Surface effect-dependent active manipulation investigation on nonlinear deformation-polarization-carrier coupling fields in a multiferroic flexoelectric piezoelectric semiconductor device considering coupled extension and bending

With the aid of plane strain assumption, classical bending theory without shear deformation, as well as linearized drift-diffusion current density model for mobile carriers, a theoretical model of magneto-thermo-mechanical coupling for multiferroic flexoelectric piezoelectric semiconductor (PS) device with surface effect is established based on nonlinear magnetostrictive constitutive model for giant magnetostrictive material Terfenol-D, phenomenological theory for PS, and zeroth-order plate equations related to coupled extensional and flexural deformations with surface effect, strain gradient, and flexoelectricity. After correctness and validity analysis of theoretical model developed, the systematic numerical analysises and discussions are carried out sequentially with emphasis on screening effect of mobile carriers, size-dependent characteristic and critical thickness induced via surface effect, strain gradient, flexoelectronics-related electronic regulation, and nonlinear active manipulation mechanism and evolution law about multi-physical fields. Numerical results indicate that a comparatively small initial state electron (hole) doping concentration can effectively improve magnetoelectric (ME) coupling effect, which is unfavorable for enhancing strain gradient and electric polarization. At nanoscale, ME coupling effect becomes stronger because of a stronger surface effect corresponds to a larger surface thermal stress modulus and surface piezomagnetic constant. When thickness of multiferroic flexoelectric PS device decreases to its critical size, the size-dependent characteristic of deformation-polarization-carrier coupling fields caused via flexoelectricity is very evident and must be fully considered. This research is of great significance for understanding flexoelectronics-related nonlinear active manipulation mechanism about mobile electron and hole transport characteristics in controllable giant magnetostrictive material exemplified by Terfenol-D based flexoelectric PS devices.