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MECH 4370, EE4371 Introduction to MEMS Extra Credit Problem (20 points) - It requires the derivation of a formula. Try it only if you finish all the above problems and you have room to challenge yourself. Consider an air-gap capacitive actuator with a movable electrode beam (blue) and a fixed bottom electrode (black). Top view: The beam is made of aluminum (L = 2 mm, w = 200 Î¼m, and 1 Î¼m thick). Assume that Aluminum's Young's modulus is 70 GPa. The beam is parallel to the fixed electrode when no external force is applied, and the initial gap distance between the two electrodes is 12 Î¼m. The width W and the length L of the top and bottom fixed electrodes are exactly the same. When a voltage is applied between the fixed electrode and the movable electrode, the electrostatic force pulls the movable electrode beam. The displacement at any position x for the beam is given by: 24E1 Derive the capacitance formula that works for the displacement of the movable electrode in the range of 0 ~ 1/3 of the initial gap. Calculate the capacitance when the deflection at the free end is 1/3 of the initial gap. Assume that the fringing electric field and squeeze film damping are negligible. Also, assume that the fixed wall is not electrically conductive.

          MECH 4370, EE4371 Introduction to MEMS

Extra Credit Problem (20 points) - It requires the derivation of a formula. Try it only if you finish all the above problems and you have room to challenge yourself.

Consider an air-gap capacitive actuator with a movable electrode beam (blue) and a fixed bottom electrode (black). 

Top view:
The beam is made of aluminum (L = 2 mm, w = 200 Î¼m, and 1 Î¼m thick). Assume that Aluminum's Young's modulus is 70 GPa. The beam is parallel to the fixed electrode when no external force is applied, and the initial gap distance between the two electrodes is 12 Î¼m. The width W and the length L of the top and bottom fixed electrodes are exactly the same.

When a voltage is applied between the fixed electrode and the movable electrode, the electrostatic force pulls the movable electrode beam. The displacement at any position x for the beam is given by:

24E1

Derive the capacitance formula that works for the displacement of the movable electrode in the range of 0 ~ 1/3 of the initial gap. Calculate the capacitance when the deflection at the free end is 1/3 of the initial gap. Assume that the fringing electric field and squeeze film damping are negligible. Also, assume that the fixed wall is not electrically conductive.

mech 4370ee4371 introduction to mems extra credit problem 20 points it requires derivation of formula try only if you finish all the above problems and you have room to challenge yourself 2 69155

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