The wafer flexure technique for the determination of the transverse piezoelectric coefficient (d31) of PZT thin films

Abstract This paper describes a simple and inexpensive method for evaluating the transverse piezoelectric coefficient ( d 31 ) of piezoelectric thin films. The technique is based upon the flexure of a coated substrate which imparts an ac two-dimensional stress to the piezoelectric film. The surface charge generated via the mechanical loading is converted to a voltage by an active integrator. Plate theory and elastic stress analyses are used to calculate the principal stresses applied to the film. The d 31 coefficient can then be determined from knowledge of the electric charge produced and the calculated mechanical stress. For 52/48 sol-gel lead zirconate titanate (PZT) thin films, the d 31 coefficient was found to range from − 5 to − 59 pC/N and is dependent on poling field.