In order to develop a new generation of electronic and optoelectronic devices based on the novel properties of nanoscale and low-dimensional materials, there remains a strong need for techniques capable of measuring electronic properties non-destructively and with high spatial resolution. In scanning microwave microscopy (SMM) the near-field impedance between a scanning probe tip and a sample of interest is measured at GHz frequencies, enabling local measurement of the free carrier density and the associated nanometer-resolved imaging of conductivity variations.
Here we use SMM to study the electronic properties in field-effect transistors of the 2D transition metal dichalcogenides MoS2, WSe2, and MoTe2. We identify significant differences in carrier density across the individual devices arising from interactions with the oxide substrate, Schottky barriers at the source and drain electrodes, as well as evidence of interlayer interaction in multilayer devices. We develop a new method combining conventional backgate control of carrier density with a high-frequency backgate bias modulation to perform SMM-based differential capacitance measurements that allow us to directly address and image the spatial inhomogeneity in the gating response. We find preferential carrier accumulation in response to gating near the source and drain electrodes while the interior of the device shows an inhomogeneous response dominated by crystal-substrate interactions.