Three-Dimensional Integrated X-ray Diffraction Imaging of a Native Strain in Multi-Layered WSe 2 .

Emerging two-dimensional (2-D) materials such as transition-metal dichalcogenides show great promise as viable alternatives for semiconductor and optoelectronic devices that progress beyond silicon. Performance variability, reliability, and stochasticity in the measured transport properties represent some of the major challenges in such devices. Native strain arising from interfacial effects due to the presence of a substrate is believed to be a major contributing factor. A full three-dimensional (3-D) mapping of such native nanoscopic strain over micron length scales is highly desirable for gaining a fundamental understanding of interfacial effects but has largely remained elusive. Here, we employ coherent X-ray diffraction imaging to directly image and visualize in 3-D the native strain along the (002) direction in a typical multilayered (∼100-350 layers) 2-D dichalcogenide material (WSe2 ) on silicon substrate. We observe significant localized strains of ∼0.2% along the out-of-plane direction. Experimentally informed continuum models built from X-ray reconstructions trace the origin of these strains to localized nonuniform contact with the substrate (accentuated by nanometer scale asperities, i.e., surface roughness or contaminants); the mechanically exfoliated stresses and strains are localized to the contact region with the maximum strain near surface asperities being more or less independent of the number of layers. Machine-learned multimillion atomistic models show that the strain effects gain in prominence as we approach a few- to single-monolayer limit. First-principles calculations show a significant band gap shift of up to 125 meV per percent of strain. Finally, we measure the performance of multiple WSe2 transistors fabricated on the same flake; a significant variability in threshold voltage and the "off" current setting is observed among the various devices, which is attributed in part to substrate-induced localized strain. Our integrated approach has broad implications for the direct imaging and quantification of interfacial effects in devices based on layered materials or heterostructures.