# Geometric Scaling of Two-Level-System Loss in Superconducting Resonators

## TL;DR

This study investigates how two-level-system dielectric loss scales in superconducting resonators, combining experimental measurements with numerical modeling to identify dominant loss sources, especially highlighting the impact of hydrogen silsesquioxane (HSQ).

## Contribution

It introduces a comprehensive approach using 3D finite-element simulations to accurately model and analyze the geometric scaling of dielectric loss in superconducting resonators, emphasizing the role of fabrication materials.

## Key findings

- HSQ is the dominant loss source with a loss tangent of 8×10⁻³.
- Finite-element modeling accurately predicts current and electric field distributions.
- Dielectric loss scales with device geometry and material interfaces.

## Abstract

We perform an experimental and numerical study of dielectric loss in superconducting microwave resonators at low temperature. Dielectric loss, due to two-level systems, is a limiting factor in several applications, e.g. superconducting qubits, Josephson parametric amplifiers, microwave kinetic-inductance detectors, and superconducting single-photon detectors. Our devices are made of disordered NbN, which, due to magnetic-field penetration, necessitates 3D finite-element simulation of the Maxwell--London equations at microwave frequencies to accurately model the current density and electric field distribution. From the field distribution, we compute the geometric filling factors of the lossy regions in our resonator structures and fit the experimental data to determine the intrinsic loss tangents of its interfaces and dielectrics. We emphasise that the loss caused by a spin-on-glass resist such as hydrogen silsesquioxane (HSQ), used for ultrahigh lithographic resolution relevant to the fabrication of nanowires, and find that, when used, HSQ is the dominant source of loss, with a loss tangent of $\delta^i_{HSQ} = 8 \times 10^{-3}$.