  The metal-insulator transition (MIT) is one of the remarkable electrical
transport properties of atomically thin molybdenum disulphide (MoS2). Although
the theory of electron-electron interactions has been used in modeling the MIT
phenomena in MoS2, the underlying mechanism and detailed MIT process still
remain largely unexplored. Here, we demonstrate that the vertical
metal-insulator-semiconductor (MIS) heterostructures built from atomically thin
MoS2 (monolayers and multilayers) are ideal capacitor structures for probing
the electron states in MoS2. The vertical configuration of MIS heterostructures
offers the added advantage of eliminating the influence of large impedance at
the band tails and allows the observation of fully excited electron states near
the surface of MoS2 over a wide excitation frequency (100 Hz-1 MHz) and
temperature range (2 K- 300 K). By combining capacitance and transport
measurements, we have observed a percolation-type MIT, driven by density
inhomogeneities of electron states, in the vertical heterostructures built from
monolayer and multilayer MoS2. In addition, the valence band of thin MoS2
layers and their intrinsic properties such as thickness-dependence screening
abilities and band gap widths can be easily accessed and precisely determined
through the vertical heterostructures.
