Design and Fabrication of Quasiperiodic and Periodic Structures via Phase Mask Interference Lithography

Abstract

Interference Lithography (IL) based techniques are attractive candidates for high thorough-put fabrication of complex 3-dimensional quasiperiodic and periodic sub-micron structures. Phase mask interference lithography reduces the experimental challenges of conventional IL by incorporating all optical elements into a single diffractive optical element. To date, the prediction of structures obtained from phase masks and the inverse problem of the design of the phase mask for a target structure are not completely solved problems, leaving gaps in rational design rules of phase masks. We offer a route to design, intuitively and effectively, several classes of simple and staggered 3D axial quasiperiodic structures as well as 3D periodic structures by considering the Fourier symmetries of the phase mask. We show that a generalized Fourier-based method allows us to predict and calculate the types of quasiperiodic 3D structures obtainable from 2D quasiperiodic phase masks, which possess high rotational symmetries (>6) incommensurate with conventional translational periodicity, and demonstrate that such a method allows for the controlled design and choice of topologically complex structural motifs into the desired structures. We then corroborate this structure prediction model with near-field scanning optical microscopy (NFSOM) measurements for transparent 2D quasiperiodic phase masks (90nm resolution). This is of particular importance for the fabrication of quasiperiodic structures because their Fourier structure is complex and very sensitive to fabrication conditions. A tandem theoretical design and NFSOM tool aids in identifying target candidate structures before fabrication, ensuring bi-continuity of the photoresist and air networks and other desired structural features. Moreover, this approach offers a more efficient selection process of masks for fabrication of complex quasiperiodic and periodic 3-D submicron structures for photonics, phononics and other applications requiring topologically complex structural motifs. Finally, we fabricate the corresponding 3D structures using phase mask based lithographic methods with pulsed lasers operating at 355nm, in SU-8 epoxy resin and show, with confocal microscopy the good agreement between the theoretically designed structures and the experimentally fabricated structures.