book of abstracts - IM2NP

A B S T R A C T S THURSDAY, JULY 1 N A N O S E A 2 0 1 0
deposition noise dominates deposition noise has been observed in computer simulations, but does not appear
to have any experimental relevance.
For an initially flat surface, the Villain-Lai-Das Sarma (VLDS) equation with nonconserved noise is obtained
for all models with random deposition and nearest-neighbor hopping. This equation is not observed in any
transient regime for typical MBE conditions. If, however, the initial surface is corrugated, the relative
magnitudes of terms in the equation of motion can be altered to the point where the VLDS equation does
indeed describe transient growth, albeit with conserved noise. This is consistent with the analysis of growth
on patterned surfaces reported by the Maryland group. We will discuss the effect of various types of patterns
on the governing growth equations and their experimental consequences.
3 – Conclusion
We have shown how our previously developed methodology for deriving regularized stochastic continuum
equations can account for much of the transient behavior seen in deposition/diffusion systems. On such
surfaces, under typical conditions, the governing equations are found to be linear. The extent to which this
can be extended to the submonolayer regime is currently being investigated. We have seen that the
patterning of a substrate can pre-empt the behavior seen on initially flat substrates. The application of RG
methods to see the complete evolution of such systems remains to be carried out. But already the systematic
derivation of growth equations for patterned substrates represents a substantial advance for these important
systems.
17H00-17H30
Modeling Facet Nucleation and Growth of Hut Clusters on Ge/Si(001).
J. A. Venables1,3, D.R. Bowler3, M.R. McKay2,4 and J. Drucker1,2 (1) Physics, 2)
Materials, Arizona State University, Tempe, Arizona, USA, 3) LCN-UCL, London, UK; 4) Lawrence
Semiconductor, Tempe, Arizona, USA).
Recent STM observations of homogenous distributions of pyramid and hut clusters on Ge/Si(001) have
shown that these clusters grow extremely slowly during annealing at intermediate temperatures, T ~ 450 oC,
when there is a super-saturation of mobile ad-particles above and within the wetting layer. Data has been
obtained on the absolute length of the clusters as a function of time L(t), and thereby the evolution of the
growth rate, over periods of order 100 hours [1]. We model this slow growth as a layer by layer (2D) facet
nucleation and growth problem, in the presence of strain-induced energies both on and around the facets.
All of these energies can markedly influence the nucleation rate of new facets. First, they justify the
observation that facet nucleation occurs from the apex of the hut, as has been observed in several other
studies [2, 3]. Second, they indicate a substantial slowing down of the nucleation rate, by many orders of
magnitude, relative to the case when such energies are not present. Finally the need to undo the stable
reconstruction on the {105} facets as each new layer is formed contributes an extra energy of order 0.5 eV
[4] to the energy of the critical nucleus.
Inclusion of these effects, with experimental values of the Ge diffusion coefficient, provides a quantitative fit
to the L(t) data, and sets bounds on step and facet energies appropriate to hut clusters. Such energies are
increasingly amenable to ab-initio calculation on reconstructed hut clusters to compare with experiment [5].
1. M.R. McKay, J.A. Venables and J. Drucker, Phys. Rev. Lett. 101, 216104 (2008); Solid State Comm. 149, 1403-1409 (2009)
2. F. Montalenti et al., Phys. Rev. Lett., 93, 216102 (2004)
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