Dynamics of thin-film piezoelectric microactuators with large vertical stroke subject to multi-axis coupling and fabrication asymmetries

The high performance and small size of MEMS based scanners has allowed various optical imaging techniques to be realized in a small form factor. Many such devices are resonant scanners, and thus their linear and nonlinear dynamic behaviors have been studied in the past. Thin-film piezoelectric materials, in contrast, provide sufficient energy density to achieve both large static displacements and high-frequency resonance, but large deformation can in turn influence dynamic scanner behavior. This paper reports on the influence of very large stroke translation of a piezoelectric vertical actuator on its resonant behavior, which may not be otherwise explained fully by common causes of resonance shift such as beam stiffening or nonlinear forcing. To examine the change of structural compliance over the course of scanner motion, a model has been developed that includes internal forces from residual stress and the resultant additional multi-axis coupling among actuator leg structures. Like some preceding vertical scanning micro-actuators, the scanner of this work has four legs, with each leg featuring four serially connected thin-film PZT unimorphs that allow the scanner to generate larger than 400 µm of vertical displacement at 14 VDC. Using an excitation near one or more resonances, the input voltage can be lowered, and complementary multi-axis rotations can be also generated, but change of the resonant frequencies with scanner height needs to be understood to maximize scanner performance. The presented model well predicts the experimental observation of the decrease of the resonant frequencies of the scanner with the increase of a dc bias voltage. Also, the effects of the magnitude and uniformity of residual stress across the scanner structure on the natural frequencies have been studied.