[23p-D316-1~17] 13.6 Nanostructures, quantum phenomena, and nano quantum devices

[23p-D316-3] Strong internal mode coupling effect in doubly clamped MEMS beam resonators through the fifth order Duffing nonlinearity

〇(D)Tianye Niu¹, Boqi Qiu¹, Naomi Nagai¹, Ya Zhang³, Kazuhiko Hirakawa^1,2 (1.IIS, Univ. of Tokyo, 2.INQIE, Univ. of Tokyo, 3.TUAT)

Keywords:MEMS technology, mode coupling, nonlinearity

Microelectromechanical (MEMS) beam resonators are very attractive for sensing applications owing to their intrinsic high sensitives. So far, there have been several studies on the internal mode coupling effect in MEMS resonators through the Duffing nonlinearity. However, most of the previous works studied only the 1:3 mode coupling, where internal mode coupling occurs when the frequency of the fundamental mode matches 1/3 of the frequency of the torsional mode due to cubic Duffing nonlinearity. In this study, we observed an internal mode coupling effect occurring between the first bending mode and the third bending mode through the fifth order Duffing nonlinearity in doubly-clamped MEMS resonators. The results show that the bending-bending mode coupling through fifth Duffing nonlinearity is much stronger than the bending-torsional mode coupling through cubic Duffing nonlinearity. In the resonance spectrum, the first bending mode is below 1/5 of the third bending mode, and one third of the first torsional mode. By increasing the driving voltage Vd, the resonance frequency f1 shifts to a higher frequency due to the hardening effect in a Duffing oscillator. When Vd is larger than 800 mV, the phase spectra show plateaus at 210 kHz, because of the bending-bending mode coupling. By keeping increasing Vd up to 1600 mV, the phase curves jump to another plateau at 225 kHz due to the bending-torsional mode coupling. In the mode coupling region (Vd > 750 mV) resonance frequencies do not increase along with Vd. The fifth harmonic mode is excited and its amplitude shows a significant increase for Vd > 750 mV in the bending-bending mode coupling region. However, in the bending-torsional mode coupling region (Vd > 1600 mV), the third harmonic mode is excited, but shows much smaller amplitudes. The results show that the bending-bending mode coupling through fifth Duffing nonlinearity is much stronger than the bending-torsional coupling due to the difference in the mode shape.