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Thermodynamic approach to the CHO deposition diagram in the diamond chemical vapour deposition process
Diamond and Related Materials, 3 (1993) 163-167
163
Thermodynamic approach to the C-H-O deposition diagram in the diamond chemical vapour deposition process Nong M. Hwang, Jun H. Hahn and Gun W. Bahng Korea Research Institute ~/ Standards and Science, PO Box 3, Taedok Science Town. Taejon, Ch'ungnam 305-606 (South Korea (Received January 20, 1993; accepted in final form May 5, 1993)
Abstract Thermodynamic analysis was made in order to evaluate the effect of the independent variables on the carbon activity in the gas phase in the C-H and C - H O systems. In the analysis, the supersaturation ratio is approximated to be the ratio of the partial pressure of carbon in the gas phase equilibrium to its equilibrium vapour pressure. The partial pressure of carbon increases with increasing carbon fraction in the reactant gases, decreasing the reactor pressure and increasing the temperature. In the C H - O system, the free energy of formation of carbon monoxide is so large that a reasonable amount of supersaturation exists only in a very narrow composition band along the carbon monoxide line. In the carbon-excess side, the supersaturation becomes very large and in the oxygen-excess side the supersaturation is reversed into very high undersaturation. These results qualitatively agree with the C - H - O deposition diagram compiled previously.
1. Introduction
The chemical vapour deposition (CVD) of diamond has been studied intensively using various processes such as hot-filament CVD [1-4] and plasma CVD [-5, 6]. In principle, the application of thermodynamics to hotfilament CVD is possible although the validity of its application to plasma CVD is suspicious. However, the effects on the microstructural evolution of the thermodynamic variables such as the concentration of carbon in hydrogen, the chamber pressure and the substrate temperature are similar for the hot-filament and the plasma CVD processes. Thus, although the thermodynamic treatment should be limited to hot-filament CVD, the results will provide some guidelines for plasma processing regarding the effect of the independent variables on the microstructural evolution. Sommer et al. [-7] and Wang et at. [-8] developed a thermodynamic analysis of diamond CVD based on a quasi-equilibrium model, where the non-equilibrium steady state depositions of diamond and graphite are analysed using equilibrium thermodynamics. Piekarczyk et al. [9] also applied thermodynamics to the diamond CVD process. They used the equilibrium concentration of carbon in the gas phase expressed by means of the so-called "solubility of the solid in the gas phase". In this paper, the deposition behaviour in the C-H and the C-H O systems is approached thermodynamically. The results of our approach are closely related to those of the previous approach such as an equilibrium
0925 9635/93/$6.00
phase diagram in the C H system [7] and the concept of the "solubility of carbon in the gas phase" [9]. However, our approach is different from the previous ones [7 9] in two respects: in the determination of the chemical potential of carbon in the gas phase and in the fact that we limit our analysis to the precipitation of graphite from the gas phase reactions. We do not apply the analysis to the formation of diamond but it will be shown that our results are closely related to features of the microstructural evolution such as the non-diamond, diamond and no growth. In a previous report [10], we suggested that the dominant nucleation of diamond over that of graphite is thermodynamically possible if the specific surface energy of diamond is only slightly lowered compared with that of graphite by some process. Since the surface energy of diamond or graphite is not considered in the thermodynamic treatment of this paper, the relative stability between diamond and graphite will not be dealt with. The driving force for deposition from the gas phase reactions is the difference in the chemical potential of carbon between the gas phase and solid carbon such as graphite or diamond. We suggest that the chemical potential of carbon in the gas phase can be approximated to be determined by the partial pressure in the gas phase equilibrium, which is the same as the solubility limit of carbon in the gas phase. Thus the supersaturation is suggested to be the ratio of the pressure of carbon in the gas phase equilibrium to its equilibrium vapour
~(') 1993 -- Elsevier Sequoia. All rights reserved
164
N. M. Hwang et al. / Thermodynamic approach to the C-H-O deposition diagram
pressure at a given temperature. The detailed description of this scheme will be published elsewhere [11]. In this paper, the thermodynamic analysis based on this scheme is applied to the C - H and C - H - O systems. The roles of the independent variables, which include the ratio of carbon to hydrogen in the reactant gases, the chamber pressure and the temperatures, are evaluated in terms of their effects on the partial pressure of carbon in the gas phase equilibrium.
