DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Direct Detection of Akhiezer Damping in a Silicon MEMS Resonator

Abstract

Abstract Silicon Microelectromechanical Systems (MEMS) resonators have broad commercial applications for timing and inertial sensing. However, the performance of MEMS resonators is constrained by dissipation mechanisms, some of which are easily detected and well-understood, but some of which have never been directly observed. In this work, we present measurements of the quality factor, Q , for a family of single crystal silicon Lamé-mode resonators as a function of temperature, from 80–300  K . By comparing these Q measurements on resonators with variations in design, dimensions, and anchors, we have been able to show that gas damping, thermoelastic dissipation, and anchor damping are not significant dissipation mechanisms for these resonators. The measured f  ·  Q product for these devices approaches 2 × 10 13 , which is consistent with the expected range for Akhiezer damping, and the dependence of Q on temperature and geometry is consistent with expectations for Akhiezer damping. These results thus provide the first clear, direct detection of Akhiezer dissipation in a MEMS resonator, which is widely considered to be the ultimate limit to Q in silicon MEMS devices.

Authors:
; ; ; ; ; ; ;
Publication Date:
Research Org.:
SLAC National Accelerator Lab. (SLAC), Menlo Park, CA (United States)
Sponsoring Org.:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1619492
Alternate Identifier(s):
OSTI ID: 1506233
Grant/Contract Number:  
AC02-76SF00515; N66001-16-1-4023
Resource Type:
Published Article
Journal Name:
Scientific Reports
Additional Journal Information:
Journal Name: Scientific Reports Journal Volume: 9 Journal Issue: 1; Journal ID: ISSN 2045-2322
Publisher:
Nature Publishing Group
Country of Publication:
United Kingdom
Language:
English
Subject:
36 MATERIALS SCIENCE; 47 OTHER INSTRUMENTATION

Citation Formats

Rodriguez, Janna, Chandorkar, Saurabh A., Watson, Christopher A., Glaze, Grant M., Ahn, C. H., Ng, Eldwin J., Yang, Yushi, and Kenny, Thomas W. Direct Detection of Akhiezer Damping in a Silicon MEMS Resonator. United Kingdom: N. p., 2019. Web. doi:10.1038/s41598-019-38847-6.
Rodriguez, Janna, Chandorkar, Saurabh A., Watson, Christopher A., Glaze, Grant M., Ahn, C. H., Ng, Eldwin J., Yang, Yushi, & Kenny, Thomas W. Direct Detection of Akhiezer Damping in a Silicon MEMS Resonator. United Kingdom. https://doi.org/10.1038/s41598-019-38847-6
Rodriguez, Janna, Chandorkar, Saurabh A., Watson, Christopher A., Glaze, Grant M., Ahn, C. H., Ng, Eldwin J., Yang, Yushi, and Kenny, Thomas W. Tue . "Direct Detection of Akhiezer Damping in a Silicon MEMS Resonator". United Kingdom. https://doi.org/10.1038/s41598-019-38847-6.
@article{osti_1619492,
title = {Direct Detection of Akhiezer Damping in a Silicon MEMS Resonator},
author = {Rodriguez, Janna and Chandorkar, Saurabh A. and Watson, Christopher A. and Glaze, Grant M. and Ahn, C. H. and Ng, Eldwin J. and Yang, Yushi and Kenny, Thomas W.},
abstractNote = {Abstract Silicon Microelectromechanical Systems (MEMS) resonators have broad commercial applications for timing and inertial sensing. However, the performance of MEMS resonators is constrained by dissipation mechanisms, some of which are easily detected and well-understood, but some of which have never been directly observed. In this work, we present measurements of the quality factor, Q , for a family of single crystal silicon Lamé-mode resonators as a function of temperature, from 80–300  K . By comparing these Q measurements on resonators with variations in design, dimensions, and anchors, we have been able to show that gas damping, thermoelastic dissipation, and anchor damping are not significant dissipation mechanisms for these resonators. The measured f  ·  Q product for these devices approaches 2 × 10 13 , which is consistent with the expected range for Akhiezer damping, and the dependence of Q on temperature and geometry is consistent with expectations for Akhiezer damping. These results thus provide the first clear, direct detection of Akhiezer dissipation in a MEMS resonator, which is widely considered to be the ultimate limit to Q in silicon MEMS devices.},
doi = {10.1038/s41598-019-38847-6},
journal = {Scientific Reports},
number = 1,
volume = 9,
place = {United Kingdom},
year = {Tue Feb 19 00:00:00 EST 2019},
month = {Tue Feb 19 00:00:00 EST 2019}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1038/s41598-019-38847-6

Citation Metrics:
Cited by: 36 works
Citation information provided by
Web of Science

Figures / Tables:

Figure 1 Figure 1: SEM image of an encapsulated Lamé-mode resonator after partial breakage of the die; this image shows the top encapsulation layer, the electrode and device layer, and the thick substrate underneath.

