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Journal of Applied Physics

Determination of the capacitance of nm scale Josephson junctions

Frank Deppe, Shiro Saito, Hirotaka Tanaka, Hideaki Takayanagi

Published Feb 13, 2004• 19 citations
Publisher

Abstract

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.

DOI
10.1063/1.1645673

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The $\mathrm{LC}$ (inductance-capacitance) resonance phenomenon in the dc SQUID (superconducting quantum interference device) creates a current peak in the $I\ensuremath{-}V$ characteristics at a voltage determined by the resonance frequency. These $I\ensuremath{-}V$ characteristics have been analyzed with the resistively shunted Josephson-junction model in the low-damping and small-oscillation regime. The resonance $I\ensuremath{-}V$ characteristics contain sufficient information to determine all circuit parameters for the dc SQUID's. Specifically, we can apply this analysis to symmetric, tunnel-junction dc SQUID's to deduce the pair-quasiparticle interference conductance ($cos\ensuremath{\theta}$ term).

Physical review. B, Condensed matter•Sep 1, 1981•0 citations
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 specific capacitance Cs of Nb/AlOx/Nb Josephson tunnel junction has been measured by means of the superconducting quantum interference device (SQUID) resonance technique. We have investigated the junctions with critical current densities Jc in the range of 0.1–18 kA/cm2 and found that 1/Cs linearly depends on a logarithm of Jc. This suggests that the barrier thickness is moderately uniform in the junction area and increases continuously during growth. The results also show that increasing Jc reduces time constants of the junction.
Measurement of Specific Capacitance for Nb/Al–AlO x_{x}x​/Nb Josephson Junctions in Single-Flux Quantum Circuit Applications
In this study, we investigate different technologies to measure the specific capacitances C8of Nb/Al-AlOx/Nb Josephson junctions. They involve measuring Fiske mode resonance in long Josephson junctions, superconducting quantum interference device (SQUID) resonance, and Josephson plasma resonance. We find a logarithmic relationship between the junction C8and its critical current density Jcin the range 0.1-2 kA/cm2using the Fiske mode resonance method. Our measured C8values using SQUID resonance and Josephson plasma resonance are compared with the results obtained by other groups via analyzing the major errors in the C8calculation. We discuss the accuracy in evaluating C8for all three techniques and suggest using Fiske mode resonance as a relatively stable method for C8extraction for the future design of our single-flux quantum circuit.
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.
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 fabricate a three-Josephson-junction flux qubit, a nonlinear superconducting circuit acting as a quantum two-level system with a macroscopic degree of freedom. First, the capacitance per unit area of the used Josephson junctions, C s =(100±25)fF/µm 2 , is determined from DC SQUID voltage steps. Next, we probe the coherence times of our qubit using a novel variant of the switching-DC-SQUID readout. At the optimal point, our device is relaxation-limited with T 1 ≅100ns and T φ ≅2µs. Ramsey and spin echo experiments reveal 1/f-noise and suggest microscopic fluctuators in the tunnel barriers as its source. As in other experiments, the 1/f-noise magnitude is ≅(10 -6 Φ 0 ) 2 . Finally, the qubit is coupled to a linear LC-resonator in a circuit quantum electrodynamics experiment. Spectroscopically, an upconversion mechanism enabled by controlled symmetry breaking is demonstrated.
The LC\mathrm{LC}LC (inductance-capacitance) resonance phenomenon in the dc SQUID (superconducting quantum interference device) creates a current peak in the $I\ensuremath{-}V$ characteristics at a voltage determined by the resonance frequency. These $I\ensuremath{-}V$ characteristics have been analyzed with the resistively shunted Josephson-junction model in the low-damping and small-oscillation regime. The resonance $I\ensuremath{-}V$ characteristics contain sufficient information to determine all circuit parameters for the dc SQUID's. Specifically, we can apply this analysis to symmetric, tunnel-junction dc SQUID's to deduce the pair-quasiparticle interference conductance ($cos\ensuremath{\theta}$ term).