A model for the nucleation of diamond clusters on Si(111) substrates

Abstract

A theoretical study of the nucleation, size, and structure of diamond phase carbon clusters on Si͑111͒ substrates is presented. Molecular mechanics analysis has been utilized to predict energetically and entropically feasible pathways for nucleation of the carbon clusters. Several mechanistic pathways for nucleation of carbon clusters are examined with CH 3 and/or C 2 H 2 as the nucleation precursors. A possible model for the nucleation mechanism of diamond-phase carbon clusters on the ␤-SiC͑111͒ surface, which forms epitaxially on Si͑111͒ substrates, is presented. The critical size of the carbon clusters is computed based on the atomistic theory of nucleation and the proposed nucleation mechanisms.

Theoretical analysis of the diffusive ion in biased plasma enhanced diamond chemical vapor deposition

“…Thus the voltage bias is effective for reactions between carbon and hydrogen or between carbon and carbon. 11,12,31 A detailed calculation of the dynamical chemical reaction for various kinetic energies of hydrogen ions is required for the further discussion of nucleus formation of diamond in the microwave CVD process.…”

“…11,12 A variety of the interface structures between the Si substrate and diamond layers formed during the bias pretreatment, such as SiC, 13,14 amorphous carbon, 15 and nanographite, 16 are directly observed by highresolution transmission electron microscopy ͑HRTEM͒. 17 The formed structures may essentially depend on the kinetic energy of the ions on the substrate surface which is dependent on the plasma parameters.…”

Silicon Etching during the HFCVD Diamond Growth

“…Moreover the reaction is highly exothermic. 11,43 Owing to the occurrence of a forced flux of methyl radicals, the factor [γ c / (1 -(γ c /2)] instead of γ c accounts to a first approximation for the non-Maxwellian distribution of the velocities when γ c is large. 44 Furthermore, it is known from comprehensive studies of the chemistry of the gas phase in the course of the diamond deposition that a quasi-equilibrium of the concentration of the hydrogen and hydrocarbon radicals is reached in the gas-phase just above the surface according to [31][32][33][34] where T is a gas temperature that ranges within the temperature of the filaments T f and the temperature of the substrate T s (T s e T , T f ) and K(T) is the constant corresponding to the equilibrium Figure 11 reports the variation of the carbon coverage with methane content using eqs 2-5.…”

“…It is clear that the nucleation mechanism must involve a set of chemical reactions with removal of molecular hydrogen through the action of gaseous hydrogen. In a recent theorical study, Mahalingam et al 11 proposed a CH 3 -based nucleation process including radical-radical surface reactions that are both energetically and entropically promoted. Furthermore, they estimated a critical diamond cluster size in the nanometer range.…”

Nucleation and growth studies of crystalline carbon phases at nanoscale.

“…However, these diagrams are not useful in understanding the nucleation on the substrate from the vapor phase. Since diamond is a metastable phase and nucleates from the gas phase heterogeneously, the classical nucleation theory for predicting the critical nuclei diameter based on carbon supersaturation is not really applicable [47]. Thus, over the years, several researchers have hypothesized structures and kinetic pathways that lead to nucleation.…”