Stress-induced electric potential barriers in thickness-stretch deformations of a piezoelectric semiconductor plate

We study the effects of equal and opposite normal stresses applied at the top and bottom surfaces of a piezoelectric semiconductor plate of crystals of class (6 mm). A first-order plate theory is established to model the stress-induced thickness-extensional deformation which is coupled to the in-plane extensional deformation of the plate. Analytical solutions are obtained for a rectangular plate under uniform or local normal stresses on the surfaces of the plate. In the case of a uniform load, a combination of parameters is identified which characterizes the strength of the coupling effect of interest, i.e., the thickness stress-induced redistribution of mobile charges. In the case of a local load applied to the central part of the plate, it is found that a local potential barrier is created. The potential barrier is accompanied by local distributions of mobile charges. The dependence of the potential barrier on various physical and geometric parameters is examined.