account for the high (18 kcal/mol) activation energy required to simulate the measured kinetics in this reduced mechanism. Rate constant k, is the same as used by Harris [ll], and k, is set to a large value so that it is not rate-limiting. Reactions s6 and s7 are included to provide a mechanism for loss of OH and 0 on the surface by abstraction of an H atom. The rate constants for these reactions are chosen to be identical to those of the analogous gas-phase reactions:
bon flames, and consists of 50 species and 218 reactions. This same mechanism has been used in previous simulations of diamond-depositing flames [17, 351, and has been used to simulate unstrained, 25torr, rich, nonsooting C,H,/O,/Ar flames with generally good results [40]. The chemical terms in the equations are evaluated with calls to the Chemkin-II [41] subroutine library, and the Chemkin thermodynamic database is employed as well. Surface Chemistry Surface reactions are included which model diamond growth and radical recombination. The surface is assumed to consist of diamond, and several different types of surface species are defined, with which gas-phase species may react. The surface species used include chemisorbed hydrogen (C,H), dangling-bond sites CC,*), chemisorbed methyl groups (C,M), chemisorbed methylene groups (C,M*), and several others. We take the surface species density to be 3 x lo-’ mol/cm*, which is the surface carbon density on the (111) surface of diamond. Rate equations are solved for the surface species to determine their steady-state surface coverages. We only allow reactions between surface- and gas-phase species (not between surface species), and therefore the set of rate equations is linear in the vector of surface coverages. This linear system is easily solved for any specified set of gas-phase concentrations at the surface, so we may regard the surface coverages as functions of the instantaneous gas-phase concentrations at the surface. With the coverages known, the net surface
0 + i-C,H,,
+ OH + i-C,H,
OH + i-C,H,,
(10)
+ H,O + i-C,H,.
(11)
TABLE 1 Surface Mechanism Used in the Simulations.”
(sl) (s2) (s3) (s4) (SS) (~6) (s7)
reaction
A
C,H+H+C,*+H, C,* + H --) C,H C,* + CH, + C,M CdM+H-+CdM*+Hz CdM*+H+CdH+H2 C,H + OH + C,* + H,O C,H+O =C,*+OH
7.8E13 2.2Ell l.OE15 2.8E7 fast 2.47E6 2.14E5
’ Rate constants are of the form k = AT”exp(-E/RT).
n
E
0 0.5 0 2.0
7.3 -2.1 18.0 7.7
2.152 2.5
Units: cm3, mol, s, kcal.
0.3217 0.924
AGO
-31.14 - 19.74
ACETYLENE
/ OXYGEN
FLAMES FOR DIAMOND
DEPOSITION
327
In addition to the reactions in Table 1, we include global reactions which destroy the radicals C, CH, CH,, and CH,(S) on the surface. We assume that these radicals are destroyed with unity probability at the surface through the global reactions 2C + H, + C,H,,
(12)
2CH -+ C,H,,
(13)
2CH, -+ C,H,,
(14)
‘mom 0.20
0.15
and 2CH,(S)
+ C,H,.
(15)
(These reactions are actually implemented as a sequence of first-order reactions, giving a destruction rate at the surface which is first-order in the radical concentration.) The product species are chosen to be major species whose concentrations are not significantly perturbed by the inclusion of these reactions. In practice, the concentrations of these and other radicals at the substrate are very low even without these reactions, and the results of the simulations are insensitive to the inclusion of these reactions. ‘Qpical Results
of the simulation results, a typical flame profile predicted by the model is shown in Figs. 7 and 8. The case shown corresponds to one flame used for the mass spectroscopy measurements. The C,HJO,/Ar ratio is 1:1.25:0.25, corresponding to an equivalence ratio of 2.0. The mass flow rate is 3.1 X 10e3 g/cm2/s, and the substrate temperature is 900 K. The pressure is 35 torr and the burner/substrate separation is 1.5 cm. Under these conditions, the peak strain rate of 220 s-l occurs 0.5 cm above the substrate, which may be taken as the velocity boundary layer thickness. The thermal boundary layer is seen to be somewhat thicker, with the temperature maximum occurring 1 cm from the substrate Most of the major species detected by mass spectrometry have flat profiles at the substrate. The exception is H,,which decreases due to thermal diffusion near the substrate. All radical species other than CH, decrease markedly near the substrate.
5 ._ r, G
0.10
S P 0.05
0
0.2
0.4
0.6
0.6
1.0
1.2
1.4
Distance from Burner (cm) Fig. 7. Predicted major species profiles in a typical flame. The flame conditions are: C#J = 2.0, 10% Ar dilution, mass flow rate per unit area = 3.1 X 10e3 g/cm*/s, substrate temperature = 900 K, pressure = 35 torr, burner to substrate separation = 1.5 cm.
