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

We present an experimental approach for cryogenic dielectric measurements on ultrathin 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 ε₁ of the dielectric function at gigahertz frequencies and sample thicknesses down to a few nanometers. We perform simulations to optimize resonator coupling and sensitivity, and we demonstrate the possibility to quantify ε₁ with a conformal mapping technique in a wide sample-thickness and ε₁-regime. Experimentally, we determine ε₁ for various thin-film samples (photoresist, MgF₂, and SiO₂) in the thickness regime of nanometer up to micrometer. 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 SrTiO₃ bulk sample, using an in situ reference method to compensate for the temperature dependence of the superconducting resonator properties.