Mesoscopic mismatch as a driving force for modified morphology above percolation

The steady-state morphology of submonolayer Si/Si(111)7×7 islands is characterized by a size-dependent transition from compact through ramified to 1D-like forms. The transition is described by the linear-chain model (LCM), which explains this shape transition in strained heteroepitaxial layers, as a mechanism for strain relaxation without dislocations. We found that above the percolation coverage _c, the entire structure adopts new steady-state morphology and reduces its typical width by a factor of e, to its optimal-energy value. The LCM predicts this value as the asymptotic behavior for infinite elongated islands. Our experimental results, which are supported by energy calculations, confirm the LCM predictions for the first time in homoepitaxy. These results are explained by a size-dependent mesoscopic mismatch between the islands and the substrate.