Two-dimensional ordering is achieved in a single layer of self-assembled Ge islands fabricated by molecular beam epitaxy on vicinal Si(001) surfaces with regular ripples caused by step bunching. The ripples with a typical period of about 120 nm lead to the long-range lineup of the Ge islands along their directions, while the strong repulsive interaction between the dense Ge islands determines their relative arrangement on different step bunches of a ripple. The ordering pattern can be tuned by the Ge coverage and the direction of the ripples. The ordering also helps to improve the size homogeneity of the Ge islands.

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We present a method to interpret reciprocal-space maps recorded in grazing-incidence small-angle x-ray scattering geometry to obtain the shape and the lateral correlation properties of buried islands. From the maps, which have been recorded for various penetration depths, the autocorrelation function is calculated, from which the island parameters are obtained by comparison with simulations based on the distorted-wave Born approximation. As a demonstration of the sensitivity of the method, measurements on self-organized SiGe islands in a Si/SiGe multilayer have been performed. It was possible to detect different shapes of the islands at the sample surface and those embedded in the multilayer. For a comparison with atomic force microscopy, we employ the same method to analyze images of the islands at the top surface.

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