A recently developed technique of transmission-mode microwave impedance microscopy (T-MIM) has greatly extended the capabilities of standard reflection-mode MIM to novel applications, such as the in operando study of nanoscale electro-acoustic devices. As is common for new techniques, systematic design principles for boosting sensitivity and balancing bandwidth are lacking. Here, we show numerically and analytically that the T-MIM signal is proportional to the reflection-mode voltage enhancement factor η of the circuit, as long as the output impedance of the local voltage source is properly treated. We show that this proportionality holds in the currently achievable "weak sampling"regime and beyond, for which we demonstrate a realistic path with commercially available superconducting components and critically coupled impedance matching networks. We demonstrate that for these next-generation designs, the sensitivity is generally maximized at a slightly different frequency from the unloaded S11 resonance, which can be explained by the maximum power transfer theorem.

Microwave impedance microscopy (MIM) is an emerging scanning probe technique for nanoscale complex permittivity mapping and has made significant impacts in diverse fields. To date, the most significant hurdles that limit its widespread use are the requirements of specialized microwave probes and high-precision cancellation circuits. Here, we show that forgoing both elements not only is feasible but also enhances performance. Using monolithic silicon cantilever probes and a cancellation-free architecture, we demonstrate Johnson-noise-limited, drift-free MIM operation with 15 nm spatial resolution, minimal topography crosstalk, and an unprecedented sensitivity of 0.26 zF/√Hz. We accomplish this by taking advantage of the high mechanical resonant frequency and spatial resolution of silicon probes, the inherent common-mode phase noise rejection of self-referenced homodyne detection, and the exceptional stability of the streamlined architecture. Our approach makes MIM drastically more accessible and paves the way for advanced operation modes as well as integration with complementary techniques.