Critical Current Of Junction Research Articles

Energy efficient half-flux-quantum circuit aiming at milli-kelvin stage operation

Half-flux-quantum (HFQ) circuits are based on 0–π superconducting quantum interference devices (SQUIDs) and is one of the energy-efficient superconductor digital circuits. The bit energy is determined by the critical current I cn of 0–π SQUID, which can be easily tuned with the loop inductance and junction critical current. In this work, an alternative π–π–π SQUID is adopted to demonstrate HFQ circuits to simplify the fabrication process and enhance circuit energy efficiency. The properties of superconductor/ferromagnet/insulator/superconductor Josephson junctions (π-JJs) are measured with temperature dependence from 4.2 K down to 10 mK. HFQ toggle flip-flops (TFFs) are successfully demonstrated at frequencies of up to 6.7 GHz and 44.5 GHz at temperatures of 4.2 K and 10 mK, respectively. Comparing the HFQ TFF with its rapid single-flux quantum counterpart under the same fabrication process, it is anticipated that the HFQ TFF will exhibit approximately 70% reduction in both static and dynamic energy dissipation. This research establishes the foundation for developing cryogenic interface control and readout circuits for large-scale quantum computing in the future.

Design and Fabrication of Low-Power Single-Flux-Quantum Circuits Toward Quantum Bit Control

we report low-power single-flux-quantum (SFQ) circuits fabricated with a lowered critical current density process and low-voltage design. We selected 250 A/cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> to obtain 2–10 μA Josephson junctions (JJs) easily using conventional facilities. Our numerical simulation shows that the expected operating frequency is 10 GHz and that we can reduce the bias voltage to 0.1–0.5 mV; power consumption can be reduced to around 1 nW per JJ. We newly developed a fabrication process featuring four planarized Nb layers and a Pd resistor layer. We obtained the correct operation of several basic SFQ circuit elements designed with the lowered critical currents to 1/2 of the conventional circuits at 4.2 K. We also evaluated the Josephson junction critical currents, specific capacitance, resistance, and inductance at 3 K and 300 mK. We observed an increase of 7% in the critical currents at 300 mK, while the other parameters were unchanged. We demonstrated a 0.5-mV Josephson transmission line where we lowered the critical currents to 1/10. We expect such low-power SFQ circuits to operate at 20 mK, providing classical, general-purpose digital processing near quantum bits.

Improving Josephson junction reproducibility for superconducting quantum circuits: junction area fluctuation

Josephson superconducting qubits and parametric amplifiers are prominent examples of superconducting quantum circuits that have shown rapid progress in recent years. As such devices become more complex, the requirements for reproducibility of their electrical properties across a chip are being tightened. Critical current of the Josephson junction Ic is the essential electrical parameter in a chip. So, its variation is to be minimized. According to the Ambegaokar–Baratoff formula, critical current is related to normal-state resistance, which can be measured at room temperature. In this study, we focused on the dominant source of non-uniformity for the Josephson junction critical current–junction area variation. We optimized Josephson junction fabrication process and demonstrated resistance variation of 9.8–4.4% and 4.8–2.3% across 22 × 22 mm2 and 5 × 10 mm2 chip areas, respectively. For a wide range of junction areas from 0.008 to 0.12 μm2, we ensure a small linewidth standard deviation of 4 nm measured over 4500 junctions with linear dimensions from 80 to 680 nm. We found that the dominate source of junction area variation limiting {mathrm{I}}_{mathrm{c}} reproducibility is the imperfection of the evaporation system. The developed fabrication process was tested on superconducting highly coherent transmon qubits (T1 > 100 μs) and a nonlinear asymmetric inductive element parametric amplifier.

Diagnosing flux penetration condition of the Mo/Au bilayer transition-edge sensor

The magnetic-field-dependence critical current Ic(Ha) is measured for the Mo/Au bilayer transition-edge sensors. A model based on a surface barrier delaying the first penetration of magnetic flux into a flat superconducting strip, including both the geometrical and Bean–Livingston barrier, in combination with two Josephson junction models with different characteristic lengths, is found to ubiquitously fit the Ic(Ha) curves of devices with various geometry designs. The bulk penetration depth, London depairing current density, Josephson junction critical current, self-field coupling coefficient, and conditions of the first vortex entry are investigated throughout the superconducting transition. The evidences of Josephson effect are observed in both Fraunhofer interference pattern and Shapiro steps.

