Analysis of process modifications for efficient diamond chemical vapor deposition

ELSEVIER

Diamond and Related Materials 5 (1996) 895-906

Analysis of process modifications for efficient diamond chemical vapor deposition Dean E. Kassmann,

Thomas

A. Badgwell

Department of Chemical Engineering, Rice University, P.O. Box 1892, Houston, TX 77251, USA

Received 19 June 1995

Abstract

A theoretical model has been developed to investigate transport phenomena and chemical kinetics in a rotating disk diamond chemical vapor deposition (CVD) reactor. The model combines mass, momentum and energy balances for the gas flow with detailed gas and surface chemical kinetics for diamond formation. The model equations are solved numerically to determine gas phase composition profiles and diamond film growth rates for hot-filament and d.c. arc-jet systems. The model is then used to investigate the potential benefits of two process modifications which may increase the efficiency of diamond CVD reactors. The first involves lowering the energy requirements by dissociating hydrogen chemically with chlorine. The second involves increasing the growth rate by injecting methane through the substrate. Combining the two modifications may allow growth of a porous diamond film at 1200 urn h-‘, using an order of magnitude less energy per carat than a conventional d.c. arc-jet reactor. Keywords: Chemical vapor deposition; Diamond;

Modeling; Chlorine-activated

1. Introduction There has been an explosive growth in research on diamond chemical vapor deposition (CVD) in the last decade [ 11. The intense interest in diamond is directly related to its unique material and electronic properties [2]. Diamond is the hardest known substance, making it a good choice for protective coatings. It has the highest room temperature thermal conductivity, making it an attractive material for heat transfer applications. Its large bandgap energy and high carrier mobilities raise the possibility of making fast integrated circuits that can operate at high temperatures. These properties are primarily due to the bonding arrangement between the carbon atoms in diamond, in which the atoms are more densely packed than in any other known substance. Forecasts of future market potential call for a 10 billion dollar per year market in the time frame of 2010 to 2020 [ 31. The commercial success of CVD diamond films is virtually guaranteed, at least on a limited basis, because the unique properties of diamond films will provide the enabling technology for many new inventions. Nevertheless, today’s CVD diamond films are extremely expensive relative to most engineering materials. To enjoy widespread commercial success, the cost of CVD diamond films must be reduced by at least an 0925-9635/96/$15.000 1996Elsevier Science S.A. All rights reserved SSDI 0925-9635(95)00441-6

chemical vapor deposition; Substrate injection

order of magnitude. Significant cost reductions will come only through an increased understanding of the physics and chemistry of diamond CVD, and through the use of numerical simulation codes to design and optimize diamond CVD reactors. This paper describes a theoretical model of the transport phenomena and chemical kinetics responsible for diamond CVD. The model equations are solved numerically to determine gas phase composition profiles and diamond film growth rates for representative hotfilament and dc. arc-jet systems. The model is then used to investigate two process modifications which may increase the efficiency of diamond CVD reactors. The first involves lowering the energy requirements by dissociating the hydrogen gas chemically using chlorine. The second involves increasing the growth rate by injecting methane through the substrate.

2. Theoretical model A theoretical model for diamond CVD was developed by combining ideas from the work of Coltrin et al. [4] and Goodwin and Gavillet [ 51. The model derivation begins with mass, momentum and energy balances for a reacting gas flow at steady state [6]. The general

896

D. E. Kassmann, T.A. BadgwelljDiamond and Related Materials 5 (1996) 895-906

transport equations are simplified by considering the effects of the low pressure where diamond CVD takes place. The most important simplifying assumptions are: (1) an ideal gas mixture; (2) a Newtonian fluid; (3) negligible energy from viscous dissipation. The simplified equations are then written for an axisymmetric domain consisting of two infinite radius disks separated by a finite distance, as shown in Fig. 1. The gases enter through the top disk and flow down onto the bottom disk where the diamond deposit is formed. Additional assumptions are invoked to simplify the model further: (1) the axial velocity II,, temperature T, species mass fractions Oj and species diffusion velocities V,j depend only on the axial position z; (2) the radial velocity u,, circumferential velocity v0 and radial pressure gradient ap/dr depend linearly on the radial position r; (3) the pressure can be written as the sum of an axial pressure pa and a radially varying term with n constant: p = pa + 0.5Ar2;

