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)


    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
    ISBN (Print)978-0-7803-7731-8
    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


    Conference12th International Conference on Solid State Sensors, Actuators and Microsystems, Transducers '03
    Abbreviated titleTransducers '03
    Country/TerritoryUnited States


    • nonlinear
    • phase noise
    • resonator
    • RF-mems


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