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Cantilever switch based on electrostatic force

  1. Dec 22, 2009 #1
    Dear all:

    I am going to design a cantilever switch which is working with electrostatic (capacitive) force.

    I want to design that. That is to find the dimension and material of that.
    I was wondering if you could kindly suggest a reference for designing this.

    Thank you very much.
  2. jcsd
  3. Dec 25, 2009 #2
    Hello Si14,

    If you can supply a roughly dimensioned sketch, perhaps I can help. I've spent about 8 years of my life designing capacitance-based sensors and electrical interfaces. I know, I should probably get out more....

    - Mike
  4. Dec 25, 2009 #3
    Hi Mike:

    Thank you very much. Here is my design.

    http://img23.imageshack.us/img23/4686/cantileverswitch.jpg [Broken]​

    As you can see, I want to use the Gate to turn the switch on/off.
    The cantilever will bend and makes contact with the Drain.
    For this design, First, I assume a=b (uniform width: simplest case)
    For that case I assumed that the spring constant of the cantilever is k=(8EI)/(l^3)

    So first, can I use this spring constant? Since I assumed that the force is distributed uniformly on the cantilever (the simplest case).

    And also I used thepull-in voltage Vpi=sqrt[(8k*g^3)/(27*eps0*A)]
    which can be applied to all capacitor cases.

    So this is my 1st step. After hearing your comments, we'll go to next step.

    Thanks a lot.
    Last edited by a moderator: May 4, 2017
  5. Dec 26, 2009 #4


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    Staff: Mentor

    Can you give an order of magnitude for the dimensions of this cell? And can you say why you are shorting out the drain and source with the contact? Are you aiming to make some sort of a mechanical oscillator?
    Last edited by a moderator: May 4, 2017
  6. Dec 26, 2009 #5
    The dimensions are my question. I didn't shorten the D/S contact on purpose.
    As I said in my previous post, this is a switch.

    BTW, can you confirm the formulas which I gave previously (spring constant, Vpi)?
    After that, I think I will be able to suggest some dimensions.

  7. Dec 26, 2009 #6


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    Staff: Mentor

    In asking for target lithographic dimensions, I assumed that you had a particular IC geometry already in mind. In IC design, we generally have a target geometry (or small range of geometries) in mind when thinking about a new IC. But perhaps it is different in MEMS design:


    As for the switch part, may I assume you are working on a MEMS relay of some sort? If so, you would not make the switch/relay out of a single MOSFET MEMS device. As I said in my previous post, it looks like the D-S would be shorted out by the closing of the switch. If you want to make a switch using MEMS electrostatic forces, then you will need to separate the attractive E-field from the switch closure. Why?
  8. Dec 26, 2009 #7
    Thanks. I am using it for MEMS application, and also I have no target dimension. The dimension could be 1mm*1mm or less.
    But this switch will work. Since I will know when the switch is on or off by measuring the current for example. So shortening between the drain and source is a part of switching mechanism.
    Also, the electrostatic force is only used to pull the cantilever downward. So it is kind of different from other electrostatci switches using only two plates.
  9. Dec 26, 2009 #8


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    Staff: Mentor

    What provides the holding force after the E-field is shorted out?
  10. Dec 26, 2009 #9
    The E-filed between the GATE and cantilever is still available. Since it is not shorted. Drain is only for sensing the short circuit. Not driving the switch.
  11. Dec 26, 2009 #10

    I understand part of your equations, but I'm having difficulty with the entirety. For force, given voltage and ideal (square) surfaces, I get:

    F=E^2 A Eps0 / 2 gap^2

    Where F - Force, E - Applied voltage, A - area of the two plates, and gap - distance between plates

    Given Force, this gives me:

    E = sqrt(2 F gap^2 / A Eps0)

    It looks like you substituted in the forces for beam deflection for F. Is this correct?

  12. Dec 26, 2009 #11
    In your first equation, I think, you should substitute E with V.

    But I didn't drive that spring constant. I used a formula for simple cantilever under uniform pressure. And then since the maximum deflection is at x=L. So I derived the k.

    Which is:

    http://img12.imageshack.us/img12/4176/springconstant.jpg [Broken]​

    But I am not sure about the: Rho=F/L

    So that's how I used that formula.
    Last edited by a moderator: May 4, 2017
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