<title>Mass-producible microtags for security applications: Tolerance analysis by rigorous coupled-wave analysis</title>

Abstract

We have developed a method for encoding phase and amplitude in microscopic computer-generated holograms (microtags) for security applications. An 8 X 8-cell phase-only and an 8 X 8-cell phase-and-amplitude microtag design have been fabricated in photoresist using the extreme-ultraviolet (13.4 nm) lithography tool developed at Sandia National Laboratories. Each microtag measures 80 by 160 microns and contains features 0.2 micrometers wide. Fraunhofer-zone diffraction patterns can be obtained from fabricated microtags without any intervening optics and compare very favorably with predicted diffraction patterns. In this paper, we present the results of a preliminary rigorous coupled-wave analysis of microtags. Microtags are modeled as sub-wavelength gratings of a trapezoidal profile. Only TE polarization is modeled. The analysis in this paper is concerned with the determination of optimal microtag design parameter values and tolerances on those parameters. The parameters are wall-slope angle, grating duty cycle, grating depth, and metal-coating thickness. Our findings indicate that diffraction-efficiency monotonically increases as the gratings are: (1) deepened and (2) coated with metal. Coating with metal achieves a more significant improvement and is easier to implement. The tolerance on the wall slope angle is very loose. The optimal grating duty cycle is between 0.5 and 0.6, depending on the presence of the metallic coating. The application of a protective coating on metal-coated microtags leads to an increase in diffraction efficiency and represents a practical configuration for these elements.