(4) the axial pressure pa is much larger than the radial term OSM, so that pa can be used in the ideal gas law to find the gas density. With these assumptions the similarity transform of Evans and Greif [7] can be applied. A suitable choice of dimensionless variables leads to the model equations shown in Table 1. The boundary conditions for the model are given in Table 2. Tables 3 and 4 define the variables used in the model and Table 5 defines the dimensionless constants. Two choices are presented in Table 1 for computing the ordinary diffusive velocity. The multicomponent diffusive velocity equation is more accurate, but may introduce problems in the numerical solution by increasing the condition number of the Jacobian matrix. For this reason Fick’s law approximation is often used initially. All of the results presented here were ultimately computed using the full multicomponent ordinary diffusion expression. The kinetic model for diamond formation presented by Coltrin and Dandy [8,9] in their studies of a d.c. arc-jet reactor was modified for use in this study. The

Z

Fig. 1. Domain for model (variables defined in Table 3).

Continuity equation Species continuity

Radial momentum balance Circumferential momentum balance Axial momentum balance Energy balance Ideal gas law Diffusion velocity sum Multicomponent Fick’s law Thermal diffusion velocity equation

Density p

Mass fraction oi

Radial velocity F

Circumferential velocity G

Axial velocity H

Temperature ~9

Pressure P,

Diffusion velocity V,

Multicomponent ordinary diffusive velocity Vy

Mixture-averaged ordinary diffusion velocity Vf

Thermal diffusion velocity VT

Mass fraction and diffusion velocity constraints

ordinary diffusion equation

equation

Description

Variable

Table 1 Model equations for diamond CVD in a rotating disk reactor

S

2

2 Sr? CI. I 2 S

898

D.E. Kassmann, T. A. Badgwell/Diamond and Related Materials 5 (1996) N-906

Table 2 Boundary conditions for model Inlet (n = dm)

Substrate (n = 0)

Density p Mass fraction wj Radial velocity F

0

Circumferential velocity G

Re, Re, + Re,

Axial velocity H

- Re, J_

Temperature 0 Pressure P,

Table 3 Variables in model Variable

Description

Units

z

Axial coordinate Radial coordinate Circumferential coordinate Inlet/substrate separation Radial velocity Circumferential velocity Axial velocity Injected velocity Temperature Axial pressure Substrate rotation speed Axial diffusion velocity for species j Gas reaction i rate Surface reaction i rate Mixture molecular weight Species i molecular weight Ideal gas constant Density Viscosity Kinematic viscosity Thermal conductivity Multicomponent diffusivity Effective binary diffusivity Thermal diffusivity Specific enthalpy Mixture heat capacity Species j heat capacity Diamond film growth rate Surface production rate of diamond Molar volume of diamond film

m m rad m ms-’ ms-’ m s-i ms-’ K Pa rad s-i m s-i kgmol rnv3 s-i kgmol m-’ s-l kg kgmol-’ kg kgmol - ’ J mol-’ K-i kg mm3 kg m-l s-l m2 s-l Jm-i s-i K-1

;

L 0, Vll 4 4 T Pa w Vzj W

R; m mj R P P Y k Dij Dj, ?T hi c, Gj g SD vD

m2 s-l mz s-l kg mm2 s-l Jkg-’ J kg-’ K-’ J kg-’ K-’ ms-’ kgmol m-’ s-i m3 kgmol-’

full set of 41 gas phase and 26 surface reactions considered here is illustrated in Table 6. The gas phase kinetics include the formation of higher hydrocarbons up to ethane, and the abstraction of methane down to molecular carbon. The surface phase kinetics include the forma-

tion of diamond directly by addition of a methyl radical (surface reaction (4)) or molecular carbon (surface reaction (13)), and the formation of graphite through addition of acetylene (surface reaction (26)). This allows the quality of the diamond film to be estimated by tracking the relative rates of diamond and graphite formation. Additional reactions were added to describe the effects of chlorine on diamond growth. Kinetic constants for the nominal diamond kinetics were provided by D.S. Dandy. Kinetic constants for the gas phase chlorine reactions were taken directly from the NIST database [lo]. Kinetic constants for the surface phase chlorine reactions were estimated by considering analogous gas phase reactions. The detailed kinetic data used for these simulations are available on request from the authors. After the model equations have been solved to determine the gas phase temperature, velocity and composition profiles, the diamond film growth rate is calculated by multiplying the surface reaction rate of diamond by the molar volume of the film: g = Snun. The model presented here differs in three ways from previously published work: (1) the axial momentum balance with body force terms is included; (2) the substrate boundary condition allows for injection of material through the substrate; (3) the model is presented in dimensionless form. The axial momentum balance is included in the model so that the effects of body forces can ultimately be examined. The effects of an axial electric field on charged species in the gas phase may be of interest, for example. In the simulations considered here, it is assumed that there are no significant body forces so that the axial momentum balance is neglected. The substrate boundary condition allows for the introduction of reactant species through the substrate. The

