Quantitative probe for in-plane piezoelectric coupling in 2D materials

Piezoelectric response in two-dimensional (2D) materials has evoked immense interest in using them for various applications involving electromechanical coupling. In most of the 2D materials, piezoelectricity is coupled along the in-plane direction. Here, we propose a technique to probe the in-plane piezoelectric coupling strength in layered nanomaterials quantitively. The method involves a novel approach for in-plane field excitation in lateral Piezoresponse force microscopy (PFM) for 2D materials. Operating near contact resonance has enabled the measurement of the piezoelectric coupling coefficients in the sub pm/V range. Detailed methodology for the signal calibration and the background subtraction when PFM is operated near the contact resonance of the cantilever is also provided. The technique is verified by estimating the in-plane piezoelectric coupling coefficients (d(11)) for freely suspended MoS(2) of one to five atomic layers. For 2D-MoS(2) with the odd number of atomic layers, which are non-centrosymmetric, finite d(11) is measured. The measurements also indicate that the coupling strength decreases with an increase in the number of layers. The techniques presented would be an effective tool to study the in-plane piezoelectricity quantitatively in various materials along with emerging 2D-materials.