Plane strain problems for flexoelectric semiconductors

Abstract

The flexoelectric effect, which is induced by strain gradients, is a pervasive phenomenon in dielectric and semiconductor materials. Flexoelectric semiconductors have considerable potential for application in the field of micro- and nanoelectronics, although their theoretical research is still in its infancy. In particular, there is a paucity of research on the exact solutions of the multiphysics field coupling problems for flexoelectric semiconductors. In light of these considerations, this paper presents the first comprehensive and rigorous investigation into the plane strain issues pertaining to flexoelectric semiconductors. The coupled governing equations for flexoelectric semiconductors under plane strain conditions are reformulated for decoupling purposes. On this basis, we derive the exact solutions to a series of plane-strain problems for flexoelectric semiconductors, including bending of beams, deformation of pressurized cylinders, cylindrical cavities, cylindrical inhomogeneities, and cylindrical inclusion problems with eigenstrain. By employing these exact solutions, we investigate the size effect of multiphysics field coupling in flexoelectric semiconductors and the influence of the initial doping concentration. Furthermore, we employ a mixed finite element method for numerical simulations of flexoelectric semiconductors. The high degree of agreement between the finite element solutions and the analytical exact solutions validates the utility of the exact solutions derived in this study as benchmark solutions for related numerical methods. This study offers insights and guidance for the design of flexoelectric semiconductor devices and provides a deeper understanding of the multiphysics field coupling behavior of flexoelectric semiconductors containing defects.