Abstract
Thermoelastic damping is one of the dominant mechanisms of structural damping in vacuum-operated microresonators. A three dimensional numerical model based on the finite element method is used for simulating thermoelastic damping in clamped–clamped microelectromechanical beam resonators. In this regards, both simple and slotted beam are considered. To understand the effect of slot positions and sizes on the resonator performance, resonant frequency and thermoelastic quality factor are calculated for both simple and slotted beams for a wide range of beam length from 10 to 400 µm. Punching slots in the resonator beam reduces the stiffness and mass of the beam which affect the resonant frequency. In addition thermo-mechanical coupling mechanisms of the resonator are affected by the slots which improve the thermoelastic quality factor. For most of the beam lengths, it is shown that the slots at the beam-anchor interface region, where the strain is high, are more effectively enhanced the thermoelastic quality factor than one at the centre of the beam region. However, the highest resonance frequency is achieved with the slots at the center region.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abdelsalam M, Wahba M, Abdelmoneum M, Duarte D, Ismail Y (2010) Supporting circuitry for a fully integrated micro electro mechanical (MEMS) oscillator in 45 nm CMOS Technology. In: Proceedings of IEEE international conference on VLSI system on chip, pp 259–236. doi:10.1109/VLSISOC.2010.5642670
Bannon FD, Clark JR, Nguyen CT-C (2000) High-Q HF microelectromechanical filters. IEEE J Solid-State Circuits 35:512–526. doi:10.1109/4.839911
Candler RN, Duwel A, Varghese M, Chandorkar SA, Hopcroft MA, Park W-T, Kim B, Yama G, Partridge A, Lutz M, Kenny TW (2006) Impact of geometry on thermoelastic dissipation in micromechanical resonant Beams. J Micro-electromech Syst 15:927–934. doi:10.1109/JMEMS.2006.879374
Dragoi V, Pabo E, Burggraf J, Mittendorfer G (2012) CMOS: compatible wafer bonding for MEMS and wafer-level 3D integration. Microsyst Technol 18:1065–1075. doi:10.1007/s00542-012-1439-7
Duwel A, Candler RN, Kenny TW, Varghese M (2006) Engineering MEMS resonators with low thermoelastic damping. J Micro-electromech Syst 16:1437–1445. doi:10.1109/JMEMS.2006.883573
Hao Z, Erbil A, Ayazi F (2003) An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations. Sens Actuators A 109:156–164. doi:10.1016/j.sna.2003.09.037
Lifshitz R, Roukes ML (2000) Thermoelastic damping in micro and nanomechanical systems. Phys Rev B: Condens Matter 61:5600–5609. doi:10.1103/PhysRevB.61.5600
Lin Y-W, Lee S, Li S-S, Xie Y, Ren Z, Nguyen CTC (2004) Series-resonant VHF micromechanical resonator reference oscillators. IEEE J Solid-State Circuits 39:2477–2491. doi:10.1109/JSSC.2004.837086
Lopez JL, Verd J, Uranga A, Giner J, Murillo G, Torres F, Abadal G, Barniol N (2009) A CMOS–MEMS RF-tunable bandpass filter based on two high-Q 22-MHz polysilicon clamped-clamped beam resonators. IEEE Electron Device Lett 30:718–720. doi:10.1109/LED.2009.2022509
Muniraj NJR (2011) MEMS based humidity sensor using Si cantilever beam for harsh environmental conditions. Microsyst Technol 17:27–29. doi:10.1007/s00542-010-1174-x
Nguyen CTC (2007) MEMS technology for timing and frequency control. IEEE Trans Ultrason Ferroelectr Freq Control 54:251–270. doi:10.1109/TUFFC.2007.240
Prabhakar S, Vengallatore S (2008) Theory of thermoelastic damping in micromechanical resonators with two-dimensional heat conduction. J Micro-electromech Syst 17:494–502. doi:10.1109/JMEMS.2008.916316
Roszhart TV (1990) The effect of thermoelastic internal friction on the Q of micromachined silicon resonators. In: Proceedings of solid-state sensor and actuator workshop technical digest, pp 13–16. doi:10.1109/SOLSEN.1990.109810
Shi H, Fan S, Xing W, Li C, Sun J, Jing Z (2013) Design and FEM simulation study of the electro-thermal excitation resonant beam with slit-structure. Microsyst Tech 19:979–987. doi:10.1007/s00542-012-1682-y
Younis ML (2011) MEMS linear and nonlinear statics and dynamics. Springer, New York
Zener C (1937) Internal friction in solids I: theory of internal friction in reeds. Phys Rev 52:230–235. doi:10.1103/PhysRev.52.230
Zener C (1938) Internal friction in solids II: general theory of thermoelastic internal friction. Phys Rev 53:90–99. doi:10.1103/PhysRev.53.90
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Asadi, S., Sheikholeslami, T.F. Effects of slots on thermoelastic quality factor of a vertical beam MEMS resonator. Microsyst Technol 22, 2723–2730 (2016). https://doi.org/10.1007/s00542-015-2652-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00542-015-2652-y