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Characterisation and optimisation of superconducting microwave resonators

T. Boehme

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

In this master's thesis, I present the design, fabrication, and characterisation of superconducting microwave resonators. These resonators are quarter-wavelength coplanar waveguide resonators, operating at resonance frequencies between 4 GHz and 8 GHz. This kind of resonator is a key component in several applications, ranging from quantum computation devices to parametric amplifiers. Minimising the losses (achieving high internal quality factors) in these resonators is important to maximise performance of the applications they are used for. During the thesis work, we have studied several possible changes to improve the resonator quality.\n\nFabrication of the resonators was done in the Nanofabrication Laboratory at Chalmers University of Technology, and consist of the following steps: cleaning a sapphire or silicon wafer, depositing a layer of superconducting niobium, photolithography, and etching the waveguide. We then measured the resonators in a cryogen-free dilution refrigerator, at a temperature of 10 mK. The measurements consisted of a power sweep, in order to quantify the quality factor at high and low excitation powers. As an example, the first resonator we fabricated had a quality factor of 4.3 x 10^4 at high power (about 10^5 photons in the resonator), and quality factor of 3.7 x 10^4 at the single-photon level.\n\nWe then investigated different loss mechanisms that we expect to negatively affect the quality factor, and how to reduce this loss. Firstly, to reduce radiation losses and magnetic vortex losses, we reduced the lateral dimensions of the resonator. Secondly, as two-level system (TLS) losses are believed to mainly reside at the surfaces of the materials and interfaces between them, we etched into the substrate to selectively move a part of the TLS away from the resonator. We also studied the effect of the meandering of the resonator on the quality factor, as well as using two different etching gasses.\n\nBy gathering all this data, we were then able to compare the different combinations to see the effect of the changing parameters. In conclusion, the reduced lateral dimensions and the removal of part of the substrate indeed reduce the losses, as expected from the theory. We also found interesting behaviour with regards to the meandering, namely that having a meandered structure negatively affects the quality factor.\n\nCombining all results, we can give a guideline for the fabrication of resonators in the future, which gave us a quality factor up to 4.9 x 10^5 at high excitation power, and 3.0 x 10^5 at the single photon level.

