发表机构
University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对AlScN-on-silicon谐振器，分离Q与f₀的压力响应，发现气体阻尼与频率平衡为不同状态，品质因数饱和不足以判定真空封装合格性，需额外约束表面介导频率老化。
AI 中文摘要
微纳机电谐振器的真空封装完整性通常通过品质因数Q评估，但Q探测的是残余气体阻尼，而非可能主导频率老化的表面态演化。本研究针对64.21 MHz Al₀.₇Sc₀.₃N-on-silicon横截面拉梅模式谐振器，在0.01至760 Torr范围内分离Q与谐振频率f₀的压力响应。在25℃及一阶热灵敏度被抑制的68.8℃频率周转点的测量显示，两者平衡时间尺度差异显著：每次压力阶跃后，Q在压力控制时间尺度内达到与历史无关的可逆稳态，且在约1 Torr以下趋近于拟合得到的压力无关上限8.5e4；而f₀的响应可低至1e-5 Torr，且仍与历史相关，在固定压力下弛豫数小时，其瞬态遵循拉伸指数动力学，与表面弛豫速率的宽分布一致，单个压力阶跃产生的频率偏移分数高达1.9 ppm。10小时锁相测量显示，在0.01至100 Torr范围内，短期时间偏差下限普遍接近1e-10 s，而长期平均时间内残余确定性弛豫占主导；在760 Torr时，气体阻尼通过降低Q劣化短期跟踪性能。这些结果确立了气体阻尼平衡与频率平衡为不同状态，因此仅品质因数饱和不足以判定精密机械频率参考的真空封装合格性，封装规格还必须约束表面介导的频率老化。
英文摘要
Vacuum package integrity in micro- and nanoelectromechanical resonators is commonly assessed through the quality factor Q, although Q probes residual-gas damping rather than the surface-state evolution that can govern frequency aging. Here, we disentangle the pressure responses of Q and the resonance frequency f0 in a 64.21 MHz Al0.7Sc0.3N-on-silicon cross-sectional Lamé-mode resonator between 0.01 to 760 Torr. Measurements at 25 °C and at the 68.8°C frequency turnover, where first-order thermal sensitivity is suppressed, reveal widely separated equilibration timescales. Following each pressure step, Q reaches a reversible, history-independent steady value on the pressure-control timescale and approaches a fitted pressure-independent ceiling of 8.5e4 below approximately 1 Torr. By contrast, f0 responds measurably down to 1e-5 Torr and remains history-dependent, relaxing for hours at fixed pressure. The transients follow stretched-exponential kinetics, consistent with a broad distribution of surface relaxation rates, and individual pressure steps produce fractional frequency shifts as large as 1.9 ppm. Ten-hour phase-locked measurements show a common short-term time-deviation floor near 1e-10 s from 0.01 to 100 Torr, whereas residual deterministic relaxation dominates at long averaging times; at 760 Torr, gas damping degrades short-term tracking through the reduced Q. These results establish gas-damping equilibrium and frequency equilibrium as distinct states. Quality-factor saturation alone is therefore insufficient to qualify vacuum packaging for precision mechanical frequency references; package specifications must also constrain surface-mediated frequency aging.
