Experimental investigation into the effect of substrate clamping on the piezoelectric behaviour of thick-film PZT elements

This paper details an experimental investigation of the clamping effect associated with thick-film piezoelectric elements printed on a substrate. The clamping effect reduces the measured piezoelectric coefficient, d(33), of the film. This reduction is due to the influence of the d(31) component in the film when a deformation of the structure occurs, by either the direct or indirect piezoelectric effect. Theoretical analysis shows a reduction in the measured d(33) of 62%, i.e. a standard bulk lead zirconate titanate (PZT)-5H sample with a manufacturer specified d(33) of 593pC/N would fall to 227.8pC/N. To confirm this effect, the d(33) coefficients of five thin bulk PZT-5H samples of 220 mum thickness were measured before and after their attachment to a metallized 96% alumina substrate. The experimental results show a reduction in d(33) of 74% from 529pC/N to 139pC/N. The theoretical analysis was then applied to existing University of Southampton thick-film devices. It is estimated that the measured d(33) value of 131pC/N of the thick-film devices is the equivalent of an unconstrained d(33) of 345pC/N.