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.