Characterizing dielectric properties of ultra-thin films using superconducting coplanar microwave resonators

Abstract

We present an experimental approach for cryogenic dielectric measurements on ultra-thin insulating films. Based on a coplanar microwave waveguide design we implement superconducting quarter-wave resonators with inductive coupling, which allows us to determine the real part ${\epsilon }_1$ of the dielectric function at GHz frequencies and for sample thicknesses down to a few nm. We perform simulations to optimize resonator coupling and sensitivity, and we demonstrate the possibility to quantify ${\epsilon }_1$ with a conformal mapping technique in a wide sample-thickness and ${\epsilon }_1$-regime. Experimentally we determine ${\epsilon }_1$ for various thin-film samples (photoresist, MgF${}_2$, and SiO${}_2$) in the thickness regime of nm up to $\mu m$. We find good correspondence with nominative values and we identify the precision of the film thickness as our predominant error source. Additionally we present a temperature-dependent measurement for a SrTiO${}_3$ bulk sample, using an in-situ reference method to compensate for the temperature dependence of the superconducting resonator properties.