Period of a comblike pattern controlled by atom supply and noise

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 V(p), is studied with the use of a phase field model. From a straight step, fluctuations of the most unstable wavelength λ(max) 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 F(u) of a current noise in diffusion as Λ∼λ(max)|lnF(u)|: such a logarithmic dependence is confirmed for the first time. A nonmonotonic V(p) dependence of Λ indicates that the comblike pattern with a small V(p) is related to an unstable growth mode of the free needle growth in a channel. The pattern is stabilized by the guiding linear source.