2. Definition of supersaturation The free energy difference between the initial state and the final equilibrium drives the overall CVD process. However, the driving force for deposition of carbon from the gas phase reactions, which should be distinguished from the driving force for the overall CVD process, is the difference in the chemical potential of carbon between the gas phase and solid carbon. Though we know the chemical potential of carbon in the solid carbon phase p~, we need to determine its chemical potential in the gas phase pg, especially adjacent to the growing surface. In this paper, we use two terms, "the gas phase equilibrium" and "the final equilibrium" or "the gassolid equilibrium". By the first we mean the equilibrium among the gas phase species excluding the condensed phases. The gas phase equilibrium is determined by the Gibbs free energy minimization excluding the thermodynamic data for the condensed phases involved. By the second term we mean the total equilibrium including the solid phase, which minimizes the total Gibbs free energy of the system including the condensed phases. We suggest that the chemical potential of carbon in the gas phase adjacent to the growing surface be approximated to be I~g = I ~ + R T ln P*
(1)
where #~ and P~ represent respectively the standard state and the partial pressure of carbon in the gas phase equilibrium. This approximation will be valid when the chemical reactions among the gas phase species are sufficiently fast. The validity of this scheme will be described in detail elsewhere [11]. P~ in eqn. (1) is directly related to the so-called "solubility of carbon in the gas phase" adopted previously by Piekarczyk et al. in their thermodynamic analysis [9]. The solubility limit of carbon in the gas phase will be the maximum amount of carbon that the gas phase can have, which is the same as P*. If the standard state of the solid carbon is set to be the same as the gas phase, the chemical potential of carbon in the solid phase is expressed as #~ =/t~ + R T In pO
(2)
and the driving force for deposition becomes A#c=-RTln\poj
(3)
The supersaturation ratio becomes
Pt
ct = p--~
(4)
Equation (3) agrees with the deposition phase diagram in the CVD process. When the composition is such that the final equilibrium predicts the solid phase, eqn. (3) becomes negative and vice versa. It should be noted that this equation exactly predicts the phase diagram for the C - H system reported by Sommer et al. [7]. This equation becomes positive and negative respectively in the compositions of carbon and hydrogen [7] where the condensed carbon does not and does exist. At the phase boundary demarcating the existence of the solid carbon [7], the driving force for deposition is predicted to be zero from eqn. (3), which indicates that neither deposition nor etching will occur. Equations (3) and (4) are the basis for the following evaluation of the supersaturation and the driving force for deposition in the C - H and C - H - O systems.
3. C - H system Normally in the hot-filament CVD process for diamond film, various forms of hydrocarbon diluted by hydrogen are used as reactants [12]. The thermodynamic independent variables in the process are the composition ratio of carbon to hydrogen, the chamber pressure and the substrate temperature. Based on the supersaturation ratio described by eqn. (4), the effect of these variables on the supersaturation can be evaluated in terms of their effect on the partial pressure of carbon in the gas phase equilibrium. The partial pressure of carbon in the gas phase can be calculated in the gas phase equilibrium, where the thermodynamic data of solid carbon are omitted in the calculation of Gibbs free energy minimization. When the condensed phase is stable, the gas phase equilibrium is metastable with respect to the gas-solid equilibrium. The thermodynamic analysis was carried out using the THERMO-CALCsoftware [13]. There are two sources that can build up the supersaturation in the hot-filament CVD process. One arises when the partial pressure of carbon in the gas phase equilibrium is higher than its equilibrium vapour pressure at the given temperature. This supersaturation can be controlled by changing the ratio of carbon to hydrogen of the reactant gases. The other arises from the temperature gradient above the substrate, i.e. supercooling. In the hot-filament CVD process, the temper-
N. M. Hwang et al.
Thermodynamic approach to the C H 0 deposition diagram
ature gradient between the filament and the substrate is steep. When the chemical reactions in the gas phase are sufficiently fast in the given temperature range, the gas phase equilibrium will be maintained throughout the temperature gradient. In this case, the supersaturation from the temperature gradient does not exist and only supersaturation from chemical reactions will exist. The driving force for deposition is relatively simple because the maximum supersaturation ratio is expressed by eqn. (4). However, when the supercooling effect exists, the supersaturation arising from supercooling should be also considered. For example, if the gas phase which is in equilibrium at the temperature T1, is supercooled at the substrate temperature T2, the supersaturation ratio would be the ratio of the partial pressure of carbon in the gas phase equilibrium at T1 to the equilibrium vapour pressure at T2. In contrast, the preparation of thin film by the evaporation method [14] uses this supersaturation arising from the temperature gradient alone without the supersaturation arising from the chemical reactions. Figure 1 shows the partial pressure of carbon with varying temperatures for four different ratios of carbon to hydrogen at a chamber pressure of 2700 Pa. For comparison the equilibrium vapour pressure of graphite or diamond is also shown. Note that since the vertical pressure axis is a logarithmic scale, the slight difference in equilibrium vapour pressure between graphite and diamond is not distinguishable. Figure 1 shows that increasing the ratio of carbon to hydrogen increases the partial pressure of carbon and thus increases the supersaturation for the precipitation of the solid carbon. For the ratio C : H = 1 : 2 0 0 , the
I0°~
,
i
i
,
'
g_ I 0 -+
S~
+
10-~s I 10 -2°