899

D. E. Kassmann. T.A. BadgwelljDiamond and Related Materials 5 (1996) 895-906 Table 4 Dimensionless

variables

in model (subscript

0 refers to inlet conditions;

subscript

I refers to injected

conditions) Description Axial coordinate

Radial

velocity

Circumferential

velocity

Axial velocity

Temperature Pressure

Diffusion

velocity

Gas reaction Surface Mixture

for species j

i rate i rate

reaction molecular

weight

Species j molecular

weight

Ideal gas constant

Density Viscosity Thermal

conductivity

Multicomponent Effective binary Thermal

diffusivity diffusivity

diffusivity

Specific enthalpy Mixture

heat capacity

Species j heat capacity

injected gas is assumed to enter the reactor with a purely axial positive velocity and with a perfectly uniform distribution across the substrate. It is assumed that there is no back diffusion of species through the substrate. The full model is presented here in dimensionless form with a choice of scaling analogous to that of Evans and Greif [ 71. Although the dimensional and dimensionless forms are mathematically identical, the dimensionless form is more useful for analysis of engineering issues such as reactor scale-up.

3. Simulation results The model equations were solved numerically on an IBM RISC/6000 workstation using a modified form of

the SPIN code [ 1l] from Sandia National Laboratories. The SPIN code solves a dimensional form of the equations in Table 1 without the axial momentum balance. The substrate boundary condition was modified to allow for injection of reactants through the substrate. The SPIN code uses a finite difference discretization of the spatial domain and a modified Newton method to solve the resulting non-linear algebraic equations. Time integration is employed to improve numerical conditioning when Newton’s method fails. The initial solution is computed on a coarse grid and then the problem is re-solved on subsequently finer and finer grids until solution gradients fall below user-supplied limits. Solutions were obtained for hot-filament, d.c. arc-jet and chlorine-activated systems, with and without substrate injection (discussed in more detail below). Table 7

D. E. Kassmann, T. A. BadgweNJDiamond and Related Materials 5 (1996) 895-906

900

Table 5 Dimensionless constants in the model Variable

Definition

Description

Re,

Spin Reynolds number Forced Reynolds number

Daf

Gas reaction i Damkohler number

Da;

Surface reaction i Damkohler number

Re,

X

A

of diamond produced. The dissociation ratio measures the moles of hydrogen (hot-filament and d.c. arc-jet) or chlorine (chlorine-activated) dissociated per mole of carbon incorporated into the diamond film. The film quality is defined as the percentage of the film which is diamond (sp3 bonding) vs. graphite (sp’) bonding. The diamond growth rate is reported in both meters per second and micrometers per hour. 3.1. Hot-jilament

Radial pressure gradient

Hot-filament reactors are widely used for diamond CVD due to their simplicity [ 11. Nominal conditions for hot-filament CVD include a pressure of 20 Torr, a substrate temperature of 900 “C and an inlet to substrate separation of 7 mm as shown in Table 7. Typical gas flow rates lead to a low inlet velocity, 0.5 m s-l for the example shown here. Under these conditions the mass transport is dominated by diffusion. The gas phase composition profile for these conditions is illustrated in Fig. 2. The inlet gas composition was estimated by assuming an inlet gas of 99.5% H, plus 0.5% CH4 in which 5% of the H2 is dissociated by the filament. This gives an inlet H atom concentration of 10%. The right side of the plot shows that H atoms entering the reactor quickly abstract hydrogen from methane to form methyl radicals (CH,). Further abstraction reactions lead to the formation of CH,, CH and atomic carbon C. Recombination reactions lead to acetylene formation (C,H,). The left side of the plot shows that the methyl radical concentration at the surface is about 1.8 x 10m3, and the C concentration is 3.2 x 10e5, which gives a net diamond growth rate of 5.0 urn h-l. The fraction of

