Directly measuring flexoelectric coefficients μ₁₁ of the van der Waals materials

Flexoelectricity originates from the electromechanical coupling interaction between strain gradient and polarization, broadly applied in developing electromechanical and energy devices. However, the study of quantifying the longitudinal flexoelectric coefficient (μ₁₁) which is important for the application of atomic-scale two-dimensional (2D) materials is still in a slow-moving stage, owing to the technical challenges. Based on the free-standing suspension structure, this paper proposes a widely applicable method and a mensurable formula for determining the μ₁₁ constant of layer-dependent 2D materials with high precision. A combination of in situ micro-Raman spectroscopy and piezoresponse force microscopy (PFM) imaging was used to quantify the strain distribution and effective out-of-plane electromechanical coupling, respectively, for μ₁₁ constant calculation. The μ₁₁ constants and their physical correlation with the variable mechanical conditions of naturally bent structures have been obtained extensively for the representative mono-to-few layered MX₂ family (M = W and Mo; X = S and Se), and the result is perfectly consistent with the estimated order-of-magnitude of the μ₁₁ value (about 0.065) of monolayer MoS₂. The quantification of the flexoelectric constant in this work not only promotes the understanding of mechanical and electromechanical properties in van der Waals materials, but also paves the way for developing novel 2D nano-energy devices and mechanical transducers based on flexoelectric effects.