Electromechanical Coupling Analysis of a Piezoelectric–Flexoelectric–Semiconductor Cantilever Beam

This paper presents a theoretical study on the electromechanical coupling response of piezoelectric–flexoelectric–semiconductor (PFS) nanocantilevers by adopting flexoelectric elasticity and semiconductor theory. A unified mechanical–electrical model is established to incorporate a strain gradient, the piezoelectric effect, semiconducting characteristics, and flexoelectricity at micro-/nanoscales. Analytical solutions for deflection, electric potential, and electron concentration are obtained under three types of electrical boundary conditions. Numerical results show that flexoelectricity significantly enhances the effective bending stiffness of the beam under open-circuit conditions with or without surface electrodes, especially in thinner structures. With a fixed external electric potential condition, the applied potential can effectively modulate the deflection by adjusting the polarization field. The induced electric potential, under the open-circuit condition with surface electrodes, exhibits a peak value at a critical thickness and flexoelectric coefficient due to the synergistic effect of the strain gradient and flexoelectricity. The electron screening effect induced by the high doping concentration is found to suppress the induced potential considerably. The present work provides a fundamental understanding of PFS coupling and provides guidance for the design of high-sensitivity micro–nano-electromechanical systems/devices.