Universal signal scaling in microwave impedance microscopy

Abstract

Microwave impedance microscopy (MIM) is an emerging scanning probe technique that measures the local complex dielectric function using near-field microwave. Although it has made significant impacts in diverse fields, a systematic, quantitative understanding of the signal's dependence on various important design parameters is lacking. Here, we show that for a wide range of MIM implementations, given a complex tip-sample admittance change ΔY, the MIM signal—the amplified change in the reflected microwave amplitude—is −G·ΔY/2Y0·η2·Vin, where η is the ratio of the microwave voltage at the probe to the incident microwave amplitude, Y0 is the system admittance, and G is the total voltage gain. For linear circuits, η is determined by the circuit design and does not depend on Vin. We show that the maximum achievable signal for different designs scales with η2 or η when limited by input power or sample perturbation, respectively. This universal scaling provides guidance on diverse design goals, including maximizing narrow-band signal for imaging and balancing bandwidth and signal strength for spectroscopy.