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# (Solved): Q2. Accelerations along the z-axis are detected by measuring the changes in the capacitance between ...

Q2. Accelerations along the z-axis are detected by measuring the changes in the capacitance between the plate (i.e., the proof mass) and the bottom electrode. The dimensions of each piece of the beam springs are

L=200\mu m,W=

5\mu m

, and

h=2\mu m

. The proofmass is also

2\mu m

thick with lateral dimensions of

500\mu m\times 500\mu m

. Ignore the mass of the beams. Assume the beam springs are aligned with the

<110>

direction of the silicon crystal and the density of silicon is

2330k(g)/(m^(3))

. Assume the gap between the proofmass and the bottom electrode is

g=1\mu m

. You can use the results from the mechanical analysis of the structure in that assignment (or the ones from the provided solutions) to answer the following questions. a) What is the capacitance of the device at rest (i.e.,

a_(z)=0

)? b) How much will the device capacitance change for

a_(z)=9.81(m)/(s^(2))

? c) How much will the proofmass move if a voltage difference of

V_(B)=1V

is applied between the bottom electrode and the proofmass?

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