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T. Voglhuber-Brunnmaier, E. Reichel, B. Jakoby, R. Beigelbeck, P.M. Mayrhofer, U. Schmid:
"Fast method for the calculation of surface bending on circular multilayered piezoelectric structures";
Poster: Sensors 2016, Orlando, Florida, USA; 10-30-2016 - 11-02-2016; in: "Proceedings of the IEEE Sensors 2016", IEEE, (2016), ISBN: 978-1-4799-8287-5; 3 pages.

A method for the fast calculation of ver-
tical displacement fields, observed on thin piezoelectric
layers of aluminium nitride (AlN) type deposited on
n-doped silicon wafers, is shown. The basic findings
are that the surface bending effect due to
d
31
,d
32
is
very strong but is largely compensated by
d
33
in the
demonstrated case. The displacements are very sensi-
tive on the piezoelectric properties and therefore the
field computation must be very accurate in this respect.
Furthermore, the anisotropy of the silicon wafer results
in noticeable deviations when assuming a rotational
symmetry for material properties. The demonstrated
approach is based on an electromechanical Green´s
function (GF) and the assumption of a uniform charge
distribution at the electrodes, which is shown to be
acceptable when the thickness of the piezoelectric layer
is much smaller than the lateral electrode dimensions.
The infinite integral encountered in the rigorous field
computations is approximated by a truncated series
that can be calculated efficiently. The validity of the
applied approximations is demonstrated by a compari-
son with results of a rigorous field calculation and with
measurement results obtained with a laser Doppler
vibrometer.