Magnetic flux-to-voltage transducer based on Josephson junction arrays

Abstract

A device and method for converting magnetic flux to voltage uses a linear Fraunhofer pattern of a 1D array of long Josephson junctions. The 1D array of Josephson junctions may include from 1 to 10.sup.9 junctions formed in a planar geometry with a bridge width within the range of 4-10 m.

Claims

1. A method for converting magnetic flux to voltage comprising using a one-dimensional planar array of long Josephson junctions on a substrate, wherein the planar array is configured in a geometry selected from line, spiral, circle, meandering line, and combinations thereof, wherein each long Josephson junction has a bridge width greater than two times the Josephson penetration depth.

2. The method of claim 1, wherein the planar geometry comprises a meandering line comprising from 10 to 10.sup.6 meanders.

3. The method of claim 1, wherein the array of Josephson junctions comprises from 1 to 10.sup.9 junctions.

4. The method of claim 1, wherein the Josephson junctions have a bridge width within a range of 4 to 100 m.

5. The method of claim 4, wherein the Josephson junctions have a junction width much narrower than the bridge width.

6. The method of claim 1, wherein the Josephson junctions have a bridge width within a range of 4 to 10 m.

7. The method of claim 1, wherein the array is arranged in series, parallel, or series-parallel.

8. The method of claim 1, wherein the array of Josephson junctions is formed from an YBCO superconductor.

9. The method of claim 1, wherein the array of Josephson junctions is formed in a superconducting material selected from the group consisting of Nb, Pb, Al, MgB.sub.2, and cuprates.

10. The method of claim 1, wherein the Josephson junctions comprise junction barriers selected from the group consisting of Superconductor-Insulator-Superconductor (SIS), Superconductor-Normal Metal-Superconductor (SNS), and Superconductor-diminished superconductor-Superconductor (SSS).

11. The method of claim 1, wherein the Josephson junctions comprise a junction selected from the group consisting of ion damage Josephson junctions, SIS trilayers, step-edge junctions, bicrystal junctions, grain boundary junctions, and ramp junctions.

12. A method for converting magnetic flux to voltage comprising using a Fraunhofer pattern of a 1D array of long Josephson junctions.

13. The method of claim 12, wherein the ID array of long Josephson junctions is configured in a planar geometry selected from line, spiral, circle, meandering line, and combinations thereof.

14. The method of claim 12, wherein the array comprises from 1 to 10.sup.9 long Josephson junctions.

15. The method of claim 12, wherein the Josephson junctions have a junction width much narrower than the bridge width.

16. The method of claim 12, wherein the junction width is less than 10 m and the bridge width is in a range of 50 to 100 m.

17. The method of claim 12, wherein the array is arranged in series, parallel, or series-parallel.

18. The method of claim 12, wherein the array of Josephson junctions is formed in a superconducting material selected from the group consisting of Nb, Pb, Al, MgB.sub.2, and cuprates.

19. The method of claim 12, wherein the Josephson junctions comprise junction barriers selected from the group consisting of Superconductor-Insulator-Superconductor (SIS), Superconductor-Normal Metal-Superconductor (SNS), and Superconductor-diminished superconductor-Superconductor (SSS).

20. The method of claim 12, wherein the Josephson junctions comprise a junction selected from the group consisting of ion damage Josephson junctions, SIS trilayers, step-edge junctions, bicrystal junctions, grain boundary junctions, and ramp junctions.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIGS. 1A and 1B are diagrammatic views of short and long Josephson junctions depicting current density distribution (prior art).

(2) FIG. 2A is a diagrammatic perspective view of a device constructed with a meandering geometry according to an embodiment of the present invention; FIG. 2B is a top plan view of an embodiment of the FMFS device; FIG. 2C is a diagrammatic view of an exemplary spiral geometry; FIG. 2D is a diagram of an exemplary double spiral configuration; and FIG. 2E is a diagram of a planar layout with groups of meanders in different orientations.

(3) FIG. 3A is a plot showing the Fraunhofer and SQUID pattern for a 101000 two dimensional SQUID array fabricated with 2 micron wide junctions.; FIG. 3B is a plot comparing the linearity of the Fraunhofer and SQUID patterns.

