Silicon nanowire polytypes: identification by Raman spectroscopy, generation mechanism, and misfit strain in homostructures.

Silicon nanowires with predominant 9R, 27T, 2H and other polytype structures with respective hexagonalities of 50, 40 and 35.3% were identified by Raman microscopy. Transmission electron microscopy indicates that intrinsic stacking faults form the basic building blocks of these polytypes. We propose a generation mechanism in which polytypes are seeded from incoherent twin boundaries and associated partial dislocations. This mechanism explains observed prevalence of polytypes and trends in stacking for longer period structures. The percentage of hexagonal planes in a polytype is extracted from its Raman spectrum after correcting the zone-folded phonon frequencies to account for changes of the in-plane lattice parameter with respect to diamond cubic (3C) Si. The correction is found to be (i) of the same order of magnitude as frequency differences between modes of low period polytypes and (ii) proportional to the hexagonality. Corrected phonon frequencies agree with experimentally found values to within 0.4 cm(-1). Homostructures in which a central polytype region is bounded by 3C regions, with the planes (111)(3C)║(0001)(polytype) parallel to the nanowire axis, are found in 112 oriented nanowires. Strain-induced shifts of the Raman modes in such structures enable a rough estimation of the lattice misfit between polytypes, which compares favorably with first-principles calculations. Considerations presented here provide a simple and quantitative framework to interpret Raman frequencies and extract crystallographic information on polytype structures.