Thermal plasma synthesis of diamond

A numerical model was used to examine experimental data in which a gas chromatograph measured the composition of gas sampled through a 70-pn orifice in the growth substrate during atmospheric-pressure RF plasma diamond CVD. Substantial discrepancies were found between the measurements and the predicted species mole fractions at the surface, but the data were in much better accord with predicted mole fractions -0.2 mm above the surface. This may possibly be due to the perturbation caused by the orifice. The model was also used to examine the predicted effects of freestream and substrate temperatures on the surface concentrations ratios of H, CH3 and C2H2. Different trends versus substrate temperature were found accoIding to whether the freestream temperature was 3000 K or 4000 K. INTRODUCTION Atmospheric-pressure plasmas generated by RF inductive coupling are one of the more promising methods for diamond CVD. Among the advantages of this method are high growth rates (10-100 pdh), the absence of electrode contamination (compared to DC arcjets), and the relative ease of atmospheric-pressure operation. Nevertheless, although there is a general understanding that the gas-phase chemical composition near the diamond growth surface crucially affects film growth, remarkably few experimental measurements have been reported for chemical species mole fractions in this environment. For atmospheric-pressure inductively-coupled RF plasmas, the only reported measurements are boundary-layer profiles of CH (1) and C2 (2) obtained by Owano et ul. using degenerate four-wave mixing spectroscopy, and our recently reported measurements (3) of several stable hydrocarbon species using a gas chromatograph for samples obtained through a small orifice located in the center of the deposition substrate. The CH measurements of Owano et ul. were shown to be in good agreement with a numerical model, whereas their measured C2 mole fractions closest to the surface lay two orders of magnitude above the predictions of the model (2). In this paper we consider two aspects of the experiments in which our recent GC measurements were obtained. First, we examine the agreement of the measured species mole fractions with a detailed numerical model. Secondly, we use the numerical model to consider the discrepancy which was reported in Ref. 3, concerning the effect of substrate temperature on film morphology-namely, that different diamond CVD environments appear to produce opposite trends regarding the effect of temperature on film morphology. EXPERIMENTAL The flow configuration for the experiments reported in Ref. 3 was the '*central jet injection" geometry of Refs. 4 and 5 , in which reactants are coaxially injected through a probe inserted directly into the coil region of an RF plasma, forming a jet which impinges on the growth substrate. Operating pressure was 1 atm, and the RF generator operated at 2.9 MHz with a plate power of 13 486 S. L. GlRSHlCK AND J. M. LARSON kW. Flow rates were 40 slm for the main argon introduced at the torch inlet, and 4 slm for both argon and hydrogen introduced through the injection probe, with methane injected through the probe at 1-5% of the hydrogen flow rate. The temperature of the molybdenum substrate was controlled using a previously described cooling system (6). The GC measurements were obtained by sampling gas through a 70-pm-diameter (before diamond growth) sonic orifice located in the center of the substrate. The pressure of the sampling line was maintained at 20 Torr, dropping to 6 Torr across the sample loop in the GC. The GC was equipped with both flame ionization and thermal conductivity detectors, and provided calibrated measurements of the mole fractions of stable species including Ar, H2, CH4, C2H2, C2H4 and C2H6. Because we wish to compare the experimental data to the numerical calculations discussed below, it is necessary to note that the interpretation of the GC measurements is complicated by two effects: (1) the perturbation and finite spatial resolution introduced by the sampling orifice, and (2) chemistry in the line which delivers the sample to the GC. Suction close to the orifice causes the flow to lose its one-dimensional character. Gas in this region is rapidly accelerated from close-tozero velocity to sonic velocity, effectively freezing the chemical composition at its value some distance above the orifice. A simple analysis using as a criterion that the Peclet number equals unity (transition from diffusion-dominated flow close to the surface to convection-dominated flow for the gas accelerating toward the orifice) at the edge of a “hemisphere of influence” indicates that the radius of this hemisphere is approximately twice the orifice diameter, or about 140 pm before diamond growth. However this analysis neglects two complicating effects: (1) the effect of viscous drag close to the surface for fluid drawn laterally toward the orifice, which may cause the geometry of the affected region to be effectively more conical than spherical; and (2) the fact that isotherms, which in the absence of the orifice would be flat and parallel to the surface, would tend in the region above the orifice to be depressed toward the orifice. Thus about 200 pm may be a more realistic estimate for the distance from the orifice for which the composition is effectively sampled. Regarding the effect of chemistry in the probe line, we conducted kinetic calculations, similar to those described in Ref. 7. If, following the discussion above, we assume that the gas composition entering the probe corresponds to the species mole fractions predicted by our numerical model at a location 200 pm above the surface, then these calculations indicate that the mole fractions of methane and acetylene are virtually unaffected by chemistry in the sampling line. As in Ref. 7, methyl radicals are predicted to recombine in the sampling line to form C2Hq and C2H6. , NUMERICAL MODEL Our general approach to modeling this system (4, 8) involves both a two-dimensional “globall’ plasma model and a one-dimensional model for the chemically-reacting boundary layer above the substrate. The plasma model solves the continuum fluid conservation equations coupled to the electromagnetic field equations, using the induction coil current rather than the plasma power as a boundary condition (9). The injected hydrocarbon (which comprises less than 0.2% of the total flow rate) is neglected in the two-dimensional model. One outcome of this calculation is the location of the 4000 K isotherm above the substrate, which we take to define the qlge of the chemically reacting boundary layer. For the argon and hydrogen flow rates corresponding to the experimental values, the calculation predicts that this boundary layer is 2.0 mm thick, and that the axial velocity at the boundary layer edge is 9.7 d s . These outputs of the two-dimensional model are used as inputs to the boundary-layer model, which utilizes the Sandia SPIN code (10) to solve the transformed one-dimensional conservation equations for stagnation-point flow, including both homogeneous gas-phase chemistry and diamond growth chemistry at the surface. Both the gas-phase reactions considered and our model for surface chemistry are described in detail in Ref. 8.