A One-Dimensional Stochastic Model of Diamond Growth
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one of the distinctive morphological patterns of growth, lateral propagation of surface steps [10,11]. It was also suggested [10] that appearance of different textures may be due to the same elementary reaction mechanism but under different regimes of kinetic competition between adsorption and surface diffusion on {100} planes. Testing these hypotheses and examining the interplay between the principal elements of the process constitutes the objective of the present study. METHOD An increasing number of elementary chemical reactions has been identified in quantumchemical calculations for surface transformations underlying diamond growth, with the outcome often determined by the surface site environment [9-11]. The large number of possible elementary reactions and their strong steric dependence requires a stochastic model to capture the interactions among different events. However, vastly differing time scales are predicted by theory for individual reaction steps, which makes detailed stochastic simulations extremely computer intensive if not impossible at present. As the first step in this direction, a simple model is developed to examine the stochastic character of the interplay between primary processes of the diamond growth chemistry. The model includes two principal simplifications: one-dimensional substrate, and grouping of the elementary reactions into a few global steps. 83 Mat. Res. Soc. Symp. Proc. Vol. 399 01996 Materials Research Society
The main chemical features of diamond growth are [9-11]: insertion of hydrocarbon precursors into surface dimers, which transforms the dimers into bridge sites; migration of the bridging CH 2 group along dimer chains; formation of next-layer dimers by combination of two (migrating) CH 2 groups from two adjacent chains; transformation of lone dimers into doubly chemisorbed C=CH2 groups; migration of these C=CH2 groups along dimer chains; and ultimately, formation of stable dimers next to already existing ones. All of these processes are governed by abstraction, addition, and local migration reactions of hydrogen atoms. The simplified, one-dimensional model traces the formation, destruction, and migration of individual dimers. Three global steps, classified according to the steric environment, are considered in the present model- adsorption, desorption, and surface migration-each of them summarizing a series of elementary reactions. For example, the adsorption step represents addition of a gaseous precursor to a radical dimer vacancy, f3-scission of the C C
dimer bond, formation of the bridged configuration, and combination of two bridge sites into a dimer, all of the processes mediated by abstraction, addition, and local migration of hydrogen atoms. A distinctive feature of diamond growth chemistry is that adsorption of major growth species is extremely slow at bridge sites, as compared to dimer sites, due to prohibitive repulsion between hydrogen atoms of the incoming gaseous species and surface hydrogens. This creates voids--unfilled vacancies along the dimer chain dir
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