Superconducting Microstrip Transmission Lines Research Articles

Cross-Talk Between Superconducting Microstrip Transmission Lines

Cross-Talk Between Superconducting Microstrip Transmission Lines

External Field Coupling to Superconducting Microstrip Transmission Line in Nonlinear Operation

External Field Coupling to Superconducting Microstrip Transmission Line in Nonlinear Operation

Fabrication Development for SPT-SLIM, a Superconducting Spectrometer for Line Intensity Mapping

Line Intensity Mapping (LIM) is a new observational technique that uses low-resolution observations of line emission to efficiently trace the large-scale structure of the Universe out to high redshift. Common mm/sub-mm emission lines are accessible from ground-based observatories, and the requirements on the detectors for LIM at mm-wavelengths are well matched to the capabilities of large-format arrays of superconducting sensors. We describe the development of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R$</tex-math></inline-formula> = <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda / \Delta \lambda = 300$</tex-math></inline-formula> on-chip superconducting filter-bank spectrometer covering the 120–180 GHz band for future mm-LIM experiments, focusing on SPT-SLIM, a pathfinder LIM instrument for the South Pole Telescope. Radiation is coupled from the telescope optical system to the spectrometer chip via an array of feedhorn-coupled orthomode transducers. Superconducting microstrip transmission lines then carry the signal to an array of channelizing half-wavelength resonators, and the output of each spectral channel is sensed by a lumped element kinetic inductance detector (leKID). Key areas of development include incorporating new low-loss dielectrics to improve both the achievable spectral resolution and optical efficiency and development of a robust fabrication process to create a galvanic connection between ultra-pure superconducting thin-films to realize multi-material (hybrid) leKIDs. We provide an overview of the spectrometer design, fabrication process, and prototype devices.

Radiation Effects on Thin Flexible Superconducting Cables

We have studied the effects of gamma radiation on flexible superconducting microstrip transmission line structures, to explore their suitability for use in harsh environments where they may be subjected to radiation. In this work, we used two conductor variants: one with only Nb and another with a conductor stack of Al/Nb/Al. Spin-on polyimide HD-4110 was used as the dielectric substrate and both the variants were encapsulated with a layer of HD-4110 to increase the robustness of the structure by protecting the superconducting trace from potential mechanical damage. The resonators were irradiated at room temperature in a vacuum sealed chamber at a pressure of 1E-6 Torr using cobalt-60 as a source of gamma radiation. Samples were exposed to doses up to 60.8 Mrad (608 kGy). Quality factors of the resonators were extracted in the frequency range from 2 to 20 GHz, at various cryogenic temperatures between 1.2 K and 4.2 K, using a closed-cycle cryostat. We observed a small increase in microwave loss for higher temperature ranges, which points to a small change in the superconducting properties of the conductors. The results of this work show that low mass, flexible superconducting cables may be suitable alternatives to bulky coaxial cables for signal transmission at cryogenic temperatures in extreme (radiation) environments.

On the Response of Multiconductor Superconducting Microstrip Lines Under Plane Wave Excitation

Superconducting microwave circuits are composed of components made from superconducting microstrip transmission lines (SMTLs). The spatial features of the superconductors provide the system operation at high speed and low noise floor. However, coupling the external electromagnetic field in these systems reduces or nullifies their performance. This article presents a general solution for evaluating the electromagnetic behavior of multiconductor SMTLs under plane wave excitation. The analysis is portrayed in the spectral domain. Using the proposed approach, the electromagnetic susceptibility of the lines is evaluated for two proximity SMTLs. It is then investigated in different scenarios where the effect of film thickness, film spacing, and operating temperature is investigated. The study reveals that by increasing the film thickness or film spacing or decreasing the operating temperature, the lines’ susceptibility is increased. Further, it is shown that for small film spacing, the susceptibility dependency on temperature or film thickness of one line can affect the susceptibility of the other line.

Modeling of Superconducting Components in Full-Wave Simulators

Designing superconducting microwave planar components cannot be well performed without utilizing a full-wave simulator. However, well-known conventional simulators, i.e., Ansoft HFSS or CST microwave studio, cannot predict the electromagnetic behavior of superconducting circuits. Therefore, this paper proposes a simulation model through utilizing which one can evaluate superconducting microwave components in conventional simulators. The model works for a film thickness up to 5λ and can be used up to millimeter-wave frequencies. The proposed model replaces the superconducting film by a sheet with appropriate impedance. The value of the equivalent sheet impedance is determined subject to the current distribution within the film. Through the proposed simulation model, the characteristic impedance and phase constant of several superconducting microstrip transmission lines are obtained using Ansoft HFSS. The results are compared with those from theoretical formulas. The agreement between the results shows that one can obtain the behavior of superconducting microwave components by simulating the structure with the proposed model.

