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A computational model for the hot-filament diamond growth environment
Workshop on diamond thin films
A notation
Mod& for the Hot-F%ment
785
Diamond Growth Environment
D.G Goodwin and G.G. Gsvillet Division of Engineering and Applied Science California Institute of Technology, Pasadena, CA 91125 A imputation model has been developed to study gas-phase che~stry and transport in diamond s thesis reactors. We consider a simplified oneilimensional geometry, which allow8 inclusion oP detailed chemical kinetics without prohibitive computational ex ense. The approach we take is similar to that used by Coltrin, Kee, and Evans to study silicon CVD(l P. We consider a showerhead gas inlet of radius R located a distance L above a substrate of the 8ame radius. The gas is assumed to leave the inlet with a uniform, purely axial velocity - uL. The fluid equations for mass, momentum, energy, and species enervation, iodudin both convective and diffusive transport, are solved for the limit R >> L to calculate axial ve!o&y, radial velocity, temperature, and species concentration profdes in the gap between the gas inlet and the substrate. By choosing the inlet gas temperature and composition to model appropriately the hot, activated gas, we may simulate the near-substrate environment for either low or high pressure diamond growth processes. We have first applied the model to simulate the hot-filament experiments of Harris and Weiner[2]. We consider hydroc~~ns up through C4 species (23 hydrocarbons plus H and HZ), and use a 56-reaction pyrolysis model, based on that of Harris[J . Following Ref. [2], we take the gas temperature at the inlet to be 2000 K, which we assume to b e representative of gas which passes near the filament. We assume the gas remains at 2000 K long enough to yield approximately equal CH4 and C,H, mole fractions (0.2 set), as has been observed experimentally [2]. The resulting gas composition is used as the boundary condition at the gas inlet for the species equations. Shown in Fi ure 1 are species mole fractions for all species exceeding 10-r, computed for the ~~~~~do~ Ref. z:21 ( = 20 Torr, 0.29 CH4 to 100 Hz, substrate temperature = 1000 K). We take L = = 1 cm Psee, which gives a Reynolds number Re = 5.3 x 10-4. The large6t mass-transfer L Peclet number concentration
uLL/D is 2.3 x 10-s.
Thus, species transport
is dominated
by diffusion, and the
profiles are independent of the assumed uL
For these conditions, the major species Hz, H, CH4, C$Ip, and CHs are only slightly affected by gas-phase chemistry. Chemistry plays a more important role in determining the con~ntratio~ at the substrate of CzH,, z = 3 - 6, which are in the range of 0.1 to 3 ppm. For these conditions, the CsH, hydrocarbons, 2 = 2 - 5, have surface concentrations near 1 ppm. However, the CsH, surface concentrations, unlike those for CZH,, fall rapidly if L is increased, and are below 0.1 ppm for L = 2 cm.
Ac~owl~gem~ts: This work is supported in part by the Office of Naval Research under Grant No. NOOO14-90-J-1386. References M.E. Coltrin, R.J. Kee, and G.H. Evans, f. Electrochem. SC. 136,819-829 (1989). 2. Appl. S.J. Harris, A.M. Weiner, and T.A. Perry, Phys. Lat. 53, 1605-1607 (1988). 1.
3. S.J. Harris, .I. Appl. Phys. 65, 30443048 (1989).
-6 0
0.1
0.2
0.3
0.4
0.5
*(cm)
Fig 1. Predicted species profiles for the experimental conditions of Ref. 2. The substrate is at x = 0
A notation
Mod& for the Hot-F%ment
785
Diamond Growth Environment
D.G Goodwin and G.G. Gsvillet Division of Engineering and Applied Science California Institute of Technology, Pasadena, CA 91125 A imputation model has been developed to study gas-phase che~stry and transport in diamond s thesis reactors. We consider a simplified oneilimensional geometry, which allow8 inclusion oP detailed chemical kinetics without prohibitive computational ex ense. The approach we take is similar to that used by Coltrin, Kee, and Evans to study silicon CVD(l P. We consider a showerhead gas inlet of radius R located a distance L above a substrate of the 8ame radius. The gas is assumed to leave the inlet with a uniform, purely axial velocity - uL. The fluid equations for mass, momentum, energy, and species enervation, iodudin both convective and diffusive transport, are solved for the limit R >> L to calculate axial ve!o&y, radial velocity, temperature, and species concentration profdes in the gap between the gas inlet and the substrate. By choosing the inlet gas temperature and composition to model appropriately the hot, activated gas, we may simulate the near-substrate environment for either low or high pressure diamond growth processes. We have first applied the model to simulate the hot-filament experiments of Harris and Weiner[2]. We consider hydroc~~ns up through C4 species (23 hydrocarbons plus H and HZ), and use a 56-reaction pyrolysis model, based on that of Harris[J . Following Ref. [2], we take the gas temperature at the inlet to be 2000 K, which we assume to b e representative of gas which passes near the filament. We assume the gas remains at 2000 K long enough to yield approximately equal CH4 and C,H, mole fractions (0.2 set), as has been observed experimentally [2]. The resulting gas composition is used as the boundary condition at the gas inlet for the species equations. Shown in Fi ure 1 are species mole fractions for all species exceeding 10-r, computed for the ~~~~~do~ Ref. z:21 ( = 20 Torr, 0.29 CH4 to 100 Hz, substrate temperature = 1000 K). We take L = = 1 cm Psee, which gives a Reynolds number Re = 5.3 x 10-4. The large6t mass-transfer L Peclet number concentration
uLL/D is 2.3 x 10-s.
Thus, species transport
is dominated
by diffusion, and the
profiles are independent of the assumed uL
For these conditions, the major species Hz, H, CH4, C$Ip, and CHs are only slightly affected by gas-phase chemistry. Chemistry plays a more important role in determining the con~ntratio~ at the substrate of CzH,, z = 3 - 6, which are in the range of 0.1 to 3 ppm. For these conditions, the CsH, hydrocarbons, 2 = 2 - 5, have surface concentrations near 1 ppm. However, the CsH, surface concentrations, unlike those for CZH,, fall rapidly if L is increased, and are below 0.1 ppm for L = 2 cm.
Ac~owl~gem~ts: This work is supported in part by the Office of Naval Research under Grant No. NOOO14-90-J-1386. References M.E. Coltrin, R.J. Kee, and G.H. Evans, f. Electrochem. SC. 136,819-829 (1989). 2. Appl. S.J. Harris, A.M. Weiner, and T.A. Perry, Phys. Lat. 53, 1605-1607 (1988). 1.
3. S.J. Harris, .I. Appl. Phys. 65, 30443048 (1989).
-6 0
0.1
0.2
0.3
0.4
0.5
*(cm)
Fig 1. Predicted species profiles for the experimental conditions of Ref. 2. The substrate is at x = 0