50 Ohm Transmission Lines with Extreme Wavelength Compression Based on Superconducting Nanowires on High-Permittivity Substrates

Abstract

We demonstrate impedance-matched low-loss transmission lines with a signal wavelength more than 150 times smaller than the free space wavelength using superconducting nanowires on high permittivity substrates. A niobium nitride thin film is patterned in a coplanar waveguide (CPW) transmission line geometry on a bilayer substrate consisting of 100 nm of epitaxial strontium titanate on high-resitivity silicon. The use of strontium titanate on silicon enables wafer-scale fabrication and maximizes process compatibility. It also makes it possible to realize a $50$ $\Omega$ characteristic impedance across a wide range of CPW widths, from the nanoscale to the macroscale. We fabricated and characterized an approximately $50$ $\Omega$ CPW device with two half-wave stub resonators. Comparing the measured transmission coefficient to numerical simulations, we determine that the strontium titanate film has a dielectric constant of $1.1 \times 10^3$ and a loss tangent of not more than 0.009. To facilitate the design of distributed microwave devices based on this type of material system, we describe an analytical model of the CPW properties that gives good agreement with both measurements and simulations.