Distortion analysis of crystalline and locally quasicrystalline 2D photonic structures with grazing-incidence small-angle X-ray scattering

In this study, grazing-incidence small-angle X-ray scattering (GISAXS) is used to collect statistical information on dimensional parameters in an area of 20 x 15 mm on photonic structures produced by nanoimprint lithography. The photonic structures are composed of crystalline and locally quasicrystalline two-dimensional patterns with structure sizes between about 100 nm and 10 mu m to enable broadband visible light absorption for use in solar-energy harvesting. These first GISAXS measurements on locally quasicrystalline samples demonstrate that GISAXS is capable of showing the locally quasicrystalline nature of the samples while at the same time revealing the long-range periodicity introduced by the lattice design. The scattering is described qualitatively in the framework of the distorted-wave Born approximation using a hierarchical model mirroring the sample design, which consists of a rectangular and locally quasicrystalline supercell that is repeated periodically to fill the whole surface. The nanoimprinted samples are compared with a sample manufactured using electron-beam lithography and the distortions of the periodic and locally quasiperiodic samples are quantified statistically. Owing to the high sensitivity of GISAXS to deviations from the perfect lattice, the misalignment of the crystallographic axes was measured with a resolution of 0.015 degrees, showing distortions of up to +/- 0.15 degrees in the investigated samples.