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# (Solved): Q4. We have used a piezoelectric material sandwiched between two metal electrodes to detect the dis ...

Q4. We have used a piezoelectric material sandwiched between two metal electrodes to detect the displacements of a silicon cantilever tip. The cantilever is

250\mu m

long,

20\mu m

wide, and

2\mu m

thick. The piezoelectric layer is

1\mu m

thick and as wide as the cantilever and is extended over the first

10\mu m

of the cantilever. For the piezoelectric material:

\epsi _(r)=1500,d_(31)=-44.2\times 10^(-12)(C)/(N)

and

d_(33)=117\times 10^(-12)(C)/(N)

. For silicon,

E=170GPa

. Ignore the effects of the metal electrodes and the piezoelectric layer in your mechanical calculations. a) Ignoring charge leakage, what is the produced charge on the top electrode if

\Delta y=1\mu m

? b) What is the corresponding voltage difference across the electrodes if

\Delta y=1\mu m

? Reminder: The produced voltage when a piezoelectric material is under stress

\sigma _(k)

is found from:

V=(d_(3k)\sigma _(k))/(\epsi _(r)\epsi _(0))h_(piezo )

, where

k=1

or 3 and

h_(piezo )

is the thickness of the piezoelectric layer.

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