We report quantitative measurements of nanoscale permittivity and conductivity using tuning-fork (TF) based microwave impedance microscopy (MIM). The system is operated under the driving amplitude modulation mode, which ensures satisfactory feedback stability on samples with rough surfaces. The demodulated MIM signals on a series of bulk dielectrics are in good agreement with results simulated by finite-element analysis. Using the TF-MIM, we have visualized the evolution of nanoscale conductance on back-gated $MoS_2$ field effect transistors and the results are consistent with the transport data. Our work suggests that quantitative analysis of mesoscopic electrical properties can be achieved by near-field microwave imaging with small distance modulation.
Download