Thermodynamic analysis of the chemical vapor deposition of diamond films

Solid State Communications, Printed in Great Britain.

0038-1098/89 $3.00 + .OO Pergamon Press plc

Vol. 69, No. 7, pp. 775-778, 1989.

THERMODYNAMIC

ANALYSIS OF THE CHEMICAL OF DIAMOND FILMS

VAPOR DEPOSITION

M. Sommer, K. Mui and F.W. Smith Department

of Physics, City College of the City University of New York, New York, NY 10031, USA (Received 7 November 1988 by G. Burns)

The chemical vapor deposition of carbon films is analyzed using the thermodynamic quasiequilibrium model and a phase diagram for the carbon-hydrogen system is obtained. When the enhanced etching of graphite by hydrogen is included in the model, a region in the phase diagram where diamond is the only stable solid phase of carbon is predicted, consistent with the experimental results of S. Matsumoto, Y. Sato, M. Tsutsumi and N. Setaka [J. Mater. Sci. 17, 3106 (1982)]. It is further predicted that higher carbon fractions (at least 5%) in the gas phase will be required for deposition of diamond at atmospheric pressure. RECENT advances in the chemical vapor deposition (CVD) of crystalline diamond films have brought about a revival of interest in this technologically unique material [l-8]. It has been demonstrated that polycrystalline diamond films can be deposited from CH,/HZ mixtures (typically with CH,/H* N 0.01) at pressures below atmospheric (typically l-100Torr) and for deposition temperatures in the range 6001000°C. It is widely believed that atomic hydrogen plays a vital role in the growth of diamond by suppressing the growth of the stable graphitic form of carbon via etching. An outstanding experimental problem which will have to be resolved if single crystal diamond films are to be obtained concerns the difficulty of nucleation of diamond on non-diamond substrates. An equally important issue in the CVD of diamond films is the need to obtain an understanding of the influence of the thermodynamics of the carbonhydrogen (C-H) system on the growth of diamond and graphite. This has not been achieved so far. A thermodynamic analysis based on the chemical equilibria of the C-H system can specify which are the stable vapor species and solid phases as functions of the important system variables: total pressure, temperature, and C/H ratio. Since graphite is the stable form of solid carbon for the pressures and temperatures now employed in the CVD of diamond, it is clear that some key kinetic factors will have to be introduced into the thermodynamic analysis in order to explain the observed relative stability of diamond. For example, the kinetic factors which lead to the enhanced etching of graphite relative to diamond will certainly have to be considered. 775

We have developed such a thermodynamic analysis of the diamond CVD process based on the quasiequilibrium (QE) model [9]. The QE model, presented below, has been used to obtain the phase diagram for the C-H system. When the enhanced etching of graphite is included, this phase diagram indicates that there can exist conditions under which diamond will be present as the only solid form of carbon. Important guidelines for the growth of diamond films will be presented, and comparisons with relevant diamond CVD experiments will be made. In the QE model, the non-equilibrium steady state depositions of diamond and graphite are analyzed using equilibrium thermodynamics. The question of whether such an approach based on the assumption of thermodynamic equilibrium is a useful starting point for an analysis of diamond CVD should be answered on the basis of comparisons between model predictions and experimental results. These comparisons will be carried out below. We note that a thermodynamic analysis [lo] of the Si-0 system has been able to explain qualitatively the observed pressure and temperature dependences of the competition between the growth of SiOZand the etching of Si via production of SiO. Kinetic theory is used from the outset in the QE model in order to express the rates at which vapor species are incident on and adsorbed species are evaporated from the substrate surface in terms of the equilibrium partial pressures of the species. These rates may involve additional non-thermodynamic parameters such as sticking (or equilibration) and desorption (or accommodation) coefficients.

