Skip to main content
SpringerLink
Log in

Modeling and analysis of MEMS disk resonators

  • Technical Paper
  • Published:
Microsystem Technologies Aims and scope Submit manuscript

Abstract

In this work a very accurate process for modeling a microdisk resonator is presented and the dynamic behavior of the resonator is investigated. Using the minimization of the Hamiltonian, the governing equation of the motion is derived. The periodic solutions in the vicinity of primary resonance are determined by means of shooting method and their stability is investigated by determining the so-called Floquet exponents of the perturbed motions. To obtain a very accurate model, the influences of intermolecular forces such as van der Waals and Casimir is included in the modeling process. The effect of the design parameters on the dynamic responses is discussed. The results indicate that, high quality factor in the ultra-high frequency (UHF), weak nonlinearity, low actuation voltage and very high pull-in voltage, make these polydiamond disk resonators the most likely leaders in the next-generation micromechanical RF filters and channelizers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  • Akgul M (2014) A micromechanical RF channelizer. University of California, Berkeley

    Google Scholar 

  • Akgul M, Schneider R, Ren Z, Chandler G, Yeh V, Nguyen CTC (2011) Hot filament CVD conductive microcrystalline diamond for high Q, high acoustic velocity micromechanical resonators. In: Frequency control and the european frequency and time forum (FCS), 2011 joint conference of the IEEE international, pp 1–6

  • Ale Ali N, Mohammadi AK (2015) Effect of thermoelastic damping in nonlinear beam model of MEMS resonators by differential quadrature method. J Appl Comput Mech 1:112–121

    Google Scholar 

  • An S, Gupta NK, Gianchandani YB (2014) A Si-micromachined 162-stage two-part Knudsen pump for on-chip vacuum. J Microelectromech Syst 23:406–416

    Article  Google Scholar 

  • Antkowiak B, Gorman J, Varghese M, Carter D, Duwel A (2003) Design of a high-Q, low-impedance, GHz-range piezoelectric MEMS resonator. In: TRANSDUCERS, Solid-State Sens Actuators Microsyst, 12th international conference, pp 841–846

  • Bannon FD, Clark JR, Nguyen CTC (2000) High-Q HF microelectromechanical filters. IEEE J Solid State Circuits 35:512–526

    Article  Google Scholar 

  • Bergström L (1997) Hamaker constants of inorganic materials. Adv Coll Interface Sci 70:125–169

    Article  Google Scholar 

  • Campbell C (1998) Surface acoustic wave devices for mobile and wireless communications. Academic Press, Dublin

    Google Scholar 

  • Chaudhuri RR, Bhattacharyya TK (2013) Electroplated nickel based micro-machined disk resonators for high frequency applications. Microsyst Technol 19:525–535

    Article  Google Scholar 

  • Chorsi MT, Azizi S, Bakhtiari-Nejad F (2015) Application of quadratic controller to control the pull-in instability of a micro-resonator. Int J Mech Mater Des 11:111–123

    Article  Google Scholar 

  • Chorsi HT, Chorsi MT, Zhang XJ (2016) Using graphene plasmonics to boost biosensor sensitivity. SPIE Biomed Opt Med Imag. https//doi.org/10.1117/2.1201610.006712

    Google Scholar 

  • Chorsi HT, Chorsi MT, Gedney SD (2017a) A conceptual study of microelectromechanical disk resonators. IEEE J Multiscale Multiphys Comput Tech 2:29–37

    Article  Google Scholar 

  • Chorsi MT, Chorsi HT, Gedney SD (2017b) Radial-contour mode microring resonators: nonlinear dynamics. Int J Mech Sci 130:258–266

    Article  Google Scholar 

  • Clark JR, Hsu WT, Nguyen CC (2000) High-Q VHF micromechanical contour-mode disk resonators. In: Electron devices meeting. IEDM’00. Technical digest. International, pp 493–496

  • Clark JR, Abdelmoneum M, Nguyen CTC (2003) UHF high-order radial-contour-mode disk resonators. In: Frequency control symposium and PDA exhibition jointly with the 17th European frequency and time forum, 2003. Proceedings of the 2003 IEEE international, pp 802–809

  • Clark JR, Hsu W-T, Abdelmoneum M, Nguyen CT (2005) High-Q UHF micromechanical radial-contour mode disk resonators. Microelectromech Syst J 14:1298–1310

    Article  Google Scholar 

  • Davis ZJ, Svendsen W, Boisen A (2007) Design, fabrication and testing of a novel MEMS resonator for mass sensing applications. Microelectron Eng 84:1601–1605

    Article  Google Scholar 

  • Doyle JF (1989) Wave propagation in structures. Springer, Berlin

  • Ghadiri M, Shafiei N, Alavi H (2017) Thermo-mechanical vibration of orthotropic cantilever and propped cantilever nanoplate using generalized differential quadrature method. Mech Adv Mater Struct 24:636–646

