Redistribution of charge carriers in a bending piezoelectric semiconductor shell subjected to mechanical loading

Piezoelectric semiconductor shells, as a new type of multifunctional material structure, have shown broad application prospects in the fields of intelligent sensing, energy harvesting, and flexible electronic devices in recent years. Understanding the distributions of charge carriers under loading is crucial for the design and performance optimization of piezotronic devices. However, the distributions of charge carriers are also influenced by the form and magnitude of external loads, owing to the nonlinear interaction between electromechanical fields and charge carriers, which has usually been ignored in previous studies. Hence, in this study, a bending n-type piezoelectric semiconductor thin shell model taking account of this nonlinear effect is established on the basis of first-order shear deformation theory. The principle of virtual work is used to derive the governing equations and boundary conditions. The accuracy and effectiveness of the nonlinear model are validated through comparisons with a linearization under the condition of a small external load and with a three-dimensional pure piezoelectric model. Numerical results show that the linear model fails to accurately describe the distribution behaviors of charge carriers as the external load increases. The distributions of charge carriers in the plane and along the thickness direction are revealed for different magnitude of uniform loads. An interesting phenomenon is found in which the electron distribution is not confined to the loading region on the middle surface, regardless of whether the loading direction is along or against the c axis. In the former case, electrons are redistributed toward the outer boundary of the loading zone within the plane, while in the latter case, the redistribution is mostly toward the upper and lower surfaces in the thickness direction. The results of this study will provide guidance for designing new shell-based piezotronic devices.