Measurement of sub pm/V in-plane piezo-coupling coefficients using lateral PFM

Piezoelectric effect, in combination with other properties of two-dimensional (2D) materials, has relevance for various electromechanical applications. 2D layers such as hBN, transition-metal dichalcogenides and many other emerging 2D materials exhibit in-plane piezoelectricity. We propose a technique to quantitatively measure the in-plane piezoelectric coupling for 2D materials. The method involves a novel approach for in-plane field excitation in lateral Piezoresponse force microscopy (PFM) to facilitate the measurement for the 2D materials. We utilize the contact resonance gain of the AFM probe to improve the detection sensitivity by more than an order of magnitude. Piezoelectric coupling coefficients as low as pm/V can be measured using the proposed method. The technique is verified by estimating the in-plane piezoelectric coupling coefficients for freely suspended MoS of one to five atomic layers. The technique is useful for quantitative characterization of the in-plane piezo-coupling in the emerging 2D-materials.