PO(0 + ~zo/~)2

Fr

(w + u,,/L)3’2y;‘2 Froude number

B

(0 + o,&3’*y;‘2

g Body force

L Pr

C,opolko

system

Prandtl number

summarizes the process conditions and simulation results for each case, and Figs. 2-6 illustrate the corresponding gas phase composition profiles. In each figure, the right side corresponds to the reactor inlet (after the hydrogen or chlorine has been dissociated), and the left side corresponds to the substrate on which the diamond film is growing. Reactor performance measures for each case are given at the bottom of Table 7. Carbon capture is defined as the fraction of carbon entering the reactor that ends up in the diamond film. The dissociation energy refers to the energy required to dissociate hydrogen (hot-filament and d.c. arc-jet) or chlorine (chlorine-activated) per carat 10”

-

CH4

- - - - -

CH3

-.-.-.-.-

C2H2 .““’

0.3

C2H

----

CH2

-..-..-..-

c

----_

CH H

-‘-‘-‘-‘-

H2

0.4

position (cm)

Fig. 2. Gas phase composition profile for a hot-filament reactor (5.66 pm h-r).

D. E. Kassmann, T. A. BadgwelljDiamond and Related Materials 5 (1996) 895-906 Table 6 Chemical

reactions

used in the model (D, diamond;

G, graphite;

901

M, third body)

Gas phase reactions

Surface

(l)C1+HZ~HC1+H (2) HCl + MsH + Cl -t M (3) Cl + CH40CH3 + HCI (4) CH, + C1*CH2 + HCl (5) CH, + Cl+CH + HCl (6) CH + CleC + HCl (7) 2CHJ + M-=-&H6 + M (8) CH, + H + M-=-CH, + M (9) CH, + H+CHJ + H2 (10) CH, + HoCH2 + H, (11)CH2+H-CH+H, (12)CH+HoC+H, (13)CH+CH29C,H2+H (14)CH+CH30CzH3+H (15)CH+CH,-=CzH4+H (16) C + CH, o&H2 + H (17)C+CH,-=C,H+H (18) CzHs + CH, oCZH, + CHz, (19) C2H, + HsCzHs + H, (20) C2H4 + Hc>CZHs + H, (21) CH, +CH,+C2H4 +H (22) H + C2H4 + M-=C,H, + M (23) CzHs + HoCH3 + CH, (24) H, + C2H-=C2H2 + H (25) H + C,H, + Me&H, + M (26) H + CZH, 9 CZH, (27) C,HS + H+CaH, + Hz (28) C2H, + CHI *C2H2 + CH, (29) C,H, + C,H 9 C,H, + C,H, (30) C2H, f CH-=CH2 + C2H, (31) CH,(SG) + M*CH, + M (32) CH,(SG) + CH,*CH, + CHa (33) CH,(SG) + C,Hs*CH, + C2H, (34) CH,(SG)+ H20CH, +H (35) CH,(SG) + H-==-CH, + H (36) CH, + CH, -=C,H, + H2 (37) C,H2 + MeC2H + H + M (38) C,H4 + M-C2HZ + H, + M (39) C,H., + Me&H3 + H + M (40)H+H+MsH,+M (41)H+H+H2-=H2+H2

(1) CH(S) + Cl+C(S,R) + HCl (2) CH,(S) + Cl+CH(S,R) + HCl (3) CH,(S) + Cl-=+CH,(S,R) + HCl (4) C(S,R)+CH,sD+CH3(S) (5) CH,(S)+HoCH(S,R)+H, (6) CH,(S) + HoCH,(S,R) + H, (7) CH,(S,R) + CH(S,R)-=-CH,(S) + CH(S) (8) C(S,R) + &Hz-=-D + HCCH(S,R) (9) CH(S) + HCCH(S,R)-=C(S,R) + H,CCH(S) (10) H,CCH(S) + C(S,R)-D + CH,(S) + CH(S,R) (11) CH,(S) + CH(S,R)+CHf(S) + CH(S,R) (12) CH(S,R) + H + CH:(S)+CH(S) + CH(S) + Hz (13) C(S,R) + C-=-D + C(S,R3) (14) C(S,R3) + CH,(S)-=-CH(S,R) + CH(S) (15) CH(S,R) + H+CH,(S) (16) C(S,R3)+ HZ-=CH,(S,R) (17) C(S,R3) + HeCH(S,RZ) (18) CH(S,RZ) + HoCH,(S,R) (19) CH,(S,R) + H+CH3(S) (20) CH(S,RZ) + H,*CH,(S) (21) CH(S,G) + G + H-=-CH(S,R) + CH(S) (22)CH(S,G)+H+C(R,G)+H, (23) C(R,G) + H-+CH(S,G) (24) CH, + C(R,G)+G + CH,(S) (25) C + C(R,G)*G + C(S,R3) (26) C,H, + C(R,G)eG + HCCH(S,R)

