Circuit-level design principles for transmission-mode microwave impedance microscopy

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 ? 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 S-11 resonance, which can be explained by the maximum power transfer theorem.

Automated summary

The recently developed technique of transmission-mode microwave impedance microscopy greatly expands the capabilities of standard reflection-mode MIM for studying nanoscale electro-acoustic devices. However, there is a lack of systematic design principles for boosting sensitivity and balancing bandwidth. This study shows that the T-MIM signal is proportional to the reflection-mode voltage enhancement factor of the circuit, as long as the output impedance of the local voltage source is properly treated. The authors demonstrate a realistic path for achieving this proportionality using commercially available superconducting components and critically coupled impedance matching networks.