Cluster shape cycles during self-similar cluster growth

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Abstract
In this paper we discuss an interesting feature of the system In on InP(001), i.e., that the shape of a significant number of large In clusters on the surface, formed during thermal decomposition of the compound semiconductor, undergo shape cycles between spherical and rectangular during cluster growth. Indications of repeated shape cycles are shown and a detailed theoretical discussion of the effect is given. The shape cycles are caused by enhanced substrate etching below clusters which results in the formation of square- or rectangular-shaped depressions. The depressions modify the energetic equilibrium condition governing cluster shapes such that cluster shapes follow the shape of the expanding depression for some time. We further demonstrate that the global cluster size distribution follows a self-similar behavior.