partial pressure of carbon is higher than its equilibrium vapour pressure over the temperature range between about 890 and about 2290 K. With increasing carbon content, this temperature range becomes wider. If the gas phase equilibrium is assumed to be maintained throughout the temperature gradient and thus only the supersaturation arising from chemical reactions is considered, deposition of the solid carbon will take place in the above temperature range. This assumption will hold at high temperatures, where the chemical reactions in the gas phase are relatively fast. The reason why the filament is not deposited by the solid carbon is that, at the normal filament temperatures of about 2500 K in the diamond CVD process [1-4], no driving force for deposition exists. For the low temperatures, where the supersaturation from the supercooling effect should be considered, the deposition can take place even for the etching condition of solid carbon predicted from the chemical reactions because of the supersaturation arising from the supercooling effect. However, it should be noted that, when the supersaturation from the chemical reaction predicts deposition, the result cannot be reversed to etching because the supercooling effect always increases the supersaturation. For composition ratios higher than C : H = 1 : 100, the evolution of a non-diamond cauliflower structure is reported [15 17]. We suggest that charged clusters are involved in the diamond CVD process [18]. On the basis of the presence of the charged clusters, the high supersaturation will increase the cluster size. It would be difficult for a large cluster to be reconstructed into crystalline diamond on the substrate. A ratio lower than C : H = 1:400 is the lower limit normally adopted in processing. Thus, for ratios much lower than this, the growth rate will be negligible or etching rather than deposition will take place. It can be said that the large supersaturation is related to the formation of the nondiamond phase and the low supersaturation and the undersaturation are related to the negligible growth rate or no growth and to the etching respectively.
4. C - H - O system
I°-'+1
~ I0-12I
no
165
I 1200
,
16100
I 2000
i
[ 2400
i
2800
Temperoture (K) Fig. 1. Variation of the partial pressure of carbon in the gas phase with temperature for four differentratios of carbon to hydrogen(total pressure, 2700 Pa): A, C : H = 1: 50; I , C : H = 1 : 100; A, C : H = 1: 200; ©, C : H = 1:400; *, vapour pressure of carbon.
The addition of oxygen or water to the C H system has been reported to have some desirable effects [19-24]. Thermodynamically, the effect of water is the same as that of oxygen except that two extra hydrogen atoms accompany the oxygen atom. Bachmann et al. [25] compiled the previously reported diamond CVD data and suggested a diamond deposition map in the C - H - O system where, irrespective of the sources of reactants and methods of processes, the deposition of diamond is possible along a narrow range of compositions centred on the carbon monoxide line and in the carbon-rich side
N. M. Hwang et al. / Thermodynamic approach to the C-H-O deposition diagram
166
of this range non-diamond deposition results while in the oxygen-rich side no growth results. Figure 2 shows the temperature dependence of the partial pressure of carbon in the gas phase equilibrium of the C - H - O system for the three different compositions C : O =49.5 : 50.5, 50:50 and 50.5:49.5 with a fixed hydrogen content of 50% under a chamber pressure of 2700 Pa. The partial pressure of carbon in the gas phase is very sensitive to the composition ratio between carbon and oxygen. Note that the partial pressure of carbon depends on the ratio of carbon to oxygen in the C - H - O system much more sensitively than on the ratio of carbon to hydrogen in the C - H system. As a result, the supersaturation or the driving force for deposition would be very sensitive to the ratio of carbon to oxygen in the C - H - O system. There exist no exact criteria of the supersaturation distinguishing non-diamond growth and no growth. However, based on the experimental data reported for the C - H system [12, 15-17], where non-diamond growth and no growth resulted respectively for high and low methane concentrations relative to hydrogen, the criteria of the supersaturation can be roughly deduced. These criteria present some problems because the partialpressure dependence of carbon on the temperature in the C - H system is different from that in the C - H - O system. However, thermodynamic calculations in the C - H - O system show that the free energy of formation of carbon monoxide from carbon and oxygen is so large that slight deviation of the composition ratio from C : O = 1:1 would result in very high supersaturation or undersaturation of carbon. When the oxygen content is larger than that of carbon, most of the carbon is used up to
form carbon monoxide and as a result the partial pressure of carbon markedly decreases. Thus no driving force for deposition of any solid carbon exists. When the carbon content is larger than that of oxygen, the excess carbon after forming carbon monoxide tends to increase abruptly the partial pressure of carbon in the gas phase and as a result a very high supersaturation is obtained. If the diamond deposition is supposed to be possible in a reasonable supersaturation range as in the C - H system, the diamond deposition region will be limited to a very narrow composition range along the carbon monoxide line. The reasonable supersaturation ranges in the C - H - O system are shown in Fig. 3. The low supersaturation region in Fig. 3 is determined by a supersaturation ratio less than unity at 1200 K which is regarded as the substrate temperature. In the C - H system, this condition is a ratio lower than C : H = 1:2000, at which composition ratio no deposition is expected. The high supersaturation region in Fig. 3 is determined by a partial pressure of carbon in the gas phase higher than that at 2500 K for the ratio C : H = 1 : 50, which ratio is reported to produce a non-diamond phase in the C - H system [12, 15-17]. 2500 K is the normally chosen filament temperature. The region produced by these criteria is along the carbon monoxide line but is much narrower than that suggested by Bachmann e t al. [25]. This discrepancy between the calculated region and that suggested by Bachmann et al. based on the compiled experimental data seems to come from the highly non-equilibrium nature of the CVD process. Especially in the plasma CVD process, the thermodynamic approach cannot be applied, because thermal equilibrium is not achieved. Nevertheless, our C
I o°
i
i
i
i
0._ c 0
I 0 -4
0 o
,~
I 0 -e
~
10-~2
j
......
