Comparable measurements and modeling of piezoelectric thin films for MEMS application

Accurate and reliable measurements of piezoelectric coefficients on thin films are required to perform thin film process development and compare different manufacturing techniques and quality especially in MEMS applications. State of the art measurements are performed by double-beam laser interferometry since many years, however the variety of parameter ranges and test conditions make it difficult to compare measurement results. Films on a substrate exhibit effective piezoelectric coefficients due to substrate clamping and the coefficient also depends on feature size and substrate thickness. This was shown by FEM simulations for the case of d_33J measurements by DBLI [1] and latest simulation and measurement results show that a considerable reduction of the measured d_33J was obtained for small electrodes and an increase for large electrodes. The measured d_33J value at large electrodes is even larger than the true d33J of the film and for small feature sizes it is lower. A feature size chosen equivalent to the substrate thickness exhibits the most exact number for the effective coefficient d_33J [2]. Furthermore nonlinearity and hysteresis of ferroelectric films requires the definition of measurement parameters to obtain comparable procedures regarding hysteresis, poling conditions, and other property nonlinearities, voltage and frequency dependency of coefficients, and large and small signal responses. For easier comparison of films a large signal coefficient (d_33,ls) is introduced as the average slope of a displacement vs. voltage measurement over the full operating voltage range. For thin film measurements it reflects the potential displacement in typical actuator applications in comparison to small-signal coefficients and allows better comparison of materials for actuation.