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IEEE Transactions on Applied Superconductivity

Analysis on the Suitability of Bi-SQUIDs for the Detection of Trapped Flux in Superconducting Circuits

Tessa Hall, Coenrad Johann Fourie

Published Nov 24, 2025• 0 citations
Publisher

Abstract

Quantised magnetic flux trapped during cooldown in superconducting integrated circuits, particularly in thin-film ground planes, couples to nearby circuit structures. The coupling from such fluxons is known to degrade circuit operating margins, or to cause outright operational failure. Measurement of the likely location of one or more trapped fluxons during circuit operation, as well as before and after defluxing steps, can help improve defluxing methods and increase circuit operating margins. A bi-SQUID is a device consisting of three Josephson junctions which demonstrates improved linearity in the voltage-flux response over conventional DC SQUIDs. Conventional DC SQUIDs are being considered as a means of implementing trapped flux detection. Due to the improved linearity of bi-SQUIDs, we investigate their suitability for the same purpose. We present simulation results comparing the sensitivity of different bi-SQUID designs and layout structures to trapped flux and compare bi-SQUID results with a conventional DC SQUID.

DOI
10.1109/tasc.2025.3636601

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•Aug 21, 2015•0 citations
Quantised magnetic flux trapped during cooldown in superconducting integrated circuits, particularly in thin-film ground planes, couples to nearby circuit structures. The coupling from such fluxons is known to degrade circuit operating margins, or to cause outright operational failure. Measurement of the likely location of one or more trapped fluxons during circuit operation, as well as before and after defluxing steps, can help improve defluxing methods and increase circuit operating margins. A bi-SQUID is a device consisting of three Josephson junctions which demonstrates improved linearity in the voltage-flux response over conventional DC SQUIDs. Conventional DC SQUIDs are being considered as a means of implementing trapped flux detection. Due to the improved linearity of bi-SQUIDs, we investigate their suitability for the same purpose. We present simulation results comparing the sensitivity of different bi-SQUID designs and layout structures to trapped flux and compare bi-SQUID results with a conventional DC SQUID.
Abstract Flux trapping in superconducting integrated circuits cause circuits to operate with reduced margins, or to fail completely. Moats are used in superconducting ground planes to create low energy locations for flux trapping. Moat design and placement strategies have been presented before, and several experiments published to evaluate moat efficiency. Although fluxons can be steered to moats to prevent trapping in or near Josephson junctions or inductive interconnects, the flux in a moat couples to nearby structures and induces dc currents in superconducting loops. In this paper, we discuss a set of numerical simulation tools for flux trapping analysis, developed under the IARPA SuperTools project. These tools are used to extract compact models for magnetic flux trapped in moats, including the magnetic coupling to superconducting structures. An open-source superconducting transient simulation engine, called JoSIM, is used to simulate these compact models. To evaluate the magnetic coupling of different moat configurations, we developed a set of a flux linkage experiments. Test structures were designed for the multi-layer MIT Lincoln Laboratory SFQ5ee process that allow for flux insertion into moats of different configurations. From experimental results we measure the effects of trapped flux, in different moat structures, on SQUID parameters and use the results to validate the compact models used by our tools.
The influence of a trapped flux quantum in a superconducting ground plane hole, called a moat, on superconducting circuit operation was analyzed. We devised a calculation model to estimate the magnetic flux threading a signal line of a superconducting integrated circuit by the trapped flux quantum in a moat placed near the signal line, by using a conventional inductance extraction tool. Assuming one flux quantum trapped in the moat, the dependence of the magnetic flux threading the signal line on the distance between the moat and the signal line were calculated. We measured the flux linkage by measuring the modulation of the I-V characteristic of a dc-SQUID with a moat near the SQUID implemented by using the 2.5 kA/cm2Nb standard process. The measured flux linkage agrees well with the analysis results using the devised calculation model. When the distance between the 1 μm × 10 μm moat and the SQUID, the signal line size of which corresponds to the typical inductance of an adiabatic flux quantum parametron (AQFP) is 1 μm and one flux quantum is trapped in the moat, the measured magnetic flux linkage threads the signal line was approximately 1.2% of the flux quantum. This flux linkage induces approximately 4% deterioration of the device margin of the AQFP. The devised calculation model and experimental results provide useful information for designing highly integrated future superconducting integrated circuits.
Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance Cs{C}_{s}Cs​ and resistance Rs{R}_{s}Rs​ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.
It has been shown that the voltage versus flux (V-Φ) relation of dc superconducting quantum interference devices (SQUIDs) operating at T=77 K is degraded considerably by thermal noise. Since degradation of modulation voltage in the V-Φ relation becomes more significant when inductance increases, a very restricted range of inductance exists which can be used at T=77 K. In order to reduce the degradation due to thermal noise and to enable the use of large inductances, a new SQUID using three Josephson junctions (3J-SQUID) is proposed. Numerical simulation shows that inductance of 3J-SQUID can be increased to twice as large as that of the conventional case without degrading modulation voltage. It is also shown that modulation voltage is highly improved by damping resistance parallel to inductance. As a result, we can expect to use inductances as large as L<500 pH if 3J-SQUID with damping resistance is employed. Large inductances available in 3J-SQUID will be useful in realizing efficient coupling of external magnetic field to the SQUID inductance.
A variety of superconductor integrated circuits composed of six ac-powered SFQ shift registers with a total of 27078 bits and 108500 Josephson junctions (JJs) per 5 mm × 5 mm chip have been designed, fabricated, and tested to characterize flux trapping, fabrication process yield, and parameter spread. The six 4513-bit registers in the circuits have a common single-phase ac clock and individual input/output drivers, allowing for their parallel testing. We have investigated flux trapping in the circuits with various geometry, size, distance between moats in active ground planes (GPs), and containing up to three additional ‘dummy’ GPs, using multiple cooldowns through the critical temperature with various cooling rates and residual magnetic fields up to ∼ 1.2 µT. For the slit-type and square moats arrayed along the sides of the register cells, we have found a negligible effect of flux sequestered in the moats on the operating margins of the registers, and a negligible probability of detrimental flux trapping outside of the moats. Circuits with 0.3-µm-wide slit moats occupying less than 2% of the circuit area were fully operational in 100% of cooldowns, supporting the viability of a very large-scale integration of superconductor digital circuits. We have also found a strong enhancement of flux trapping outside the moats in circuits with closely spaced GPs and determined a critical distance,${{{\boldsymbol{t}}}_{\boldsymbol{c}}} \approx $0.6 µm, between them. The presence of two or more GPs spaced below thetcrendered the circuits nonoperational in 100% of cooldowns. We have measured 30 chips with over 3M JJs and determined individual cell operating margins in 138 registers to characterize the fabrication-related parameter spread and detect fabrication defects and flux-trapping events. By finding outlier bit-cells in the statistical distribution of the individual cell margins, we detected about one fabrication defect per million JJs, in most cases causing magnetic flux trapping in the affected cell.The circuits have been fabricated in the SFQ5ee fabrication process at MIT Lincoln Laboratory (MIT LL).
The standard operation of a dc SQUID leads to oscillatory electric fields that emit electromagnetic radiation and can change the state of the measured sample. A stationary SQUID could be advantageous when back action on the measured sample has to be avoided. We study a superconducting loop that encloses a magnetic flux, connected to a superconducting and to a normal electrode, when a fixed electric current between the electrodes flows through the loop. The considered circuit does not contain Josephson junctions. We find that in a very broad range of parameters the current flow converges to a stationary regime. The potential difference between the electrodes depends on the magnetic flux, so that measuring this voltage would provide information on the enclosed flux. The influence of thermal noise was estimated. The sizes of the voltage and of the power dissipation could be appropriate for the design of a practical fluxmeter. We found narrow ranges of flux at which the voltage varies sharply with the flux.