Analyzing Radiated Susceptibility of Superconducting Microstrip Transmission Line Under Plane Wave Excitation

Several studies have been conducted on an externally-excited microstrip transmission line; however, no study, to the best knowledge of the researchers, has examined the superconducting microstrip transmission lines (SMTL), which are the main part of the superconducting circuits. This article aims to investigate the radiated susceptibility of SMTL under plane wave excitation. The analysis is based on modeling the superconducting film as a current sheet with specified impedance. It is revealed that the equivalent sheet impedance depends on the current distribution within the film; hence, London's second equation is employed to obtain an integral equation to acquire the current distribution and, subsequently, the equivalent sheet impedance. Then, the susceptibility of the SMTL is calculated after applying the boundary condition at the equivalent impedance surface. The procedure is performed using spectral-domain approach and verified by COMSOL software. Finally, the susceptibility of the SMTL is examined at different temperatures and for different film thicknesses. The results show that the lower temperature makes the SMTL more susceptible to an external electromagnetic field. Moreover, the same behavior is observed for increased film thickness.

Second-generation Micro-Spec: A compact spectrometer for far-infrared and submillimeter space missions

Micro-Spec is a direct-detection spectrometer which integrates all the components of a diffraction-grating spectrometer onto a ≈10-cm2 chip through the use of superconducting microstrip transmission lines on a single-crystal silicon substrate. The second generation of Micro-Spec is being designed to operate with a spectral resolution of at least 512 in the far-infrared and submillimeter (420–540 GHz, 714–555 μm) wavelength range, a band of interest for NASA's experiment for cryogenic large-aperture intensity mapping called EXCLAIM. EXCLAIM will be a balloon-borne telescope that is being designed to map the emission of redshifted carbon monoxide and singly-ionized carbon lines over a redshift range 0<z<3.5 and it will be the first demonstration of the Micro-Spec technology in a space-like environment. This work reviews the status of the Micro-Spec design for the EXCLAIM telescope, with emphasis on the spectrometer's two-dimensional diffractive region, through which light of different wavelengths is focused on kinetic inductance detectors along the instrument focal plane. An optimization process is used to generate a geometrical configuration of the diffractive region that satisfies specific requirements on size, operating spectral range and performance. An initial optical design optimized for EXCLAIM is presented in terms of geometric layout, spectral purity and efficiency.

Electromagnetic models for multilayer superconducting transmission lines

Thin-film superconducting transmission lines play important roles in many signal transmission and detection systems, including qubit coupling and read-out schemes, electron spin resonance systems, parametric amplifiers, and various ultra high sensitivity detectors. Here we present a rigorous method for computing the electromagnetic behaviour of superconducting microstrip transmission lines and coplanar waveguides. Our method is based on conformal mapping, and is suitable for both homogeneous superconductors and proximity-coupled multilayers. We also present an effective conductivity approximation of multilayers, thereby allowing the multilayers to be analysed using existing electromagnetic design software. We compute the numerical results for Al–Ti bilayers and discuss the validity of our full computation and homogeneous approximation.

Second-Generation Design of Micro-Spec: A Medium-Resolution, Submillimeter-Wavelength Spectrometer-on-a-Chip

Micro-Spec (µ-Spec) is a direct-detection spectrometer which integrates all the components of a diffraction-grating spectrometer onto a \(\sim \) 10-cm\(^2\) chip through the use of superconducting microstrip transmission lines on a single-crystal silicon substrate. A second-generation µ-Spec is being designed to operate with a spectral resolution of 512 in the submillimeter (500–1000 µm, 300–600 GHz) wavelength range, a band of interest for several spectroscopic applications in astrophysics. High-altitude balloon missions would provide the first test bed to demonstrate the µ-Spec technology in a space-like environment and would be an economically viable venue for multiple observation campaigns. This work reports on the current status of the instrument design and will provide a brief overview of each instrument subsystem. Particular emphasis will be given to the design of the spectrometer’s two-dimensional diffractive region, through which the light of different wavelengths is focused on the detectors along the focal plane. An optimization process is employed to generate geometrical configurations of the diffractive region that satisfy specific requirements on spectrometer size, operating spectral range, and performance. An optical design optimized for balloon missions will be presented in terms of geometric layout, spectral purity, and efficiency.

