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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, f m T 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 α m, 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 α m ∝ T 1 to the high frequency Landau–Rumer scattering regime α m ∝ T 4, 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.

Identical GaN/AlN resonant tunneling diode structures were grown on free-standing bulk GaN at substrate temperatures of 760 °C, 810 °C, 860 °C, and 900 °C via plasma-assisted molecular beam epitaxy. Each sample displayed negative differential resistance (NDR) at room temperature. The figures-of-merit quantified were peak-to-valley current ratio (PVCR), yield of the device with room-temperature NDR, and peak current density (Jp). The figures-of-merit demonstrate an inverse relationship between PVCR/yield and Jp over this growth temperature series. X-ray diffraction and transmission electron microscopy were used to determine the growth rates, and layer thicknesses were used to explain the varying figures-of-merit. Due to the high yield of devices grown at 760 °C and 810 °C, the PVCR, peak voltage (Vp), and Jp were plotted vs device area, which demonstrated high uniformity and application tunability. Peak current densities of up to 1.01 MA/cm2 were observed for the sample grown at 900 °C. publishedVersion

We systematically demonstrate that one-dimensional phononic crystal (1-D PnC) tethers can significantly reduce tether loss in micromechanical resonators to a point where the total energy loss is dominated by intrinsic mechanisms, particularly phonon damping. Multiple silicon resonators are designed, fabricated, and tested to provide comparisons in terms of the number of periods in the PnC and the resonance frequency, as well as a comparison with conventional straight-beam tethers. The product of resonance frequency and measured quality factor (f×Q) is the critical figure of merit, as it is inversely related to the total energy dissipation in a resonator. For a wide range of frequencies, devices with PnC tethers consistently demonstrate higher f×Q values than the best conventional straight-beam tether designs. The f×Q product improves with increasing number of PnC periods, and at a maximum value of 1.2 × 1013 Hz, approaches limiting values set by intrinsic material loss mechanisms.