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 put emphasis on 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. We find that, when used, HSQ is the dominant source of loss, with a loss tangent of .

Highlights

  • Several modern circuits rely on superconducting devices with high microwave characteristic impedance and low dissipation

  • High impedance is usually implemented using the kinetic inductance of a chain of Josephson junctions [1,2,3] or with sub-micron-width wires made of a disordered superconductor such as NbN [4], NbTiN [5], or granular Al [6,7,8]

  • These results confirms that the porous amorphous silicon oxide structure of developed HSQ [32, 33] is a major source of dielectric loss, and a process that allows for the removal of the HSQ mask would lead to significant improvements in device performance

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Summary

Introduction

Several modern circuits rely on superconducting devices with high microwave characteristic impedance and low dissipation. To accurately capture the physics, we instead perform 3D finite-element simulations of the current density and electric and magnetic fields at microwave frequencies, from which we extract the various filling factors This reveals that, while the metal-air (MA) interface has a small filling factor, the loss of the HSQ top dielectric is large enough to represent the largest combined loss, in agreement with measurements. Combining measurements of the loss and numerical simulation of the filling factors of the different interfaces, we determine the value of the loss tangent of HSQ: diHSQ = 8 ́ 10-3 , i.e. four times that of SiOx [27, 29, 35], which would have been the assumption due to the similarities between spin-on-glass resists and silicon oxide.

Modelling of TLS loss
Filling factor simulations
Discussion
Conclusion
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