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IEEE Transactions on Applied Superconductivity

Contribution of Quantum Susceptance in SIS Junction Capacitance Measurement

Takafumi Kojima, M. Kroug, Yoshinori Uzawa, Yuto Kozuki, Wenlei Shan

Published Mar 28, 2019• 3 citations
Publisher

Abstract

In this paper, we present an investigation of the contribution of quantum susceptance in capacitance measurements of superconductor-insulator-superconductor tunnel junctions. We directly measured the one-port S-parameter S11by utilizing a 4-K probe station in combination with a network analyzer. We observed a bias voltage dependence of the measured junction susceptance which demonstrates the contribution of quantum susceptance. Calculation results performed, based on a simple equivalent circuit model, were in excellent agreement with the measurements. Experiment and analysis methods suggested here enable the quantitative verification of the contribution of quantum susceptance and are an effective way of extracting the junction's geometric capacitance.

DOI
10.1109/tasc.2019.2908092

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In this paper, we present an investigation of the contribution of quantum susceptance in capacitance measurements of superconductor-insulator-superconductor tunnel junctions. We directly measured the one-port S-parameter S11by utilizing a 4-K probe station in combination with a network analyzer. We observed a bias voltage dependence of the measured junction susceptance which demonstrates the contribution of quantum susceptance. Calculation results performed, based on a simple equivalent circuit model, were in excellent agreement with the measurements. Experiment and analysis methods suggested here enable the quantitative verification of the contribution of quantum susceptance and are an effective way of extracting the junction's geometric capacitance.
Superconductor-Insulator-Superconductor (SIS) tunnel junctions are widely used as the mixing component in mm and sub-mm receivers for radio astronomy and environmental science. SIS mixers offer superior noise performance close to the quantum limit for frequencies up to 1 THz. An important property of an SIS junction is the intrinsic specific capacitance (Cs), which is defined by the geometrical capacitance (Cj) divided by the junction area (A). In order to prevent loss of the RF signal, a tuning circuitry is required to resonate out the Cj. The RF bandwidth of an SIS mixer is determined by the quality factor of the resulted resonator-like tuning circuitry, Q = ωRnCj, where Rn is the normal resistance of the junction and ω is the angular frequency. In order to increase the RF bandwidth of the mixer, junctions with lower specific resistance (RnA) and hence thinner insulator layer are required. For the practical SIS mixers, junctions with RnA 100 Ω.µm2 (often as low as 20 Ω.µm2) are typically used. In this RnA range, the published data on the Cs vs. RnA are often spread and not consistent between different sources. Therefore, at this limit, the design of an accurate tuning circuitry becomes challenging. Hence, there is a well-recognized demand for accurate measurement of Cs.\nSo far, all the developed characterisation methods measured the specific capacitance effect indirectly, e.g., in a resonant circuit. In this context, the specific capacitance was extracted by fitting the measurement data into a theoretical model. In this thesis, a new method was developed, which directly measures the junction capacitance at microwave frequencies (1 - 7 GHz) with estimated uncertainty varying from ±2% to ±11% depending on the junction area. In this measurement method, an original calibration approach was suggested and implemented.\nUsing this method, the capacitance of 34 junctions with various RnA values ranging from 8 to 68 Ω.µm2 was measured. The observed scatter in the specific capacitance is discussed. We argue that, it is the tunnel barrier (thickness) nonuniformity, which is responsible for the observed spread of the Cs data. The nonlinear capacitance as a result of the Kramers-Kronig transformation of the dc IV characteristic of the SIS junction was shown to be a significant contribution for RnA 40 Ω.µm2 even at frequencies as low as 1-7 GHz. The extracted specific capacitance from the measurements was corrected for the nonlinear capacitance. The obtained Cs(RnA) data agrees well with the model relation Cs = a/ln(RnA), where a =0.227 for the RnA 40 Ω.µm2. \n
We have made the first direct measurement of the quantum susceptance that arises from the nondissipative part of quasiparticle tunneling in a superconductor-insulator-superconductor tunnel junction. The junction is coupled to an antenna and a superconducting microstrip stub to form a resonator; the resonant frequency is determined from the response of the junction to broadband radiation from a Fourier-transform spectrometer. A 19% shift of the resonant frequency, from 73 to 87 GHz, is observed, which arises from the change of the quantum susceptance of the junction with dc bias voltage. This shift is in excellent agreement with calculations based on the Werthamer-Tucker theory, which includes the quantum susceptance. We also demonstrate that it is essential to include the quantum susceptance in our theoretical computation to explain the photon-assisted-tunneling steps, which have negative dynamic conductance. Such steps are observed when the junction is pumped at slightly below the resonant frequency of the capacitor and the stub. The quantum susceptance should exist in all tunnel devices whose nonlinear I-V characteristics are due to elastic tunneling.
The need for operating frequencies well into THz region with higher sensitivity and wider bandwidth pushes superconductor-insulator-superconductor (SIS) technology towards junctions with more transparent barrier and higher current densities. Obtaining accurate knowledge of the specific capacitance, which is related to the transparency of the junctions, leads to a precise design of the tuning circuitry. Previously, characterization of the SIS junction’s specific capacitance involved complex measurements providing data relying on various model fitting. Herein, we present the characterization of the specific capacitance by directly measuring the impedance of the SIS tunnel junction at microwave frequencies (~3 GHz).
This paper presents a method for measuring the capacitance of superconductor-insulator-superconductor (SIS) junctions with a 4-K probe station. The probe station can be used to perform on-wafer characterization of sample lots at frequencies ranging from dc to microwave. In our study, we evaluated SIS junctions that had a variety of areas, and estimated the capacitance after subtracting the parasitic elements of the probe contact pad. The results show that the RNC products for the evaluated junctions were uniform within +/-5% across the wafer.
The microwave response of the dc quasiparticle tunneling current in Josephson tunnel junctions, where the Josephson current is suppressed by an external magnetic field, has been studied quantitatively in order to clarify its characteristics as a probe for the measurement of the junction capacitance. Extensive experiments for both small and long junctions are carried out for distinguishing between microwave behaviors of lumped and distributed constant junctions. It is shown that the observed voltage dependence of the dc quasiparticle tunneling current modified by an applied rf field is in good agreement with a theoretical result which takes into account the influence of the microwave circuit connected to the junction. The comparison between theory and experiment gives the magnitude of the internal rf field in the junction. Together with the applied rf field, this internal rf field leads to the junction rf impedance which is dominated by the junction capacitance in our experimental condition. In the case of lumped junctions, this experimental rf impedance is in reasonable agreement with the theoretical one with the junction capacitance estimated from the Fiske step of the distributed junction fabricated on the same substrate; the obtained ratio of the experimental impedance to the theoretical one is approximately 0.6–1.7. In the case of distributed junctions, however, experimental values of their characteristic impedances are approximately 0.2–0.3 of theoretical values calculated by assuming the one-dimensional junction model and taking account of the standing-wave effect in the junction.
Superconductor-insulator-superconductor (SIS) junction geometrical capacitance with out of phase current I/sub kk/ impedance component forms sufficient junction reactance X/sub SIS/=( omega C+B/sub Q/)/sup -1/. It is suggested that the way to resonate out both omega C and B/sub Q/ is by using an additional identical SIS junction connected to the first through a long line impedance inverter and RF+DC biased symmetrically to the first. Pumped I-V curves without quantum reactance and frequency impedance patterns of the system are calculated. Calculations demonstrated the presence of high and even negative induced dynamic resistance regions at high-order quasiparticle steps for the case of SIS junction reactance complete compensation. The suggested method may be used in SIS mixers and detectors for a better RF matching.