Measuring 2D semiconductors with Kelvin Probe Force Microscopy: caution and success

We explore the Kelvin Probe Force Microscopy (KPFM) response of 2D semiconductors, using both simple models based on Fermi-Dirac statistics and experiments on back-gated, hBN-encapsulated, monolayer WSe₂. KPFM is a probe microscopy technique meant to measure the contact potential difference between the conductive probe and the sample surface. In these measurements, the tip can have as high as 3V amplitude ac bias and be positioned 10's of nm or less from the surface. At first, it seems that the KPFM technique could not possibly yield accurate data on a 2D semiconductor, as the easily gated channel would be slammed asymmetrically between n-doped and p-doped regimes by the tip's electric field. However, in experimental data, changes in the measured KPFM signal with back gate voltage correspond well to the expected change in chemical potential. We will discuss how typical experimental parameters can lead to quantitative results on 2D semiconductors. This makes it a useful measurement of relative chemical potentials and bandgaps in 2D materials, allowing their suitability for novel junctions to be directly measured.