Efficient Modeling of Thin Piezoelectric Layer Deflections

A method for the fast calculation of vertical 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 d31, d32 is very strong but is largely compensated by d33 in the demonstrated case. The displacements are very sensitive 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 comparison with results of a rigorous field calculation and with measurement results obtained with a laser Doppler vibrometer.

Details can be found in:

Voglhuber-Brunnmaier, T., Reichel, E. K., Jakoby, B., Beigelbeck, R., Mayrhofer, P. M., & Schmid, U. (2016). Fast method for the calculation of surface bending on circular multilayered piezoelectric structures. In 2016 IEEE SENSORS (pp. 1-3). IEEE.