Shape transition in growth of strained islands: Spontaneous formation of quantum wires

Strained epitaxial layers tend initially to grow as dislocation-free islands. Here we show that such islands, as they increase in size, may undergo a shape transition. Below a critical size, islands have a compact, symmetric shape. But at larger sizes, they adopt a long thin shape, which allows better elastic relaxation of the island's stress. We have observed such elongated islands, with aspect ratios greater than 50:1, in low energy electron microscopy studies of growth of Ag on Si(001). These islands represent a novel approach to the fabrication of ``quantum wires.''