(4) FIG. 4A is an optical micrograph of single junction devices fabricated with different bridge widths according to an embodiment of the invention; FIG. 4B is a diagrammatic view of the device of FIG. 4A.

(5) FIGS. 5A-5G are plots of critical current versus flux demonstrating the evolution of bridge width and the increasingly linear behavior with increasing bridge width.

(6) FIG. 6A-6D illustrate increasing linearity and skew in the central peak with increasing bridge width.

(7) FIGS. 7A-7F provide results of a simulation investigating the effects of critical current non-uniformity on a long Josephson junction amplifier for a standard deviation =0.05 and 0.10.

(8) FIGS. 8A-8F show results of a simulation investigating the effects of lithographically-defined junction area non-uniformity on a 100 junction array for a standard deviation =0.05 and 0.10.

(9) FIGS. 9A-9F show results of a simulation combining both the effects of lithographically-defined junction area non-uniformity and critical current non-uniformity on a long Josephson junction amplifier.

(10) FIG. 10A-10B are plots of the junction period of the magnetic field pattern vs. junction width.

(11) FIG. 11 is a plot of junction sensitivity as a function of junction width.

(12) FIG. 12 is a plot showing increased junction linearity with junction width.

(13) FIG. 13 is a diagrammatic view of a wide bridge device according to an embodiment of the invention.

(14) FIG. 14 is a plot of the estimated sensitivity of the wide bridge device of FIG. 13.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

(15) A Fraunhofer magnetic field sensor (FMFS)-based device is formed from an array of Josephson junctions to produce increased voltage yield, improved sensitivity, and signal-to-noise ratio well beyond that obtainable from SQUID devices. The inventive devices are capable of operation above the boiling point of liquid nitrogen, can be very densely spaced 500 nm, easily manufactured, are uniform to better than 10% variation with excellent temporal stability. Utilization of wide junctions greatly simplifies photolithography while increasing sensitivity and linearity. The voltage obtainable by large linear arrays according to the FMFS junction technology is unsurpassed due to the large number of junctions possible.

(16) FIG. 2A diagrammatically illustrates an example of a FMFS-based device 10 fabricated on 1 cm1 cm substrate 16 consisting of a series array 8 of Josephson junctions 12 arranged in a meander geometry. Each of the junctions 12 is a long Josephson junction, i.e., one in which the junction width is larger than .sub.J so that the current is concentrated at the edges. (See, e.g., FIG. 1B.) Lines of Josephson junctions 12 define a meander leg 20, with pairs of meander legs 20 joined by superconducting bridge switch-backs 18. For simplicity in illustration, in FIG. 2A, each meander leg 20 is shown as having ten (10) Josephson junctions 12, however, it will be readily apparent to those in the art that the number of junctions within a meander leg or within the entire meander structure will be selected based on a number of factors including, but not limited to, fabrication methods and desired device characteristics. Selection of appropriate numbers of junctions, inter-junction spacing, numbers of meanders and their dimensions will be within the level of skill in the art based on the examples described herein. Contacts 14 disposed at the switch-backs 18 and at the meander ends 22 provide for external connection. The contacts 14 may be gold bond pads or other appropriate conductors.

(17) FIG. 2B provides a diagrammatic top view of an embodiment of a FMFS-based device 110 shown with a larger number N of meanders 28, but otherwise configured using with the same basic elements as described with reference to FIG. 1B. The meanders may number on orders of magnitude of 10 to 10.sup.6 or more, with junctions numbering from a single junction to billions (10.sup.9) or more, limited only by practical fabrication constraints, to achieve the desired performance, with the substrate size being scaled as needed.

(18) Modestly estimating 400 meanders (25 micron periodicity) with 200 switch-backs and an inter-junction spacing of 0.5 microns would yield a total of 810.sup.6 junctions. Assuming a typical single junction I.sub.CR product of 100 A1 Ohms=100 V and 50% modulation of the critical current to zero, this would yield 400 Volts. If only 25% of this signal has a usable linear range, it would still yield 100 V/10 T, or equivalently 10.sup.7 V/T, which is two orders of magnitude better than a SQUID with the added benefits of dynamic range, linearity and a bandwidth from DC to GHz. An additional benefit Fraunhofer devices may have over SQUID devices is lower noise properties.