    Article  Google Scholar 

  • Guo J-G, Zhao Y-P (2004) Influence of van der Waals and Casimir forces on electrostatic torsional actuators. Microelectromech Syst J 13:1027–1035

    Article  Google Scholar 

  • Hao Z, Pourkamali S, Ayazi F (2004) VHF single-crystal silicon elliptic bulk-mode capacitive disk resonators-part I: design and modeling. Microelectromech Syst J 13:1043–1053

    Article  Google Scholar 

  • Israelachvili JN (2011) Intermolecular and surface forces: revised third edition. Academic Press, Cambridge

  • Khorramabadi H, Gray PR (1984) High-frequency CMOS continuous-time filters. IEEE J Solid State Circuits 19:939–948

    Article  Google Scholar 

  • Lee H, Meissner H, Meissner O (2006) Adhesive-free bond (AFB) CVD diamond/sapphire and CVD diamond/YAG crystal composites. In: Defense and security symposium, pp 62160O–62160O-8

  • Li SS, Lin YW, Ren Z, Nguyen CC (2006) Disk-array design for suppression of unwanted modes in micromechanical composite-array filters. In: Micro electro mechanical systems, MEMS 2006, 19th IEEE international conference, Istanbul, pp 866–869

  • Li SS, Lin YW, Ren Z, Nguyen CT (2007) An MSI micromechanical differential disk-array filter. In: Solid-state sensors, actuators and microsystems conference. TRANSDUCERS 2007. International, pp 307–311

  • Linxi D, Quan Y, Jinyan B, Jiaping T (2014) Analysis of reliability factors of MEMS disk resonator under the strong inertial impact. J Semicond 35:074014

    Article  Google Scholar 

  • Liu X, Katehi LP, Chappell WJ, Peroulis D (2009) A 3.4–6.2 GHz continuously tunable electrostatic MEMS resonator with quality factor of 460–530. In: Microwave symposium digest, 2009. MTT’09. IEEE MTT-S International, pp 1149–1152

  • Meirovitch L (1997) Principles and techniques of vibrations, vol 1. Prentice Hall, New Jersey

  • Nayfeh AH, Balachandran B (2008) Applied nonlinear dynamics: analytical, computational and experimental methods. Wiley, Hoboken

  • Nayfeh AH, Younis MI, Abdel-Rahman EM (2007) Dynamic pull-in phenomenon in MEMS resonators. Nonlinear Dyn 48:153–163

    Article  MATH  Google Scholar 

  • Nguyen CT (1995) Micromechanical resonators for oscillators and filters. In: Ultrasonics symposium. Proceedings, IEEE, pp 489–499

  • Nguyen CT (2004) Vibrating RF MEMS for next generation wireless applications. In: Custom integrated circuits conference. Proceedings of the IEEE 2004, pp 257–264

  • Nguyen CTC (2006) Integrated micromechanical circuits for RF front ends. In: Solid-state device research conference. ESSDERC 2006. Proceeding of the 36th European, pp 7–16

  • Nguyen CT-C (2007) MEMS technology for timing and frequency control. Ultrason Ferroelectr Freq Control IEEE Trans 54:251–270

    Article  Google Scholar 

  • Otis BP, Rabaey JM (2003) A 300-μW 1.9-GHz CMOS oscillator utilizing micromachined resonators. Solid-State Circuits IEEE J 38:1271–1274

    Article  Google Scholar 

  • Ouakad HM, Younis MI (2014) On using the dynamic snap-through motion of MEMS initially curved microbeams for filtering applications. J Sound Vib 333:555–568

    Article  Google Scholar 

  • Ouakad HM, Sedighi HM, Younis MI (2017) One-to-one and three-to-one internal resonances in MEMS shallow arches. J Comput Nonlinear Dyn

  • Overhoff S (2009) Selecting high-linearity mixers for wireless base stations. Electron Eng Product World 4:029

    Google Scholar 

  • Ozdogan M, Towfighian S (2016a) Nonlinear dynamic behavior of a bi-axial torsional MEMS mirror with sidewall electrodes. Micromachines 7:42

    Article  Google Scholar 

  • Ozdogan M, Towfighian S (2016b) A MEMS microphone using repulsive force sensors. In: 21st design for manufacturing and the life cycle conference, vol 4; 10th international conference on micro- and nanosystems charlotte, North Carolina, USA, 21–24 Aug 2016

  • Park CI (2008) Frequency equation for the in-plane vibration of a clamped circular plate. J Sound Vib 313:325–333

    Article  Google Scholar 

  • Pepakayala V, Green SR, Gianchandani YB (2014) Passive wireless strain sensors using microfabricated magnetoelastic beam elements. J Microelectromech Syst 23:1374–1382

