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IEEE Transactions on Applied Superconductivity

Optimization of the Double-Barrier Josephson Junction Switching Dynamics

Serhii E. Shafranjuk, John B. Ketterson

Published Mar 1, 2004• 3 citations
Publisher

Abstract

The switching dynamics of a double-barrier Josephson junction is analyzed as a function of the microscopic properties of its electrodes. In particular, it is found that the nonstationary behavior of the Josephson phase difference is very sensitive to dissipation mechanisms acting inside the intrinsic shunt. The leading factor that determines the dissipation is the local electron density of states N(E) inside the electrodes. The roles of junction geometry, electrode purity, and interface quality are discussed and how they affect the details of N(E), hence the resulting phase dynamics. The microscopic analyses allow optimization of the performance of double-barrier Josephson junction-based rapid-single-flux-quantum circuits in two ways: 1) decreasing the switching time of Josephson elements and 2) reducing the excess wiring. Such an analysis is facilitated with the aid of a lumped circuit representation which generalizes the nonlinear resistive-shunted-junction model.

DOI
10.1109/tasc.2004.824329

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The switching dynamics of a double-barrier Josephson junction is analyzed as a function of the microscopic properties of its electrodes. In particular, it is found that the nonstationary behavior of the Josephson phase difference is very sensitive to dissipation mechanisms acting inside the intrinsic shunt. The leading factor that determines the dissipation is the local electron density of states N(E) inside the electrodes. The roles of junction geometry, electrode purity, and interface quality are discussed and how they affect the details of N(E), hence the resulting phase dynamics. The microscopic analyses allow optimization of the performance of double-barrier Josephson junction-based rapid-single-flux-quantum circuits in two ways: 1) decreasing the switching time of Josephson elements and 2) reducing the excess wiring. Such an analysis is facilitated with the aid of a lumped circuit representation which generalizes the nonlinear resistive-shunted-junction model.
Double-barrier Josephson junctions, with outer electrodes of superconducting Nb and a central thin layer of non-superconducting Al, are being developed as self-shunted junctions for high-frequency superconducting integrated circuits. This paper presents a simplified phenomenological model of the behaviour of such junctions (often called SINIS, for superconductor-insulator-normal-insulator-superconductor) based on the resistively shunted junction model, using Josephson coupling between the layers and the time-dependent Ginzburg-Landau equation to describe the dynamics of the weak induced energy gap in the Al layer. This analysis shows how non-hysteretic I - V characteristics can be obtained but suggests some limitations in their high-frequency performance. Predictions for critical current generally agree with prior experiments. The technological implications of this model are discussed.
The continuous development of superconducting electronics is encouraging several studies on hybrid Josephson junctions (JJs) based on superconductor-ferromagnet-superconductor (SFS) heterostructures, as either spintronic devices or switchable elements in quantum and classical circuits. Recent experimental evidence of macroscopic quantum tunneling and of an incomplete 0-$\ensuremath{\pi}$ transition in tunnel-ferromagnetic spin-filter JJs could also enhance the capabilities of SFS JJs as active elements. Here, we provide a self-consistent electrodynamic characterization of NbN\mathrm{Nb}\mathrm{N}NbN/GdN\mathrm{Gd}\mathrm{N}GdN/NbN\mathrm{Nb}\mathrm{N}NbN spin-filter JJs as a function of the barrier thickness, disentangling the high-frequency dissipation effects due to the environment from the intrinsic low-frequency dissipation processes. The fitting of the III-VVV characteristics at 4.2 K and at 300 mK by using the tunnel-junction-microscopic model allows us to determine the subgap resistance Rsg{R}_{\mathrm{sg}}Rsg​, the quality factor QQQ, and the junction capacitance CCC. These results provide the scaling behavior of the electrodynamic parameters as a function of the barrier thickness, which represents a fundamental step for the feasibility of tunnel-ferromagnetic JJs as active elements in quantum and classical circuits, and are of general interest for tunnel junctions other than conventional SIS JJs.
