  Strain engineering offers unique control to manipulate the electronic band
structure of two-dimensional materials (2DMs) resulting in an effective and
continuous tuning of the physical properties. Ad-hoc straining 2D materials has
demonstrated novel devices including efficient photodetectors at
telecommunication frequencies, enhanced-mobility transistors, and on-chip
single photon source, for example. However, in order to gain insights into the
underlying mechanism required to enhance the performance of the next-generation
devices with strain(op)tronics, it is imperative to understand the nano- and
microscopic properties as a function of a strong non-homogeneous strain. Here,
we study the strain-induced variation of local conductivity of a few-layer
transition-metal-dichalcogenide using a conductive atomic force microscopy. We
report a novel strain characterization technique by capturing the electrical
conductivity variations induced by local strain originating from surface
topography at the nanoscale, which allows overcoming limitations of existing
optical spectroscopy techniques. We show that the conductivity variations
parallel the strain deviations across the geometry predicted by molecular
dynamics simulation. These results substantiate a variation of the effective
mass and surface charge density by .026 me/% and .03e/% of uniaxial strain,
respectively. Furthermore, we show and quantify how a gradual reduction of the
conduction band minima as a function of tensile strain explains the observed
reduced effective Schottky barrier height. Such spatially-textured electronic
behavior via surface topography induced strain variations in atomistic-layered
materials at the nanoscale opens up new opportunities to control fundamental
material properties and offers a myriad of design and functional device
possibilities for electronics, nanophotonics, flextronics, or smart cloths.