(19) The general architecture of a FMFS-based device according to the invention can include anywhere from single long Josephson junction up to millions of junctions in series. In addition, series-parallel junction arrays may be used where the Josephson junctions in parallel are connected in such a way that they do not exhibit SQUID properties, i.e., large .sub.L factor (=I.sub.0(2L/.sub.0100), large inductance, and/or out of plane. (See, e.g., Tesche and Clarke, J. Low Temp. Phys., Vol. 29, No. 3/4, 1977.) The SQUID properties can be avoided by using a sufficiently large inductance connecting the junctions in the parallel direction.

(20) While the examples described herein refer to YBCO (YBa.sub.2Cu.sub.3O.sub.7-) superconductors, the inventive devices may be formed using virtually any superconducting material in which a Josephson junction may be made, including Nb, Pb, Al, MgB2, cuprates, etc. Any junction barrier-type may also be used, including, but not limited to Superconductor-Insulator-Superconductor (SIS), Superconductor-Normal Metal-Superconductor (SNS), and Superconductor-diminished superconductor-Superconductor (SSS). In addition, while the exemplary embodiments describe ion damage Josephson junctions, the junctions may be formed using any other known method, including, but not limited to SIS trilayer, step-edge junctions, bicrystal junctions, grain boundary junctions, ramp junctions, and others.

(21) Appropriate configurations of the planar array of Josephson junctions extend far beyond the meandering line geometry described in the exemplary embodiment. The configuration of the junction array may follow any planar geometry, including lines, spirals, circles, meanders, combinations thereof, or any shape that is appropriate for a specific antenna. FIGS. 2C-2E illustrate a few possible planar geometry configurations, showing a spiral (FIG. 2C), a double spiral (FIG. 2D) or groups of meanders in different orientations (FIG. 2E). Many other configurations are possible. The planar geometry may optionally include flux focusing elements, or other elements such as flux input elements for current-to-voltage transduction. The device may include any number of elements arranged in a series or parallel relationship. The structures may be resonant or non-resonant, with the broadest bandwidth being achieved with non-resonant structures.

(22) With regard to the junction spacing, there is no limit to the spacing for the invention described. For any given junction technology, any range of spacings that can produce Josephson junctions will be within the scope of the invention. The highest density of junctions is set by the practical fabrication limits. For a high voltage output in a small area, a high density junction technology is most desirable. For improved coupling of the device to external HF fields, a large area is desirable. For an RF device, a distributed array of a limited number of junctions is preferred. For example, with 1 Ohm junctions matching a 50 Ohm load, radio frequency power is most efficiently transduced for approximately 50 junctions rather than millions.

(23) The inventive FMFS-based device uses the Fraunhofer patterns of a 1D array in contrast to a 2D array used in a SQUID array. FIG. 3A shows the magnetic field response of a 2D 101000 junction array (SQUID array). Josephson junctions exhibit both interference and diffraction. Small oscillation (quantum interference) from the SQUID areas and large oscillation (quantum diffraction) are determined by the junction area. The sharp Fraunhofer modulation of the SQUID transfer function is an indicator that the junctions have uniform areas and critical currents. A 1D array exhibits only the Fraunhofer pattern, which is far more linear that the SQUID pattern and has a dynamic range that is about 1,000 times larger. FIG. 3B illustrates how the Fraunhofer regime (upper line1200 junction array) is very linear compared to a SQUID array (lower line51000 junction array) while having a much larger dynamic range. (Note that the upper axis scale (in T) corresponds to the SQUID pattern while the lower axis scale (in mT) corresponds to the Fraunhofer pattern, as indicated by the double arrows.) To achieve the same sensitivity as a SQUID, it is simply a matter of increasing the number of junctions to scale up the voltage.

