Elucidating Piezoelectricity and Strain in Monolayer MoS at the Nanoscale Using Kelvin Probe Force Microscopy.

Strain engineering modifies the optical and electronic properties of atomically thin transition metal dichalcogenides. Highly inhomogeneous strain distributions in two-dimensional materials can be easily realized, enabling control of properties on the nanoscale; however, methods for probing strain on the nanoscale remain challenging. In this work, we characterize inhomogeneously strained monolayer MoS via Kelvin probe force microscopy and electrostatic gating, isolating the contributions of strain from other electrostatic effects and enabling the measurement of all components of the two-dimensional strain tensor on length scales less than 100 nm. The combination of these methods is used to calculate the spatial distribution of the electrostatic potential resulting from piezoelectricity, presenting a powerful way to characterize inhomogeneous strain and piezoelectricity that can be extended toward a variety of 2D materials.