Save / Share:

Works referenced in this record:

An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations
journal, December 2003

  • Hao, Zhili; Erbil, Ahmet; Ayazi, Farrokh
  • Sensors and Actuators A: Physical, Vol. 109, Issue 1-2
  • DOI: 10.1016/j.sna.2003.09.037

Thermal expansion coefficient of single-crystal silicon from 7 K to 293 K
journal, November 2015


Effect of etch holes on quality factor of bulk-mode micromechanical resonators
journal, January 2008


Attachment losses of high Q oscillators
journal, July 2004

  • Photiadis, Douglas M.; Judge, John A.
  • Applied Physics Letters, Vol. 85, Issue 3
  • DOI: 10.1063/1.1773928

Internal Friction in Solids II. General Theory of Thermoelastic Internal Friction
journal, January 1938


MEMS technology for timing and frequency control
journal, January 2007

  • Nguyen, Clark
  • IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 54, Issue 2, p. 251-270
  • DOI: 10.1109/TUFFC.2007.240

Quality factors in micron- and submicron-thick cantilevers
journal, March 2000

  • Yasumura, K. Y.; Stowe, T. D.; Chow, E. M.
  • Journal of Microelectromechanical Systems, Vol. 9, Issue 1
  • DOI: 10.1109/84.825786

Support loss in the radial bulk-mode vibrations of center-supported micromechanical disk resonators
journal, March 2007


Wide-range temperature dependence studies for devices limited by thermoelastic dissipation and anchor damping
conference, June 2017

  • Rodriguez, J.; Gerrard, D. D.; Chandorkar, S.
  • 2017 19th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS)
  • DOI: 10.1109/TRANSDUCERS.2017.7994244

Internal Friction in Solids. I. Theory of Internal Friction in Reeds
journal, August 1937


Temperature dependence of acoustic attenuation in silicon
journal, June 1995


Anchor Loss in Hemispherical Shell Resonators
journal, February 2017

  • Darvishian, Ali; Shiari, Behrouz; Cho, Jae Yoong
  • Journal of Microelectromechanical Systems, Vol. 26, Issue 1
  • DOI: 10.1109/JMEMS.2016.2636080

High Q diamond hemispherical resonators: fabrication and energy loss mechanisms
journal, July 2015

  • Bernstein, Jonathan J.; Bancu, Mirela G.; Bauer, Joseph M.
  • Journal of Micromechanics and Microengineering, Vol. 25, Issue 8
  • DOI: 10.1088/0960-1317/25/8/085006

Piezoresistive Readout Mechanically Coupled Lamé Mode SOI Resonator With $Q$ of a Million
journal, August 2015

  • Zhu, Haoshen; Xu, Yuanjie; Lee, Joshua E-Y
  • Journal of Microelectromechanical Systems, Vol. 24, Issue 4
  • DOI: 10.1109/JMEMS.2015.2414441

Effect of phonon interactions on limiting the f.Q product of micromechanical resonators
conference, June 2009

  • Tabrizian, R.; Rais-Zadeh, M.; Ayazi, F.
  • TRANSDUCERS 2009 - 2009 International Solid-State Sensors, Actuators and Microsystems Conference
  • DOI: 10.1109/SENSOR.2009.5285627

Limits of quality factor in bulk-mode micromechanical resonators
conference, January 2008

  • Chandorkar, S. A.; Agarwal, M.; Melamud, R.
  • 2008 IEEE 21st International Conference on Micro Electro Mechanical Systems
  • DOI: 10.1109/MEMSYS.2008.4443596

Thermal energy loss mechanisms in micro- to nano-scale devices
conference, May 2011

