The introduction of mechanical strain is a well-established technique for engineering electronic and optical properties in a broad range of semiconductor materials. In atomically thin materials such as graphene and mono- or few-layer transition metal dichalcogenides (TMDCs), the deliberate introduction and engineering of strain becomes an even more powerful approach for controlling material properties due to the high levels of elastic strain that can be accommodated and the feasibility of achieving precise, highly inhomogeneous strain distributions at the nanoscale. Full realization of and control over these possibilities will require the ability to characterize and control strain, and accompanying changes in electronic, optical, electromechanical, or other properties, in such materials at the nanoscale. To this end, we have used a variety of proximal probe microscopy and spectroscopy techniques to characterize strain and associated material properties in TMDC materials with nanoscale spatial resolution.

We first describe the use of tip-enhanced Raman spectroscopy (TERS) and tip-enhanced photoluminescence (TEPL) to characterize strain and optical properties of atomically thin MoS₂ to which local strain has been applied via transfer onto a nanopatterned substrate. In these studies, plasmonic modes at the apex of a metal-coated scanning probe tip are excited by laser illumination at or near the plasmon resonance wavelength, enabling Raman scattering and photoluminescence signals to be detected from nanoscale volumes with precise positional control. In tip-induced resonant Raman spectroscopy of monolayer and bilayer MoS₂, we observe large enhancements in Raman signal levels measured for MoS₂ associated with excitation of plasmonic gap modes between an Au-coated probe tip and Au substrate surface onto which MoS₂ has been transferred. Transitions in exciton photoluminescence intensity between monolayer and bilayer regions of MoS₂ are observed and discussed. Significant differences in nanoscale Raman spectra between monolayer and bilayer MoS₂ are also observed. The origins of specific resonant Raman peaks, their dependence on MoS₂ layer thickness, and spatial resolution associated with the transition in Raman spectra between monolayer and bilayer regions are described. In TERS and TEPL studies of bilayer MoS₂ with inhomogeneous strain created by transfer to a nanopatterned Au-coated substrate, we observe clear shifts in Raman peak positions and intensities which we correlate with MoS₂ phonon deformation potentials and strain-induced changes in electronic structure and phonon dispersion.

We then present an example of previously unobserved physical behavior that can arise in connection with nanoscale variations in strain in atomically thin TMDC materials, specifically in the area of electromechanical coupling – the interplay between strain and dielectric polarization in materials. Piezoelectricity, in which there is a linear relationship between dielectric polarization (or an applied electric field) and strain in materials lacking inversion symmetry, is the most well-known of such phenomena. Flexoelectricity, in which strain gradients induce a dielectric polarization field (or its converse, in which gradients in an applied electric field induce strain), is present in all materials but has been much less thoroughly studied, in large part due to the difficulty of achieving sufficiently large strain gradients in conventional crystalline materials. Atomically thin TMDCs offer unique opportunities to explore these and related phenomena. For example, in-plane piezoelectricity was theoretically predicted and subsequently observed experimentally to occur in monolayer and odd-layer MoS₂, arising due to the reduction in crystal symmetry in the atomically thin limit. Here, we discuss piezoresponse force microscopy measurements in which out-of-plane electromechanical response, which we have tentatively attributed to flexoelectricity, is observed in monolayer MoS₂ and other TMDCs. The estimated effective flexoelectric coefficients are found to be very consistent with those predicted by a simple physical model, and lead to electromechanical coupling response comparable in size to piezoelectric effects in the same materials.