In the design of electronic applications (for example, rapid single flux quantum (RSFQ) circuits), the properties of Josephson junctions (JJs) provided by technology are the major requirement. The characteristic voltage IcRn an dt he dynamic parameter βc are non-negligibly important, bu tt he external shunted junctions are only completely described by including the parasitic inductance between the junction area and the shunt resistor. The first publications of the RSFQ circuit technique were closely followed by many studies on the dynamic influence of this inductance. It has been pointed out that no practical value of this parameter has to be taken into account in the circuit design and optimization process. The operation of RSFQ logic circuits made of high-temperature superconductors (HTS) are strongly influenced by thermal noise. Our paper contains the determination of the digital bit-error rate for all different types of JJs by using a Fokker–Planck equation for describing the influence of thermal fluctuations. Ou ra nalysis shows that the parasitic inductance cannot be neglected in terms of noise. The intrinsic shunted junctions like high current density-, SINIS- and all kinds of HTS-JJs provide the best noise immunity for a fixed temperature.
Within the framework of the microscopic model of tunneling, we modeled the behavior of the Josephson junction shunted by the superconductor--insulator--normal-metal (SIN) tunnel junction. The electromagnetic impedance of the SIN junction includes both the frequency-dependent damping and reactance, which affect the circuit dynamics. We calculated the dc $I\text{\ensuremath{-}}V$ curves and transient characteristics and show their differences to the characteristics obtained within the simpler models. The correct operation of the basic single-flux-quantum circuits, i.e., the Josephson transmission line and the toggle flip-flop, based on such SIN-shunted Josephson junctions with small damping at low frequencies, has also been modeled.
The results relative to macroscopic quantum tunneling rate, out of the metastable state of Josephson junctions, are examined in view of determining the effect of dissipation. We adopt a simple criterion in accordance to which the effect of dissipation can be evaluated by analyzing the shortening of the semiclassical traversal time of the barrier. In almost all the considered cases, especially those with relatively large capacitance values, the relative time shortening turns out to be about 20% and with a corresponding quality factor Q ≃ 5.5. However, beyond the specific cases here considered, still in the regime of moderate dissipation, the method is applicable also to different situations with different values of the quality factor. The method allows, within the error limits, for a reliable determination of the load resistance RL, the less accessible quantity in the framework of the resistively and capacitively shunted junction model, provided that the characteristics of the junction (intrinsic capacitance, critical current, and the ratio of the bias current to the critical one) are known with sufficient accuracy.
Measurements of macroscopic quantum tunnelling (MQT) in intrinsic Josephson junctions (IJJs) suggest that they may be suitable as qubits. An advantage of using IJJs over trilayers is the absence of any artificial barrier and hence the possible absence of decohering two-level fluctuators. A disadvantage is that it is difficult to fabricate single IJJs. Hence all IJJ MQT experiments have been carried out on arrays of many IJJs in series. Since MQT is suppressed by dissipation, it is important (a) to understand the role of dissipation on the dynamics of IJJs and (b) to consider how the dissipation and the dynamics change as a function of the number of junctions in the array which are in the voltage state. We have measured distributions of the nth-order switching current in TlBaCaCuO IJJ arrays, where n indicates switching from n to n+1 junctions being in the voltage state. The junctions show conventional underdamped behaviour at temperatures below some temperature T*, with a suppression of the width of the distribution above T*. We find that T* depends upon n. For n = 0 (i.e. switching from the supercurrent branch), T* is less than 4.2 K. For n > 0, we measured T* values between 20 K and 40 K. Calculations and simulations show that a change in T* results from a change in Q. Analysis suggests that the Q of the IJJs is determined by the environmental impedance when all junctions in the array are in the zero-voltage state, whereas having one junction or more in the voltage state isolates the array from the environment leading to a higher Q. We discuss our data in the context of possible qubit applications.