High-T_c SQUID Optimization: Exploring Competing Design and Operating Parameters

Improving the design of superconducting quantum interference devices (SQUIDs) for quantum sensing applications can involve a compromise between competing device parameters. For SQUIDs made from high-temperature superconductors (HTS), accurate modelling for optimization should include the device geometry, material properties and their temperature dependences, as well as thermal noise. We outline here a lumped element model that calculates the voltage response to magnetic flux of a hairpin SQUID and use it to explore the effect of these parameters on optimizing the SQUID voltage output. We first validate our model by showing close agreement with current-voltage and voltage-flux measurements performed on Yttrium Barium Copper Oxide hairpin SQUIDs with different geometries by including structures such as the bias leads. We show the effect of track width on the kinetic to geometric inductance ratios ( <tex-math notation="LaTeX">κ</tex-math> ) for a range of film thicknesses and temperatures, to aid researchers how to optimize SQUID designs. Then, through numerical simulations, we show on how (i) the voltage modulation depth decreases exponentially with the total inductance, independent of the asymmetry ratio; (ii) narrower superconducting tracks lead to a broader temperature operation range, <tex-math notation="LaTeX">Δ T ~ 30</tex-math> K, while wider tracks operate in a narrower temperature range, <tex-math notation="LaTeX">Δ T ~ 10</tex-math> K, but are more sensitive to temperature changes; and (iv) the optimal bias current, which maximises the device performance, depends on the operating temperature.