Capacitive Lamé Mode Resonators in $65\ \mu \mathrm{m}$-Thick Monocrystalline Silicon Carbide with Q-Factors Exceeding 20 Million

This paper reports on the implementation of a capacitive in-plane Lamé mode resonator in $65\ \mu \mathrm{m}$-thick monocrystalline 4H silicon carbide on insulator (SiCOI) with ultra-low dissipation. Boasting the highest $f\cdot Q$ in Lamé mode resonators to date, this work is a stepping stone toward realizing a myriad of high-performance instruments and sensors in monocrystalline SiC. In addition to providing chemical and environmental robustness, SiC exhibits extremely low levels of intrinsic dissipation, potentially enabling $f\cdot Q\mathrm{s}\ 30\times$ higher than those achievable in silicon (Si). However, attaining quantum-limited microresonators demands scrupulous processing and careful, deliberate design. With this in view, Lamé mode square resonators are excellent candidates to probe the fundamental phonon dissipation limits of SiC. Acoustically-engineered anchoring tethers composed of 1D phononic crystal (PnC) strips localize the acoustic vibration, limiting losses to the substrate. Electrostatically-transduced Lamé mode resonators are fabricated by deep reactive ion etching (DRIE) of fusion bonded SiCOI substrates, displaying a $Q$-factor of 20 Million (M) at 6.27 MHz with $f\cdot Q=1.25 \times 10^{14}$ Hz, over 4× above the Akhiezer limit set in (100) Si substrates. With further process optimization, these resonators can theoretically achieve $Q\mathrm{s}$ in excess of 100M at room temperature. Across the temperature range −45° to 85°C, the thermal coefficient of frequency (TCF) of on-axis 4H-SiC Lamé modes is −12 ppm/°C.