Fabrication and Characterization of Superconducting Resonators
Summary
Superconducting microwave resonators are of interest for detection of light, quantum computing applications and materials characterization. This work presents a detailed procedure for fabrication and characterization of superconducting microwave resonator scattering parameters.
Abstract
Superconducting microwave resonators are of interest for a wide range of applications, including for their use as microwave kinetic inductance detectors (MKIDs) for the detection of faint astrophysical signatures, as well as for quantum computing applications and materials characterization. In this paper, procedures are presented for the fabrication and characterization of thin-film superconducting microwave resonators. The fabrication methodology allows for the realization of superconducting transmission-line resonators with features on both sides of an atomically smooth single-crystal silicon dielectric. This work describes the procedure for the installation of resonator devices into a cryogenic microwave testbed and for cool-down below the superconducting transition temperature. The set-up of the cryogenic microwave testbed allows one to do careful measurements of the complex microwave transmission of these resonator devices, enabling the extraction of the properties of the superconducting lines and dielectric substrate (e.g., internal quality factors, loss and kinetic inductance fractions), which are important for device design and performance.
Introduction
Advances in astrophysical instrumentation have recently introduced superconducting microwave resonators for the detection of infrared light.1–4 A superconducting resonator will respond to infrared radiation of energy E = hv > 2Δ (where h is Planck's constant, v is the radiation frequency and Δ is the superconducting gap energy). When the resonator is cooled to a temperature well below the superconductor critical temperature, this incident radiation breaks Cooper pairs in the resonator volume and generates quasiparticle excitations. The increase in the density of quasiparticle excitations changes the kinetic inductance, and thus the complex surface impedance of the superconductor. This optical response is observed as a shift in the resonance frequency to lower frequency and a reduction in the quality factor of the resonator. In the canonical read-out scheme for a microwave kinetic inductance detector (MKID), the resonator is coupled to a microwave feedline and one monitors the complex transmission through this feedline at a single microwave frequency tone on resonance. Here, the optical response is observed as a change in both the amplitude and phase of transmission5 (Figure 1). Frequency-domain multiplexing schemes are capable of reading out arrays of thousands of resonators.6-7
To successfully design and implement superconducting-resonator-based instrumentation, the properties of these resonant structures need to be characterized accurately and efficiently. For example, precision measurements of the noise properties, quality factors Q, resonance frequencies (including their temperature dependence) and optical response properties of superconducting resonators are desired in the context of MKID device physics,8 quantum computing,9 and the determination of low-temperature materials properties.10
In all of these cases, the measurement of the circuit's complex transmission scattering parameters is desired. This work concentrates on the determination of the resonator's complex transmission coefficient, S21, whose amplitude and phase can be measured with a vector network analyzer (VNA). Ideally, the VNA reference plane (or test port) would be directly connected to the device under test (DUT), but a cryogenic setting normally requires the use of additional transmission line structures to realize a thermal break between RT (~300 K) and the cold stage (~0.3 K in this work; see Figure 2). Additional microwave components such as directional couplers, circulators, isolators, amplifiers, attenuators, and associated interconnecting cables may be needed to appropriately prepare, excite, read out and bias the device of interest. The phase velocities and dimensions of these components vary when cooling from room to cryogenic temperatures, and therefore they affect the observed response at the device calibration plane. These intervening components between the instrument and the device calibration plane influence the complex gain and need to be appropriately accounted for in the interpretation of the measured response.11
In theory, a scheme is needed that sets the measurement reference plane, identical to the one employed during calibration, at the DUT. To reach this target, one could measure the calibration standards over multiple cool-downs; however, this poses constraints on the stability of the VNA and the repeatability of the cryogenic instrument, which are difficult to attain. To mitigate these concerns, one could place the necessary standards in the cooled test environment and switch between them. This is, for example, similar to what is found in microwave probe stations, where the sample and calibration standards are cooled to 4 K by a continuous liquid helium flow or a closed-cycle refrigeration system.12 This method was demonstrated at sub-kelvin temperatures but requires a low-power, high-performance microwave switch in the test band of interest.13
An in-situ calibration procedure is therefore desired which accounts for the instrumental transmission response between the VNA reference plane and the device calibration plane (Figure 2) and which overcomes the limitations of the methods described above. This cryogenic calibration method, presented and discussed in detail in Cataldo et al.11, allows one to characterize multiple resonators over a frequency range wide compared to the resonator line width and inter-resonator spacing with an accuracy of ~1%. This paper will focus on the details of the sample fabrication and preparation processes, experimental test set-up and measurement procedures used to characterize superconducting microwave resonators with planar line geometries.11
Protocol
Representative Results
Discussion
The single-flip fabrication process provides a means for realizing superconducting resonators on both sides of a thin 0.45-µm single-crystal Si substrate. One may be motivated to use a single-crystal Si dielectric because it has more than an order of magnitude lower loss than deposited dielectrics (such as Si3N4) with loss tangents in the 4.0-6.5-GHz range < 1 x 10-5. 23-24 The ability to pattern features on both sides of this substrate allows one to employ a microstri…
Declarações
The authors have nothing to disclose.
Acknowledgements
The authors acknowledge funding support from the National Aeronautics and Space Administration (NASA)'s ROSES and APRA programs. GC also acknowledges the Universities Space Research Association for administering his appointment at NASA.
Materials
| Microposit S-1811 Photoresist | Shipley | ||
| BCB | Dow | 3022-35 | |
| SOI wafers | SOITec | Fabricated with SmartCutTM process | |
| Mo | Kamis | 99.99% | |
| Nb | Kamis | 99.95% (excludes Ta) | |
| E-6 metal etch w/AES | Fujifilm | CPG Grade | |
| Acetone | JT Baker | 9005-05 | CMOS Grade |
| HF dip (1:10) | JT Baker | 5397-03 | |
| PMMA | Microchem | 950 PMMA A2 | |
| GE 7031 | General Electric | Low-temperature adhesive | |
| Cryogenic Microwave Amplifier | MITEQ | AF S3-02000400-08-CR-4 | 2-4 GHz, gain ~30dB |
| NbTi Semi-rigid SMA cables | Coax. Co. | SC-086/50-NbTi-NbTi | |
| Circulator | PamTech | CTD1229K | return loss > -20 dB from 2-4 GHz |
| RF attenuator | Weinschel | Model-4M | 7 dB attenuation |
| Flexible SMA cables | Teledyne-Storm | R94-240 | ACCU-TEST |
| Vector Network Analyzer | Agilent | N5242A PNA-X | |
| Liquid He-4 cryogen | Praxair | ||
| Liquid N2 cryogen | Praxair |
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