a.
~
10-~6
0 13..
10-2°
1200
1600
2000
Temperature
2400
2800
H
H20
0
(K)
Fig. 2. Variation of the partial pressure of carbon in the gas phase with temperature for three different ratios of carbon to oxygen with 50% H (total pressure, 2700 Pa): II, N(C):N(O)=0.495:0.505; A, N(C) : N(O) = 0.500 : 0.500; O, N(C) : N(O) = 0.505 : 0.495; ,k, vapour pressure of carbon.
Fig. 3. C-H-O systemshowing the region divided on the basis of the present criteria for supersaturation:--, calculated results;--- results of Bachmann et al. The upper full line is determined by a partial pressure of carbon in the gas phase equilibrium higher than that at 2500 K for the ratio C : H = 1: 50 and the lower full line by supersaturation less than unity at 1200K.
N. M. Hwang et al. / Thermodynamic approach to the C H 0 deposition diagram
thermodynamic analysis indicates that the free energy of formation of carbon monoxide is so large and, as a result, the supersaturation is so sensitively affected by the ratio of carbon to oxygen that a prediction based on thermodynamics can be at least qualitatively applied even to the highly non-equilibrium plasma process. On the basis of the suggestion of the charged clusters in the diamond CVD process [18], for a fixed number of ions the supersaturation will affect the cluster size, which will in turn affect the microstructural evolution and the growth kinetics. Caution is also needed to interpret the effect of the addition of oxygen because oxygen has a relatively high electron affinity and will have a tendency to become a negative ion, which will produce a charged carbon cluster in the supersaturated carbon gas.
5. Conclusion Based on the thermodynamic calculations, the effect of the independent variables on the driving force for deposition or etching of solid carbon in the C-H and C - H - O systems can be estimated. The thermodynamic treatment here was based on thermal equilibrium, while a real diamond CVD process such as plasma CVD takes place under highly non-equilibrium conditions. However, the thermodynamic analysis indicates that the non-diamond growth region and no-growth regions, which were classified solely on the basis of experimental data, at least qualitatively correspond to the high supersaturation and to the low supersaturation or undersaturation respectively, in both the C-H and C - H - O systems. Diamond deposition is possible only in the composition region where an appreciable amount of supersaturation exists.
Acknowledgments The authors appreciate the financial support from the Korea Ministry of Science and Technology. All the thermodynamic analyses were done using the substance database and the Poly-3 module of the THERMO-CALC
167
program developed at the Royal Institute of Technology in Sweden.
References 1 B. V. Derjaguin and D. B. Fedoseev, Growth of Diamond and Graphite from the Gas Phase, Nauka, Moscow, 1977, Chapter 4. 2 S. Matsumoto, Y. Sato, M. Tsutsumi and N. Setaka, J. Mater. Sci., 17 (1982) 3106. 3 S. Matsumoto, Y. Sato, M. Kamo and N. Setaka, Jpn. J. Appl. Phys., 21 (1982) L183. 4 A. Sawabe and T. Inuzuka, Thin Solid Films, 137 (1986) 89. 5 K. Suzuki, A. Sawabe, H. Yasuda and T. Inuzuka, Appl. Phys. Lett., 50 (1987) 728. 6 M. Kamo, Y. Sato, S. Matsumoto and N. Setaka, .I. Cryst. Growth. 62 (19831 642. 7 M. Sommer, K. Mui and F. W. Smith, Solid State Commun., 69 (1989) 775. 8 R. B. Wang, M. Sommer and F. W. Smith, J. Cryst. Growth, 119 (1992) 271. 9 W. Piekarczyk, R. Roy and R. Messier, J. Cryst. Growth, 98 (1989) 765. I0 N. M. Hwang, G. W. Bahng and D. N. Yoon, Diamond Relat. Mater., 1 (1992) 191. 11 N. M. Hwang, Diamond Relat. Mater., submitted for publication. 12 K. E. Spear, J. Am. Ceram. Soc., 72 (1989) 171. 13 B. Sundman, B. Jansson and J. O. Andersson, CALPHAD, 9 (1985) 153. 14 R. Glang, in L. I. Maissel and R. Glang (eds.), Handbook of Thin Film Technology, McGraw-Hill, New York, 1983. 15 K. Kobashi, K. Nishimura, Y. Kawate and T. Horiuchi, Phys. Rev. B,38 (1988) 4067. 16 M. Yoshikawa, G. Katagiri, H. Ishida, A. Ishitani, M. Oho and K. Matsumura, Appl. Phys. Lett., 55 (1989) 2608. 17 D. S. Knight, R. Weimer, L. Pilione and W. B. White, Appl. Phys. Lett., 56 (1990) 1320. 18 N. M. Hwang, D. W. Moon, K. S. Lim and M. Y. Wey, presented at Diamond '92, Heidelberg, August 31 September 4, 1992. 19 T. Kawato and K. Kondo, dpn. J. Appl. Phys., 26 {1987) 1429. 20 C. P. Chang, D. L. Flamm, D. E. Ibbotson and J. A. Mucha, 3. Appl. Phys., 63 (1988) 1744. 21 Y. Saito, K. Sato, H. Tanaka, K. Fujita and S. Matsuda, J. Mater. Sci., 23 (1988) 842. 22 J. A. Mucha, D. L. Flamm and D. E. lbbotson, d. Appl. Phys., 65 (1989) 3448. 23 W. A. Yarbrough, M. A. Stewart and J. A. Cooper, SurL Coat. Technol., 39-40 (1989) 241. 24 A. R. Badzian, P. K. Bachmann, T. Hartnett, T. Badzian and R. F. Messier, in P. Oelhafen and P. Koidll (eds.), Diamond and Diamondlike Films, European Materials Researeh Society Symposium Proceedings, Vol. 17, Editions de Physique, Paris, 1987, p. 63. 25 P. K. Bachmann, D. Leers and H. Lydtin, Diamond Relat. Mater., 1 (1991) 1.
