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Period of a comblike pattern controlled by adatom supply and noise

M. Kawaguchi, H. Miura, K. Kishi, M. Sato, and M. Uwaha, Phys. Rev. E 91, 012409 (9pages) (2015).

Pattern formation of a step on a growing crystal surface induced by a straight line source of atoms, which is escaping from the step at a velocity Vp, is studied with the use of a phase field model. From a straight step, fluctuations of the most unstable wavelength λmax grow. Competition of intrusions leads to coarsening of the pattern, and survived intrusions grow exponentially. With sufficient strength of the crystal anisotropy, a regular comblike pattern appears. This peculiar step pattern is similar to that observed on a Ga-deposited Si(111) surface. The final period of the intrusions, Λ, is determined when the exponential growth ends. The period depends on the strength Fu of a current noise in diffusion as Λ∼λmax| ln Fu|: such a logarithmic dependence is confirmed for the first time. A nonmonotonic Vp dependence of Λ indicates that the comblike pattern with a small Vp is related to an unstable growth mode of the free needle growth in a channel. The pattern is stabilized by the guiding linear source.