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 alpha from alpha similar to 4 degrees to alpha similar to 54 degrees. Experiments show that the pit-inclination angle critically affects island positioning. While for shallow pits (pit-sidewall inclination angle alpha < similar to 30 degrees) islands are observed solely within the pits, at higher angles islands grow outside the pits. In particular a progressive (complete at alpha similar to 54 degrees) 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 alpha. The theoretical results show that there exists an elastic driving force for island positioning inside shallow enough pits, which reaches its maximum at alpha similar to 20 degrees and changes sign for alpha > 40 degrees. At the same time, the calculations indicate a progressive relaxation of the wetting layer (WL) outside the pit with increasing alpha. The consistency between numerical results and experimental observations gives a clear indication on the important role played by the elastic relaxation in this system.