163
Thermodynamic approach to the C-H-O deposition diagram in the diamond chemical vapour deposition process Nong M. Hwang, Jun H. Hahn and Gun W. Bahng Korea Research Institute ~/ Standards and Science, PO Box 3, Taedok Science Town. Taejon, Ch'ungnam 305-606 (South Korea (Received January 20, 1993; accepted in final form May 5, 1993)
Abstract Thermodynamic analysis was made in order to evaluate the effect of the independent variables on the carbon activity in the gas phase in the C-H and C - H O systems. In the analysis, the supersaturation ratio is approximated to be the ratio of the partial pressure of carbon in the gas phase equilibrium to its equilibrium vapour pressure. The partial pressure of carbon increases with increasing carbon fraction in the reactant gases, decreasing the reactor pressure and increasing the temperature. In the C H - O system, the free energy of formation of carbon monoxide is so large that a reasonable amount of supersaturation exists only in a very narrow composition band along the carbon monoxide line. In the carbon-excess side, the supersaturation becomes very large and in the oxygen-excess side the supersaturation is reversed into very high undersaturation. These results qualitatively agree with the C - H - O deposition diagram compiled previously.
1. Introduction
The chemical vapour deposition (CVD) of diamond has been studied intensively using various processes such as hot-filament CVD [1-4] and plasma CVD [-5, 6]. In principle, the application of thermodynamics to hotfilament CVD is possible although the validity of its application to plasma CVD is suspicious. However, the effects on the microstructural evolution of the thermodynamic variables such as the concentration of carbon in hydrogen, the chamber pressure and the substrate temperature are similar for the hot-filament and the plasma CVD processes. Thus, although the thermodynamic treatment should be limited to hot-filament CVD, the results will provide some guidelines for plasma processing regarding the effect of the independent variables on the microstructural evolution. Sommer et al. [-7] and Wang et at. [-8] developed a thermodynamic analysis of diamond CVD based on a quasi-equilibrium model, where the non-equilibrium steady state depositions of diamond and graphite are analysed using equilibrium thermodynamics. Piekarczyk et al. [9] also applied thermodynamics to the diamond CVD process. They used the equilibrium concentration of carbon in the gas phase expressed by means of the so-called "solubility of the solid in the gas phase". In this paper, the deposition behaviour in the C-H and the C-H O systems is approached thermodynamically. The results of our approach are closely related to those of the previous approach such as an equilibrium
0925 9635/93/$6.00
phase diagram in the C H system [7] and the concept of the "solubility of carbon in the gas phase" [9]. However, our approach is different from the previous ones [7 9] in two respects: in the determination of the chemical potential of carbon in the gas phase and in the fact that we limit our analysis to the precipitation of graphite from the gas phase reactions. We do not apply the analysis to the formation of diamond but it will be shown that our results are closely related to features of the microstructural evolution such as the non-diamond, diamond and no growth. In a previous report [10], we suggested that the dominant nucleation of diamond over that of graphite is thermodynamically possible if the specific surface energy of diamond is only slightly lowered compared with that of graphite by some process. Since the surface energy of diamond or graphite is not considered in the thermodynamic treatment of this paper, the relative stability between diamond and graphite will not be dealt with. The driving force for deposition from the gas phase reactions is the difference in the chemical potential of carbon between the gas phase and solid carbon such as graphite or diamond. We suggest that the chemical potential of carbon in the gas phase can be approximated to be determined by the partial pressure in the gas phase equilibrium, which is the same as the solubility limit of carbon in the gas phase. Thus the supersaturation is suggested to be the ratio of the pressure of carbon in the gas phase equilibrium to its equilibrium vapour
~(') 1993 -- Elsevier Sequoia. All rights reserved
164
N. M. Hwang et al. / Thermodynamic approach to the C-H-O deposition diagram
pressure at a given temperature. The detailed description of this scheme will be published elsewhere [11]. In this paper, the thermodynamic analysis based on this scheme is applied to the C - H and C - H - O systems. The roles of the independent variables, which include the ratio of carbon to hydrogen in the reactant gases, the chamber pressure and the temperatures, are evaluated in terms of their effects on the partial pressure of carbon in the gas phase equilibrium.