open surface sites is 20%. There is no visible boundary layer near the surface because this is a diffusive system. The performance data at the bottom of Table 7 show that the hot-filament system is qualitatively different from the other systems considered here. The carbon capture for the hot-filament case is 54%, which indicates that just over one-half of the entering carbon atoms are incorporated into the film. The dissociation energy of 128 kJ carat-’ is much lower than for the other systems, which translates into a simpler reactor configuration with lower operating costs. The dissociation ratio shows that just over lo5 hydrogen atoms must be dissociated for each carbon atom deposited as diamond. The film quality of 99.55% indicates that the film is essentially pure sp3-bonded diamond. The predicted growth rate of 5.0 urn h-i is much lower than for the other systems,

reactions

which is the price paid for running a diffusive system. Low growth rates are the primary barrier to the widespread industrial use of hot-filament systems. 3.2. D.c. arc-jet system In contrast with hot-filament systems, d.c. arc-jet reactors rely on a high flux of atomic hydrogen to achieve high diamond growth rates. The hydrogen flux is provided by direct dissociation of molecular hydrogen in a d.c. plasma gun using equipment that is expensive to purchase and operate. Because of the higher growth rates that can be achieved, however, a recent economic study predicted that this may be the most cost effective method for future CVD diamond production, despite the high capital and energy costs [3]. Representative

902

D. E. Kassmann, T. A. Badgwell/Diamond and Related Materials 5 (1996) 895-906

Table 7 Summary of simulation results Process variable

Hot-filament (Fig. 2)

D.c. arc-jet (Fig. 3)

Chlorine-activated (Fig. 4)

D.c. arc-jet sub. inj. (Fig. 5)

Chlorine-activated sub. inj. (Fig. 6)

Inlet gas velocity (m s-i) Substrate injected CH, velocity (m s-r) Inlet/substrate separation (m) H inlet mole fraction H, inlet mole fraction CH4 inlet mole fraction Cl inlet mole fraction Inlet temperature (K) Substrate temperature (K) Pressure (Pa) [ Torr] Inlet rotation rate (rev mini) Substrate rotation rate (rev min-‘) H mole fraction near surface CH, mole fraction near surface C mole fraction near surface C,H, mole fraction near surface C( S,R) mole fraction (open sites) Carbon capture Dissociation energy (kJ carat -‘) Dissociation ratio Film quality (%) Diamond growth rate (m s-l) [pm h-l]

0.514 0 7 x 1o-3 0.0943 0.8958 0.0099 0 2173 1173 2670 [20] 0 0 6.79 x 1O-3 1.83 x 1O-3 3.19 x 1o-s 5.04 x 1o-3 0.200 0.541 128 1.15 x lo5 99.55 1.39 x 1o-g

2000 0 0.15 0.300 0.695 0.005 0 2500 1200 4000 [30] 1000 1000 2.88 x lo-’ 4.39 x 1o-4 3.72 x lo-“ 3.03 x 10-a 0.224 1.54 x 10-a 2.83 x lo5 2.56 x lo* 99.95 1.01 x 10-s

2000 0 0.15 0 0.695 0.005 0.300 1773 1200 4000 c301 1000 1000 2.01 x lo-* 5.64 x 1O-4 5.37 x 10-4 1.84 x 1O-3 0.263 1.75 x 10-z 1.39 x 10s 2.24 x 10’ 99.98 1.62 x 10-s

2000 1.25 0.15 0.250 0.750 0 0 2500 1100

2000 1.25 0.15 0 0.50 0 0.50 1773 1100

4000 c301 0 0

6670 [SO] 0 0

1.80 x 1.50 x 7.81 x 2.32 x 0.160 5.10 x 2.51 x 2.26 x 99.95 9.53 +

c5.001

[36.4]

