Crossover from Dimer Nucleation to Adatom Exchange During Submonolayer Epitaxy
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ABSTRACT The nucleation and growth of islands in the early stages of epitaxial growth is studied with kinetic Monte Carlo Simulations and self-consistent mean field rate equations. Specifically, adatom exchange and irreversible dimer formation are allowed to compete equally as the origin of two-dimensional islands. The island size distribution and number density are found to satisfy a dynamic crossover scaling form. The critical island size evolves from one to zero with increasing temperature, decreasing flux, and increasing coverage.
INTRODUCTION In the early stages of epitaxial growth, atoms deposited onto a crystalline substrate can diffuse freely until they are trapped by defects such as steps and impurities or en.counter other diffusing species and nucleate islands. Alternatively, the diffusing atoms can exchange with a substrate atom forming an immobile "island" of only one atom which acts as a trapping site for other diffusing monomers [1, 2, 3]. This process has been observed for numerous metal on metal hetero-epitaxial systems [3]-[7]. An analogous situation occurs if the diffusing species are molecules instead of atoms. Recent work on the chemical vapor deposition of Fe on Si(100) [8], for example, reveal that adsorbed precursor molecules dissociate leaving behind a single Fe atom. This relatively immobile Fe atom acts as a trapping site for preferential dissociation of additional diffusing molecules [8]. Because of their qualitative similarity, in this paper the terms "diffusing monomer" and "exchange" can be used interchangably with "diffusing molecule" and "dissociation". A systematic study of the scaling properties of the island number densities in the early stages of growth (submonolayer) may provide important information on the relevant atomistic processes. For example, if islands form from adatom collisions, the total number density of islands Nnc1 often has a simple power law dependence on the ratio of the surface diffusion rate D and deposition flux F [9, 10],
N,ý,
(i > 0)
-
(1)
where the critical island size i is one atom less than the size at which an island, on average, grows more rapidly than it decays. Using this equation, it is possible to measure the diffusion constant D and the critical island size by simply counting the number of islands on the substrate [11, 12]. Conversely, if islands form by exchange (i = 0) the number density Nexc is independent of the deposition flux and predicted by Ref. [3] to obey approximately N
Ok Dc 37
Mat. Res. Soc. Symp. Proc. Vol. 399 01996 Materials Research Society
(2)
where he is the rate of adatom exchange and 0 is the coverage. A systematic study using Eq. 2 can measure the ratio of the energy barrier for exchange to the energy barrier for diffusion. Eqs. 1 is approximately valid for coverages ranging from about 0.05 monolayers to the onset of coalescence. The coverage dependence of Eq. 2 is derived from a simplified rate theory which assumes constant rate coefficients (see below). The island size distribution function (n8 (9)) (defined as t
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