Two dimensional Superconducting Quantum Interference Filter (SQIF) arrays using 20,000 YBCO Josephson Junctions
(bottom row) Alex Grancea, Shane Keenan, Simon Lam, Cathy Foley.
Emma Mitchell1, Kirsty Hannam1, Jeina Lazar1, Keith Leslie1, Chris Lewis1,
Alex Grancea2, Shane Keenan1, Simon Lam1, Cathy Foley1
1CSIRO Manufacturing, Lindfield, NSW, Australia,
2CSIRO Data61, Epping, NSW, Australia.
Josephson junctions form the essential magnetic sensing element at the heart of most superconducting electronics. A Josephson junction consists of two superconducting electrodes separated by a thin barrier . Provided the barrier width is less than the superconducting coherence length, Cooper pairs can tunnel quantum mechanically from one electrode to the other coherently when the temperature is below the critical temperature of the two electrodes. Due to the macroscopic quantum coherence of the Cooper pairs in the superconducting state, Josephson junctions not only detect magnetic fields and RF radiation over an extremely wide frequency band, but can also emit radiation. The highly sensitive response of the Josephson junction current to magnetic fields is the key to many of its applications, including magnetometers, absolute magnetic field detectors and low noise amplifiers. More recent applications also include small RF antennas which utilize the Josephson junction’s broadband (dc- THz) detection abilities.
The dc SQUID, or Superconducting Quantum Interference Device, consists of two Josephson junctions connected together in parallel via a superconducting loop. The SQUID is an extremely sensitive flux-to voltage transducer, but despite this simplicity, an exact solution of this problem can only be given in the case of negligible inductance of the loop containing the two junctions. When the SQUID is biased with a current and an external magnetic field is applied, the voltage response oscillates periodically with applied magnetic field (Figure 1a). The period of the oscillation is inversely proportional to the loop area. SQUIDs have been connected together into arrays of increasing size and complexity to improve device sensitivity.
Feynman et al. (1966) first predicted  an enhancement in the SQUID interference effect by having multiple (identical) junctions in parallel, analogous to a multi-slit diffraction grating. This enhancement was originally observed using superconducting point contact junctions  and has been further developed using series arrays of low temperature superconducting (LTS) Nb SQUIDs. More recently 1D arrays of SQUIDs with incommensurate loop areas (non-identical and variable spread) with a non-periodic voltage response were suggested . The voltage response of these superconducting quantum interference filters (SQIFs) is then analogous to a non-conventional optical grating where different periodic responses from individual SQUIDs with different loop areas are summed. This results in a voltage response to a magnetic field in which a dominant anti-peak develops at zero applied field due to constructive interference of the individual SQUID responses. Weaker non-periodic oscillations occur at non-zero fields where the individual SQUID responses destructively interfere. The magnitude and width of the anti-peak for a SQIF is governed by the range and distribution of SQUID loop areas and inductances.
In our recent work  we demonstrate high temperature superconducting (HTS) two dimensional SQIF arrays based on 20,000 YBCO step-edge Josephson junctions connected together in series and parallel (Figure 1b). The maximum SQIF response we measured had a peak-to-peak voltage of ~ 1mV and a sensitivity of (1530 V/T) using a SQIF design with twenty sub-arrays connected in series with each sub-array consisting of 50 junctions in parallel connected to 20 such rows in series. The variation in loop areas within each subarray had a pseudo- random distribution with a mean loop area designed to have an inductance factor βL = 2LIc/Φ0 ~1 . Figure 2a shows part of our array with four whole sub-arrays visible. At higher magnification the variation of individual loop areas is evident (Figure 2b) with the rows of step-edge junctions indicated by arrows.
Figure 2: (a) Part of the 20,000 YBCO step-edge junction SQIF array showing four complete sub-arrays of 1,000 junctions each (b) one sub-array at higher magnification showing rows of junctions (arrows) and variable loop areas (darker material is the YBCO).
