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Applied Physics Letters

A method for determining the specific capacitance value of mesoscopic Josephson junctions

Sheng-Shiuan Yeh, Kuan‐Wen Chen, Tao-Hsiang Chung, Dai-Yang Wu, Ming-Chou Lin, Jyh-Yang Wang, I‐Lin Ho, Cen-Shawn Wu, Watson Kuo, Chii‐Dong Chen

Published Dec 3, 2012• 5 citations
Publisher

Abstract

An approach for precise determination of capacitance values and energy level spacing of mesoscopic Josephson junctions is proposed. Quantized levels arising from plasma oscillation manifest themselves in the current peaks in the current-voltage characteristics of a nearby probe Josephson junction. From peak spacing, the specific capacitance of aluminum junctions is determined to be 35 fF/μm2. In addition, magnetic field dependence of quantum states can be described quantitatively by a theory that takes the effect of field induced surface current into account.

DOI
10.1063/1.4769999

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IEEE Transactions on Applied Superconductivity•Aug 20, 2014•0 citations
An approach for precise determination of capacitance values and energy level spacing of mesoscopic Josephson junctions is proposed. Quantized levels arising from plasma oscillation manifest themselves in the current peaks in the current-voltage characteristics of a nearby probe Josephson junction. From peak spacing, the specific capacitance of aluminum junctions is determined to be 35 fF/μm2. In addition, magnetic field dependence of quantum states can be described quantitatively by a theory that takes the effect of field induced surface current into account.
Superconducting three-Josephson-junction flux qubits (3JFQB) are possible candidates for the basic elements of a (future) scalable quantum computer. An important design parameter is the capacitance of their Josephson junctions. We estimate the capacitance per junction area (specific capacitance) of junctions typically used in 3JFQBs, i.e., of Al/AlOx/Al junctions with 5–10 Å thick oxide layers. The capacitance is obtained by analyzing resonant voltage steps in the current–voltage characteristics of specifically designed dc superconducting quantum interference devices (SQUIDs). The junction area is deduced from scanning electron microscope images. We find that the specific capacitance of our junctions is Cs=100±25 fF/μm2. Finally we compare this result to capacitance estimates obtained with 3JFQB microwave spectroscopy and find that the SQUID resonance method provides a much higher accuracy.
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.
The capacitance of a Josephson tunnel junction is an important parameter, which determines its plasma frequency ωp and thus the energy level spacing in the quantum regime. When a microwave signal at the frequency of ω is applied to a current-biased junction in its zero-voltage state, the escape rate from this state is somehow enhanced. The enhancement is expected to go through a pronounced maximum when ωp=ω. Making use of such microwave generated resonant activation in the thermal regime, we have developed a time-resolved measurement scheme for determining the junction capacitance with an uncertainty of less than 2%.
By introducing the entangled state representation and Feynman assumption that `electron pairs are bosons, ..., a bound pair acts as a Bose particle', we construct an operator Hamiltonian for a mesoscopic inductance-capacitance (LC) circuit including a Josephson junction, then we use the Heisenberg equation of motion to derive the current equation and the voltage equation across the inductance as well as across the Josephson junction. The result manifestly shows how the junction voltage is affected by the capacitance coupling. In this way the Cooper-pair number-phase quantization for this system is completed.
This paper examines the quantization of mesoscopic circuit including Josephson junctions. Following Feynman's assumption, via the Hamilton dynamic approach and by virtue of the entangled state representation, it constructs Hamiltonian operator for the double-Josephson-junction mesoscopic circuit coupled by a capacitor. Then it uses the Heisenberg equation of motion to derive the induction voltage across each Josephson junction. The result manifestly shows how the voltage is affected by the capacitance coupling.
Parametric Characterization and Macroscopic Quantum Tunneling of Nb/AlOx/Nb\hbox{Nb}/\hbox{AlO}_{\rm x}/\hbox{Nb}Nb/AlOx​/Nb Josephson Junctions
Parameters ofNb/AlOx/Nb\hbox{Nb}/\hbox{AlO}_{\rm x}/\hbox{Nb}Nb/AlOx​/NbJosephson including its critical current and capacitance which determine the dynamic energy consumption and speed of the superconducting electronics have been measured. The critical current of a22×22 μm222 \times 22 \ \mu\hbox{m}^{2}22×22 μm2junction is1801±52 μA1801 \pm 52 \ \mu\hbox{A}1801±52 μAcalculated from the dependent curve between the lifetime of zero-voltage and switching current. The specific capacitance is0.051±0.008 pF/μm20.051 \pm 0.008 \ \hbox{pF}/\mu\hbox{m}^{2}0.051±0.008 pF/μm2obtained by observing Fiske self-resonant step when applied several Gauss magnetic field. Critical current distributions had been measured as a function of temperature from 900 mK to 40 mK. The distribution widths become independent of temperature below 200 mK, which indicates the transition between thermal activation and macroscopic quantum tunneling of junction phase.