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‘redictions of the quasiequilibrium model for oration rates R, for H, H,, CH4 and C, H, and m rates R, for solid carbon (graphite and I) as functions of temperature T for the interf a CH,/H, mixture with solid carbon. The ves refer to graphite, while the dashed curves liamond. The fluxes of H, and CH, reaching ice are 2.61 x lo** and 2.64 x 10” cm-* s-‘, ely. key assumption of the QE model is that remical equilibrium exists between the solid uface and the vapor species desorbed from it. the case, then the composition (i.e. partial I) of the mixture of gases in equilibrium with ce can be obtained from the equilibrium conof the generalized reactions ( y/2) H,(g) +, C,H,(g), yH(g) c* C,H,(g),

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nposing conservation of H atoms arriving at ing the surface. In addition to determining e the important vapor species in the C-H he question of whether deposition or etching :arbon (diamond or graphite) occurs can be within the framework of the QE model by ig the flux of carbon atoms reaching the sub,face from the CH4/HZ mixture with the total .om flux leaving the surface via the production llatile hydrocarbons C,H,(g), equations (1). g. 1 the predictions of the QE model for the vaporation R, of H,, H, CHI and C2H2 from ce of solid carbon for a given incoming flux gen equivalent to 5.22 x lo** H atoms cm-* ven as functions of temperature T. For both ind diamond, the dominant reaction product p to about 600K, and then H, dominates I K to above 2500 K. Above about 1’700K, :omes the dominant hydrocarbon product.

Fig. 2. Predicted phase diagram for the C-H system for a total pressure = 36Torr. Phase boundaries between the regions where solid carbon exists and where no condensed phases exist are shown for both graphite (g) and diamond (d). CH, dominates in the gas phase below about 1700 K, while C,H, dominates at higher T. We note that, as expected, the partial pressures of CH, and C2H2 are higher for diamond than for graphite. Other hydrocarbons (i.e. C2H,, CH, etc.) have been included in the model but are not shown in Fig. 1 since their evaporation rates are not significant when compared to those of H,, H, CHI and C2H2. For simplicity, at this stage of the model all sticking and desorption coefficients have been set equal to 1. When CH, is added to the incoming flux of hydrogen, solid carbon (graphite or diamond) will be deposited on the surface when the incoming C flux exceeds the flux of C atoms leaving the surface due to etching. The resulting rates of deposition Rd of graphite and diamond corresponding to an incoming flux of carbon atoms equal to 2.64 x 10” cm-' s-’ incident on the surface are also shown in Fig. 1. Under these conditions corresponding to an incident atom ratio rc = C/ (C + H) = 4.9 x 10-3, it is apparent that graphite will be deposited in the temperature range from 850 to above 2500 K while diamond can be deposited between 910 and 2325 K. With the total pressure constant at 36Torr, the phase diagram for the C-H system shown in Fig. 2 can be obtained. For this pressure, graphite and diamond can be deposited only for values of rc greater than approximately 2 x lo-’ and 5 x 10p5, respectively. Even when allowed, solid carbon will only be deposited in the range of temperatures between TL and TH. Etching of solid carbon dominates below TL via production of CH, and above TH via production of C2H2. Due to the higher free energy of diamond in the

Vol. 69, No. 7 2.41

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Fig. 3. Predicted phase diagram for the C-H system modified to include the enhanced etching of graphite by hydrogen. Also shown are the experimental results of Matsumoto ef al. [3]. Open squares refer to the observation of well-defined diamond particles, while the open and filled circles correspond to small, poorlydefined diamond particles and to large particles apparently covered with graphitic deposits, respectively. The curve labelled d(760) corresponds to the phase boundary for diamond at 760Torr. temperature and pressure range of interest, the region of stability of diamond lies completely within the region of stability of graphite, as shown in Fig. 2. There must exist, however, kinetic factors which favor the growth of diamond over graphite and which therefore should be incorporated into the QE model. From an analysis of the previous study of Balooch and Olander [l l] of the reactions of atomic and molecular hydrogen with graphite, we have found that the etching of graphite in atomic H via the production of CH, is actually enhanced above the rate predicted by the QE model between 450 and 800 K. This observation indicates that the actual region of stability of graphite must be smaller than that shown in Fig. 2. Although it is not possible at this point to determine conclusively which kinetic factors are leading to the observed enhanced etching of graphite by hydrogen, possible candidates include (1) a desorption coefficient q,&(g) for H, on graphite less than unity, and (2) H atoms tightly bound to the graphite surface. In the first case, production of CH, leading to etching would be enhanced while the production of H, would be dimin-. ished. In the second case, the recombination of H atoms to form H, would be inhibited. Further work is clearly necessary in order to identify the dominate kinetic factor(s). In Fig. 3 we present a comparison between the experimental results of Matsumoto et al. [3] and the predictions of our thermodynamic analysis where we

