Size-Dependent Behavior of Piezoelectric Circular Ultrathin Films With Consideration of Surface Effects for NEMS Applications

In this paper, size-dependent electromechanical behavior of circular nanoplates made of piezoelectric materials is studied with consideration of materials surface properties. Gurtin-Murdoch theory for solid surfaces is used to generalize the classical plate model through an analytical method. Closed-form solutions based on Bessel functions with modified arguments are given for some normalized parameters that represent different physical aspects of the problem. In addition to general parametric analysis and for more exploration, ZnO nanoplates are also examined as pointing up case studies. It is shown that external electric loading can control the size-dependent behavior of piezoelectric nanoplates without any requirement for high-precision devices to be applied. This concept is more observable in thinner nanoplates with considerable size-dependent behaviors. Next, it is shown that surface residual stresses can make the piezoelectric nanoplates with especial geometries to get self-unstable. The numerical results illustrate a contradiction at macroscale which can be used for measurement of surface residual stresses without coping with difficulties of nanoscale experimental setups. An inverse formulation is also proposed for verification of the results with relevant experiments confirming capability of the presented procedure in size-dependent analysis of nanostructures.