Joint influence of multiple cylindrical PN and Schottky junctions on the propagation characteristics of shear cylindrical waves in a multilayered piezoelectric semiconductor concentric cylinder structure

Cylindrical structures are widely employed in micro-resonators, sensors, and energy harvesting devices owing to their high space utilization and efficient electromechanical coupling, especially with the advancement of microelectromechanical systems and high-frequency communication technologies. Multilayer concentric cylindrical structures with cylindrical PN and Schottky junctions, which are the core carriers of micro high-power devices, can regulate the behavior of elastic waves through the surface and interface effects of the junction regions, providing new solutions for high-performance acoustic-electric devices. This study theoretically investigates the propagation of shear cylindrical waves in an infinitely long, multilayered piezoelectric semiconductor concentric cylinder structure containing multiple PN and Schottky junctions. The work aims to comprehensively examine the influence of mechano-electric-carrier coupling on wave energy efficiency and to quantify the critical steady-state carrier concentration along with the synergistic multi-junction effects. By considering the coupling among mechanical displacement, electric potential, and charge carrier perturbation, the fundamental governing equations for this structure are meticulously derived in the cylindrical coordinate system. Subsequently, integrating the physical attributes of cylindrical junctions, a mathematical model for the propagation of shear cylindrical waves is established. Leveraging the spectral method, the calculation problem of the dispersion and attenuation curves of shear cylindrical waves is transformed into the calculation problem of the eigenvalues of the square matrix, which shows the joint influence of the multiple cylindrical PN and Schottky junctions on the dispersion and attenuation characteristics of the shear cylindrical waves. Through numerical computations of the dispersion and attenuation curves, it is evident that cylindrical Schottky and PN junctions respectively manifest surface and interface effects. These effects serve to reduce wave attenuation and inhibit the conversion of mechanical energy into electrical energy. Specifically, an increase in the steady-state charge carrier concentration intensifies these effects, leading to the attainment of a peak value.