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tentatively choose q&(g) as the key kinetic parameter. Matsumoto et al. [3] studied the growth of diamond particles from CH,/H, mixtures via hot filament CVD at total pressures of about 36 Torr. They have presented SEM micrographs of the diamond particles deposited both at a fixed deposition temperature Td of 800” C for varying CH, concentrations and also at a fixed CH, concentration for varying Td. The data points presented in Fig. 3 shown as open squares refer to the observation of well-defined diamond particles, while the open and filled circles correspond to small, poorly-defined diamond particles and to large particles apparently covered with graphitic deposits, respectively. In order to arrive at a possible explanation for the results of Matsumoto et al. [3], we have redetermined the phase boundary for graphite using a value of r&,(g) = 0.2, which is within the range of values (0.03 to 1) needed to explain the results of Balooch and Olander [ 111.With this assumption concerning r&,(g), the region of stability for graphite now lies within that of diamond, which is unchanged from Fig. 2. The predictions of the modified QE model are thus consistent with the experimental results of Matsumoto et al. [3], as shown in Fig. 3, as the conditions leading to the deposition of well-defined diamond particles fall within the region where only diamond is predicted to be stable. The deposition conditions for the small, poorly-defined diamond particles lie near to the boundary for etching of diamond, while those for the graphite-covered particles lie in or near the region where graphite is stable. In addition, Matsumoto et al. [3] noted that no diamond growth could be observed at a pressure of 760Torr under their deposition conditions. The QE model predicts that the etching-growth boundaries for both diamond and graphite shift to higher values of rc as the pressure P is increased, and this is illustrated in Fig. 3 where the boundary for diamond corresponding to 760Torr is presented. The deposition conditions used by Matsumoto et al. [3] now correspond to the etching region, so that the observed absence of diamond growth at 760Torr is successfully explained by the QE model. The QE model as modified to include the observed [l l] enhanced etching of graphite by hydrogen has thus been able to both clarify and even explain qualitatively the CVD of diamond films under the conditions presently being used. It is clear now why the observed ranges of parameters (600-1000’ C, l-100 Tori-, 0.5 2% CH,) have been successful for diamond deposition in terms of the diamond stability region present in the phase diagram of Fig. 3. The model can provide insights into how to optimize the diamond deposition rates and also into how the deposition of diamond can be expected to vary with the available experimental

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VAPOR DEPOSITION

parameters. For example, the QE model shows that growth at lower temperatures or higher pressures will require higher carbon atom ratios rc (at least 0.05) in order to remain in the diamond stability region. In addition, the effect of adding oxygen to the reacting gases can be readily explored via the QE model by incorporating CO, CO, and H,O as possible reaction products. In order for the QE model to make more quantitative predictions for growth or etching rates, realistic values for the sticking coefficients of the reactants (H, H,, CH,, etc.) and for the desorption coefficients of the products (H, H,, CH,, C,H,) will be required. We are presently investigating the effects on diamond deposition of varying these parameters and also of varying the reactant gas mixture by including additional gases such as 02, HF, CF,, etc. Experiments are under way to test these predictions of the QE model. Acknowledgement -This

research has been supported in part by the US Department of Energy under grants DE-FG02-84ER45168 and DE-FG02-87ER45317.

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