Dual-Ring Method: Lateral Piezoelectric Coefficient (e31,f) Measurement on Unstructured Thin Films

In the literature, measurement of piezoelectric properties is often absent in work describing the processing of these materials. For a measurement to be used in process development and control, it should preferably be performed shortly after the process itself. However, there are only a few methods available to characterize the piezoelectric constants on an unstructured thin film. Furthermore, these methods do not measure the lateral piezoelectric coefficient
${e}_{31,{f}}$
, although it is the most important piezoelectric parameter for many devices. In this article, a new method is introduced to enable the measurement of the lateral piezoelectric coefficient on unstructured wafers. For the measurement, the entire wafer is bent. The charge generated by the wafer bending is used to calculate the piezoelectric constant. An analytical formula is derived to establish the relation between geometry, substrate properties, force, and charge. This formula is compared with finite-element analyses (FEAs). FEA is used to investigate the impact of geometric variations on the measurement. The method is evaluated on sputtered aluminum nitride and shows a good correlation with the four-point bending method. As the output signal of the new method is some magnitudes higher compared to the well-known Berlincourt method. The requirements for the measurement equipment are much less stringent, resulting in the need for only a few basic tools that are accessible to researchers without access to specialized laboratories.