(24) Using photolithographic processes an array comprising a large number (on the order of hundreds to multiple millions) of Josephson junctions is formed on a substrate. The FMFS devices may be fabricated by a number of different process, including conventional photolithographic processes as are known in the art, and the photolithographic processes described by S. A. Cybart, et al. in Very Large Scale Integration of Nanopatterned YBa.sub.2Cu.sub.3O.sub.7- Josephson Junctions in a Two-Dimensional Array, Nanoletters, 2009, Vol. 9, No. 10, 3581-3585, which is incorporated herein by reference.

(25) Briefly, the process described by Cybart, et al., involves the steps of thermal co-evaporation of a superconducting, e.g., YBCO, thin film on a sapphire wafer followed by deposition of a gold contact layer. The films are patterned using photolithography and argon ion (Ar.sup.+) milling to fabricate a microstrip. The gold layer over the junctions was removed using a subsequent photolithography step and chemical gold etch, leaving the contact pads. The junctions are fabricated by coating the wafer with a layer of photoresist, which is then hardbaked, to serve as the primary ion stopping layer. A thin (e.g., 25 nm) layer of germanium (Ge) may be electron-beam evaporated on top of the resist to also serve as an etch stop. A layer of poly(methyl methacrylate) (PMMA) resist is spun onto the Ge layer for electron-beam lithographic patterning. Using an e-beam writer, such as a 100 keV Leica VB6-HR nanowriter, or similar conventional e-beam system, lines are written into the PMMA over the locations intended for the junctions. This pattern is transferred into the Ge layer by reactive ion etching (RIE) in a HBrCl.sub.2 plasma etcher. The pattern in the Ge is transferred to the resist using low temperature (100 C.), low pressure (5 mTorr) oxygen RIE. Following etching, the wafers are implanted to induce ion damage in the areas not protected by the mask. The implant dose will depend on the desired junction parameters.

(26) An alternative fabrication method is disclosed in co-pending International Application No. PCT/US2015/035426, filed Jun. 11, 2015, which is incorporated herein by reference. The process is also described by S. A. Cybart, et al., in Nano Josephson superconducting tunnel junctions in YBa.sub.2Cu.sub.3O.sub.7-67 directly patterned with a focused helium ion beam, Nature Nanotechnology, 2015, 10(598-602), published on-line 27 Apr. 2015.

(27) FIG. 4A is an optical micrograph taken at 2 magnification of a test sample chip with FMFS-based devices fabricated from YBCO strips of varying bridge widths. FIG. 4B provides a diagrammatic view of the same structure, with the bridge widths indicated. As previously described, bridge width W impacts to Josephson penetration depth, determining whether the junction is considered long or short. The actual junctions are too small to be seen in the photographic image, but are indicated by the black Xs. In FIG. 4B, the junctions are illustrated as the light gray areas in the centers of the wider strips (not shown in the narrower strips.) The devices 30-39 have bridge widths W of 50 m, 30 m, 15 m, 10 m, 8 m, 6 m, 5 m and 4 m, from top to bottom of the image. Bond pads 14 are shown in both images, with the voltage and current connections for the 50 m bridge indicated in FIG. 4B.

(28) FIGS. 5A-5G provide the results of the evaluation of bridge width and its impact on device response. FIG. 5A shows the critical current versus flux pattern for a 2 m bridge width at a temperature of 4K. FIG. 5B is a plot of critical current versus flux for a 3 m bridge width at a temperature of 4K. FIGS. 5C and 5D are plots of critical current versus flux for a 4 m bridge width at 4K and 77K, respectively. FIG. 5E shows the pattern for a 6 m bridge width at 80K. FIG. 5F provides the results of an 8 m bridge at 80K. FIG. 5G provides the results for a 10 m bridge at 80K. The Josephson penetration depth for this set of experiments is around 34 m. Looking at the evolution of the patterns, it can be seen that the degree of roundness of the center peaks diminishes (i.e., becomes sharper) as bridge width increases. For bridge widths greater than 6 m, the curves in the pattern are replaced by a linear slope. The shape of the pattern is the most important, because the sensitivity and the dynamic range can be adjusted by the number of junctions in series. What is demonstrated by these results is that the shorter junctions have a round center peak whereas in the longer junctions, the center peak transitions to a triangle. The increased sharpness of the slope with increasing bridge width corresponds to greater sensitivity due to the larger area (=BA). It should be noted that the data were obtained using different devices. Also, the operating temperature can be tuned anywhere within a range of 4K to 80K.

