Development of a microwave capacitive method for the spectroscopy of the complex permittivity

Abstract

We describe a vector network analyzer-based method to study the electromagnetic properties of nanoscale dielectrics at microwave frequencies (1 MHz–40 GHz). The complex permittivity spectrum of a given dielectric can be determined by placing it in a capacitor accessed on its both electrodes by coplanar waveguides. However, inherent propagation delays along the signal paths together with frequency-dependent effective surface of the capacitor at microwave frequencies can lead to significant distortion in the measured permittivity, which in turn can give rise to artificial frequency variations of the complex permittivity. We detail a fully analytical rigorous correction sequence with neither recourse to extrinsic loss mechanisms nor to arbitrary parasitic signal paths. We illustrate our method on 3 emblematic dielectrics: ferroelectric morphotropic lead zirconate titanate, its paraelectric pyrochlore counterpart, and strontium titanate. Permittivity spectra taken at various points along the hysteresis loop help shedding light onto the nature of the different dielectric energy loss mechanisms. Thanks to the analytical character of our method, we can discuss routes to extend it to higher frequencies and we can identify unambiguously the sources of potential artifacts.