Electrostatic effects of inhomogeneous strain in monolayer transition metal dichalcogenides



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Two-dimensional materials are only a few atoms thick, exhibiting novel properties due to their reduced dimensionality. Strain engineering can be used to modify optical and electronic properties, and highly inhomogeneous strain distributions in two-dimensional materials can be easily realized, allowing for their properties to be tuned on the nanoscale. This work is primarily focused on transition metal dichalcogenides, which have received much attention owing to their semiconducting nature, placing them in a key role among two-dimensional materials. Monolayer transition metal dichalcogenides exhibit a significant piezoelectric effect that can couple with spatially inhomogeneous strain distributions to influence electronic and optical behavior. In this work, inhomogeneous strain and piezoelectricity in transition metal dichalcogenides are studied. We first examine the luminescence behavior of monolayer MoS₂ and WSe₂ in the presence of strain and strain gradients generated via nanoindentation. The strain distribution and piezoelectricity resulting from indentation of monolayer MoS₂ and WSe₂ is modeled, and the interaction between the piezoelectric effect and strain distribution is demonstrated to result in charge densities reaching 10¹² e/cm², with electrostatic potential variations on the order of ±0.1V across the suspended monolayer in the modeled geometry. These results have potential implications for luminescence and exciton transport behavior in monolayer transition metal dichalcogenides with spatially varying strain. We then characterize monolayer MoS₂ which is inhomogeneously strained via a nanopatterned substrate. Kelvin probe force microscopy and electrostatic gating are used to measure the spatial distribution of the conduction band edge energy which can be correlated to in-plane hydrostatic strain. This method demonstrates the capability to resolve the strain distribution on length scales less than 100nm. A method for determining the distribution of the full in-plane strain tensor from the in-plane hydrostatic strain distribution is also presented. The combination of these methods is able to successfully calculate the spatial distribution of the electrostatic potential resulting from piezoelectricity that agrees well with experimental results. These methods present a powerful way to characterize inhomogeneous strain distributions and piezoelectricity that can be extended towards characterization of a variety of 2D materials.


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