(29) FIGS. 6A-6D provide an additional example of how linearity and skew in the central peak increase with increasing bridge width. Single junctions with bridge widths of 4, 6, 8 and 10 m were tested at 77K, with the results plotted in FIGS. 6A-6D, respectively. Devices larger than 10 microns did not function properly because the width became too large.

(30) A close-spaced series array with 1000 meanders, 10 m bridge width, and 100 nm junction spacing fabricated on a 1 cm1 cm area chip would produce a device having 10.sup.9 junctions. Using the results shown in FIG. 6D, the I.sub.CR product for a single junction (250 A0.13) would be 32.5 V. Modulation of the critical current to zero (a change in magnetic field of 35 T) for a single junction corresponds to 1 V/T, which, for 10.sup.9 junctions produces 1 V/nT.

(31) To investigate the effects that non-uniform critical currents might have on the linearity and dynamic range of such an array, we simulated a linear array of I.sub.C(B) patterns by summing the voltages of triangular shaped functions of different amplitudes for both a 0.10 and 0.05 critical current standard deviation. FIG. 7A illustrates the voltage-flux characteristic of each junction for =0.05, FIG. 7B shows the results for each junction for =0.10. For all junctions summed, the results are shown in FIGS. 7C and 7D for =0.05 and 0.10, respectively. FIGS. 7E and 7F plot the slopes of all junctions for =0.05 and 0.10, respectively. Based on these results, there appeared to be little or no effect on range or linearity for either case. Our current junctions have been demonstrated with standard deviations in critical current of around 0.12. To simulate variation in junction area, triangles of different periodicity were evaluated for a 100 junction array. The results, provided in FIGS. 8A-8F, indicate that linearity is not affected and dynamic range is only slightly reduced for a 0.10 standard deviation in junction area compared to 0.05. As in the previous simulation, FIGS. 8A and 8B show the voltage-flux characteristic for each junction for a variation in junction area of =0.05 and 0.10, respectively, FIGS. 8C and 8D provide the characteristic for the sum of all 100 junctions for =0.05 and 0.10, and FIGS. 8E and 8F provide the slope of all junctions for =0.05 and 0.10, respectively.

(32) The effect of a combination of variations in both effects (critical current non-uniformity and junction area variation) on a long Josephson junction amplifier is demonstrated in the simulation results shown in FIGS. 9A-9F. Area variation is determined by lithographic error (which is very small, especially for long junctions) to be 0.02 standard deviation from the mean area. The derivative shows a very small reduction in dynamic range, which can easily be compensated for by adding more junctions. FIGS. 9A and 9B show the voltage-flux characteristics for each junction for a variation in junction area of .sub.A=0.05 and 0.10, and a variation in critical current of .sub.I=0.10 and 0.20, respectively. FIGS. 9C and 9D provide the characteristics for the sum of all 100 junctions for .sub.A=0.05 and 0.10, and .sub.I=0.10 and 0.20. FIGS. 9E and 9F provide the slope of all junctions for .sub.A=0.05 and 0.10, and .sub.I=0.10 and 0.20, respectively.

(33) FIG. 10A-10B are plots of the junction period of the magnetic field pattern vs. junction width, demonstrating how larger bridge width substantially reduces the field period and, hence, increases sensitivity. The upper line in each plot is proportional to 1/w.sup.2, where w is the bridge width.

(34) Sensitivity can be defined as the slope of the magnetic field pattern operated in voltage mode dV/dB. To evaluate sensitivity, the device is biased with a static current above the critical current and voltage is detected. In FIG. 11, sensitivity is plotted as a function of junction width, demonstrating that sensitivity increases with width.

(35) The linearity of a device can be analyzed by fitting a straight line (IcB) from the center peak to the first minimum of the steeper side and determining the residual sum of squares from the fit. As shown in FIG. 12, the residual sum of squares of each fit decreases as the junction width increases, indicating improved linearity with increasing width.

