High-performance magnetostatic wave resonators through deep anisotropic etching of GGG substrates

Microscale resonators are fundamental and necessary building blocks for modern radio communication filters for mobile devices. The resonator's Q factor ($Q$) determines the insertion loss while coupling ($K_t^2$) governs the fractional bandwidth. The product $k_t^2 \times Q$ is widely recognized as the definitive figure of merit for microresonators. Magnetostatic wave resonators based on Yttrium Iron Garnet (YIG) are a promising technology platform for future communication filters. They have shown considerably better performance in terms of $Q$ when compared to the commercially successful acoustic resonators in the $>$7 GHz range. However, the coupling coefficients of these resonators have been limited to $<$3 %, primarily due to the restricted design space imposed by microfabrication challenges related to the patterning of gadolinium gallium garnet (GGG), the substrate material used for growing single crystal YIG. This paper reports novel resonator designs enabled by breakthrough bulk micromachining technology for anisotropic etching of GGG, leading to coupling >8 % in the 6-20 GHz frequency range. We use the same technology platform to show resonant enhancement of effective coupling, reaching up to 23 \% at 10.5 GHz. The frequency of resonant coupling can be tuned by design during the fabrication process. The resonant coupling results in an unprecedented $k_t^2 \times Q$ figure of merit of 191 at 10.5 GHz and 222 at 14.7 GHz. The technology platform presented in this paper supports both tunable filter architecture and switched filter banks that are currently being used in consumer mobile devices.