Nonlinear mechanical effects in silicon longitudinal mode beam resonators

Ville Kaajakari (Corresponding Author), Tomi Mattila, Antti Lipsanen, Aarne Oja

Research output: Contribution to journalArticleScientificpeer-review

82 Citations (Scopus)


The fundamental nonlinear mechanical effects in micromachined single-crystal silicon resonators are investigated. Longitudinal mode beam resonators are chosen for the analysis due to their simple geometry and high quality factor (Q > 100 000). Analytical model for the resonator is developed in terms of nonlinear engineering Young’s modulus that incorporates both geometrical and material effects. For comparison with the theory, beam resonators were fabricated in two different crystalline directions. The measured nonlinearity is larger for beams in [1 1 0] direction than for beams in [1 0 0] direction in agreement with the theoretical prediction. The results provide a quantitative value for the appearance of the material-induced nonlinear effects in single-crystal silicon microresonators.
Original languageEnglish
Pages (from-to)64 - 70
Number of pages7
JournalSensors and Actuators A: Physical
Issue number1
Publication statusPublished - 2005
MoE publication typeA1 Journal article-refereed


  • bulk acoustic wave devices
  • hysteresis
  • nonlinearities
  • microresonators
  • nonlinear oscillators
  • micromechanical oscillators
  • microelectromechanical resonators
  • resonators

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