As an example
0
0.2
0.4 Distance
0.6
0.6
1.0
1.2
1.4
from Burner (cm)
Fig. 8. Prediced minor species profiles in a typical flame. The flame conditions are the same as in Fig. 7.
328
N. G. GLUMAC
RESULTS Fluorescence
The OH fluorescence measurements were carried out for a single flame with P = 34 torr, 4 = 1.67, total flow rate = 4 slm, TB = 993 K, T, = 1068 K, burner to substrate distance L = 0.92 cm. The flow rate corresponds to a cold gas velocity of 2.2 m/s. The maximum strain rate calculated from the flame model is 340 s-’. This flame is similar to (but slightly leaner than) a flame used for diamond deposition [19]. Temperatures measured at four different locations in the flame are shown in Fig. 9 along with the predictions of the flame code. The error bars show the statistical uncertainties in the linear fit to Boltzmann data, using 2u uncertainties in the peak areas. Absorption of the laser beam by the flame was below our detection limits, which is about 4%. From calculations assuming 4% absorption of the strongest line, we calculate a maximum temperature correction of -35 K. That is, the reported temperature is at most 35 K larger than the actual temperature. The uncertainty varies from f 100 to f 175 K. Within this level of uncertainty, the agreement of experiment and theory is good. Figure 9 also shows the calculated temperature for a flame with the same input flame parameters and no substrate. It can be seen that the predicted peak temperature of the flame with a
2500
1
0
0.2
x
I
I
0.4
0.6
’
I
0.5
Distance from Burner (cm)
Fig. 9. Comparison of OH rotational temperature data with predictions of the model. The solid curve shows the predicted flame temperature with the substrate in place, and the dashed curve shows the predicted temperature with no substrate.
AND D. G. GOODWIN
substrate present is lower than that of the flame with no substrate, and our measurements support this prediction as well. The agreement in the temperature profile between prediction and measurement is slightly better than that observed in many unstrained burner-stabilized flames. There are at least two possible reasons for this. First, in unstrained flames, the temperature overprediction is usually largest in the postflame zone where heat losses due to radial conduction and radiation have accumulated enough to be appreciable. The predicted temperature profile in the reaction zone of the flame is often much closer to the measured profile. In the strained flames at 34 torr, the reaction zone covers a substantial portion of the gap width, and there is only few mm of the gap which can be considered a postflame region. Thus, because of the lack of a large postflame zone, better agreement between predicted and measured temperatures is anticipated. Second, in the region of the flame past the reaction zone, the primary heat loss mechanism is axial conduction downstream towards the relatively cool substrate. This gas-phase conduction is included in the model. It is possible that the heat loss to the substrate dominates any heat losses by radiation in these strained flames. In that case, better agreement in such flames is expected because the dominant heat loss mechanisms in the postflame gases are accounted for, whereas in the unstrained flames the heat loss mechanisms in the postflame gases typically are neglected. Relative OH concentrations were obtained by measuring the relative area of the Qr(6) line at each location and correcting for the variation in Boltzmann fraction. The realtive concentrations are shown in Fig. 10, normalized to theory at x = 3 mm. Again, agreement with theory is good. The predicted effect of the substrate, in this case, is to reduce the OH concentration to 5% of its maximum value at x = 8 mm. This is compared to the case of a flame without the substrate in which the OH concentration at 8 mm is 95% of its maximum value. Our measurements are in agreement with the 5% prediction. The measured relative OH profile is insensitive to surface chemistry, however. If the mea-
ACETYLENE
/ OXYGEN
FLAMES FOR DIAMOND
DEPOSITION
329
0.6 -
A j
0.4 -
A
A
A
IL s P
_
5.0 -
_______--------
0.2 -
-
2.5 -
0.2
0.4
0.6
0.6
Distance from Burner (cm)
Fig. 10. Comparison of OH number density profiles with the predictions of the model. The measured values are normalized to the theoretical predictions at x = 0.3 cm. The curves are predictions of the model as follows: solid line, surface chemistry included; dotted line, no surface chemistry; dashed line, no substrate.
sured values are normalized to the predicted OH concentration profile obtained by neglecting surface chemistry, the experimental data fit equally well. Thus, though there are significant predicted differences in the absolute OH concentration when the surface chemistry mechanism is altered, our data cannot be used to evaluate the accuracy of the surface mechanism. However, the data clearly show the decrease in OH near the substrate due to the lower gas temperature.
