Precise measurement of the transverse piezoelectric coefficient for thin films on anisotropic substrate

In this study, we propose a reliable measurement method for the effective transverse piezoelectric coefficient for thin films especially on anisotropic substrate. This coefficient for piezoelectric Pb(Zr, Ti)O3 (PZT) thin films was calculated by measuring the electric field-induced tip displacement of unimorph cantilevers composed of PZT thin films and Si substrates. We evaluated the reliability of the proposed measurement method by comparing it with numerical analysis and confirmed that the relative error of the piezoelectric coefficient (e31, f) was less than 1%. We prepared 16 different unimorph cantilevers composed of identical PZT films on different Si beam geometries that had various substrate thicknesses and cantilever widths. Although the effective transverse piezoelectric coefficient e31, f of PZT thin films ranged from −6.5 to −14 C/m2 as a function of the applied voltage, the difference among the 16 samples with an applied voltage of 25 V was within 10%. These results demonstrate that the proposed measurement method has sufficient reliability and can be used to evaluate the effective transverse piezoelectric coefficient e31, f of thin films.