FIAS Scientific Report 2011 - Frankfurt Institute for Advanced Studies ...

Fractals on a surface
Collaborators: A.V. Solov’yov 1 , V. Dick 1 , C. Bréchignac 2 , I.A. Solov’yov 3
1 Frankfurt Institute for Advanced Studies, 2 CNRS, France, 3 UIUC, Urbana, USA
Main results:
We developed a theoretical tool for studying post-growth processes occurring in nanofractals grown on a surface.
A method was developed which accounts for the internal dynamics of particles in a fractal. We demonstrated
that particle diffusion and detachment controls the shape of the emerging stable islands on a surface.
Fig. 1. Arrangement of deposited particles on a surface.
The important processes which govern pattern
formation on a surface are indicated by arrows: F
is the particle deposition rate, Γ is the diffusion rate
of a free particle, Γd is the diffusion rate of a particle
along the periphery of an island, and Γe is the
detachment rate of a particle from the island.
Fig. 2: Formation of islands with different morphologies on a surface during the particle deposition process: (a)
formation of compact islands (low particle deposition rate); (b) formation of fractals with thick branches (intermediate
particle deposition rate); (c) formation of the fractal structures with thin branches (fast particle deposition rate).
We demonstrated that the morphology of islands on a surface is mainly governed by the characteristic time
needed for the newly deposited particles to reach the growth region (nucleation time) and by the characteristic
time needed for a particle to find an optimum position within an island (rearrangement time). To get an in
depth understanding of the self-organization and fragmentation processes on a surface we have investigated
how various essential parameters of the system influence the diffusion of clusters on a surface. In particular,
we considered the cluster size, the binding energy between clusters and the substrate and the temperature.
We considered different scenarios of fractal post-growth relaxation and analyzed the time evolution of the
island’s morphology. The result of calculations were compared with available experimental observations, and
experiments in which the post-relaxation of deposited macrostructure can be probed were suggested.
Related publications in 2011:
1. V.V. Dick, I.A. Solov’yov and A.V. Solov’yov, Fragmentation pathways of nanofractal structures on
surfaces, Phys. Rev. B84, 115408 (2011).
2. V.V. Dick, Mechanism of nano-fractal structure formation and post-growth evolution, Dissertation,
Goethe-Universität Frankfurt am Main (2011).
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