[58.4]

c3431

1.41 x 10-Z 1.27 x 1O-2 3.58 x 1O-4 1.82 x 1O-3 0.214 0.107 1.88 x lo4 3.04 x 10’ 99.95 3.33 x 10-7 [12001

conditions for a d.c. arc-jet reactor were taken from the paper by Coltrin and Dandy [S]. As can be seen in Table 7, the distinguishing features of a d.c. arc-jet system are the high inlet velocity and high inlet mole fraction of atomic hydrogen. Under these conditions, the primary mass transport mechanism is convection. Fig. 3

lo-* lo4 10’ 10-s

illustrates the gas phase composition profile for these conditions, which matches fig. 13(b) of Coltrin and Dandy’s paper [ 81. There is a chemical boundary layer near the inlet (right side of plot) where atomic hydrogen attacks methane to form methyl radicals. The concentration of hydrogen atoms is so high that additional

-

CH4

-----

CH3

-.-‘-.-.-

CZHZ

.““’ ----

10.0

5.0

lo-’ lo-* 1O-5 1O-2

..”

CZH CH2

-..-..-..-

c

-

CH

-‘-.-‘-‘-

HZ

15.0

position (cm) Fig. 3. Gas phase composition profile for a d.c. arc-jet reactor (36.4 nrn h-l).

D. E. Kassmann,

T. A. BadgwelllDiamond

and Related Materials 5 (1996) 895-906

abstraction reactions lead to a surface concentration of atomic carbon of 3.7 x 10e4, an order of magnitude higher than in the hot-filament case. A thin boundary layer with sharp species gradients forms near the surface, as expected for a convective system. The predicted diamond growth rate of 36 nm h-i is due primarily to the direct addition of atomic carbon. The performance data at the bottom of Table 7 reveal that 0.15% of the incoming carbon ends up in the film. Raw material costs for d.c. arc-jet systems can be significantly reduced by improving the carbon capture, either by introducing methane in a more efficient way or by recycling unreacted methane. The dissociation energy of 2.8 x 10’ kJ carat-’ is three orders of magnitude higher than for the hot-filament case, which indicates that the capital and operating costs for this system will be very high. Lowering the energy costs is another way to improve significantly the economics of d.c. arc-jet systems. 3.3. Chlorine-activated

CVD

The chlorine-activated CVD (CACVD) process was developed in an effort to lower the energy requirements for diamond CVD [ 121. In a chlorine-activated system, atomic hydrogen is created indirectly by allowing atomic chlorine to attack molecular hydrogen. This is advantageous because the chlorine-chlorine bond (243 kJ mol-‘) can be dissociated with about half the energy required to break a hydrogen-hydrogen bond (436 kJ mol- ‘). Chlorine can be dissociated thermally at 1700 K in a graphite heater, which can potentially be scaled to larger areas more reliably than a conventional filament or plasma system. The price paid for using a

903

CACVD system is that chlorine and its byproducts must be processed. It should be possible with additional processing to recover valuable byproducts such as aqueous HCl or AlCl, from the reactor effluent, however, while recycling unused hydrogen back to the reactor. The basic CACVD process has been demonstrated experimentally as discussed by Pan et al. [ 121. In order to evaluate the potential performance of a CACVD reactor, the imaginary d.c. arc-jet system analyzed in the previous section was converted to a CACVD system. This was accomplished by taking the process conditions from the d.c. arc-jet simulation, replacing the inlet atomic hydrogen with atomic chlorine and lowering the inlet temperature from 2500 K to 1773 K. Fig. 4 illustrates the predicted gas phase composition profile. The right side of Fig. 4 shows that atomic hydrogen is formed very quickly as atomic chlorine attacks molecular hydrogen. From this point on, the gas phase composition profiles look quite similar to the d.c. arc-jet case, except that the lower inlet temperature favors additional abstraction of hydrocarbons to form atomic carbon, at the expense of acetylene formation. The fraction of open surface sites increases from 22% to 26% due to additional abstraction of surface hydrogen by chlorine atoms. The combination of these effects leads to a slightly higher diamond growth rate of about 58 pm h-i. Performance numbers for the CACVD case show that carbon capture is increased by an order of magnitude over the d.c. arc-jet system to 1.8% due to the lower inlet temperature and higher growth rate. The dissociation energy is cut by one-half to 1.4 x lo5 kJ carat-‘. The dissociation ratio shows that 2.2 x 10’ molecules of chlorine must be dissociated for each mole of carbon

___

CH4

-----.-‘-

CH3 - -

CZHZ CZH

----

CH2 C

-----

5.0

10.0

profile for a chlorine-activated

HZ (..

