Nonlinearities in single-crystal silicon micromechanical resonators

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

doi:10.1109/SENSOR.2003.1217080

Nonlinearities in single-crystal silicon micromechanical resonators

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

Helsinki University of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-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 E_m/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 language	English
Title of host publication	TRANSDUCERS 2003- The 12th International Conference on Solid-State Sensors, Actuators and Microsystems
Publisher	IEEE Institute of Electrical and Electronic Engineers
Pages	1574-1577
Volume	2
ISBN (Print)	978-0-7803-7731-8
DOIs	https://doi.org/10.1109/SENSOR.2003.1217080
Publication status	Published - 2003
MoE publication type	A4 Article in a conference publication
Event	12th International Conference on Solid State Sensors, Actuators and Microsystems, Transducers '03 - Boston, United States Duration: 8 Jun 2003 → 12 Jun 2003 Conference number: 12

Conference

Conference	12th International Conference on Solid State Sensors, Actuators and Microsystems, Transducers '03
Abbreviated title	Transducers '03
Country/Territory	United States
City	Boston
Period	8/06/03 → 12/06/03

Keywords

nonlinear
phase noise
resonator
RF-mems

Access to Document

10.1109/SENSOR.2003.1217080

Cite this

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

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title = "Nonlinearities in single-crystal silicon micromechanical resonators",

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.",

keywords = "nonlinear, phase noise, resonator, RF-mems",

author = "Ville Kaajakari and Tomi Mattila and Jyrki Kiiham{\"a}ki and Hannu Kattelus and Aarne Oja and Heikki Sepp{\"a}",

note = "Project code: T3SU00015; 12th International Conference on Solid State Sensors, Actuators and Microsystems, Transducers '03, Transducers '03 ; Conference date: 08-06-2003 Through 12-06-2003",

year = "2003",

doi = "10.1109/SENSOR.2003.1217080",

language = "English",

isbn = "978-0-7803-7731-8",

volume = "2",

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booktitle = "TRANSDUCERS 2003- The 12th International Conference on Solid-State Sensors, Actuators and Microsystems",

publisher = "IEEE Institute of Electrical and Electronic Engineers",

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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, IEEE Institute of Electrical and Electronic Engineers, pp. 1574-1577, 12th International Conference on Solid State Sensors, Actuators and Microsystems, Transducers '03, Boston, Massachusetts, United States, 8/06/03. https://doi.org/10.1109/SENSOR.2003.1217080

Nonlinearities in single-crystal silicon micromechanical resonators. / Kaajakari, Ville; Mattila, Tomi ; Kiihamäki, Jyrki et al.
TRANSDUCERS 2003- The 12th International Conference on Solid-State Sensors, Actuators and Microsystems. Vol. 2 IEEE Institute of Electrical and Electronic Engineers, 2003. p. 1574-1577.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Nonlinearities in single-crystal silicon micromechanical resonators

AU - Kaajakari, Ville

AU - Mattila, Tomi

AU - Kiihamäki, Jyrki

AU - Kattelus, Hannu

AU - Oja, Aarne

AU - Seppä, Heikki

N1 - Conference code: 12

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - nonlinear

KW - phase noise

KW - resonator

KW - RF-mems

U2 - 10.1109/SENSOR.2003.1217080

DO - 10.1109/SENSOR.2003.1217080

M3 - Conference article in proceedings

SN - 978-0-7803-7731-8

VL - 2

SP - 1574

EP - 1577

BT - TRANSDUCERS 2003- The 12th International Conference on Solid-State Sensors, Actuators and Microsystems

PB - IEEE Institute of Electrical and Electronic Engineers

T2 - 12th International Conference on Solid State Sensors, Actuators and Microsystems, Transducers '03

Y2 - 8 June 2003 through 12 June 2003

ER -

Nonlinearities in single-crystal silicon micromechanical resonators

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