Mass Spectrometry
Absolute surface mole fractions for C,H,, CH,, H,, and CO were obtained at several equivalence ratios ranging from 1.67 to 2.25. For these measurements, the experimental parameters are as follows: P = 35 torr, total flow rate = 3.91 slm, T, = 900 K, T, = - 840 K, L = 15 mm, Ar dilution = 10%. The results of these measurements are shown in Figs. 11-13. For H, and CO, the results match the predictions of the model to within the lo%-15% experimental uncertainty, although for CO the agreement is only slightly within experimental uncertainty. The gas mixture used to calibrate the relative sensitivity factors for Ar and CO was a 2.1% CO in Ar mixture, which has an At-/CO ratio significantly different than that in the flame. For this reason, the uncertainty in
Fig. 11. Comparison of measured H, and CO surface mole fractions with the predictions of the model. The symbols represent experimental data, and the curves are predictions of the flame model with a substrate present (solid line), and with no substrate (dashed line).
the CO mole fraction measurement may be slightly larger than for the other species. Since the mass peak of 15 amu was used for the detection of CH,, there may be substantial contributions to the measured signal from CH, and other hydrocarbon radicals that recombine with other radicals to produce methane in the probe. Additionally, some signal contribution may be obtained from larger hydrocarbons which fragment into methyl radicals in the mass spectrometer. Thus, it is anticipated that in using the measured signal at the mass peak of 15 amu, the methane concentration is overestimated. Indeed, the measured methane con-
0.06
(
I
I
1.6
1.6
I
I
I
2.0
2.2
2.4
e
Fig. 12. Comparison of measured C,H, surface mole fractions with the predictions of the model. The symbols represent experimental data, and the curves are predictions of the flame model with a substrate present (solid line), and with no substrate (dashed line).
330
N. G. GLUMAC AND D. G. GOODWIN
1.5,
g E
4
2m
I
I
I
1
I
l.O-
0.5 -
s
0 -”
1
.,..
I
I
1.6
I
1.6
2.0
I
I
2.2
2.4
0
Fig. 13. Comparison of measured CH, surface mole fractions with the predictions of the model. The symbols represent experimental data, and the curves are predictions of the flame model for Xcu4 (solid line), and Xcu, + xCH 3 (dashed line).
centration shows better agreement with the sum of predicted surface CH, and CH, concentrations (as shown in Fig. 131, which would be expected if a substantial fraction of CH, radicals recombine to form CH, in the probe. For C,H, and CH, there is larger statistical uncertainty in the measurements, especially at low values of equivalence ratio, due to the fact that both hydrocarbons are only present in amounts near or below our detection limit (- lop4 mole fraction). Even with the larger uncertainty, the predicted rise in both C,H, and CH, mole fractions with increasing 4 is similar to the rise observed in the experiments, although the measured onset of significant residual hydrocarbons at the substrate occurs at a lower 4 than predicted by the model. The model shows that the effect of the substrate is to shift the onset to lower equivalence ratio, due to the lower flame temperature. The experimental results may indicate that the oxidation of acetylene in the low-temperature boundary layer region near the substrate is not well-modeled by the present mechanism. This is potentially an important deficiency of the model, since diamond film quality is sensitively dependent on the hydrocarbon to atomic hydrogen ratio at the substrate [12, 131. CONCLUSIONS Experimental temperature,
observations of OH rotational OH axial profiles, and stable
species surface concentrations have reproduced many of the flame features predicted by our stagnation-point flame model. The OH rotational temperature measurements suggest that the model-predicted temperature is good at least to within 175 K throughout the gap region. The predicted OH relative concentration profile shows excellent agreement with the LIF measurements. The mass spectrometry data also indicates that the model is capable of predicting some major species (e.g., CO and H,) to within experimental uncertainties. The dependence of C,H, and CH, at the substrate on equivalence ratio is predicted reasonably well, although the measurements show the onset of residual hydrocarbons at the substrate occurring at a lower equivalence ratio than predicted. No conclusions can be drawn about the accuracy of the surface chemistry mechanism, although the model predictions indicate that an absolute measurement of OH concentration a few mm above the substrate may be sensitive to changes in OH surface chemistry. Such a measurement might be useful in refining surface reaction rates for OH. The authors would like to thank Dr. Jay Jeffries for several helpful discussions on rotational temperature measurements. i%12 work was supported in part by grants from the National Science Foundation and Norton Corporation. REFERENCES Murayama, M., Kojima, S., and U&da, Phys. 69:7924-7926
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Received 6 April 1995; revised 19 September 1995