Long- to short-junction crossover and field-reentrant critical current in Al/Ag-nanowires/Al Josephson junctions

We have probed the superconducting proximity effect through long high-quality monocrystalline Ag nanowires, by realizing Josephson junctions of different lengths, with different superconducting materials. Thanks to the high number of junctions probed, both the contact resistance and electron diffusion constant could be determined, enabling a comparison of the measured critical current to theoretical expectation, over the entire regime from short to long diffusive junction. Although the length dependence of the critical current is as expected, the amplitude of the $R_{N}I_c$ product is smaller than predicted by theory. We also address the magnetic field dependence of the critical current. The quasi-gaussian decay of the critical current with field expected of a long narrow junction is observed for all superconducting contacts we used except for aluminum. We present the striking non-monotonous effect of field on the critical current of junctions with aluminum contacts, and analyze it in terms of improved quasiparticle thermalization by a magnetic field.

A density-functional theory study of the Al/AlOx/Al tunnel junction

The aluminum oxide tunnel junction is a key component of the majority of superconducting quantum devices. For high-quality, reproducible, and scalably manufacturable qubits, the ability to fabricate Josephson junctions (JJs) with a targeted critical current and high uniformity is essential. We use first-principles modeling to assess fundamental aspects of the atomic structure of both amorphous and crystalline aluminum oxide tunnel junctions and relate the structure to predicted performance metrics. We use modified ab initio molecular dynamics to develop realistic models of the tunnel junction, from which interface roughness and local thickness fluctuations are analyzed in an unbiased manner by training a neural network to identify the boundary between metal and oxide. We show that the effective thickness of the insulating part of the junction can be different from the apparent physical thickness. We calculate the rate of Cooper pair tunneling for the atomically resolved electrostatic potential using direct numerical solution in 3D, which shows a channeling effect that impacts the junction critical current. The predicted critical current is a useful JJ design parameter that can be accessed from the ab initio calculations without fitting parameters. To assess the limits of uniformity and fabrication choices (e.g., oxidation vs epitaxy), we compare the amorphous junctions to crystalline models, which show order of magnitude more efficient tunneling compared to the amorphous case, underlining the connection between atomistic structure and Cooper pair tunneling efficiency. Further, this work provides a foundation for ab initio materials design and evaluation to help accelerate future development of improved tunnel junctions.

IV-characteristics and power of emission from stacks of long Josephson junctions with Gaussian spread of critical currents

The creation of sources of coherent emission in the terahertz region of frequencies from stacks of intrinsic Josephson junctions in high-temperature superconductors becomes the recently important problem of applied nanoscience. We investigated numerically IV-characteristics of stacks of three and four long Josephson junctions and power of emission from edges of the stack at different small Gaussian standard deviations of critical currents. We found the split zero-field steps in IV-characteristics. Positions of zero-field steps in the IV-curve can be described by a simple analytical expression in the theory of electrical properties of stacks of Josephson junctions placed in the external magnetic field. Maxima of coherent emission appear at voltages corresponding to the frequencies of the resonance of the in-phase collective modes of the whole stack with modes of geometrical resonances. We found maximal tolerant standard deviations of critical currents at which this resonance exists (from 1 to 10% of averaged critical currents of junctions).

Bi-SQUID Loading

Loading impact on the bi-SQUID output signal linearity has been studied. As the load impedance decreases, the maximum attainable linearity drops. This effect is minimized when the impedance is approximately the same at both signal and Josephson oscillation frequencies. The impedance value is allowed to be as low as 4RN to RN (normal Josephson junction resistance) to support linearity level no less than 70 to 60 dB, respectively. This is the level that can be considered realistically attainable given that the junction critical currents and inductances are fixed by fabrication and cannot be tuned during operation.

SNS Josephson Junctions With Tunable Ta–N Barriers

We report on the fabrication and characterization of Nb/Ta-N/Nb Josephson junctions grown by room temperature magnetron sputtering on 150-mm diameter Si wafers. Junction characteristics depend upon the Ta-N barrier composition, which was varied by adjusting the N2 flow during film deposition. Higher N 2 flow rates raise the barrier resistance and increase the junction critical current. This work demonstrates the viability of Ta-N as an alternative barrier to aluminum oxide, with the potential for large scale integration.

Timing Characterization for RSFQ Cell Library

As superconducting circuits grow in complexity, full transient simulation and verification at the Josephson junction level using analog circuit simulators become increasingly computationally expensive. To enable faster functional and timing verification using timing back annotation and static timing analysis, logic models of rapid single flux quantum library cells are developed using hardware description languages like Verilog together with the required timing characteristics. These include propagation delays and minimum pin-to-pin pulse arrival time separation at various process and operating corners. These timing parameters must satisfy required margins and yield using Monte Carlo simulations with statistical variations. For each library cell, these timing parameters depend not only on the adjacent cells but also on their internal states. These delay variations are driven by bias current redistribution, load inductance, and load junction critical currents. We present our methodology for extracting these timing parameters to enable timing back annotation and static timing analysis. We demonstrate our methodology with a parallel counter as a reference circuit and show that timing back annotated simulation can closely match results from full circuit simulation.

