How pit facet inclination drives heteroepitaxial island positioning on patterned substrates

We demonstrate the possibility of growing SiGe islands on patterned Si(001) substrates with pits having a continuous variation of the sidewall inclination angle α from α ∼ 4° to α ∼ 54°. Experiments show that the pit-inclination angle critically affects island positioning. While for shallow pits (pit-sidewall inclination angle α < ∼30°) islands are observed solely within the pits, at higher angles islands grow outside the pits. In particular a progressive (complete at α ∼ 54°) decoration of the pit rim by several islands is observed. We use elasticity theory to compare strain relaxation of a single island inside and outside the pit, as a function of α. The theoretical results show that there exists an elastic driving force for island positioning inside shallow enough pits, which reaches its maximum at α ∼ 20° and changes sign for α > 40°. At the same time, the calculations indicate a progressive relaxation of the wetting layer (WL) outside the pit with increasing α. The consistency between numerical results and experimental observations gives a clear indication on the important role played by the elastic relaxation in this system.