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arXiv:2002.12801 · Journal of Physics Condensed Matter

Effects of device geometry and material properties on dielectric losses in superconducting coplanar-waveguide resonators

Valtteri Lahtinen, Mikko Möttönen

Published Jun 2, 2020• 17 citations
arXivHTMLPDF

Abstract

Superconducting coplanar-waveguide (CPW) resonators are one of the key devices in circuit quantum electrodynamics (cQED). Their performance can be limited by dielectric losses in the substrate and in the material interfaces. Reliable modeling is required to aid in the design of low-loss CPW structures for cQED. We analyze the geometric dependence of the dielectric losses in CPW structures using finite-element modeling of the participation ratios of the lossy regions. In a practical scenario, uncertainties in the the dielectric constants and loss tangents of these regions introduce uncertainties in the theoretically predicted participation ratios. We present a method for combining loss simulations with measurements of two-level-system-limited quality factors and resonance frequencies of CPW resonators. Namely, we solve an inverse problem to find model parameters producing the measured values. High quality factors are obtainable by properly designing the cross-sectional geometries of the CPW structures, but more accurate modeling and design methods for low-loss CPW resonators are called for major future improvements. Our nonlinear optimization methodology for solving the aforementioned inverse problem is a step in this direction.

DOI
10.1088/1361-648x/ab98c8

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Superconducting coplanar-waveguide (CPW) resonators are one of the key devices in circuit quantum electrodynamics (cQED). Their performance can be limited by dielectric losses in the substrate and in the material interfaces. Reliable modeling is required to aid in the design of low-loss CPW structures for cQED. We analyze the geometric dependence of the dielectric losses in CPW structures using finite-element modeling of the participation ratios of the lossy regions. In a practical scenario, uncertainties in the the dielectric constants and loss tangents of these regions introduce uncertainties in the theoretically predicted participation ratios. We present a method for combining loss simulations with measurements of two-level-system-limited quality factors and resonance frequencies of CPW resonators. Namely, we solve an inverse problem to find model parameters producing the measured values. High quality factors are obtainable by properly designing the cross-sectional geometries of the CPW structures, but more accurate modeling and design methods for low-loss CPW resonators are called for major future improvements. Our nonlinear optimization methodology for solving the aforementioned inverse problem is a step in this direction.
Superconducting quantum computing systems, including coplanar waveguide (CPW) resonators and qubits, are highly susceptible to energy dissipation from two-level systems (TLS) within bulk and interfacial dielectrics. CPW resonators serve as an ideal platform for characterizing these material losses at the single-photon excitation level. Building on recent experimental evidence that interface engineering can mitigate TLS losses, this study employs simulations to evaluate resonator quality factors across various interface modifications. Our results demonstrate that reducing losses at the substrate–air (SA) interface can increase the internal quality factor Qi by up to three orders of magnitude. While etching the SA interface also enhances Qi, material loss remains the dominant dissipation mechanism. Furthermore, we find that other lossy interfaces have a significantly smaller impact on the quality factor compared to the SA interface. These simulation results align with established experimental findings, providing a robust framework for refining resonator design. This work offers precise guidelines for TLS mitigation, essential for enhancing coherence times and developing more reliable superconducting quantum processors.
© 2019 American Physical Society. Superconducting quantum-computing architectures comprise resonators and qubits that experience energy loss due to two-level systems (TLSs) in bulk and interfacial dielectrics. An understanding of these losses is critical to improving performance in superconducting circuits. In this work, we present a method for quantifying the TLS losses of different bulk and interfacial dielectrics present in superconducting coplanar-waveguide (CPW) resonators. By combining statistical characterization of sets of specifically designed CPW resonators on isotropically etched silicon substrates with detailed electromagnetic modeling, we determine the separate loss contributions from individual material interfaces and bulk dielectrics. This technique for analyzing interfacial TLS losses can be used to guide targeted improvements to qubits, resonators, and their superconducting fabrication processes.
Superconducting coplanar waveguide (SCPW) resonators have a wide range of applications due to the combination of their planar geometry and high quality factors relative to normal metals. However, their performance is sensitive to both the details of their geometry and the materials and processes that are used in their fabrication. In this paper, we study the dependence of SCPW resonator performance on materials and geometry as a function of temperature and excitation power. We measure quality factors greater than 2 × 106 at high excitation power and 6 × 105 at a power comparable to that generated by a single microwave photon circulating in the resonator. We examine the limits to the high excitation power performance of the resonators and find it to be consistent with a model of radiation loss. We further observe that while in all cases the quality factors are degraded as the temperature and power are reduced due to dielectric loss, the size of this effect is dependent on resonator materials and geometry. Finally, we demonstrate that the dielectric loss can be controlled in principle using a separate excitation near the resonance frequencies of the resonator.
Improving the performance of superconducting qubits and resonators generally results from a combination of materials and fabrication process improvements and design modifications that reduce device sensitivity to residual losses. One instance of this approach is to use trenching into the device substrate in combination with superconductors and dielectrics with low intrinsic losses to improve quality factors and coherence times. Here, we demonstrate titanium nitride coplanar waveguide resonators with mean quality factors exceeding two million and controlled trenching reaching 2.2 μm in the silicon substrate. Additionally, we measure sets of resonators with a range of sizes and trench depths and compare these results with finite-element simulations to demonstrate quantitative agreement with a model of interface dielectric loss. We then apply this analysis to determine the extent to which trenching can improve resonator performance.
Superconducting coplanar waveguide (CPW) resonators are powerful and versatile tools used in areas ranging from radiation detection to circuit quantum electrodynamics. Their potential for low intrinsic losses makes them attractive as sensitive probes of electronic properties of bulk materials and thin films. Here we use superconducting MoRe CPW resonators to investigate the high-frequency (up to 0.3 GHz) and low-temperature (down to 3.5 K) permittivity of SrTiO3{\mathrm{SrTiO}}_{3}SrTiO3​, a nonlinear dielectric on the verge of a ferroelectric transition (quantum paraelectricity). We perform a quantitative analysis of its dielectric properties as a function of external dc bias (up to $\ifmmode\pm\else\textpm\fi{}15\phantom{\rule{0.16em}{0ex}}\mathrm{V}$), rf power, and mode number and discuss our results within the framework of the most recent theoretical models. We also discuss the origin of a fatigue effect that reduces the tunability of the dielectric constant of SrTiO3{\mathrm{SrTiO}}_{3}SrTiO3​, which we relate to the presence of oxygen vacancies.
Abstract Coplanar waveguide (CPW) resonators have shown considerable success in circuit quantum electrodynamics research. However, their susceptibility to an external magnetic field limits their general functionality. In addition, electrical voltage gating for devices coupled to a CPW resonator necessitates alterations to the ground plane, changing the resonator characteristics. To avoid these problems, we fabricated and measured quarter wavelength differentially driven coplanar stripline (CPS) resonators made of NbTiN. We measured multiple devices with varying geometrical parameters in these novel resonators and analyse changes in their internal quality factor and two-level system losses. Furthermore, we establish the resilience of the resonators to an applied magnetic field by tracking the resonance frequency shift, without optimisation of the resonator geometry. Due to their flexible design and high magnetic field resilience, CPS resonators are particularly well-suited to study superconductor-semiconductor heterophysics where voltage gating or a magnetic field are necessary.