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.

X–Ka Band Epitaxial ScAlN/AlN/NbN/SiC High-Overtone Bulk Acoustic Resonators

“…The temperature trend for representative mode frequencies (Fig. 6) exhibits a parabolic trend with an extracted turnover temperature of 40 K. The non-linear temperature trends for f×Q and mode frequencies are consistent with prior work on SiC epi-HBARs [19].…”

“…3(a) are baseline-corrected and normalized for comparison, using standard MATLAB functions. As expected, the epi-HBAR has a stronger response at lower temperatures, because of the decreased propagation losses [18], [19]. The data in Fig.…”

“…5) are also extracted for all acoustic modes [21]. As expected, best extracted data lie within the transducer envelopes [19]. We believe that the noisy f×Q values (> 30 GHz) are a result of the weak signal and un-optimized electrical impedance matching.…”

“…The f×Q increases inversely with temperature, up to a point near 150 K, but saturates at > 10 14 Hz for all modes (Fig. 5), indicating that loss is not limited by frequency-and temperature-dependent anharmonic phonon scattering [18], [19]. The low temperature loss might be a result of diffraction losses [22], interface scattering [23], or another temperature independent loss mechanism.…”

Investigation of support transducer enabled higher-order radial bulk mode MEMS resonator and low phase noise oscillator

“…The inset in figure 8 shows the quality factor variation trend of the resonator with temperature sweep. Similar nature of frequency drift and the existence of a turnover point have been observed in [33][34][35][36]. As reported in [37][38][39], the resonant tank behaviour with temperature sweep is dependent on the doping concentration of the silicon being used.…”