Manufacturing Tolerance Analysis, Fabrication, and Characterization of 3-D Submillimeter-Wave Electromagnetic-Bandgap Crystals

Abstract

The sensitivity of the characteristic band edge frequencies of three different 500-GHz electromagnetic-bandgap crystals to systematic variations in unit cell dimensions has been analyzed. The structures studied were square bar woodpiles made with dielectric having epsiv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ap12 and epsiv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> =37.5 and two wide bandgap epsiv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> =37.5 crystals designs proposed by Fan and Johnson and Joannopoulos. These epsiv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> values correspond to high-resistivity silicon and a zirconium-tin-titanate ceramic, respectively. For the woodpiles, the fractional frequency bandgap varied very little for dimensional deviations of up to plusmn5% from the optimum. The bandgaps of the Fan and Johnson and Joannopoulos structures were affected to a greater extent by dimensional variations, particular sensitivity being exhibited to the air-hole radius. For all crystals, the effect of increasing the amount of dielectric in the unit cell was to shift the bandgap edges to lower frequencies. Both silicon and ceramic woodpiles, along with a ceramic Fan structure, were fabricated and dimensionally characterized. Mechanical processing with a semiconductor dicing saw was used to form the woodpiles, while the Fan structure required both dicing and UV laser drilling of circular thru-holes. Good agreement with predicted normal incidence transmissions were found on the low-frequency side of the bandgap in all cases, but transmission values above the upper band edge were lower than expected in the ceramic structures