High-Quality Factor Superconducting Flexible Resonators Embedded in Thin-Film Polyimide HD-4110

We present the design, fabrication procedure, and measurement results of Nb superconducting microstrip transmission line resonators fabricated using thin-film polyimide HD-4110, including both nonembedded and embedded versions. These resonators were used to characterize the microwave dielectric loss tangent of 20 $\mu$ m thick polyimide HD-4110 at deep cryogenic temperatures. We observed high-quality factors ( Q ) up to 21 040 at 1.2 K in the frequency range of 2–21 GHz for nonembedded resonators, indicating that the dielectric loss tangent can be less than 5 $\times$ 10−5. Embedded resonators with an additional 20 $\mu$ m thick encapsulation layer also exhibited Q values as high as $\sim 19$ 200. Dielectric and conductor (quasiparticle) loss have been compared between the two types of resonators. This study provides information applicable to the design of future high-density, flexible, multilayer superconducting cables, which are of great interest for potential applications in cryogenic electronics systems, including quantum computers.

Microwave Loss Measurements of Copper-Clad Superconducting Niobium Microstrip Resonators on Flexible Polyimide Substrates

In this work, we investigated how different under- and capping layers on patterned Nb films impacted the RF losses of flexible thin-film superconducting microstrip transmission line resonators measured in a frequency range from 2 to 20 GHz. We studied how different thicknesses of Ti(10 and 50 nm) under-layer, used for adhesion, impacts conductor losses. We also studied Cu(20, 50, 100, and 200 nm) capping layers and how they affect conductor loss. These studies were carried out on 20- $\mu$ m-thick spin-on polyimide (PI-2611) thin films and characterized at various cryogenic temperatures between 1.2 and 4.2 K. The results indicate normal-superconductor (Ti/Nb) and superconductor-normal (Nb/Cu) bilayer structures have increased surface resistance, which leads to an increase in microwave loss when compared to Nb-only signal traces. We quantified this additional loss by extracting resonator quality factors for weakly coupled resonators with various conductor stack-ups. Our experimental results can help inform decisions regarding material stack-ups when designing multiconductor multilayer superconducting flexible cables intended for use with ultralow-temperature electronic systems.

Parametric Amplification in a Superconducting Microstrip Transmission Line

Broadband parametric amplifiers (PAs), which utilize the nonlinear kinetic inductance of superconducting transmission lines, provide new access to ultimate sensing capability for radio astronomical observation and microwave quantum electronics. In this paper, the parametric amplification is investigated with a time-domain numerical method. The results present direct images of the traveling waves, which clarify the distinctively different features of the parametric gain in uniform and impedance-perturbed nonlinear transmission lines. The results indicate that the traveling-wave PAs (TWPAs) are susceptible to impedance mismatching because of the lack of isolation between the input and the output ports. In the experimental part of this paper, we tested, for the first time, microstrip TWPAs based on NbTiN. A parametric gain was observed at liquid helium temperature.

Nonlinear Circuit Model for Discontinuity of Step in Width in Superconducting Microstrip Structures and Its Impact on Nonlinear Effects

Superconducting materials are known to exhibit nonlinear effects and to produce harmonic generation and intermodulation distortion in superconductive circuits. In planar structures, these nonlinearities depend on the current distribution on the strip which is mainly determined by the structure of the device. This paper investigates the current distribution at the step-in-width discontinuity in superconducting microstrip transmission lines, which is computed by a numerical approach based on a 3-D finite-element method. This current distribution is used to obtain the parameters of the nonlinear circuit model for the superconducting microstrip step-in-width discontinuity. The proposed equivalent nonlinear circuit can be solved using the harmonic balance method. Examples of two superconducting structures which contain the steps in width are given and validated by comparison with electromagnetic full-wave results. The proposed model can be used for effective optimization of the superconducting microwave filter resonators in order to minimize their nonlinear distortions.

Modeling of unusual nonlinear behaviors in superconducting microstrip transmission lines

There are unusual nonlinear behaviors in superconducting materials, especially at low temperatures. This paper describes the procedure to reliably predict this nonlinearity in superconducting microstrip transmission lines (SMTLs). An accurate nonlinear distributed circuit model, based on simultaneously considering of both quadratic and modulus nonlinearity dependences, is proposed. All parameters of the equivalent circuit can be calculated analytically using proposed closed-form expressions. A numerical method based on Harmonic Balance approach is used to predict nonlinear phenomena like intermodulation distortions and third harmonic generations. Nonlinear analyses of the SMTLs at the different temperatures and the input powers have been presented. This proposed model can describe the unusual behaviors of the nonlinearity at low temperatures, which are frequently observed in the SMTLs.

