Field-effect transistors (FETs) are the backbone of modern semiconductor devices. The same concept of electrostatic modulation of carrier densities has also been very fruitful for the exploration of electronic properties in advanced quantum materials. Using a non-invasive microwave impedance microscope with ~100nm resolution and ~1nS sensitivity, we have visualized the metal-insulator transitions of various materials in the FET configuration. The images acquired at different gate voltages of MoS2 and HgTe devices clearly show the spatial evolution of conductance at the edge and bulk of the sample. Strong electrical inhomogeneity is observed in the MIM images, revealing the fluctuations of disorder potential in the 2D layer. I will also discuss the conductance mapping in ion-gel-gated electric double-layer transistors and 2D devices under laser illumination. The combination of novel FETs and impedance microscopy paves the way to study phase transitions in complex materials induced by electrostatic field effects.

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