2. Definition of supersaturation The free energy difference between the initial state and the final equilibrium drives the overall CVD process. However, the driving force for deposition of carbon from the gas phase reactions, which should be distinguished from the driving force for the overall CVD process, is the difference in the chemical potential of carbon between the gas phase and solid carbon. Though we know the chemical potential of carbon in the solid carbon phase p~, we need to determine its chemical potential in the gas phase pg, especially adjacent to the growing surface. In this paper, we use two terms, "the gas phase equilibrium" and "the final equilibrium" or "the gassolid equilibrium". By the first we mean the equilibrium among the gas phase species excluding the condensed phases. The gas phase equilibrium is determined by the Gibbs free energy minimization excluding the thermodynamic data for the condensed phases involved. By the second term we mean the total equilibrium including the solid phase, which minimizes the total Gibbs free energy of the system including the condensed phases. We suggest that the chemical potential of carbon in the gas phase adjacent to the growing surface be approximated to be I~g = I ~ + R T ln P*
(1)
where #~ and P~ represent respectively the standard state and the partial pressure of carbon in the gas phase equilibrium. This approximation will be valid when the chemical reactions among the gas phase species are sufficiently fast. The validity of this scheme will be described in detail elsewhere [11]. P~ in eqn. (1) is directly related to the so-called "solubility of carbon in the gas phase" adopted previously by Piekarczyk et al. in their thermodynamic analysis [9]. The solubility limit of carbon in the gas phase will be the maximum amount of carbon that the gas phase can have, which is the same as P*. If the standard state of the solid carbon is set to be the same as the gas phase, the chemical potential of carbon in the solid phase is expressed as #~ =/t~ + R T In pO
(2)
and the driving force for deposition becomes A#c=-RTln\poj
(3)
The supersaturation ratio becomes
Pt
ct = p--~
(4)
Equation (3) agrees with the deposition phase diagram in the CVD process. When the composition is such that the final equilibrium predicts the solid phase, eqn. (3) becomes negative and vice versa. It should be noted that this equation exactly predicts the phase diagram for the C - H system reported by Sommer et al. [7]. This equation becomes positive and negative respectively in the compositions of carbon and hydrogen [7] where the condensed carbon does not and does exist. At the phase boundary demarcating the existence of the solid carbon [7], the driving force for deposition is predicted to be zero from eqn. (3), which indicates that neither deposition nor etching will occur. Equations (3) and (4) are the basis for the following evaluation of the supersaturation and the driving force for deposition in the C - H and C - H - O systems.
3. C - H system Normally in the hot-filament CVD process for diamond film, various forms of hydrocarbon diluted by hydrogen are used as reactants [12]. The thermodynamic independent variables in the process are the composition ratio of carbon to hydrogen, the chamber pressure and the substrate temperature. Based on the supersaturation ratio described by eqn. (4), the effect of these variables on the supersaturation can be evaluated in terms of their effect on the partial pressure of carbon in the gas phase equilibrium. The partial pressure of carbon in the gas phase can be calculated in the gas phase equilibrium, where the thermodynamic data of solid carbon are omitted in the calculation of Gibbs free energy minimization. When the condensed phase is stable, the gas phase equilibrium is metastable with respect to the gas-solid equilibrium. The thermodynamic analysis was carried out using the THERMO-CALCsoftware [13]. There are two sources that can build up the supersaturation in the hot-filament CVD process. One arises when the partial pressure of carbon in the gas phase equilibrium is higher than its equilibrium vapour pressure at the given temperature. This supersaturation can be controlled by changing the ratio of carbon to hydrogen of the reactant gases. The other arises from the temperature gradient above the substrate, i.e. supercooling. In the hot-filament CVD process, the temper-
