Not yet reviewed by Pith; the record is open.

Electrostatic modification of functional materials by electrolytic gating has demonstrated a remarkably wide range of density modulation, a condition crucial for developing novel electronic phases in systems ranging from complex oxides to layered chalcogenides. Yet little is known microscopically when carriers are modulated in electrolyte-gated electric double-layer transistors (EDLTs) due to the technical challenge of imaging the buried electrolyte-semiconductor interface. Here, we demonstrate the real-space mapping of the channel conductance in ZnO EDLTs using a cryogenic microwave impedance microscope. A spin-coated ionic gel layer with typical thicknesses below 50 nm allows us to perform high resolution (on the order of 100 nm) sub-surface imaging, while maintaining the capability of inducing the metal-insulator transition under a gate bias. The microwave images vividly show the spatial evolution of channel conductance and its local fluctuations through the transition, as well as the uneven conductance distribution established by a large source-drain bias. The unique combination of ultra-thin ion-gel gating and microwave imaging offers a new opportunity to study the local transport and mesoscopic electronic properties in EDLTs.