Probing Effective Out-of-Plane Piezoelectricity in van der Waals Layered Materials Induced by Flexoelectricity

Many van der Waals layered 2D materials, such as h-BN, transition metal dichalcogenides (TMDs), and group-III monochalcogenides, have been predicted to possess piezoelectric and mechanically flexible natures, which greatly motivates potential applications in piezotronic devices and nanogenerators. However, only intrinsic in-plane piezoelectricity exists in these 2D materials and the piezoelectric effect is confined in odd-layers of TMDs. The present work is intent on combining the free-standing design and piezoresponse force microscopy techniques to obtain and directly quantify the effective out-of-plane electromechanical coupling induced by strain gradient on atomically thin MoS₂ and InSe flakes. Conspicuous piezoresponse and the measured piezoelectric coefficient with respect to the number of layers or thickness are systematically illustrated for both MoS₂ and InSe flakes. Note that the promising effective piezoelectric coefficient (d^eff ₃₃) of about 21.9 pm V⁻¹ is observed on few-layered InSe. The out-of-plane piezoresponse arises from the net dipole moment along the normal direction of the curvature membrane induced by strain gradient. This work not only provides a feasible and flexible method to acquire and quantify the out-of-plane electromechanical coupling on van der Waals layered materials, but also paves the way to understand and tune the flexoelectric effect of 2D systems.