N. M. Hwang et al.
Thermodynamic approach to the C H 0 deposition diagram
ature gradient between the filament and the substrate is steep. When the chemical reactions in the gas phase are sufficiently fast in the given temperature range, the gas phase equilibrium will be maintained throughout the temperature gradient. In this case, the supersaturation from the temperature gradient does not exist and only supersaturation from chemical reactions will exist. The driving force for deposition is relatively simple because the maximum supersaturation ratio is expressed by eqn. (4). However, when the supercooling effect exists, the supersaturation arising from supercooling should be also considered. For example, if the gas phase which is in equilibrium at the temperature T1, is supercooled at the substrate temperature T2, the supersaturation ratio would be the ratio of the partial pressure of carbon in the gas phase equilibrium at T1 to the equilibrium vapour pressure at T2. In contrast, the preparation of thin film by the evaporation method [14] uses this supersaturation arising from the temperature gradient alone without the supersaturation arising from the chemical reactions. Figure 1 shows the partial pressure of carbon with varying temperatures for four different ratios of carbon to hydrogen at a chamber pressure of 2700 Pa. For comparison the equilibrium vapour pressure of graphite or diamond is also shown. Note that since the vertical pressure axis is a logarithmic scale, the slight difference in equilibrium vapour pressure between graphite and diamond is not distinguishable. Figure 1 shows that increasing the ratio of carbon to hydrogen increases the partial pressure of carbon and thus increases the supersaturation for the precipitation of the solid carbon. For the ratio C : H = 1 : 2 0 0 , the
I0°~
,
i
i
,
'
g_ I 0 -+
S~
+
10-~s I 10 -2°
partial pressure of carbon is higher than its equilibrium vapour pressure over the temperature range between about 890 and about 2290 K. With increasing carbon content, this temperature range becomes wider. If the gas phase equilibrium is assumed to be maintained throughout the temperature gradient and thus only the supersaturation arising from chemical reactions is considered, deposition of the solid carbon will take place in the above temperature range. This assumption will hold at high temperatures, where the chemical reactions in the gas phase are relatively fast. The reason why the filament is not deposited by the solid carbon is that, at the normal filament temperatures of about 2500 K in the diamond CVD process [1-4], no driving force for deposition exists. For the low temperatures, where the supersaturation from the supercooling effect should be considered, the deposition can take place even for the etching condition of solid carbon predicted from the chemical reactions because of the supersaturation arising from the supercooling effect. However, it should be noted that, when the supersaturation from the chemical reaction predicts deposition, the result cannot be reversed to etching because the supercooling effect always increases the supersaturation. For composition ratios higher than C : H = 1 : 100, the evolution of a non-diamond cauliflower structure is reported [15 17]. We suggest that charged clusters are involved in the diamond CVD process [18]. On the basis of the presence of the charged clusters, the high supersaturation will increase the cluster size. It would be difficult for a large cluster to be reconstructed into crystalline diamond on the substrate. A ratio lower than C : H = 1:400 is the lower limit normally adopted in processing. Thus, for ratios much lower than this, the growth rate will be negligible or etching rather than deposition will take place. It can be said that the large supersaturation is related to the formation of the nondiamond phase and the low supersaturation and the undersaturation are related to the negligible growth rate or no growth and to the etching respectively.
4. C - H - O system
I°-'+1
~ I0-12I
no
165
I 1200
,
16100
I 2000
i
[ 2400
i
2800
Temperoture (K) Fig. 1. Variation of the partial pressure of carbon in the gas phase with temperature for four differentratios of carbon to hydrogen(total pressure, 2700 Pa): A, C : H = 1: 50; I , C : H = 1 : 100; A, C : H = 1: 200; ©, C : H = 1:400; *, vapour pressure of carbon.
