Analysis of influence of buffer layers on microwave propagation through high-temperature superconducting thin films

Methods of analysis of microwave propagation through superconducting thin films with buffer layers on dielectric substrates have been discussed. Expressions describing the transmission coefficient S₂₁ through the structure and the complex conductivity sigma of a superconductor in an analytical form have been derived. The derived equations are valid for microwave propagation in waveguides as well as in free space with relevant definition of impedances. Using the obtained solutions, the influences of buffer layers' parameters (thickness, relative permittivity and loss tangent) on the transmission coefficient has been investigated using MATLAB. Simulations have been performed for 10 GHz transmission through YBa₂Cu₃O₇ films on sapphire with SrTiO₃ and CeO₂ buffer layers and on silicon with CaF₂ and YSZ buffer layers. To illustrate the simulations, measurements of the transmission through YBCO film on sapphire with SrTiO₃ buffer layer have been performed. It has been shown that even lossy buffer layers have very little impact (smaller than 1% in magnitude and 0.3% in phase) on the transmission coefficient through superconducting thin films, providing their thickness is below 10 mu m