We
report an observation of arrays of self-assembled Si ridges
grown by vapor–liquid–solid mechanism in a molecular
beam epitaxy (MBE) chamber. The growth experiments are conducted on
Si(100) substrates using Au droplets as seeds for growth of Si ridges.
We show that at a sufficiently low flux of Si atoms, gold droplets
are propelled forward along two orthogonal ⟨011⟩ directions
by the growing silicon ridges. The reticular growth closely resembles
a self-avoiding random walk in two dimensions, as we confirmed by
using Monte Carlo simulation. The result is a formation of a network
of Si ridges with a topological complexity and connectivity that depends
on the growth time as well as the starting diameter of the Au droplets.
On the basis of our experimental results, we elaborate on the role
of diffusion in the MBE growth of Si ridges.