Optimization of Time- and Code-Division-Multiplexed Readout for Athena X-IFU.

Readout of a large, spacecraft-based array of superconducting transition-edge sensors (TESs) requires careful management of the layout area and power dissipation of the cryogenic-circuit components. We present three optimizations of our time- (TDM) and code-division-multiplexing (CDM) systems for the X-ray Integral Field Unit (X-IFU), a several-thousand-pixel-TES array for the planned Athena-satellite mission. The first optimization is a new readout scheme that is a hybrid of CDM and TDM. This C/TDM architecture balances CDM's noise advantage with TDM's layout compactness. The second is a redesign of a component: the shunt resistor that provides a dc-voltage bias to the TESs. A new layout and a thicker Pd-Au resistive layer combine to reduce this resistor's area by more than a factor of 5. Third, we have studied the power dissipated by the first-stage SQUIDs (superconducting quantum-interference devices) and the readout noise versus the critical current of the first-stage SqUIDs. As a result, the X-IFU TDM and C/TDM SQUIDs will have a specified junction critical current of 5 μA. Based on these design optimizations and TDM experiments described by Durkin, et al. (these proceedings), TDM meets all requirements to be X-IFU's backup-readout option. Hybrid C/TDM is another viable option that could save spacecraft resources.

Automated Verification and Optimization of SFQ Superconducting Circuits

New tools have been created to allow a superconducting design flow for schematic design, verification, and optimization. These tools integrate with the Cadence design environment. In single flux quantum superconducting electronics, individual component values, such as wire inductances, Josephson junction critical currents, and bias currents, must be optimized to allow for maximum deviance from the designer value, which is also known as the device margin. One tool is used to create a description of the proper circuit behavior. Included with this tool is the ability to automatically create the description from a Cadence netlist. The other tool is an automated device margin circuit schematic verification and optimization tool, which widens device margins while maintaining proper circuit behavior derived from the first tool. Additionally, this optimization tool can automatically correct the circuit schematic using the proper circuit behavior description. In this paper, the functionality of the language used to create the description of the proper circuit behavior is presented. Several circuits are then verified and optimized based on their correct behavior.

Radiation comb generation with extended Josephson junctions

We propose the implementation of a Josephson radiation comb generator based on an extended Josephson junction subject to a time dependent magnetic field. The junction critical current shows known diffraction patterns and determines the position of the critical nodes when it vanishes. When the magnetic flux passes through one of such critical nodes, the superconducting phase must undergo a π-jump to minimize the Josephson energy. Correspondingly, a voltage pulse is generated at the extremes of the junction. Under periodic driving, this allows us to produce a comb-like voltage pulses sequence. In the frequency domain, it is possible to generate up to hundreds of harmonics of the fundamental driving frequency, thus mimicking the frequency comb used in optics and metrology. We discuss several implementations through a rectangular, cylindrical, and annular junction geometries, allowing us to generate different radiation spectra and to produce an output power up to 10 pW at 50 GHz for a driving frequency of 100 MHz.

Noise of dc-SQUIDs with planar sub-micrometer Nb/HfTi/Nb junctions

We have fabricated Nb-based dc-SQUIDs with sub-micrometer planar Nb/HfTi/Nb junctions in order to investigate their noise performance. The SQUIDs are of simple coplanar design, their nominal inductance is ca. 15 pH. Electron beam lithography and chemical-mechanical polishing have been used to realize junctions with cross sections areas as low as about 100 × 100 nm2. The SQUIDs exhibit pronounced excess noise increasing towards lower frequencies. This apparent flux noise arises from fluctuations of the junction critical currents or resistances. The Nb/HfTi/Nb junction critical currents are found to be strongly temperature dependent. Upon cooling below ca. 4 K the SQUIDs start to show current–voltage characteristics with negative differential resistances, and their flux noise increases significantly. Estimation of the HfTi barrier electron temperature indicates that the degradation of the SQUID properties towards lower temperature is caused by self-heating effects.

Manipulating Josephson junctions in thin-films by nearby vortices

It is shown that a vortex trapped in one of the banks of a planar edge-type Josephson junction in a narrow thin-film superconducting strip can change drastically the dependence of the junction critical current on the applied field, Ic(H). When the vortex is placed at certain discrete positions in the strip middle, the pattern Ic(H) has zero at H=0 instead of the traditional maximum of ‘0-type’ junctions. The number of these positions is equal to the number of vortices trapped at the same location. When the junction–vortex separation exceeds ∼W, the strip width, Ic(H) is no longer sensitive to the vortex presence. The same is true for any separation if the vortex approaches the strip edges.

