Redistributions of charge carriers in a bending piezoelectric semiconductor shell subjected to mechanical loadings

Piezoelectric semiconductor shell, as a new type of multifunctional material structure, has shown broad application prospects in the fields of intelligent sensing, energy harvesting and flexible electronic devices in recent years. Clarifying the distribution behaviors of charge carriers after loading are crucial for the design and performance optimization of piezotronic devices. However, the distribution characteristics of charge carriers are also influenced by the form and magnitude of external loads due to the nonlinear interaction between electromechanical fields and charge carriers, which is usually ignored in previous studies. Hence, a bending n-type piezoelectric semiconductor thin shell model including this nonlinear effect is established in this study. The principle of virtual work is used to derive the governing equations and boundary conditions. Besides, the accuracy and effectiveness of present model are validated. Numerical results show that the linear model fails to accurately describe the distribution behaviors of charge carriers as the external load increases. Moreover, the distribution characteristics of charge carriers in the plane and along the thickness direction are revealed in different magnitude of uniform loads. An interesting phenomenon is found that the electron concentration will not be locked in the loading region on the middle surface regardless of whether the loading direction is along or against the c-axis. The former is redistributed towards the outer boundary of the loading zone within the plane, while the latter is mostly redistributed towards the upper and lower surfaces in thickness direction. The studies will provide guidance for designing new shell-based piezotronic devices.