Electric control of a phononic crystal constituted of Piezoelectric layers using Schottky diode

A one-dimensional piezoelectric phononic crystal (PPC) consisting of a periodic pattern made of two perfectly bonded materials: one active (piezoelectric), the other passive (elastic) and exhibiting a strong acoustic impedance contrast is studied. We are interested in the tunability of piezoelectric inclusions in order to control the propagation of ultrasonic waves in the MHz range from a nonlinear electrical component connected to the terminals of the piezoelectric elements. After modeling the dynamic resistance of the Schottky diode, based on the piezoelectricity equations, a one-dimensional analytical model is proposed to take into account the resistive impedance effect of this diode connected to the electrodes of the active plate. Thus, we have shown that the application of various electrical boundary conditions (EBCs) on the electrodes (open-circuit, short_circuit, connecting an electrical load) allows to change the effective properties of the piezoelectric plate in particular and those of the PPC in general. The dispersion of the waves is then electrically tuned and, depending on the applied EBCs, we have demonstrated numerically the possibility of opening Bragg or hybridization gaps in the PPC band structure.