e(31),(f) determination for PZT films using a conventional 'd(33)' meter

A new and simple method is described for the determination of the piezoelec tric coefficients d(33,f) and e(31,f) for piezoelectric films deposited on substrates using a conventional point-loading 'd(33)' or 'Berlincourt' piez ometer. An analytical mathematical model is developed which simulates the d ynamical flexure of such films when a ring-supported sample is subject to c entral loading. Classical plate theory and elastic analysis are used to cal culate the stresses in doped lead zirconate titanate (PZT) him for differen t radii of supporting rings, enabling both piezoelectric coefficients to be determined through a simple modification to the piezometer. The analytical model for the radial stresses has been evaluated in comparison with the re sults of finite element analysis and has shown a good correlation. The new measurement technique has been applied to both thick films of PZT and thin films of manganese-doped lead zirconate titanate (PMZT) on silicon substrat es. The values of d(33,f) and e(31,f) obtained experimentally are found to be similar to these that have been determined by more elaborate methods.