Evidence for nonclassical nucleation at solid surfaces in diamond deposition from the gas phase
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In the framework of a previously developed kinetic model, a discriminating criterion is established to distinguish between classical and nonclassical nucleation of diamond at solid surfaces. The two-step model gives the non-steady-state nucleation density function in terms of the rate constants for active site —• germ, germ —* active site, and germ —• nucleus kinetic steps. The criterion states that a//3 > 6 is a necessary condition for classical nucleation at surfaces to occur, a and (3 being functions of the rate constants which can be obtained by appropriate analysis of the experimental data. This criterion is applied to recent results on diamond nucleation at silicon surfaces and indicates nonclassical results. The expression of the nonequilibrium Zeldovich factor, Z, is also found in the form Z = [1 + K/ndYl, K and nd being the rate constants for the germ —> nucleus and germ —> active site steps, respectively. An estimation of the rate constants is reported and the corresponding Zeldovich factor is evaluated to be 0.6 for nucleation at both Si(100) and S i ( l l l ) substrates.
I. INTRODUCTION
AG can be higher than zero and the definition of a critical nucleus, as the cluster of the new phase formed with maximal work, still retained. 6 In the following we shall address the term classical to a nucleation whenever the free energy change occurring during the critical cluster formation is positive. On the contrary, the term nonclassical will refer to those nucleation processes occurring at AG < 0. Transient nucleation in a condensed system has been extensively examined in the literature (Refs. 7 and 8 and references therein). The transient or induction time is the time required to attain a steady state nucleation regime. Nucleation at surfaces is usually assumed to occur only at particular sites called "active sites" or "nucleation sites." Since the density of active sites at the substrate The nucleus dimension indicates when the consurface is a finite number, the nucleation rate goes to tinuum approximation can be applied to describe zero when the nucleation process reaches completion. the nucleation process. For a macroscopic nucleus This implies that a steady state nucleation regime can be the continuum approach is used and the work of established for a finite interval of time only. formation of critical cluster expressed in the form AG = (16T7 1, K — vn) when the continuum approximation can be applied Z — {AG(ra)/37rk7>i2}1/2.8'12'15'16
J. Mater. Res., Vol. 8, No. 7, Jul 1993
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M. Tomellini: Evidence for nonclassical nucleation at solid surfaces in diamond deposition from the gas phase
Although the term Zeldovich factor usually refers to the value of Z as obtained in the continuum limit, we shall retain this name in the nonclassical case as well. The relationship between the Zeldovich factor and the K, nd, nf rate constants is established on the basis of the steady state regime as predicted by the twostep model for nucleation. According to Eqs. (l)-(3)
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