Creating Two-Dimensional Quasicrystal, Supercell, and Moiré Lattices with Laser Interference Lithography: Implications for Photonic Bandgap Materials

We extend the patterning capability of laser interference lithography (LIL) to fabricate complex two-dimensional quasicrystal lattices, superlattices, and Moiré lattices. Traditional interference lithography is typically used to create single-pitch linear gratings or simple square or hexagonal patterns. In this work, we demonstrate how using multiple exposures at various defined orientations and with different interference pitch values results in a cumulative surface pattern that encompasses a diverse group of complex lattice structures. We demonstrate the fabrication of quasicrystal lattices of symmetry order ranging from 2-fold to 22-fold by repeated exposure of a one-dimensional interference pattern over multiple fixed sample rotation angles. More complex superlattice structures are prepared by overlapping two-dimensional lattices at controlled offset angles. Overlapping interference patterns with different pitch values and at different offsets are used to create various sophisticated incommensurate Moiré lattices. The increasing complexity of these surfaces is determined using a numerical algorithm to predict their structure. The structure and optical diffraction of these lattices were measured and compared to model results. This work extends the capabilities of LIL to provide access to a wide variety of complex nanostructures with tunable periodicity and controllable symmetry. We anticipate that these structures will prove useful in the fabrication of surfaces and devices based upon periodic two-dimensional nanostructures, including photonic bandgap materials with tunable band gaps, as platforms for plasmonic devices with complex engineered structures, as novel diffractive optical elements, and as templates for controlling the self-assembly and crystallization of colloidal crystals.