Determining the temperature-dependent London penetration depth in HTS thin films and its effect on SQUID performance

The optimum design of high-sensitivity Superconducting Quantum Interference Devices (SQUIDs) and other devices based on thin high-temperature superconductor (HTS) films requires accurate inductance modeling. This needs the London penetration depth λ to be well defined, not only at 77K, but also for any operating temperature, given the increasingly widespread use of miniature low-noise single-stage cryocoolers. Temperature significantly affects all inductances in any active superconducting device, and cooling below 77 K can greatly improve device performance; however, accurate data for the temperature dependence of inductance and λT for HTS devices are largely missing in the literature. We report here inductance measurements on a set of 20 different thin-film YBa ₂Cu ₃O _7−x SQUIDs at 77K with thickness t=220 or 113nm. By combining experimental data and inductance modeling, we find an average penetration depth λ 77=nm at 77K, which was independent of t. Using the same methods, we derive an empirical expression for λ for a further three SQUIDs measured on a cryocooler from 50 to 79=K. Our measured value of λ7 and our inductance extraction procedures were then used to estimate the inductances and the effective areas of directly coupled SQUID magnetometers with large washer-style pickup loops. The latter agrees better than 7% with experimentally measured values, validating our measured value of λ and our inductance extraction methods.