Long-range periodicity and disorder in two-dimensional arrays of metallic dots studied by x-ray diffraction

High-resolution x-ray diffraction was employed to investigate the ordering of Au dots grown on silicon substrates using molecular-beam epitaxy and electron-beam lithography. A mapping near the origin of the reciprocal space yielded that the mean distances between the next neighbors in two mutually perpendicular directions are 2μm as intended in the deposition process. The reciprocal space mapping also confirmed the rectangular shape of the dots. In a further step, the samples were rotated in their plane to turn the trace of the diffraction plane into a general direction regarding the direction of the dots. This rotation created an artificial modulation, i.e., an additional long-range periodicity, which was exploited to study the ordering of dots in submillimeter scale. Diffraction phenomena observed near the origin of the reciprocal space are concurrently explained using the kinematic diffraction theory and the crystallographic representation.