Some studies on the deformation of the membrane in an RF MEMS switch

Vijaya Raghav Ambati, Andreas Asheim, Jan Bouwe van den Berg, Yves van Gennip, Tymofiy Gerasimov, Andriy Hlod, Bob Planqué, Martin van der Schans, Sjors van der Stelt, Michelangelo Vargas Rivera, Erwin Vondenhoff

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    Abstract

    Radio Frequency (RF) switches of Micro Electro Mechanical Systems (MEMS) are appealing to the mobile industry because of their energy efficiency and ability to accommodate more frequency bands. However, the electromechanical coupling of the electrical circuit to the mechanical components in RF MEMS switches is not fully understood. In this paper, we consider the problem of mechanical deformation of electrodes in RF MEMS switch due to the electrostatic forces caused by the difference in voltage between the electrodes. It is known from previous studies of this problem, that the solution exhibits multiple deformation states for a given electrostatic force. Subsequently, the capacity of the switch that depends on the deformation of electrodes displays a hysteresis behaviour against the voltage in the switch. We investigate the present problem along two lines of attack. First, we solve for the deformation states of electrodes using numerical methods such as finite difference and shooting methods. Subsequently, a relationship between capacity and voltage of the RF MEMS switch is constructed. The solutions obtained are exemplified using the continuation and bifurcation package AUTO. Second, we focus on the analytical methods for a simplified version of the problem and on the stability analysis for the solutions of deformation states. The stability analysis shows that there exists a continuous path of equilibrium deformation states between the open and closed state.
    Original languageEnglish
    Title of host publicationProceedings of the 63rd European Study Group Mathematics with Industry
    Subtitle of host publicationEnschede, The Netherlands, 28 January – 1 February, 2008
    EditorsOnno Bokhove, Johann Hurink, Gjerrit Meinsma, Chris Stolk, Michel Vellekoop
    Place of PublicationAmsterdam
    PublisherCentrum voor Wiskunde en Informatica
    Pages65-84
    Number of pages20
    ISBN (Print)978-90-365-2779-8
    Publication statusPublished - 28 Jan 2008
    Event63rd European Study Group Mathematics with Industry, SWI 2008 - University of Twente, Enschede, Netherlands
    Duration: 28 Jan 20081 Feb 2008
    Conference number: 63

    Publication series

    NameCWI Syllabus
    PublisherCWI (Centrum voor Wiskunde en Informatica)

    Conference

    Conference63rd European Study Group Mathematics with Industry, SWI 2008
    Abbreviated titleSWI
    CountryNetherlands
    CityEnschede
    Period28/01/081/02/08

    Fingerprint

    Switches
    Membranes
    Electrodes
    Electrostatic force
    Electric potential
    Electromechanical coupling
    Frequency bands
    Energy efficiency
    Hysteresis
    Numerical methods
    Networks (circuits)
    Industry

    Keywords

    • MSC-34K28
    • EWI-14950
    • METIS-255156
    • MSC-74A60
    • IR-65338
    • CR-G.1

    Cite this

    Ambati, V. R., Asheim, A., van den Berg, J. B., van Gennip, Y., Gerasimov, T., Hlod, A., ... Vondenhoff, E. (2008). Some studies on the deformation of the membrane in an RF MEMS switch. In O. Bokhove, J. Hurink, G. Meinsma, C. Stolk, & M. Vellekoop (Eds.), Proceedings of the 63rd European Study Group Mathematics with Industry: Enschede, The Netherlands, 28 January – 1 February, 2008 (pp. 65-84). (CWI Syllabus). Amsterdam: Centrum voor Wiskunde en Informatica.
    Ambati, Vijaya Raghav ; Asheim, Andreas ; van den Berg, Jan Bouwe ; van Gennip, Yves ; Gerasimov, Tymofiy ; Hlod, Andriy ; Planqué, Bob ; van der Schans, Martin ; van der Stelt, Sjors ; Vargas Rivera, Michelangelo ; Vondenhoff, Erwin. / Some studies on the deformation of the membrane in an RF MEMS switch. Proceedings of the 63rd European Study Group Mathematics with Industry: Enschede, The Netherlands, 28 January – 1 February, 2008. editor / Onno Bokhove ; Johann Hurink ; Gjerrit Meinsma ; Chris Stolk ; Michel Vellekoop. Amsterdam : Centrum voor Wiskunde en Informatica, 2008. pp. 65-84 (CWI Syllabus).
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    abstract = "Radio Frequency (RF) switches of Micro Electro Mechanical Systems (MEMS) are appealing to the mobile industry because of their energy efficiency and ability to accommodate more frequency bands. However, the electromechanical coupling of the electrical circuit to the mechanical components in RF MEMS switches is not fully understood. In this paper, we consider the problem of mechanical deformation of electrodes in RF MEMS switch due to the electrostatic forces caused by the difference in voltage between the electrodes. It is known from previous studies of this problem, that the solution exhibits multiple deformation states for a given electrostatic force. Subsequently, the capacity of the switch that depends on the deformation of electrodes displays a hysteresis behaviour against the voltage in the switch. We investigate the present problem along two lines of attack. First, we solve for the deformation states of electrodes using numerical methods such as finite difference and shooting methods. Subsequently, a relationship between capacity and voltage of the RF MEMS switch is constructed. The solutions obtained are exemplified using the continuation and bifurcation package AUTO. Second, we focus on the analytical methods for a simplified version of the problem and on the stability analysis for the solutions of deformation states. The stability analysis shows that there exists a continuous path of equilibrium deformation states between the open and closed state.",
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    Ambati, VR, Asheim, A, van den Berg, JB, van Gennip, Y, Gerasimov, T, Hlod, A, Planqué, B, van der Schans, M, van der Stelt, S, Vargas Rivera, M & Vondenhoff, E 2008, Some studies on the deformation of the membrane in an RF MEMS switch. in O Bokhove, J Hurink, G Meinsma, C Stolk & M Vellekoop (eds), Proceedings of the 63rd European Study Group Mathematics with Industry: Enschede, The Netherlands, 28 January – 1 February, 2008. CWI Syllabus, Centrum voor Wiskunde en Informatica, Amsterdam, pp. 65-84, 63rd European Study Group Mathematics with Industry, SWI 2008, Enschede, Netherlands, 28/01/08.

