Self-organized ordering of Si1-xGexnanoscale islands studied by grazing incidence small-angle x-ray scattering

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Abstract
Highly regular islands of strained Si1-xGex have been grown on Si (001) by liquid phase epitaxy (LPE). The islands themselves are {111}-faceted truncated pyramids with a narrow base-width size distribution and coherent behaviour. In this study we report on the state of lateral ordering within a single layer of Si1-xGex islands. Grazing incidence small-angle x-ray scattering (GISAXS) was used to investigate the ordering as a function of island coverage. At very low island coverage the array behaves like a two-dimensional liquid exhibiting an increased number of island dimers which orient along the island base diagonal 100. On increasing the coverage these dimers develop into extended chains of islands oriented along 100. At high coverage there is strong ordering along both the 100 and the 110 directions. The self-organised ordering can be explained by two possible mechanisms: (i) that the observed ordering is driven by the anisotropy of the elastic constants where short-range order along the soft 100 directions is expected, and (ii) that there is an underlying two-dimensional ripple pattern in the wetting layer aligned along the 100 directions. At later stages of growth this pattern transforms into pseudomorphic islands.