Low-loss GHz frequency phononic integrated circuits in Gallium Nitride for compact radio-frequency acoustic wave devices

Guiding and manipulating GHz frequency acoustic waves in $\mu$m-scale waveguides and resonators opens up new degrees of freedom to manipulate radio frequency (RF) signals in chip-scale platforms. A critical requirement for enabling high-performance devices is the demonstration of low acoustic dissipation in these highly confined geometries. In this work, we show that gallium nitride (GaN) on silicon carbide (SiC) supports low-loss acoustics by demonstrating acoustic microring resonators with frequency-quality factor ($fQ$) products approaching $4*10^{13}$ Hz at 3.4 GHz. The low dissipation measured exceeds the $fQ$ bound set by the simplified isotropic Akhiezer material damping limit of GaN. We use this low-loss acoustics platform to demonstrate spiral delay lines with on-chip RF delays exceeding 2.5 $\mu$s, corresponding to an equivalent electromagnetic delay of $\approx$ 750 m. Given GaN is a well-established semiconductor with high electron mobility, our work opens up the prospect of engineering traveling wave acoustoelectric interactions in $\mu$m-scale waveguide geometries, with associated implications for chip-scale RF signal processing.