Theory of Directed Nucleation of Strained Islands on Patterned Substrates

We develop a theoretical model to elucidate the nucleation of strained islands on patterned substrates. We show that island nucleation is directed to the preferred sites by a much lower energy barrier and smaller critical size. Strain relaxation directs island nucleation to the bottom of a pit rather than the top of a ridge as commonly perceived, while large surface energy anisotropy favors nucleation at both places. The theory explains some puzzling experimental results and provides useful guidelines for future experiments.