Single-dopant band bending fluctuations in MoSe$_2$ measured with electrostatic force microscopy

In this work, we experimentally demonstrate two-state fluctuations in a metal-insulator-semiconductor (MIS) device formed out of a metallic atomic force microscopy tip, vacuum gap, and multilayer MoSe$_2$ sample. We show that noise in this device is intrinsically bias-dependent due to the bias-dependent surface potential, and does not require that the frequency or magnitude of individual dopant fluctuations are themselves bias-dependent. Finally, we measure spatial nonhomogeneities in band bending (charge reorganization) timescales.