High-Quality Superconducting Planar Resonators: Geometric Optimization and Surface Participation Analysis

This study explores the use of various geometries in superconducting planar resonators to achieve high intrinsic quality factors, crucial for applications such as bosonic quantum computation. We fabricated resonators using epitaxially grown titanium nitride (TiN) on silicon wafers, achieving intrinsic quality factors of Q_i = 1.0 × 10⁷ at the single-photon level and Q_i = 9.0 × 10⁷ at high power. These results significantly outperform traditional coplanar waveguide (CPW) resonators.

To understand these improvements, we conducted a comprehensive numerical analysis using the finite element solver COMSOL. We calculated surface participation ratios—the fraction of electric field energy stored in dissipative surface layers—at critical interfaces: metal-air, metal-substrate, and substrate-air. Our findings show that our resonators have lower surface participation ratios compared to CPWs, explaining their superior quality factors and reduced coupling to two-level systems.