A pure bending semiconductor beam that exhibits a non-homogeneous cross section variation enhanced flexoelectric coupling effect is investigated in this paper from the point of view of theoretical analysis and numerical calculations. According to the macroscopic theory of flexoelectric semiconductors, a one-dimensional bending model for a simple-supported beam with variable cross section is developed. The semi-analytical method, which is composed of cosine series and supplementary functions, is introduced to solve the partial differential equations with variable coefficients. Before the analysis, the convergence and correctness of the semi-analytical method are demonstrated systematically. The calculated results show that both the electric potential and the charge carrier distribute non-homogeneously in the entire beam under a pair of symmetric bending moments. It is revealed that more carriers, a larger electric potential, and more charges tend to concentrate in the zone near the ends. After introducing a dimensionless carrier density, this paper systematically investigates the non-homogeneous cross section variation effect on the flexoelectric coupling for charge carrier redistribution. It is indicated that more perturbation carriers in a non-uniform beam are produced by the enhanced flexoelectric coupling. The demonstration of this concept could be potential guidance for designing new semiconductor devices.

Based on the three-dimensional (3D) linear elasticity theory of piezoelectric semiconductor (PS) structures, inspired by the variational principle and the Mindlin plate theory, a two-dimensional (2D) higher-order theory and equations for thin-film devices are established for a rectangular coordinate system, in which Newton’s law (i.e., stress equation of motion), Gauss’s law (i.e., charge equation of electrostatics), Continuity equations (i.e., conservation of charge for holes and electrons), drift–diffusion theory for currents in semiconductors, and unavoidable thermo-deformation-polarization-carrier coupling response in external stimulus field environment are all considered. As a typical application of these equations, the static characteristic analysis of electromechanical fields for the extensional deformation of a PS thin-film device with thermal field excitations is carried out by utilizing established zeroth-order equations and the double trigonometric series solution method. It is revealed that the extensional deformations, electric potential, electron and hole concentration perturbations, and their current densities can be controlled actively via artificially tuning thermal fields of external stimuli. Especially, a higher temperature rise can induce a deeper potential well and a higher potential barrier, which can play a vital role in driving effectively motions and redistributions of electrons and holes. Overall, the derived 2D equations as well as the quantitative results provide us some useful guidelines for investigating the thermal regulation behavior of PS thin-film devices.

To study how in-plane stresses affect the mechano-electro-charge carrier coupling properties in piezoelectric semiconductor plates, this work establishes a mathematical model based on the phenomenological theory of n-type piezoelectric semiconductors and the first-order shear deformation theory. The differential quadrature method is adopted to solve the two-dimensional boundary value problem. For plates with simply supported and electrically shorted boundaries, displacement, electric potential, and perturbation carrier density exhibit biaxial symmetry. Rotation, electric field, and electric current density are symmetric about one midline and antisymmetric about the orthogonal midline. In addition, owing to the screening effect of redistributed carriers, both electric potential and electric field decline with an increase in initial carrier density. This study mainly focuses on the regulation of electro-elastic fields by in-plane stress. Numerical results show that compressive stress reduces effective bending stiffness, while tensile stress improves it. Field strength rises with increasing load magnitude. The total carrier density displays a near-exponential growth trend. The variation pattern remains nearly unchanged when the initial carrier density exceeds 1020 m−3. Further investigations into the forced vibration of piezoelectric semiconductor rectangular plates demonstrate that the change in equivalent stiffness induced by in-plane stress effectively adjusts the natural frequency of the structure. Potential barriers and wells form inside the plate at resonant frequencies. Current flow is thus restricted to regions outside these potential barriers and wells. The obtained mechanisms provide theoretical guidance for the design of smart piezotronic devices.