(36) From these above-described tests, we learned that using a wider bridge gives greater sensitivity, however the junction should be 10 m or less. Therefore, one approach for an optimized device is to create a junction contained inside of a much larger bridge. FIG. 13 illustrates an example of a 50 m wide bridge with an approximately 10 m junction inside. To build this, on substrate 50, we use a low ion dose to write the junction 54 and a very large dose to write insulating barriers 52 on the sides. The area within the dashed lines 56 corresponds to the effective junction area. FIG. 14 is a plot of the estimated sensitivity of the wide bridge device of FIG. 13 for bridge widths ranging from 4 m up to 100 m for a constant 6 m junction width, where the junction period (left axis) is plotted against bridge width as indicated by the black dots, and junction sensitivity (right axis) is plotted against bridge width, indicated by the black squares.

(37) Using the approaches described herein, a device for converting magnetic flux to voltage can be fabricated on a small substrate using relatively straightforward lithographic processes. A FMFS-based transducer can be used as a magnetic antenna, amplifier, magnetometer, magnetic field sensor or for satellite communication with very high linearity, ultra wide bandwidth, large dynamic range and high sensitivity. Such a device provides significant advantages over existing SQUID-based technologies because it is simpler and more easily commercialized. A significant additional advantage lies in the fact that the supporting electronics required for implementation of an FMFS-based antenna, amplifier and/or a magnetometer are greatly simplified relative to existing SQUID-based technologies. The inventive approach describe above is not limited to antenna-like applications, but may be used in any application requiring magnetic field sensing with high linearity and wide bandwidth, including biomedical magnetic imaging and magnetic microscopes.

(38) References (incorporated herein by reference):

(39) 1. V. Martin et al., Magnetometry based on sharpened high Tc GBJ Fraunhofer patterns, IEEE Trans. Appl. Supercond. 7(2):3079-3082, 1997.

(40) 2. J. Clarke and A. Braginski (Eds.), The SQUID Handbook: Fundamentals and Technology of SQUIDs and SQUID Systems, Volume I, and The SQUID Handbook: Applications of SQUIDs and SQUID Systems, Volume II, Wiley-VCH Verlag GmbH & Co., 2006.

(41) 3. A. V. Shadrin, et al., Fraunhofer regime of operation for superconducting quantum interference filters, Appl. Phys. Lett. 93(26):262503, 2008.

(42) 4. C. D. Tesche and J. Clarke, dc SQUID: Noise and Optimization, J. Low Temp. Phys., 29(3/4):301-331, 1977.

(43) 5. K. Chen, et al., Planar thin film YBa.sub.2Cu.sub.3O.sub.7- Josephson junction pairs and arrays via nanolithography and ion damage, Appl. Phys. Lett. 85(14): 2863-2865, 2004.

(44) 6. K. Chen, et al., Study of closely spaced YBa.sub.2Cu.sub.3O.sub.7- Josephson junction pairs, IEEE Trans. on Appl. Supercond., 15(2):149-152, 2005.

(45) 7. S. A. Cybart, et al., Planar YBa.sub.2Cu.sub.3O.sub.7- ion damage Josephson junctions and arrays, IEEE Trans. on Appl. Supercond., 15(2): 241-244, 2005,

(46) 8. S. A. Cybart et al., Temporal Stability of YBaCuO Nano Josephson Junctions from Ion Irradiation, IEEE Trans. on Appl. Supercond., 23(3): 1100103, 2013.

(47) 9. S. A. Cybart, et al. Very Large Scale Integration of Nanopatterned YBa.sub.2Cu.sub.3O.sub.7- Josephson Junctions in a Two-Dimensional Array, Nanoletters, 2009, 9(10): 3581-3585.

(48) 10. S. A. Cybart, et al., Nano Josephson superconducting tunnel junctions in YBa.sub.2Cu.sub.3O.sub.7- directly patterned with a focused helium ion beam, Nature Nanotechnology, 2015, 10 (598-602), 27 Apr. 2015.