Design and Modeling of Piezoelectric Nanofilm Actuators for Low-Voltage Powered Microrobots

Piezoelectric actuators are essential for sub-millimeter robots and reconfigurable microstructures owing to their advantages, including the ability to operate in air and high-speed response. However, the substantial performance degradation observed in piezoelectric actuators with sub-micrometer thickness poses a critical challenge for the design of low-voltage microactuators capable of achieving large bending curvature. Here we develop a coupled analytical-numerical framework for designing multilayer lead zirconate titanate (PZT) nanofilm microactuators under a low voltage constraint (≤5 V). An analytical multilayer beam model is extended to incorporate thickness-dependent material properties and an interfacial dead layer that reduces the effective electric field at small thicknesses. This enables rapid exploration of curvature and the neutral-axis position as functions of the thicknesses of PZT, electrodes, and the dielectric layer. Two- and three-dimensional finite-element simulations provide complementary predictions of neutral-axis location, voltage-dependent curvature response, and eigenmode shapes. The resulting design maps reveal a non-monotonic optimum for PZT thickness in the few-hundred-nanometer range to maximize the curvature change at low voltages and identify ultrathin top electrodes as a key design lever that enhances bending by reducing parasitic stiffness while shifting the neutral axis favorably. These findings offer quantitative guidelines for designing low-voltage, high-curvature piezoelectric microactuators for microrobotic systems.