Intrinsic quality factors approaching 10 million in superconducting planar resonators enabled by spiral geometry

Abstract This study investigates the use of spiral geometry in superconducting resonators to achieve high intrinsic quality factors, crucial for applications in quantum computation and quantum sensing. We fabricated Archimedean Spiral Resonators (ASRs) using domain-matched epitaxially grown titanium nitride (TiN) on silicon wafers, achieving intrinsic quality factors of $Q_{\mathrm{i}} = (9.6 \pm 1.5) \times 10^{6}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>(</mml:mo> <mml:mn>9.6</mml:mn> <mml:mo>±</mml:mo> <mml:mn>1.5</mml:mn> <mml:mo>)</mml:mo> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> </mml:math> at the single-photon level and $Q_{\mathrm{i}} = (9.91 \pm 0.39) \times 10^{7}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>(</mml:mo> <mml:mn>9.91</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.39</mml:mn> <mml:mo>)</mml:mo> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> </mml:msup> </mml:math> at high power, which is more than twice as high as those for coplanar waveguide (CPW) resonators under identical conditions on the same chip. We conducted a comprehensive numerical analysis using COMSOL to calculate surface participation ratios (PRs) at critical interfaces: metal-air, metal-substrate, and substrate-air. Our findings reveal that ASRs have lower PRs than CPWs, explaining their superior quality factors and reduced coupling to two-level systems (TLSs).