ELSEVIER Journal of Crystal Growth 177 (1997) 171 173

j . . . . . . . . C R Y S T A L G R O W T H

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Thermodynamic prediction of deposition parameters for diamond synthesis in atmospheric oxyacetylene flames

Wei David Zhang, Yong-Zhong Wan, Ji-Tao Wang* Department of Electronic Engineering, Fudan Universi~, Shanghai 200 433, People's Republic of China

Received 30 September 1996; accepted 29 November 1996

Abstract

The suitable ranges of substrate temperature and gas flow ratio for diamond synthesis in atmospheric oxyacetylene flames are theoretically predicted by a non-equilibrium thermodynamic coupling model. The suitable range of substrate temperature is widest for flow ratio R close to unity, and will be narrowed rapidly when flow ratio deviates from unity. When the substrate temperature is between 1000 and 1250 K, the corresponding R range is about between 0.8 and 1.1. Diamond synthesis is allowed thermodynamically for flow ratio beyond 1.1 though the kinetic rate might be very low.

PACS: 81.05.Tp; 81.15.Gh; 81.30.Dz

Keywords: Diamond; Vapor deposition; Thermodynamics; Oxyacethylene flame

Diamond films have been synthesized by chem- ical vapor deposition (CVD) using a number of different techniques, including hot filament or plasma assisted CVD, DC plasma jet, oxyacetylene flame, and laser excited CVD [1]. Of these methods, the oxyacetylene combustion synthesis of diamond first reported by Hirose is attractive for its simplicity and low cost of equipment, as well as high growth rates [-2-6]. Substrate temperature (T) and flow ratio of oxygen to acetylene (R) are two key parameters for diamond deposition in flames.

* Corresponding author.

Many researchers have examined the effects of two key-parameters on the growth, but obtained some- what different results. Hirose et al. [2] found dia- mond deposition under acetylene-rich conditions with the range of R = 0.7-1.0; Hanssen [3] also believed diamond film growth occurred under oxy- gen-rich conditions with R values up to 1.05; Kosky [4] presented a graph of the maximum substrate temperature locus at which solid carbon can form in flames, and drew the maximum desirable sub- strate temperature of about 1300 K for diamond deposition. However, Snail [53 achieved ho- moepitaxial growth of diamond in flames at tem- peratures of 1773 K. Ruo-Bao Wang [6] attempted

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172 Wei David Zhang et al. / Journal of Crystal Growth 177 (1997) 171 173

to account for constraints of substrate temperature and flow ratio of oxygen to acetylene for diamond growth with the quasi-equilibrium model, but was not successful.

A nonequilibrium thermodynamic coupling model proposed by Ji-Tao Wang has been successfully applied to vapor-grown diamond in C H and C-H-O systems [7-9]. Regions of temperature and composition parameter space, consistent with much reported experimental data, were predicted in which diamond is thermodynamically stable relative to graphite or other nondiamond carbon. In this letter, we apply the model to diamond syn- thesis in atmospheric oxyacetylene flames, and cal- culate the phase diagram for solid carbon deposition in flames. The suitable ranges of sub- strate temperature and flow ratio of oxygen to acetylene for diamond growth are theoretically drawn from the phase diagram.

The principle ideas of our nonequilibrium ther- modynamic coupling model are (1) During dia- mond deposition process, super-equilibrium atomic hydrogen (SAH) or/and other activated particles exist in the mixture where the gas phase is in a nonequilibrium state. (2) The association of SAH into molecular hydrogen is very favorable thermo- dynamically. Through a nonequilibrium thermo- dynamic coupling reaction, the association of SAH provides the driving force for diamond synthesis from the gas phase or even from graphite (via gaseous intermediates e.g. CH4, CH3, C2H2 • " ") at low pressures. (3) The phase diagram should be calculated using a thermodynamic program minim- izing entropy production of the system for a nonequilibrium system [10]. The gas-phase tem- perature in atmospheric flames is about 3500 K, the activated temperature is chosen to be 3500 K for the phase diagram calculation here, not 2400 K used in the hot filament process [7-9]. The phase diagram for solid carbon deposition in atmospheric oxyacetylene flames is obtained, as shown in Fig. 1. The horizontal axis represents gas flow ratio of oxygen to acetylene (R), and the vertical axis rep- resents substrate temperature (T).

