Concurrent Optimization of Diffraction Fields from Binary Phase Mask for Three-Dimensional Nanopatterning

Obtaining a high resolution of a three-dimensional (3D) nanostructure is crucial in nanoengineering. For proximity-field nanopatterning (PnP), a type of nanostructure fabrication with a continuous transfer of interference, the geometry of the phase mask primarily determines the resolution of a fabricated nanostructure by modulating the phase shift of coherent lights. Currently, phase masks for PnP are limited to the intuitive design focusing on reducing zeroth (0th) order efficiency with a single variable design. Herein, the concurrent optimization method, using particle swarm optimization, calculates the optimum phase mask with an improved figure of merit for maximizing the electric field intensity contrast. For the high-contrast 3D nanopatterning, we inversely designed the desired electric-field intensity map and calculated the required phase mask. The calculated optimum phase mask for PnP fabricates the hexagonal nanochannel array with high uniformity in lattice and pore shape owing to its selective intensity control. In contrast to the minimized zeroth diffraction design, which cannot modify the intensity in a specific region, the inverse design can selectively maximize or minimize the intensity in the target regions. This concurrent optimization using the inverse design method increases the degree of freedom for the nanostructure of PnP, and it can fabricate the proper nanostructure applicable to various fields such as energy devices, structural materials, and semiconductor devices.