Measurement and modeling of Ar/H2/CH4 arc jet discharge chemical vapor deposition reactors II: Modeling of the spatial dependence of expanded plasma parameters and species number densities

Detailed methodology and results are presented for a two-dimensional (r,z) computer model applicable to dc arc jet reactors operating on argon/hydrogen/hydrocarbon gas mixtures and used for chemical vapor deposition of micro- and nanocrystalline diamond and diamondlike carbon films. The model incorporates gas activation, expansion into the low pressure reactor chamber, and the chemistry of the neutral and charged species. It predicts the spatial variation of temperature, flow velocities and number densities of 25 neutral and 14 charged species, and the dependence of these parameters on the operating conditions of the reactor such as flows of H2 and CH4 and input power. Selected outcomes of the model are compared with experimental data in the accompanying paper [C. J. Rennick et al., J. Appl. Phys. 102, 063309 (2007)]. Two-dimensional spatial maps of the number densities of key radical and molecular species in the reactor, derived from the model, provide a summary of the complicated chemical processing that occurs. In the vortex region beyond the plume, the key transformations are CH4→CH3↔C2H2↔large hydrocarbons; in the plume or the transition zone to the cooler regions, the chemical processing involves C2Hx↔(CHy and CHz), C3Hx↔(CHy and C2Hz), (C2Hy and C2Hz)↔C4Hx↔(CHy and C3Hz). Depending on the local gas temperature Tg and the H/H2 ratio, the equilibria of H-shifting reactions favor C, CH, and C2 species (in the hot, H-rich axial region of the plume) or CH2, C2H, and C2H2 species (at the outer boundary of the transition zone). Deductions are drawn about the most abundant C-containing radical species incident on the growing diamond surface (C atoms and CH radicals) within this reactor, and the importance of chemistry involving charged species is discussed. Modifications to the boundary conditions and model reactor geometry allow its application to a lower power arc jet reactor operated and extensively studied by Jeffries and co-workers at SRI International, and comparisons are drawn with the reported laser induced fluorescence data from these studies