Effects of the thin-film thickness on superconducting NbTi microwave resonators for on-chip cryogenic thermometry

Abstract Superconducting microwave resonators have recently gained a primary importance in the development of cryogenic applications, such as circuit quantum electrodynamics, electron spin resonance spectroscopy and particles detection for high-energy physics and astrophysics. In this work, we investigate the influence of the film thickness on the temperature response of microfabricated Nb 50 Ti 50 superconducting resonators. S-shaped split ring resonators (S-SRRs), approximately <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mn>20</mml:mn> </mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mtext>nm</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mn>150</mml:mn> </mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mtext>nm</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> thick, are designed to be electromagnetically coupled with standard Cu coplanar waveguides (CPWs) and their microwave properties are characterised at temperatures below <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mtext>K</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> . The combined contributions of the kinetic inductance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>T</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> increase and the decreasing loaded quality factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">L</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , for thinner films, induce an optimum condition on the temperature sensitivity and resolution of the resonators. A noise equivalent temperature as low as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0.53</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.09</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mtext>K</mml:mtext> <mml:mstyle scriptlevel="0"/> <mml:msup> <mml:mtext>Hz</mml:mtext> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> , at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mtext>Hz</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> , is reported for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mn>100</mml:mn> </mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mtext>nm</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> thick resonators at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mn>4.2</mml:mn> </mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mtext>K</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> . We also asses the possibility of implementing a multiplexed frequency readout, allowing for the simultaneous temperature tracking of several sensors along a single CPW. Such results demonstrate the possibility to perform a distributed cryogenic temperature monitoring, with a sub- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mtext>K</mml:mtext> </mml:mrow> </mml:math> resolution. Thus, the application of superconducting S-SRRs, eventually benefiting from an even higher <mml:math xmlns:mml="http://www.w3.org/1998/Math