----

HCL

15.0

reactor

H

-.-‘-‘-‘. ... . .

position (cm) Fig. 4. Gas phase composition

CH

(58.4 pm h-‘)

D. E. Kassmann, T. A. BadgweN/Diamond and Related Materials 5 (1996) 895-906

904

incorporated into the diamond film, about the same as the d.c. arc-jet case. The diamond quality is also improved due to the lower surface acetylene concentration. The net result is that the economics of diamond deposition may be significantly improved by converting a d.c. arc-jet reactor to use the CACVD process.

substrate injection may also prove difficult to implement in a real system, it is nonetheless instructive to consider the implications of this mathematically ideal case. Substrate injection will disrupt the film morphology as opposed to disrupting the gas flow field. Because the injected flow enters the chamber through holes in the substrate, the resulting film morphology will depend strongly on the distribution of substrate holes and the gas flow rates that are used. A very fine distribution of holes may lead to the growth of a perforated or porous diamond film. The conditions used by Dandy and Coltrin [9] for fig. 3(b) of their paper were employed to test the implications of substrate injection. Dandy and Coltrin [ 91 report a predicted growth rate of about 73 pm h-’ when methane is introduced into the free stream 1 cm above the substrate. Fig. 5 shows the predicted gas phase composition profile when the same amount of methane is introduced through the substrate instead. Only the region from the substrate out to 1 cm is shown in Fig. 5 because this is the only place where the gas phase composition changes significantly. Indeed, one of the major potential benefits of substrate injection (and free-stream injection) is to decouple atomic hydrogen generation from methyl radical generation, leading to a wider range of possible inlet to substrate distances and increased flexibility in choosing the process conditions such as pressure. Introducing methane at the substrate leads to a methyl radical concentration of 1.5 x lo-’ near the substrate, some two orders of magnitude higher than in the nominal d.c. arc-jet case. The methyl radical concentration peaks slightly above the substrate, allowing methyl radicals to diffuse back to the surface. The concentration of atomic

3.4. D.c. arc-jet system with substrate injection All three cases considered so far show that methyl radicals are formed very quickly by hydrogen abstraction, but are consumed by subsequent gas phase reactions on their journey towards the substrate. Therefore higher growth rates and carbon capture may be possible if methyl radicals can be formed closer to the substrate. In a recent paper, Dandy and Colt& [9] investigated the possibility of injecting methane into the gas phase near the surface, a method referred to here as free-stream injection. They predict that the diamond growth rate in a d.c. arc-jet reactor may be increased by as much as 75% by injecting the methane into the gas stream just outside the substrate boundary layer. Dandy and Coltrin [9] report a predicted growth rate of about 73 pm h-i for the case described in fig. 3(b) of their paper. While free-stream injection shows great promise for improving growth rates, it may be difficult to implement this concept in a real reactor without disrupting the flow field or introducing other asymmetries that result in a non-uniform deposit. Another possibility is to inject methane directly through the substrate, with a uniform purely axial flow opposing the bulk fluid motion. This is described in the model by the P,W,jH, term in the substrate boundary condition of Table 2. While uniform

~

CH4

-----

CH3

-.-.-.-‘-

CZHZ C2H

----

CM

-..-‘.-‘.-

c

-

CH

-.-‘-.-‘-

H2

._ 0.0

0.2

0.4

0.6

0.8

1.0

position (cm)

Fig. 5. Gas phase composition profile for a d.c. arc-jet reactor with substrate injection (343 pm h-l).

905

D.E. Kassmann, T.A. BadgwellJDiamond and Related Materials 5 (1996) 895-906

4. Conclusions

carbon is decreased near the surface, however, leading to a predicted diamond growth rate of 340 pm h-’ due almost entirely to methyl radical addition. Performance predictions show that the carbon capture is three times higher than in the nominal d.c. arc-jet case, and the dissociation energy and dissociation ratio are an order of magnitude lower due to the increased growth rate. The diamond quality is unchanged. All of this results from creating methyl radicals in the optimum location, just above the substrate.