    Some studies on the deformation of the membrane in an RF MEMS switch. / Ambati, Vijaya Raghav; Asheim, Andreas; van den Berg, Jan Bouwe; van Gennip, Yves; Gerasimov, Tymofiy; Hlod, Andriy; Planqué, Bob; van der Schans, Martin; van der Stelt, Sjors; Vargas Rivera, Michelangelo; Vondenhoff, Erwin.

    Proceedings of the 63rd European Study Group Mathematics with Industry: Enschede, The Netherlands, 28 January – 1 February, 2008. ed. / Onno Bokhove; Johann Hurink; Gjerrit Meinsma; Chris Stolk; Michel Vellekoop. Amsterdam : Centrum voor Wiskunde en Informatica, 2008. p. 65-84 (CWI Syllabus).

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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    AU - Ambati, Vijaya Raghav

    AU - Asheim, Andreas

    AU - van den Berg, Jan Bouwe

    AU - van Gennip, Yves

    AU - Gerasimov, Tymofiy

    AU - Hlod, Andriy

    AU - Planqué, Bob

    AU - van der Schans, Martin

    AU - van der Stelt, Sjors

    AU - Vargas Rivera, Michelangelo

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    N2 - Radio Frequency (RF) switches of Micro Electro Mechanical Systems (MEMS) are appealing to the mobile industry because of their energy efficiency and ability to accommodate more frequency bands. However, the electromechanical coupling of the electrical circuit to the mechanical components in RF MEMS switches is not fully understood. In this paper, we consider the problem of mechanical deformation of electrodes in RF MEMS switch due to the electrostatic forces caused by the difference in voltage between the electrodes. It is known from previous studies of this problem, that the solution exhibits multiple deformation states for a given electrostatic force. Subsequently, the capacity of the switch that depends on the deformation of electrodes displays a hysteresis behaviour against the voltage in the switch. We investigate the present problem along two lines of attack. First, we solve for the deformation states of electrodes using numerical methods such as finite difference and shooting methods. Subsequently, a relationship between capacity and voltage of the RF MEMS switch is constructed. The solutions obtained are exemplified using the continuation and bifurcation package AUTO. Second, we focus on the analytical methods for a simplified version of the problem and on the stability analysis for the solutions of deformation states. The stability analysis shows that there exists a continuous path of equilibrium deformation states between the open and closed state.

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    KW - MSC-34K28

    KW - EWI-14950

    KW - METIS-255156

    KW - MSC-74A60

    KW - IR-65338

    KW - CR-G.1

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    A2 - Stolk, Chris

    A2 - Vellekoop, Michel

    PB - Centrum voor Wiskunde en Informatica

    CY - Amsterdam

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    Ambati VR, Asheim A, van den Berg JB, van Gennip Y, Gerasimov T, Hlod A et al. Some studies on the deformation of the membrane in an RF MEMS switch. In Bokhove O, Hurink J, Meinsma G, Stolk C, Vellekoop M, editors, Proceedings of the 63rd European Study Group Mathematics with Industry: Enschede, The Netherlands, 28 January – 1 February, 2008. Amsterdam: Centrum voor Wiskunde en Informatica. 2008. p. 65-84. (CWI Syllabus).