Patterns of diamond nucleation from the gas phase
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On the basis of an analysis of experimental data on nucleation rates performed in the preceding paper in this issue, patterns of the process of diamond nucleation from the gas phase on Si(100) substrates have been drawn. A kinetic scheme is proposed which is apparently able to describe the complex behavior of the system in the temperature range 750 K-1225 K, at (CH 4 /H 2 ) ratios between 0.5 and 2% and at a total pressure of 100 mbar. The model postulates a distribution function of the nucleation centers over the heats of adsorption of active gaseous species and introduces a cut-off criterion based on the necessary condition that adjacent active sites coexist for times longer than the characteristic time of germ growth. Nucleation centers, active sites, germs, and nuclei have been defined by simple molecular models and their rates of transformation discussed, using available literature data.
I. INTRODUCTION In recent work on diamond deposition from the gas phase on a Si(100) substrate, by the hot filament chemical vapor deposition technique, it has been shown1'2 that uncoupling crystal growth from nucleation makes it possible to study these two processes separately and to apply independent kinetic treatments to crystallite growth and to nucleation. Crystal growth rates have been investigated experimentally in Ref. 1 and the results analyzed in terms of a simplified Frenklach and Spear mechanism.3'4 Nucleation rates have been examined in Ref. 2 and analyzed by a model kinetics developed in Ref. 5. Further information on the nucleation process has been obtained by a procedure consisting of consecutive depositions at two different temperatures or at two gas compositions.6 The results of Refs. 1 and 2 have shown that it is possible to derive, from the particle size distribution of the diamond deposits and from the independently measured crystal growth rates, the density functions N(t), namely the surface density of the nuclei as a function of time during deposition. These density functions are sigmoids which have been fitted by means of the kinetic equation derived in Ref. 5:
N(t) =
— a (a — (1)
Woo is the density of nuclei at t = oo, and a and /3 are constants that contain the reaction probabilities of the various steps of the kinetic scheme. The fits of experimentally derived N(t) functions to Eq. (1) yielded the dependence of N^ and of a and /3 on substrate temperature T, gas composition T = (CH 4 /H 2 ), and scratching conditions of the substrate surface by the diamond paste. 798 http://journals.cambridge.org
J. Mater. Res., Vol. 8, No. 4, Apr 1993 Downloaded: 29 Mar 2015
It is the purpose of the present paper to re-examine this kinetic scheme in the light of the results of Refs. 2 and 6 with the aim of defining a molecular model of the nucleation process compatible with the observations reported in these references. These observations will be summarized below.
II. THE OBSERVED BEHAVIOR OF THE N(t) FUNCTIONS The block diagram of Fig. 1 contains the model of the kinetics of nucleation discussed in Ref. 5. Ac
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