Universality and scaling in two-step epitaxial growth in one dimension

Irreversible one-dimensional (1D) epitaxial growth at small coverages via the recently suggested two-step growth protocol [Tokar and Dreyssé, Surf. Sci. 637-638, 116 (2015)] has been studied with the use of the kinetic Monte Carlo and the rate-equation techniques. It has been found that similar to the two-dimensional (2D) case the island capture zones could be accurately approximated with the Gamma probability distribution (GD). Coverage independence of the average island sizes grown at the first step that was also found in two dimensions was observed. In contrast to 2D case, the shape parameter of the GD was also found to be coverage-independent. Using these two constants as the input, an analytical approach that allowed for the description of the commonly studied statistical distributions to the accuracy of about 2% has been developed. Furthermore, it was established that the distributions of the island sizes and the interisland gaps grown via the two-step protocol were about 50% narrower than in the case of nucleation on random defects, which can be of practical importance. Equivalence between the GD shape of the island size distribution in the scaling regime and the linear dependence of the capture numbers on the island size in the rate-equation approach has been proved.