  • Duwel, A. E.; Lozow, Jeff; Fisher, Christopher J.
  • SPIE Defense, Security, and Sensing, SPIE Proceedings
  • DOI: 10.1117/12.885130

Elastic PMLs for resonator anchor loss simulation
journal, January 2005

  • Bindel, David S.; Govindjee, Sanjay
  • International Journal for Numerical Methods in Engineering, Vol. 64, Issue 6
  • DOI: 10.1002/nme.1394

Working equations for piezoelectric actuators and sensors
journal, January 1999

  • Weinberg, M. S.
  • Journal of Microelectromechanical Systems, Vol. 8, Issue 4
  • DOI: 10.1109/84.809069

Approaching the intrinsic quality factor limit for micromechanical bulk acoustic resonators using phononic crystal tethers
journal, July 2017

  • Gokhale, Vikrant J.; Gorman, Jason J.
  • Applied Physics Letters, Vol. 111, Issue 1
  • DOI: 10.1063/1.4990960

Temperature Dependence of the Elastic Constants of Doped Silicon
journal, June 2015

  • Ng, Eldwin J.; Hong, Vu A.; Yang, Yushi
  • Journal of Microelectromechanical Systems, Vol. 24, Issue 3
  • DOI: 10.1109/JMEMS.2014.2347205

Temperature Dependence of Quality Factor in MEMS Resonators
journal, June 2008

  • Kim, Bongsang; Hopcroft, Matthew A.; Candler, Rob N.
  • Journal of Microelectromechanical Systems, Vol. 17, Issue 3
  • DOI: 10.1109/JMEMS.2008.924253

Evidence of Surface Loss as Ubiquitous Limiting Damping Mechanism in SiN Micro- and Nanomechanical Resonators
journal, November 2014


A HARPSS polysilicon vibrating ring gyroscope
journal, June 2001

  • Ayazi, F.; Najafi, K.
  • Journal of Microelectromechanical Systems, Vol. 10, Issue 2
  • DOI: 10.1109/84.925732

Bulk and Surface Thermoelastic Dissipation in Micro-Hemispherical Shell Resonators
journal, April 2015

  • Sorenson, Logan; Shao, Peng; Ayazi, Farrokh
  • Journal of Microelectromechanical Systems, Vol. 24, Issue 2
  • DOI: 10.1109/JMEMS.2014.2333528

The effect of release-etch holes on the electromechanical behaviour of MEMS structures
conference, January 1997

  • Rabinovich, V. L.; Gupta, R. K.; Senturia, S. D.
  • Proceedings of International Solid State Sensors and Actuators Conference (Transducers '97)
  • DOI: 10.1109/SENSOR.1997.635400

Study on thermoelastic dissipation in bulk mode resonators with etch holes
conference, March 2012

  • Tu, Cheng; Lee, Joshua E-Y
  • 2012 7th IEEE International Conference on Nano/Micro Engineered and Molecular Systems (NEMS)
  • DOI: 10.1109/NEMS.2012.6196821

Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators
journal, November 2013

  • Ghaffari, Shirin; Chandorkar, Saurabh A.; Wang, Shasha
  • Scientific Reports, Vol. 3, Issue 1
  • DOI: 10.1038/srep03244

A Unified Epi-Seal Process for Fabrication of High-Stability Microelectromechanical Devices
journal, June 2016

  • Yang, Yushi; Ng, Eldwin J.; Chen, Yunhan
  • Journal of Microelectromechanical Systems, Vol. 25, Issue 3
  • DOI: 10.1109/JMEMS.2016.2537829

Characterization of MEMS Resonator Nonlinearities Using the Ringdown Response
journal, April 2016

  • Polunin, Pavel M.; Yang, Yushi; Dykman, Mark I.
  • Journal of Microelectromechanical Systems, Vol. 25, Issue 2
  • DOI: 10.1109/JMEMS.2016.2529296

Mode- and Direction-Dependent Mechanical Energy Dissipation in Single-Crystal Resonators due to Anharmonic Phonon-Phonon Scattering
journal, March 2016


Direct Detection of Anchor Damping in MEMS Tuning Fork Resonators
journal, October 2018

  • Rodriguez, Janna; Chandorkar, Saurabh Arun; Glaze, Grant M.
  • Journal of Microelectromechanical Systems, Vol. 27, Issue 5
  • DOI: 10.1109/JMEMS.2018.2859958

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.