Precise determination of piezoelectric longitudinal charge coefficients for piezoelectric thin films assisted by finite element modeling

A determination method to identify the piezoelectric longitudinal charge coefficient d
₃₃
for thin films on substrate is presented. Finite Element (FE) simulations and measurements at PZT on bulk silicon show correlations of the substrate characteristics and electrode size subject to the displacement of an electric actuated piezoelectric material. FE models are used to identify the d
₃₃
independent of the substrate and electrode characteristic. Thereby the piezoelectric longitudinal charge coefficient of 1.1 μm PLD deposited Pb(Zr
_0.52
Ti
_0.48
)O
₃
(PZT) is calculated d
₃₃
= 272.5 pm/V and a small standard deviation of σ = 4 pm/V for different sample geometries is analyzed.