Input–output description of microwave radiation in the dynamical Coulomb blockade

We study microwave radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. An input–output formalism for the radiation field is established, using a perturbation expansion in the junction's critical current. Using output field operators solved up to the second order, we estimate the spectral density and the second-order coherence of the emitted field. For typical transmission line impedances and at frequencies below the main emission peak at the Josephson frequency, radiation occurs predominantly due to two-photon emission. This emission is characterized by a high degree of photon bunching if detected symmetrically around half of the Josephson frequency. Strong phase fluctuations in the transmission line make related nonclassical phase-dependent amplitude correlations short lived, and there is no steady-state two-mode squeezing. However, the radiation is shown to violate the classical Cauchy–Schwarz inequality of intensity cross-correlations, demonstrating the nonclassicality of the photon pair production in this region.

Simulation of Series Arrays of Superconducting Quantum Interference Devices

The voltage as a function of applied magnetic field (V-B) was calculated for arrays of superconducting quantum interference devices (SQUIDs) connected in series. Comparisons were made between arrays of equal area SQUIDs and superconducting quantum interference filters (SQIFs). The areas for the SQIFs were varied exponentially, so that the V-B had a sharp minimum at zero field. We used equations for the dc SQUID based on resistively shunted junctions, with typical parameters for YBa2Cu3O7 - δ ion damage Josephson junctions. The maximum transfer coefficient of the central minimum VB = (∂V/∂B)max of the SQIF decreases as the area range increases. We find that the equal area array is more robust to the effects of non-uniform junction critical currents than the SQIF, for the junction parameters and SQUID area distributions chosen. Furthermore, we find that slight variations (~5%) to the area due to fabrication irregularities have little effect on the central minimum of V-B for either device.

Penetration depth of MgB2 measured using Josephson junctions and SQUIDs

The penetration depth of MgB2 was measured using two methods of different mechanisms. The first method used MgB2 Josephson junctions and the magnetic field dependence of the junction critical current. The second method deduced the penetration depth from the inductance of a MgB2 microstrip used to modulate the voltage of a MgB2 DC SQUID. The two methods showed a consistent value of the low-temperature penetration depth for MgB2 to be about 40 nm. Both the small penetration depth value and its temperature dependence are in agreement with a microscopic theory for MgB2 in the clean limit.

Comparison of measurements and simulations of series-parallel incommensurate area superconducting quantum interference device arrays fabricated from YBa2Cu3O7− δ ion damage Josephson junctions

We have fabricated series-parallel (two-dimensional) arrays of incommensurate superconducting quantum interference devices (SQUIDs) using YBa2Cu3O7−δ thin film ion damage Josephson junctions. The arrays initially consisted of a grid of Josephson junctions with 28 junctions in parallel and 565 junctions in series, for a total of 15 255 SQUIDs. The 28 junctions in the parallel direction were sequentially decreased by removing them with photolithography and ion milling to allow comparisons of voltage–magnetic field (V–B) characteristics for different parallel dimensions and area distributions. Comparisons of measurements for these different configurations reveal that the maximum voltage modulation with magnetic field is significantly reduced by both the self inductances of the SQUIDs and the mutual inductances between them. Based on these results, we develop a computer simulation model from first principles which simultaneously solves the differential equations of the junctions in the array while considering the effects of self inductance, mutual inductance, and non-uniformity of junction critical currents. We find that our model can accurately predict V–B for all of the array geometries studied. A second experiment is performed where we use photolithography and ion milling to split another 28 × 565 junction array into 6 decoupled arrays to further investigate mutual interactions between adjacent SQUIDs. This work conclusively shows that the magnetic fields generated by self currents in an incommensurate array severely reduce its performance by reducing the maximum obtainable modulation voltage.

Long Josephson tunnel junctions with doubly connected electrodes

In order to mimic the phase changes in the primordial Big Bang, several "cosmological" solid-state experiments have been conceived, during the last decade, to investigate the spontaneous symmetry breaking in superconductors and superfluids cooled through their transition temperature. In one of such experiments the number of magnetic flux quanta spontaneously trapped in a superconducting loop was measured by means of a long Josephson tunnel junction built on top of the loop itself. We have analyzed this system and found a number of interesting features not occurring in the conventional case with simply connected electrodes. In particular, the fluxoid quantization results in a frustration of the Josephson phase, which, in turn, reduces the junction critical current. Further, the possible stable states of the system are obtained by a self-consistent application of the principle of minimum energy.