    Article  Google Scholar 

  • Pinto F (2014) Engines powered by the forces between atoms. Am Sci 102:280

    Article  Google Scholar 

  • Rao SS (2017) Vibration of continuous systems. Wiley, Hoboken

  • Rennick RC (1973) An equivalent circuit approach to the design and analysis of monolithic crystal filters. IEEE Trans Sonics Ultrason 20:347–353

    Article  Google Scholar 

  • Rocheleau TO, Naing TL, Ren Z, Nguyen CTC (2012) Acoustic whispering gallery mode resonator with Q > 109,000 at 515 MHz. In: Micro electro mechanical systems (MEMS), 2012 IEEE 25th international conference, pp 672–675

  • Sakr MM, El-Shafie MK, Ragai HF (2006) Analysis and modeling of RF-MEMS disk resonator. In: MEMS, NANO and smart systems, the 2006 international conference, pp 19–22

  • Sedighi HM, Shirazi KH (2015) Dynamic pull-in instability of double-sided actuated nano-torsional switches. Acta Mech Solida Sin 28:91–101

    Article  Google Scholar 

  • Sedighi HM, Daneshmand F, Zare J (2014) The influence of dispersion forces on the dynamic pull-in behavior of vibrating nano-cantilever based NEMS including fringing field effect. Arch Civil Mech Eng 14:766–775

    Article  Google Scholar 

  • Sedighi HM, Shirazi KH, Changizian M (2015) Effect of the amplitude of vibrations on the pull-in instability of double-sided actuated microswitch resonators. J Appl Mech Tech Phys 56:304–312

    Article  MathSciNet  MATH  Google Scholar 

  • Seleim A, Towfighian S, Delande E, Abdel-Rahman E, Heppler G (2012) Dynamics of a close-loop controlled MEMS resonator. Nonlinear Dyn 69:615–633

    Article  Google Scholar 

  • Senturia SD, Azuru N, White J (1997) Simulating the behavior of MEMS devices: computational methods and needs. IEEE Comput Sci Eng 4(1):30–43

    Article  Google Scholar 

  • Sepúlveda-Alancastro N (2005) Polycrystalline diamond RF MEMS resonator technology and characterization. Michigan State University, East Lansing

  • Shafiei N, Kazemi M, Ghadiri M (2016) Nonlinear vibration of axially functionally graded tapered microbeams. Int J Eng Sci 102:12–26

    Article  MathSciNet  Google Scholar 

  • Soedel W (2004) Vibrations of shells and plates. CRC Press, Boca Raton

  • Tabrizian R, Rais-Zadeh M, Ayazi F (2009) Effect of phonon interactions on limiting the fQ product of micromechanical resonators. In: Solid-state sensors, actuators and microsystems conference, TRANSDUCERS 2009 international, pp 2131–2134

  • Taghizadeh M, Mobki H (2014) Bifurcation analysis of torsional micromirror actuated by electrostatic forces. Arch Mech 66:95–111

    MathSciNet  MATH  Google Scholar 

  • Wang J, Butler JE, Feygelson T, Nguyen CT (2004a) 1.51-GHz nanocrystalline diamond micromechanical disk resonator with material-mismatched isolating support. In: Micro electro mechanical systems, 2004. 17th IEEE international conference (MEMS), pp 641–644

  • Wang J, Ren Z, Nguyen CT (2004b) 1.156-GHz self-aligned vibrating micromechanical disk resonator. Ultrason Ferroelectr Freq Control IEEE Trans 51:1607–1628

    Article  Google Scholar 

  • Younis MI (2011) MEMS linear and nonlinear statics and dynamics, vol. 20. Springer, Berlin

  • Zand MM, Ahmadian M (2010) Dynamic pull-in instability of electrostatically actuated beams incorporating Casimir and van der Waals forces. Proc Inst Mech Eng Part C J Mech Eng Sci 224:2037–2047

    Article  Google Scholar 

  • Zare J (2014) Pull-in behavior analysis of vibrating functionally graded micro-cantilevers under suddenly DC voltage. J Appl Comput Mech 1:17–25

    Google Scholar 

Download references

Author information

Author notes

  1. Meysam T. Chorsi, Hamid T. Chorsi contributed equally to this work.

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Connecticut, Storrs, CT, 06269, USA

    Meysam T. Chorsi

  2. Department of Biomedical Engineering, University of Connecticut, Storrs, CT, 06269, USA

    Meysam T. Chorsi

  3. Thayer School of Engineering, Dartmouth College, Hanover, NH, 03755, USA

    Hamid T. Chorsi

Authors
  1. Meysam T. Chorsi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamid T. Chorsi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Meysam T. Chorsi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chorsi, M.T., Chorsi, H.T. Modeling and analysis of MEMS disk resonators. Microsyst Technol 24, 2517–2528 (2018). https://doi.org/10.1007/s00542-017-3645-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00542-017-3645-9

Search

Navigation