A theoretical model has been developed to investigate transport phenomena and chemical kinetics in a rotating disk diamond CVD reactor. The model combines mass, momentum and energy balances for the gas flow with the detailed gas and surface chemical kinetics for diamond formation. The model equations were solved numerically to determine the gas phase composition profiles and diamond film growth rates for hot-filament and d.c. arc-jet systems. The model was then used to investigate the potential benefits of two process modifications which may increase the efficiency of diamond CVD. The first involves lowering the energy requirements by dissociating hydrogen chemically with chlorine. The second involves increasing the growth rate by injecting methane through the substrate. From the simulation work performed to date, the following conclusions may be drawn: (1) dissociating hydrogen chemically may cut energy costs per carat by a factor of two; (2) injecting methane through the substrate may allow methyl radicals to form in the optimum location, just above the substrate, improving carbon capture and leading to a significantly higher growth rate; (3) an optimized reactor using chlorine activation and substrate injection of methane may allow growth of a porous diamond film at 1200 pm h-’ while using an order of magnitude less energy per carat than a conventional d.c. arc-jet system. A combination of these modifications may provide the order of magnitude decrease in production costs required to make widespread use of diamond films economically feasible.

3.5. Chlorine-activated CVD with substrate injection A final simulation run was performed to evaluate the benefits of combining the chlorine-activated and substrate injection concepts. This was accomplished by modifying the imaginary d.c. arc-jet process with substrate injection to incorporate chlorine activation. Further optimization to increase the growth rate led to an inlet chlorine concentration of 50% and a pressure of 50 Torr. Fig. 6 illustrates the predicted gas phase composition profile for this case. The substrate boundary layer is thinner due to the increased pressure. The nearsurface carbon radical concentration is 3.6 x 10m4, nearly five times higher than the previous case, resulting in a predicted diamond growth rate of 1200 pm h-l. Carbon capture is an order of magnitude higher, at 1 l%, the same order of magnitude as in the hot-filament case. The dissociation energy is reduced to 1.9 x lo4 kJ carat - *, an order of magnitude lower than in the nominal d.c. arc-jet case. This shows that it may be possible to grow a porous diamond film at 1200 pm h-’ using an order of magnitude less energy per carat than a conventional d.c. arc-jet reactor.

~

CH4

-------.-.-

CH3 -

CZH2 CZH

----

CH2 C

0.4

-

CH

-----

H

-‘-‘-‘-.-

H2

----

HCL

0.6

position (cm) Fig. 6. Gas phase composition

profile for a chlorine-activated

reactor

with substrate

injection,

adjusted

for high growth

rate (1200 pm h-l)

906

D. E. Kassmann, T. A. Badgwell/Diamond and Related Materials 5 (1996) 895-906

We are presently working to improve the numerical solution of the dimensionless one-dimensional model and to extend the model to a general three-dimensional geometry. Experimental work is underway to test the efficiency of substrate injection and to develop high quality experimental data with which to test the model predictions.

[S] J.E. Field, The Properties of Diamonds, Academic Press, New York, 1979. [3] J.V. Busch and J.P. Dismukes, Trends and market perspectives for CVD diamond, Diamond Relat. Mater., 3 (1994) 295-302. [4] M.E. Coltrin, R.J. Kee and G.H. Evans, A mathematical model of the fluid mechanics and gas-phase chemistry in a rotating disk chemical vapor deposition reactor, J. Electrochem. SOL, 136 (1989) 819-829. [S]

Acknowledgements

[6]

The authors thank Mike Coltrin of Sandia National Laboratories and David Dandy of Colorado State University for providing the software and data required to duplicate their simulation work. The authors also wish to thank Robert H. Hauge for his insight into the chemistry of diamond CVD and chlorine activation and the Shell Foundation for their generous financial support.

[7] [S]

[9]

[lo] [ 111

References [l]

J.C. Angus, A. Argoitia, R. Gat, Z. Li, M. Sunkara, L. Wang and Y. Wang, Chemical vapour deposition of diamond, Philos. Trans. R. Sot. London, Ser. A, 342 (1993) 195-208.

[12]

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