MINIMUM-ENERGY PATHS FOR ELEMENTARY REACTIONS IN LOW-PRESSURE DIAMOND-FILM FORMATION

We have determined minimum-energy paths on the Brenner empirical hydrocarbon potential-energy hypersurface for a number of important elementary reactions that include hydrogen atom abstraction and migration, C2H2, C2H, and hydrogen atom addition to a carbon radical site, and six-membered, carbon ring closure. Our results show that the reaction barrier for addition of C2H2 or C2H via C(s)-C single-bond formation at some radical site is within range of the expected thermal energies. Although both addition processes are exothermic, the energies released are very different. For C2H2 addition, DELTAE is -0.66 eV, whereas DELTAE = -3.5 eV for C2H addition if the end carbon atom forms the bond. If C2H chemisorbs via the C-H carbon, DELTAE = -1.58 eV. The reaction profiles show that the formation of a second C-C bond for chemisorbed C2H2 to an adjacent radical site is a near barrierless, exothermic process. However, if hydrogen atom migration is a prerequisite to formation of the second C-C bond, the overall process is associated with a barrier that can be as large as 1.62 eV (37.4 kcal/mol). The potential barrier for creation of a radical site via hydrogen atom abstraction at an sp3 carbon is 0.53 eV (12.2 kcal/mol). Consequently, radical sites required for C2H2 addition or ring closure are more likely to be created by abstraction reactions than by hydrogen atom migrations. Ring closures between two radical sites are found to be near barrierless processes. If, however, hydrogen atom release accompanies the ring closure, the overall process is associated with a barrier of at least 1.34 eV (30.9 kcal/mol). Chemisorption of ethynyl radicals (C2H) is found to lead to a more stable surface species that is less likely to undergo desorption than is the case for acetylene addition. In addition, the ethynyl radical provides a second radical site for subsequent reactions which may obviate the need for hydrogen migration or abstraction. The results indicate that hydrogen abstraction is very likely the rate-determining step in low-pressure, diamond-film growth.