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•Dec 16, 2010•1 citation
In this master's thesis, I present the design, fabrication, and characterisation of superconducting microwave resonators. These resonators are quarter-wavelength coplanar waveguide resonators, operating at resonance frequencies between 4 GHz and 8 GHz. This kind of resonator is a key component in several applications, ranging from quantum computation devices to parametric amplifiers. Minimising the losses (achieving high internal quality factors) in these resonators is important to maximise performance of the applications they are used for. During the thesis work, we have studied several possible changes to improve the resonator quality.\n\nFabrication of the resonators was done in the Nanofabrication Laboratory at Chalmers University of Technology, and consist of the following steps: cleaning a sapphire or silicon wafer, depositing a layer of superconducting niobium, photolithography, and etching the waveguide. We then measured the resonators in a cryogen-free dilution refrigerator, at a temperature of 10 mK. The measurements consisted of a power sweep, in order to quantify the quality factor at high and low excitation powers. As an example, the first resonator we fabricated had a quality factor of 4.3 x 10^4 at high power (about 10^5 photons in the resonator), and quality factor of 3.7 x 10^4 at the single-photon level.\n\nWe then investigated different loss mechanisms that we expect to negatively affect the quality factor, and how to reduce this loss. Firstly, to reduce radiation losses and magnetic vortex losses, we reduced the lateral dimensions of the resonator. Secondly, as two-level system (TLS) losses are believed to mainly reside at the surfaces of the materials and interfaces between them, we etched into the substrate to selectively move a part of the TLS away from the resonator. We also studied the effect of the meandering of the resonator on the quality factor, as well as using two different etching gasses.\n\nBy gathering all this data, we were then able to compare the different combinations to see the effect of the changing parameters. In conclusion, the reduced lateral dimensions and the removal of part of the substrate indeed reduce the losses, as expected from the theory. We also found interesting behaviour with regards to the meandering, namely that having a meandered structure negatively affects the quality factor.\n\nCombining all results, we can give a guideline for the fabrication of resonators in the future, which gave us a quality factor up to 4.9 x 10^5 at high excitation power, and 3.0 x 10^5 at the single photon level.
We report our development on design, fabrication and characterization of various superconducting resonators for quantum device applications. The resonators are developed mainly for superconducting qubit implementation in circuit QED structure, but future application will include photon detectors such as microwave kinetic inductance detectors. First we designed and fabricated half-wavelength coplanar waveguide resonators with niobium thin film on a high resistive silicon wafer, with the fundamental frequencies in the range of 1 to 8 GHz. The loaded quality factors are controlled by the coupling capacitors, and the lower bound of the intrinsic quality factor was measured down to 7 mK in the dilution refrigerator. We have also designed quarter-wavelength resonators and lumped LC resonators coupled to a transmission line, and characterized multiple resonators in a single transmission line. For the 3D transmon qubit application, we designed and fabricated a rectangular box resonator with superconducting aluminum. The intrinsic quality factor of the box resonator exceeds three million at 7 mK. We will also present basic results on the integration of a transmon qubit in the superconducting resonator.
The loss in superconducting microwave resonators at low-photon numbers and low temperatures is not well understood but has implications for achievable coherence times in superconducting qubits. We have fabricated single-layer resonators with a high quality factor by patterning a superconducting aluminum film on a sapphire substrate. Four resonator geometries were studied with resonant frequencies ranging from 5 to 7 GHz: a quasi-lumped element resonator, a coplanar strip waveguide resonator, and two hybrid designs that contain both a coplanar strip and a quasi-lumped element. Transmitted power measurements were taken at 30 mK as a function of frequency and probe power. We find that the resonator loss, expressed as the inverse of the internal quality factor, decreases slowly over four decades of photon number in a manner not merely explained by loss from a conventional uniform spatial distribution of two-level systems in an oxide layer on the superconducting surfaces of the resonator.
The sensitivity of a kinetic inductance detector is determined by the performance of the cavity circuit and therefore a high quality factor and low phase noise are required. We developed superconducting niobium coplanar waveguide resonators for kinetic inductance detectors at a resonance frequency of 6 GHz. The length of the resonators is adjusted to a quarter of a wavelength which corresponds to ≈ 5.3 mm in our geometry. Different layouts with coplanar waveguide transmission line topology for the resonator were designed and simulated. Some parameters of the device fabrication process were varied. The niobium thin films were deposited by magnetron sputtering on sapphire substrates kept at ambient temperature. The resonators were patterned by photolithography and reactive ion etching and measured at helium temperatures. Because of the quarter wave geometry with one shorted end the reflection parameter was measured. We have studied the influence of the coupling capacitances on quality factor. The optimization includes microwave simulations and implementation in different resonator structures. The measurements of optimized devices showed a very high quality factor above one million (10 6 ). The obtained results and perspective on further development of resonators will be discussed.
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.
We successfully designed and fabricated an absorption-type of superconducting coplanar waveguide (CPW) resonators. The resonators are made from a niobium film (about 160 nm thick) on a high-resistance Si substrate, and each resonator is fabricated as a meandered quarter-wavelength transmission line (one end is short to the ground and another end is capacitively coupled to a through feedline). With a vector network analyzer we measured the transmissions of the applied microwave through the resonators at ultra-low temperature. The obtained loaded quality factors are significantly high, i.e. up to ∼10 6 . When the temperature increases slowly from the base temperature (20 mK), the resonance frequencies of the resonators are blue shifted and the quality factors are lowered slightly. In principle, this type of device can integrate a series of CPW resonators with a common feedline, making it a promising candidate as the data bus for coupling distant solid-state qubits and the sensitive detector of single photons.
Measurements are made on superconducting Niobium on Sapphire and oxidized Silicon microwave coplanar resonators for quantum bit experiments. Device geometry and materials are investigated and quality factors in excess of a million have been observed. The resonant frequency as a function of temperature of a coplanar resonator is characterised in terms of the change in the number density of superconducting electrons. At lower temperatures, the resonant frequency no longer follows this function, and evidence is shown that this is associated with the resonant coupling of the resonant frequency with two level systems in the substrate. At T<2.2 K the resonant frequency scales logarithmically with the temperature, indicating that two level systems distributed in the volume of the Silicon Dioxide affect the electric permittivity. Applying higher input microwave power levels is shown to saturate these two level systems, essentially decoupling them from the CPR resonance. This is observed as an increase in resonant frequency and Q factor. The resonant frequency is also shown to have a high sensitivity to a magnetic field applied perpendicular to the plane of the coplanar resonator, with a quadratic dependence for the fundamental, second and third harmonics. Frequency shift of hundreds of linewidths are obtained. Coplanar resonator are fabricated and measured with current control lines built on chip, and these have shown to produce frequency shifts of tens of Kilohertz.