Bending of nanoscale ultrathin substrates by growth of strained thin films and islands

Mechanical bending is ubiquitous in heteroepitaxial growth of thin films where the strained growing film applies effectively an "external" stress to bend the substrate. Conventionally, when the deposited film is much thinner than the substrate, the bending increases linearly with increasing film thickness following the classical Stoney formula. Here we analyze the bending of ultrathin (nanometer range) substrates induced by growth of coherently strained thin films. The behavior deviates dramatically from the classical linear dependence: when the film thickness becomes comparable to the substrate thickness the bending decreases with increasing film thickness. This complex bending behavior can be understood by considering evolution of strain sharing between the film and substrate. We demonstrate experimentally such counterintuitive bending of a nanoscale thin Si substrate induced by a coherently strained Ge film, in the form of islands, grown on silicon-on-insulator substrate. Larger dome islands, representing a thicker film, induce much less bending of the substrate than smaller hut islands, representing a thinner film, in direct contrast to their behavior on thick Si. We explain these observations by properly considering the island shape and strain relaxation within the island.