Gold nanoparticles are widely used for catalytic growth of different semiconductor nanowires. It is important therefore to have a full appreciation of the factors influencing the size distribution of such particles on semiconductor substrates. Here, we describe some interesting phenomena observed during low-temperature deposition of Au onto InAs(111)B substrates where Au islands are solid. In particular, we find a bimodal character of the size distribution of these islands. We then develop a nucleation model which is based on a specific form of the island formation energy. The model yields a self-limiting growth behavior in which the growth rate of large islands is suppressed e.g. due to dislocations. We show that the regime of self-regulated nucleation with a few pulses is observed for short growth times, leading to a bimodal size distribution or even a more complex shapes. For longer growth times, the system acquires a steady-state regime with a time-independent supersaturation and hence the pulses disappear.
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