Temperature evolution of frequency and anharmonic phonon loss for multi-mode epitaxial HBARs

Abstract

This Letter reports measured cryogenic temperature trends for over 300 longitudinal phonon modes spanning >10 GHz in an epitaxial GaN/NbN/SiC high overtone bulk acoustic resonator (epi-HBAR). We present temperature profiles from 7.2 K to 200 K for the mode frequency (f), the quality factor (Q), the figure of merit (f×Q), and the phonon loss or attenuation coefficient (α). We show that for all m phonon modes, fmT follows an identical parabolic trend, with a zero-slope turnover temperature of 35 K. Thus, the epi-HBAR comb spectrum can be considered an ensemble of modes with the same temperature dependencies, potentially enabling the design of precise multi-mode temperature-stable RF oscillators and clocks operating at GHz frequencies. Using temperature trends for (f×Q)m and αm, we provide strong evidence that the epi-HBARs are fundamentally limited by anharmonic phonon scattering in the materials that make up the epi-HBAR. Crucially, we unambiguously demonstrate the evolution of this anharmonic phonon scattering from the low frequency Akhiezer scattering regime αm∝T1 to the high frequency Landau–Rumer scattering regime αm∝T4, using hundreds of phonon modes in the same device. Finally, we show that at extremely low temperatures, other emergent loss mechanisms overshadow anharmonic phonon scattering. This finding motivates further investigation into the root causes of these limiting mechanisms for precision RF signal processing, quantum acoustodynamics, and other applications that require extremely low loss micromechanical devices.