Nonlinearities in single-crystal silicon micromechanical resonators

Ville Kaajakari, Tomi Mattila, Jyrki Kiihamäki, Hannu Kattelus, Aarne Oja, Heikki Seppä

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

19 Citations (Scopus)

Abstract

The fundamental performance limit of single-crystal silicon resonators set by device nonlinearities is characterized. Using Leeson's model for near carrier phase noise, the nonlinearity is shown to set the scaling limit in miniaturizing oscillators. A circuit model based on discretization of distributed mass and nonlinear elasticity is introduced to accurately simulate the large amplitude vibrations. Based on published data for the third-order silicon stiffness tensor, the fundamental material nonlinearity limit is estimated. This theoretical limit is compared to measured nonlinearities in bulk acoustic wave (BAW) micromechanical resonators. The material set and measured nonlinearities are of same order-of-magnitude showing that the maximum vibration amplitude of studied BAW microresonators is near the fundamental limit. The maximum strain for single-crystal silicon resonators set by hysteresis limit is estimated to be 2·10-3 (fracture limit 10-2), which corresponds to the maximum energy density of Em/V=3·105 J/m3. This value is at least two orders-of-magnitude higher than for shear-mode quartz resonators, which partially compensates for the small size of MEMS components.
Original languageEnglish
Title of host publicationTRANSDUCERS 2003- The 12th International Conference on Solid-State Sensors, Actuators and Microsystems
PublisherIEEE Institute of Electrical and Electronic Engineers
Pages1574-1577
Volume2
ISBN (Print)0-7803-7731-1
DOIs
Publication statusPublished - 2003
MoE publication typeA4 Article in a conference publication
Event12th International Conference on Solid State Sensors, Actuators and Microsystems, Transducers '03 - Boston, United States
Duration: 8 Jun 200312 Jun 2003
Conference number: 12

Conference

Conference12th International Conference on Solid State Sensors, Actuators and Microsystems, Transducers '03
Abbreviated titleTransducers '03
CountryUnited States
CityBoston
Period8/06/0312/06/03

Keywords

  • nonlinear
  • phase noise
  • resonator
  • RF-mems

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    Kaajakari, V., Mattila, T., Kiihamäki, J., Kattelus, H., Oja, A., & Seppä, H. (2003). Nonlinearities in single-crystal silicon micromechanical resonators. In TRANSDUCERS 2003- The 12th International Conference on Solid-State Sensors, Actuators and Microsystems (Vol. 2, pp. 1574-1577). IEEE Institute of Electrical and Electronic Engineers. https://doi.org/10.1109/SENSOR.2003.1217080