CoSi2 clusters of constant height on a Si(100) surface grow in a square shape at first, but at a critical size a shape transition to clusters with large aspect ratios occurs. With each cluster connected to an implanted layer of cobalt by a thermally induced defect that serves as a diffusion channel, clusters can grow independently with a continuous supply of cobalt. When the cobalt supply is limited, clusters grow up to a specific volume and then have time to adjust their height, assuming their minimum-energy shape. Although calculations indicate that this should be a square pyramid, experiments indicate that a more elongated cluster corresponds to equilibrium.