Effects of flexoelectricity and strain gradient on bending vibration characteristics of piezoelectric semiconductor nanowires

In this paper, the governing equation of a piezoelectric semiconductor (PSC) is derived after a consideration of flexoelectricity and the strain gradient effect. A one-dimensional first-order beam model is obtained through integration across its section. Based on this model, theoretical analysis is carried out for a cantilever PSC nanowire subjected to a time-harmonic transverse shear force. The effects of flexoelectricity and the strain gradient on bending vibration characteristics are investigated, including the natural frequencies and distributions of physical quantities. The results show that the strain gradient effect on the natural frequency and stiffness of a PSC nanowire is greater than that of flexoelectricity, while with regard to the influence on electric potential and carrier concentration, the reverse is true. Our findings shed light on the design and optimization of PSC devices such as energy harvesters at the nanoscale.