The Josephson junctions in our samples are step-edge junctions formed when a grain boundary develops between the YBCO electrodes that grow epitaxially when a thin film is deposited over a small step approximately 400nm high with an angle of ~38o, etched into the supporting MgO substrate [7, 8]. It is well documented that HTS Josephson junctions are difficult to fabricate in large numbers across a substrate. However, step-edge junctions have the advantage of being relatively simple and inexpensive to fabricate and can be placed, at high surface density almost anywhere on a substrate. To date, we have made 2D arrays showing a SQIF response with 20,000 up to 67,000 step-edge junctions on a 1cm2 substrate.
Two dimensional SQIF arrays allow for large numbers of junctions to be placed in high density across a chip, enabling increases in the output voltage and sensitivity of the device. 2D arrays also allow for impedance matching of the array to external electronics by varying the ratio of junctions in parallel to those in series, by virtue of the junction normal resistance, Rn.
In addition, we demonstrated that the sensitivity of the SQIF depends strongly on the mean junction critical current, Ic, in the array, and the inductance (area) of the average loop in the array. In both cases keeping these parameters small such that βL < 1 is necessary for improving the SQIF sensitivity, but can be difficult to achieve with HTS junctions in which the typical spread in Ic can be 30%. The SQIF response also depends on the number of junctions; a linear increase in the SQIF sensitivity with junction number was measured for our SQIF designs.
We were also able to demonstrate RF detection at 30 MHz using our HTS SQIFs at 77 K . More recently a broadband SQIF response from DC to 140 MHz was demonstrated following improvements to our SQIF sensitivity (unpublished). This follows on from reports of near field RF detection to 180 MHz using 1000 low temperature superconducting (LTS) junctions , where more complex and expensive cryogenic requirements limit the LTS array applications outside the laboratory.
 B.D. Josephson, "Possible new effects in superconductive tunneling". Physics Letters, 1, 251 (1962). Abstract.
 Richard P. Feynman, Robert B. Leighton, Matthew Sands, “The Feynman lectures on Physics, Vol III” (Addison-Wesley, 1966).
 J.E. Zimmerman, A.H. Silver, "Macroscopic quantum interference effects through superconducting point contacts", Physical Review, 141, 367 (1966). Abstract.
 J. Oppenländer, Ch. Häussler, N. Schopohl, "Non-Φo periodic macroscopic quantum interference in one-dimensional parallel Josephson junction arrays with unconventional grating structures", Physical Review B, 63, 024511 (2000). Abstract.
 E.E. Mitchell, K.E. Hannam, J. Lazar, K.E. Leslie, C.J. Lewis, A. Grancea, S.T. Keenan, S.K.H. Lam, C.P. Foley, “2D SQIF arrays using 20,000 YBCO high RN Josephson junctions”, Superconductor Science and Technology, 29, 06LT01 (2016). Abstract.
 “The SQUID Handbook, Vol. I Fundamentals and technology of SQUIDs and SQUID systems", eds. John Clarke and Alex I. Braginski (Wiley, 2004).
 C.P. Foley, E.E. Mitchell, S.K.H. Lam, B. Sankrithyan, Y.M. Wilson, D.L. Tilbrook, S.J. Morris, "Fabrication and characterisation of YBCO single grain boundary step edge junctions", IEEE Transactions on Applied Superconductivity, 9, 4281 (1999). Abstract.
 E.E. Mitchell, C.P. Foley, “YBCO step-edge junctions with high IcRn”, Superconductivity Science and Technology, 23, 065007 (2010). Abstract.
 G.V. Prokopenko, O.A. Mukhanov, A. Leese de Escobar, B. Taylor, M.C. de Andrade, S. Berggren, P. Longhini, A. Palacios, M. Nisenoff, R. L. Fagaly, “DC and RF measurements of serial bi-SQUID arrays”, IEEE Transactions on Applied Superconductivity, 23, 1400607 (2013). Abstract.