Closed Form Formulas for Distributed Circuit Model of Discontinuities in HTS Microstrip Transmission Lines

A distributed circuit model for different kinds of discontinuities in high temperature superconducting (HTS) microstrip transmission lines (TLs), is proposed. In each case, closed form formula for lumped element model is presented based on the configuration of the discontinuity and the characterizations of HTS microstrip TLs. These discontinuities consist of steps in width, open ends, gaps and 90-degree bends. In the case of normal conductor microstrip TLs there are a lot of numerical and analytical equations that can accurately model them, however those formulas are not efficient for HTS TLs. Thus modified relations are extracted utilizing the superconducting characterizations to obtain much more accurate formulas. Additionally temperature dependence of HTS TLs is considered in the relations. Moreover regarding the kinetic inductance in HTS TLs a closed form formula is proposed for characteristic impedance of HTS TLs. Furthermore correction factors based on fringe fields is used to optimize all formulas. Using these formulations can lead to modeling and analysis of some superconducting microwave devices such as resonators, microwave filters, couplers, etc. In contrast to EM analysis, using the distributed circuit model is much easier for analysis of HTS microwave devices. The accuracy of the proposed model is confirmed in comparison with some electromagnetic full-wave simulations. This full analytical approach shows great accuracy in this test case as well.

High resolution on-chip thermometry using a microstrip-coupled transition edge sensor

Our recent work demonstrated highly efficient coupling of broadband thermal photon radiation between the termination resistors of a superconducting microstrip transmission line measured using a transition edge sensor (TES). A simple modification of this scheme is presented that permits rapid thermometry of micron-scale objects at temperatures below 3 K. Broadband photon noise gives a limiting temperature sensitivity of 3.8 μK for a 1 s integration time for measurements at 0.5 K. In practice, phonon noise in the thermal link between the TES and the heat bath limits the achievable temperature resolution to about 30 μK for a typical TES with noise equivalent power of 2×10−17 W/Hz with the same integration time.

Full Wave Analysis of Normal and Superconducting Microstrip Transmission Lines

Full Wave Analysis of Normal and Superconducting Microstrip Transmission Lines

On-chip characterization of low-noise microstrip-coupled transition edge sensors

Transition edge sensors (TESs) are used extensively in millimeter-wave and submillimeter-wave astronomy. The next technological push is to reduce the noise equivalent powers from 10−17 to 10−20 W Hz−1/2 in order to take full advantage of the exceptionally low backgrounds associated with cooled-aperture space telescopes. We describe a lab-on-a-chip (LoC) for measuring the small-signal and noise properties of ultralow-noise microstrip-coupled TESs. The LoC comprises two suspended SiNx membranes, one of which supports a single-mode, variable-temperature blackbody source, and the other a microstrip-coupled TES. The two devices are connected by a superconducting microstrip transmission line. The temperature of the source is determined by Johnson noise thermometry using superconducting quantum interference device readout. In this paper, we describe the theory, layout, operation, and calibration of the experimental system and report on two prototype devices. The LoC concept has many advantages, and already we have been able to assess the optical efficiencies of our TESs. We have started to gain an appreciation of the losses associated with 100–300 GHz microminiature superconducting microstrip transmission lines at low temperatures. The next phase of our work is to apply the technique to ultralow-noise detectors, to study fluctuation phenomena in multimode devices, and to investigate the behavior of more complicated integrated circuits.

Electrical and Thermal Characterization of Membrane-Isolated, Antenna-Coupled, TES Bolometers for the SPIDER Experiment

We have fabricated and measured the thermal and DC electrical properties of transition-edge sensing (TES) bolometers to be employed on the SPIDER experiment, a balloon-based observatory for studying the polarization of the cosmic microwave background (CMB). The bolometers consist of Al and Ti thermistors in series and a termination resistor which couples to an on-chip, polarization sensitive, 150 GHz slot-array antenna through a superconducting microstrip transmission line. Several important parameters were measured. Transition temperature measurements were performed by measuring the Johnson noise in the Ti thermistor. Current-voltage characteristic measurements were performed at various temperatures allowing for the deduction of the thermal conductance and the temperature coefficient of resistance. Electrical noise equivalent power was measured to sub-Hertz frequencies. Finally, the time constant of the bolometers was measured within the Al and Ti transitions where electrothermal feedback speeds up the bolometer response compared with the natural time constant measured just above the Ti transition temperature. The results of these measurements are within the design specifications for SPIDER.