The addition of oxygen or water to the C H system has been reported to have some desirable effects [19-24]. Thermodynamically, the effect of water is the same as that of oxygen except that two extra hydrogen atoms accompany the oxygen atom. Bachmann et al. [25] compiled the previously reported diamond CVD data and suggested a diamond deposition map in the C - H - O system where, irrespective of the sources of reactants and methods of processes, the deposition of diamond is possible along a narrow range of compositions centred on the carbon monoxide line and in the carbon-rich side
N. M. Hwang et al. / Thermodynamic approach to the C-H-O deposition diagram
166
of this range non-diamond deposition results while in the oxygen-rich side no growth results. Figure 2 shows the temperature dependence of the partial pressure of carbon in the gas phase equilibrium of the C - H - O system for the three different compositions C : O =49.5 : 50.5, 50:50 and 50.5:49.5 with a fixed hydrogen content of 50% under a chamber pressure of 2700 Pa. The partial pressure of carbon in the gas phase is very sensitive to the composition ratio between carbon and oxygen. Note that the partial pressure of carbon depends on the ratio of carbon to oxygen in the C - H - O system much more sensitively than on the ratio of carbon to hydrogen in the C - H system. As a result, the supersaturation or the driving force for deposition would be very sensitive to the ratio of carbon to oxygen in the C - H - O system. There exist no exact criteria of the supersaturation distinguishing non-diamond growth and no growth. However, based on the experimental data reported for the C - H system [12, 15-17], where non-diamond growth and no growth resulted respectively for high and low methane concentrations relative to hydrogen, the criteria of the supersaturation can be roughly deduced. These criteria present some problems because the partialpressure dependence of carbon on the temperature in the C - H system is different from that in the C - H - O system. However, thermodynamic calculations in the C - H - O system show that the free energy of formation of carbon monoxide from carbon and oxygen is so large that slight deviation of the composition ratio from C : O = 1:1 would result in very high supersaturation or undersaturation of carbon. When the oxygen content is larger than that of carbon, most of the carbon is used up to
form carbon monoxide and as a result the partial pressure of carbon markedly decreases. Thus no driving force for deposition of any solid carbon exists. When the carbon content is larger than that of oxygen, the excess carbon after forming carbon monoxide tends to increase abruptly the partial pressure of carbon in the gas phase and as a result a very high supersaturation is obtained. If the diamond deposition is supposed to be possible in a reasonable supersaturation range as in the C - H system, the diamond deposition region will be limited to a very narrow composition range along the carbon monoxide line. The reasonable supersaturation ranges in the C - H - O system are shown in Fig. 3. The low supersaturation region in Fig. 3 is determined by a supersaturation ratio less than unity at 1200 K which is regarded as the substrate temperature. In the C - H system, this condition is a ratio lower than C : H = 1:2000, at which composition ratio no deposition is expected. The high supersaturation region in Fig. 3 is determined by a partial pressure of carbon in the gas phase higher than that at 2500 K for the ratio C : H = 1 : 50, which ratio is reported to produce a non-diamond phase in the C - H system [12, 15-17]. 2500 K is the normally chosen filament temperature. The region produced by these criteria is along the carbon monoxide line but is much narrower than that suggested by Bachmann e t al. [25]. This discrepancy between the calculated region and that suggested by Bachmann et al. based on the compiled experimental data seems to come from the highly non-equilibrium nature of the CVD process. Especially in the plasma CVD process, the thermodynamic approach cannot be applied, because thermal equilibrium is not achieved. Nevertheless, our C
I o°
i
i
i
i
0._ c 0
I 0 -4
0 o
,~
I 0 -e
~
10-~2
j
......
a.
~
10-~6
0 13..
10-2°
1200
1600
2000
Temperature
2400
2800
H
H20
0
(K)
Fig. 2. Variation of the partial pressure of carbon in the gas phase with temperature for three different ratios of carbon to oxygen with 50% H (total pressure, 2700 Pa): II, N(C):N(O)=0.495:0.505; A, N(C) : N(O) = 0.500 : 0.500; O, N(C) : N(O) = 0.505 : 0.495; ,k, vapour pressure of carbon.
Fig. 3. C-H-O systemshowing the region divided on the basis of the present criteria for supersaturation:--, calculated results;--- results of Bachmann et al. The upper full line is determined by a partial pressure of carbon in the gas phase equilibrium higher than that at 2500 K for the ratio C : H = 1: 50 and the lower full line by supersaturation less than unity at 1200K.
N. M. Hwang et al. / Thermodynamic approach to the C H 0 deposition diagram
thermodynamic analysis indicates that the free energy of formation of carbon monoxide is so large and, as a result, the supersaturation is so sensitively affected by the ratio of carbon to oxygen that a prediction based on thermodynamics can be at least qualitatively applied even to the highly non-equilibrium plasma process. On the basis of the suggestion of the charged clusters in the diamond CVD process [18], for a fixed number of ions the supersaturation will affect the cluster size, which will in turn affect the microstructural evolution and the growth kinetics. Caution is also needed to interpret the effect of the addition of oxygen because oxygen has a relatively high electron affinity and will have a tendency to become a negative ion, which will produce a charged carbon cluster in the supersaturated carbon gas.
5. Conclusion Based on the thermodynamic calculations, the effect of the independent variables on the driving force for deposition or etching of solid carbon in the C-H and C - H - O systems can be estimated. The thermodynamic treatment here was based on thermal equilibrium, while a real diamond CVD process such as plasma CVD takes place under highly non-equilibrium conditions. However, the thermodynamic analysis indicates that the non-diamond growth region and no-growth regions, which were classified solely on the basis of experimental data, at least qualitatively correspond to the high supersaturation and to the low supersaturation or undersaturation respectively, in both the C-H and C - H - O systems. Diamond deposition is possible only in the composition region where an appreciable amount of supersaturation exists.
Acknowledgments The authors appreciate the financial support from the Korea Ministry of Science and Technology. All the thermodynamic analyses were done using the substance database and the Poly-3 module of the THERMO-CALC
167
program developed at the Royal Institute of Technology in Sweden.
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