Flexoelectronics of a centrosymmetric semiconductor cylindrical nanoshell

Cylindrical shell-type semiconductors are essential for sensing and energy harvesting when integrated into surfaces of certain equipment, such as spacecraft, marine devices, and portable electronics, where mechanical forces play a significant impact on charge transport. Traditionally, such functionalities are only manifested in piezoelectric or pyroelectric crystals that possess non-centrosymmetry. Here, we theoretically investigate electronic behaviors driven by strain gradient-induced flexoelectric polarization in a centrosymmetric semiconductor cylindrical nanoshell, expanding the flexoelectronics in shell structures. The governing equations and accompanying boundary conditions are formulated simultaneously using the principle of virtual work and the fundamental lemma of the calculus of variation. Electromechanical interactions through static bending and forced vibration analyses of the newly developed model are systematically investigated. Under localized force excitation, the distribution of mobile charges is manipulated by tuning loading magnitudes and areas. The effects of doping levels on electric potentials and mobile charges are explored to show the interaction mechanism between flexoelectric and semiconducting properties. Moreover, the natural frequencies and modes of all mechanical displacements, electric potentials, and carrier concentration perturbations within the shell are identified. This paper provides a new approach for designing shell-shaped sensors and energy harvesters specifically for centrosymmetric semiconductors.