We performed detailed studies of the current–voltage (I–V) characteristics in graphene/MoS2/metal vertical field-effect transistors. Owing to its low density of states, the Fermi level in graphene is very sensitive to its carrier density and thus the external electric field. Under the application of a bias voltage VB between graphene and the metal layer in the graphene/MoS2/metal heterostructure for driving current through the van der Waals interface, the electric field across the MoS2 dielectric induces a shift in the Fermi level of graphene. When the Fermi level of graphene coincides with the Dirac point, a significant nonlinearity appears in the measured I–V curve, thus enabling us to perform spectroscopy of the Dirac point. By detecting the Dirac point for different back-gate voltages, we revealed that the capacitance of the nanometer-thick MoS2 layer can be determined from a simple DC transport measurement.

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Note that these parameters mainly affect the current amplitude and the position of the Dirac point at VB = 0 V. The main results of the paper, such as the appearance of the inflection point in the I–V curve and the determination of the dielectric constant by using Eq. (3), are not seriously influenced by these parameters.

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