Surface-mediated frequency aging beyond quality-factor saturation in an AlScN-on-silicon resonator
Abstract
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.
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BibTeX
@misc{yousuf2026surfacemediated,
title = {{Surface-mediated frequency aging beyond quality-factor saturation in an AlScN-on-silicon resonator}},
author = {S M Enamul Hoque Yousuf and Mahmudul Hasan and Shruti Mishra and Sourav Mukherjee and Jinghan Gao and Roozbeh Tabrizian},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28959},
eprint = {2608.28959},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28959},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Surface-mediated frequency aging beyond quality-factor saturation in an AlScN-on-silicon resonator
AU - S M Enamul Hoque Yousuf
AU - Mahmudul Hasan
AU - Shruti Mishra
AU - Sourav Mukherjee
AU - Jinghan Gao
AU - Roozbeh Tabrizian
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.28959
UR - https://arxiv.org/abs/2608.28959
AB - 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.
ER -