How pit facet inclination drives heteroepitaxial island positioning on patterned substrates

Abstract

We demonstrate the possibility of growing SiGe islands on patterned Si(001) substrates with pits having a continuous variation of the sidewall inclination angle \ensuremath{\alpha} from \ensuremath{\alpha} \ensuremath{\sim} 4\ifmmode^\circ\else\textdegree\fi{} to \ensuremath{\alpha} \ensuremath{\sim} 54\ifmmode^\circ\else\textdegree\fi{}. Experiments show that the pit-inclination angle critically affects island positioning. While for shallow pits (pit-sidewall inclination angle \ensuremath{\alpha} \ensuremath{\sim}30\ifmmode^\circ\else\textdegree\fi{}) islands are observed solely within the pits, at higher angles islands grow outside the pits. In particular a progressive (complete at \ensuremath{\alpha} \ensuremath{\sim} 54\ifmmode^\circ\else\textdegree\fi{}) 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 \ensuremath{\alpha}. The theoretical results show that there exists an elastic driving force for island positioning inside shallow enough pits, which reaches its maximum at \ensuremath{\alpha} \ensuremath{\sim} 20\ifmmode^\circ\else\textdegree\fi{} and changes sign for \ensuremath{\alpha} > 40\ifmmode^\circ\else\textdegree\fi{}. At the same time, the calculations indicate a progressive relaxation of the wetting layer (WL) outside the pit with increasing \ensuremath{\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.