The figure shows a side view of an electrostatically operated switch. It consists of an elastic cantilever beam (the source contact S), a gate electrode used to close the switch (G), and a drain contact D which is in electrical contact with the source when the switch is closed. The main question in this assignment is to estimate the voltage VGS needed to close the switch.
For reasons of simplicity you may model the deformation of the beam by assuming that the beam is straight and is connected to the support by a torsional spring with a stiffness a. The length of the beam (support to middle gate contact) is L. The drain contact is located at L/2. The initial distance between source and gate is g, while the initial distance between source and drain is g / 3. You may assume that the gate-source actuator plates stay parallel all the time which is a good approximation for L >> g.
Please derive first an expression for the required VGS. Next estimate the numerical value for the case where g = 1 µm, a / L2 = 1 N/m and the area of the gate electrode A = 25 µm2.
Finally, what happens if we gradually reduce the voltage form the calculated VGS back to zero?