Three regions-gas-phase region or no deposition region, diamond growth region and nondiamond carbon growth region are presented in Fig. 1. The appearance of the diamond growth region is in

V I--

2400

2000

1600

1200

800

400 0.6

Non-diamond ~ / Gas phase carbon growth l region region fl

• • • • X

• • • & • × x

t " •• • Diamond ~ • growth region

I I I I I I

0.7 0.8 0.9 1 1.1 1.2 1.3

R

Fig. 1. The calculated phase diagram of temperature vs. gas flow ratio for solid carbon deposition in atmospheric flames. Also shown are the experimental results reported by Hirose, Weimer, Snail, Hanssen, and Phillips et al. Solid triangles, solid circles and crosses represent diamond, nondiamond carbon and no deposition, respectively.

agreement with the analysis of the nonequilibrium thermodynamic coupling model. According to the model, the graphite phase will be activated to be a higher energy state by super-equilibrium atomic hydrogen and oxygen than before, and it is unstable with respect to diamond if the coupling parameter is not too small [7, 8]. Therefore, the growth of diamond is in preference to graphite or other non- diamond carbon inside diamond growth region. In the view of chemical kinetics, Badzian and Fren- klach also demonstrated that the growth of graph- ite is covered by the diamond phase or is much lower than the growth of diamond at low pressures [11, 12].

Fig. 1 shows that the substrate temperature and gas-flow ratio for diamond growth are interdepen- dent. The suitable range of R is about between 0.8 and 1.1 for a fixed substrate temperature of 1000 K. If the temperature rises, the R range will become narrower. When the substrate temperature is above 1250 K, the R value tends to unity. The R range is wide for temperatures between 580 and 1000 K; however, nondiamond carbon should be deposited for arbitrary flow ratio when the substrate temper- ature is below about 580 K due to the existence of only a nondiamond carbon growth region. Sub- strate temperatures between 1000 and 1250 K are

Wei David Zhang et al. / Journal of C~stal Growth 177 (l 997) 171-173 173

normally used for diamond deposition in oxyacety- lene flames, the corresponding R range is about between 0.8 and 1.1, which is consistent with re- ported experimental results [13]. When diamond is synthesized at a fixed R value, there is a limiting range of substrate temperature for diamond growth. For example, the suitable range of substra- te temperature is between about 640 and 1300 K when R equals 0.93, which is in good agreement with Hirose's experimental results [2]. The widest temperature range for diamond growth occurs an R value near unity. The temperature range narrows rapidly when R deviates from unity.

It is noted that the diamond growth region in Fig. 1 extends up to a gas-flow ratio of 1.1. However, no one has successfully achieved diamond growth at R values beyond 1.1 in atmospheric flames until now. Clearly, in the light of thermodynamics, dia- mond synthesis is allowed for R values beyond 1.1 according to Fig. 1, but the kinetic growth rate might be very low.

Some experimental results reported by Hirose [2], Hanssen [3], Weimer [14], Snail [15], and Phillips [16] are presented in Fig. 1. The experi- mental results of diamond growth all lie in the diamond growth region. Reported nondiamond carbon growth results lie in nondiamond carbon growth region with a few exceptions. The results of no deposition all lie in gas-phase region of the phase diagram. Given possible errors in flow controller calibrations and in the pyrometer readings, there is good agreement between these experimental results and our thermodynamic pre- dictions.

In conclusion, the substrate temperature (T) and gas flow ratio of oxygen to acetylene (R) for dia- mond deposition in atmospheric oxyacetylene flames are theoretically predicted according to a non-equilibrium thermodynamic coupling model. When the substrate temperature is between 1000 and 1250 K, the corresponding R range is between about 0.8 and 1.1. For diamond synthesis at a fixed

R value, the range of substrate temperature greatly depends on the R value. The suitable T range is widest for R value close to unity, and will be nar- rowed rapidly when the R value deviates from unity. Diamond synthesis is allowed thermodyn- amically for R values beyond 1.1 though the kinetic rate might be very low.

This work was supported by the National Natu- ral Science Foundation of China.

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