Fractalization of silicon islands at a coverage close to 0.5 monolayers

Fractal islands are normally observed when the growth is a result of many random coalescence events of small islands or atoms with the growing cluster. In this paper, we show that fractalization can be observed also for growing islands at a coverage which is close to 0.5 monolayers. This was shown for a Si(1 1 1) surface covered by 0.53 monolayer of silicon. This fractalization is explained by the simple conservative Ising model, where the diffusion of a single atom is simulated by a single spin flip. In this model, fractal islands are observed over a finite scaling range where smaller islands have a dimension of 2 and larger ones are fractal. The fractal dimension and the scaling range are dependent on the fraction (equivalent to coverage) p of spin up (or down). Both the dimension and range increase as p approaches 0.5. We show that the growth of the clusters is in agreement with a classical t0.33 law [Phys. Rev. B 34 (1986) 7845].