  The understanding of various types of disorders in atomically thin transition
metal dichalcogenides (TMDs), including dangling bonds at the edges, chalcogen
deficiencies in the bulk, and charges in the substrate, is of fundamental
importance for their applications in electronics and photonics. Because of the
imperfections, electrons moving on these two-dimensional (2D) crystals
experience a spatially non-uniform Coulomb environment, whose effect on the
charge transport has not been microscopically studied. Here, we report the
mesoscopic conductance mapping in monolayer and few-layer MoS2 field-effect
transistors (FETs) by microwave impedance microscopy (MIM). The spatial
evolution of the insulator-to-metal transition is clearly resolved.
Interestingly, as the transistors are gradually turned on, electrical
conduction emerges initially at the edges before appearing in the bulk of MoS2
flakes, which can be explained by our first-principles calculations. The
results unambiguously confirm that the contribution of edge states to the
channel conductance is significant under the threshold voltage but negligible
once the bulk of the TMD device becomes conductive. Strong conductance
inhomogeneity, which is associated with the fluctuations of disorder potential
in the 2D sheets, is also observed in the MIM images, providing a guideline for
future improvement of the device performance.
