Using Geometry To Sense Current - Nano Letters (ACS Publications)

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Using geometry to sense current Adam Nykoruk McCaughan, Nathnael Solomon Abebe, Qing-Yuan Zhao, and Karl K. Berggren Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b03593 • Publication Date (Web): 29 Nov 2016 Downloaded from http://pubs.acs.org on December 1, 2016

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Using geometry to sense current Adam N. McCaughan†, Nathnael S. Abebe, Qing-Yuan Zhao, Karl K. Berggren* Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA. ytron, superconductivity, electronics, current crowding, memory, nondestructive readout, fluxon

We describe a superconducting three-terminal device that uses a simple geometric effect known as current crowding to sense the flow of current and actuate a readout signal. The device consists of a "Y"-shaped current combiner, with two currents (sense and bias) entering separately through the top arms of the "Y", intersecting, and then exiting together through the bottom leg of the "Y"'. When current is added to or removed from one of the arms (e.g., the sense arm), the superconducting critical current in the other arm (i.e., the bias arm) is modulated. The current in the sense arm can thus be determined by measuring the critical current of the bias arm, or inversely, the sense current can be used to modulate the state of the bias arm. The dependence of the bias critical current on the sense current occurs due to the geometric current crowding effect, which causes the sense current to interact locally with the bias arm. Measurement of the critical current in the bias arm does not break the superconducting state of the sense arm or of the bottom leg, and thus quantized currents trapped in a superconducting loop were able to be repeatedly measured without changing the state of the loop. Current crowding is a universal effect in

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nanoscale superconductors, and so this device has potential for applicability across a broad range of superconducting technologies and materials. More generally, any technology in which geometrically-induced flow crowding exists in the presence of a strong nonlinearity might make use of this type of device.

Traditional superconducting electronic devices have exploited nonlinear two-terminal devices based on tunnel junctions or nanowires for photodetection, magnetic-field sensing, and largescale classical and quantum computing

1–4

. Because of the inconvenience of sensing and

amplifying signals with a two-terminal device, researchers have tried to develop a number of three-terminal superconducting devices

5–8

based on a variety of microscopic physical

mechanisms, including integration with thermal

9,10

, semiconducting

11

, and magnetic

12–14

systems. However, existing three-terminal device proposals have had two main problems that have prevented their wide adoption: (1) they required the combination of superconducting materials with tunnel barriers or complex materials, e.g., semiconducting or magnetic materials, which led to significant engineering challenges in materials growth, device design, and device fabrication; and (2) during operation, they typically induced a voltage in series with the supercurrent-carrying wire, thus interfering with and disturbing the signal to be sensed. These problems have prevented the broad applicability of these existing devices.

Here, we demonstrate the yTron, a device that consists of a "Y"-shaped current combiner, with two currents (sense and bias) that enter through the upper arms of the "Y", join at the intersection point of the Y, and then exit together at the bottom terminal of the "Y". This geometry--mixing two inputs at a sharp intersection point—is analogous to Y-shaped combiners in fluid flow systems, where variations in the input pressures can produce turbulence and mixing at the


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intersection 15–17. In the yTron, the sense supercurrent can be measured nondestructively because the recently-described current-crowding effect in superconductors directly modifies the Gibbsfree-energy barrier of the bias arm 18–22. Previously, it has been possible to measure supercurrents nondestructively, but typically these techniques were indirect, e.g., requiring coupling to an induced magnetic field as in the SQUID amplifier23,24, or measurement of a macroscopic material parameter that was modified by the supercurrent

1,4,25,26

. In contrast, the yTron allows non-

destructive and direct sensing of supercurrent. Although topologically distinct, this device bears closest resemblance to an underdamped (i.e. latching) version of the superconducting lowinductance undulatory galvanometer (SLUG)

27,28

. The SLUG is a relative of the SQUID

amplifier in which the phase of the readout SQUID is shifted by galvanically injected currents rather than by coupling to a magnetic field. The SLUG is capable of producing quantum-limited amplification, but like the SQUID, requires fabrication of two Josephson junctions, while the yTron requires only the patterning of a single thin-film superconducting layer.


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Figure 1. Illustration of the yTron geometric current crowding and its effect on the Gibbs free energy barrier to vortex entry. (a,d,g) The sense arm is biased with the same current density as the bias nanowire, and there is minimal current crowding at the intersection. The current contributions yield a current density J that is nearly uniform in the bias arm, and the resulting vortex energy barrier Gb is positive. (b,e,h) The sense current Is is reduced and current begins to crowd on the bias arm side in the vicinity of the intersection, reducing Gb. (c,f,i) Is is set to zero, and as a result the current streamlines in the bias arm curve sharply around the intersection, indicating significant crowding. Under these bias conditions, Gb is reduced below zero and flux (vortices) flows across the bias arm.


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The functionality of the yTron arises from the strong nonlinear dependence of the current distribution in the bias arm on the sense current--unlike most superconducting devices, it requires no tunnel junctions or loops. Due to current crowding, supercurrent flowing into the sense arm diverts briefly into the bias arm region on its way towards the source terminal. This diversion produces zero net current flux into the bias arm, but it does modify the local distribution of current density along the width of the bias arm. Near the intersection of the Y, the current density in the bias arm thus depends strongly on the magnitude of the sense current. Ultimately, the modification of the current density by the sense current produces changes in the Gibbs free energy barrier to vortex entry along the width of bias arm, either raising or lowering the barrier to vortex entry. Once the barrier is reduced to zero, it becomes energetically favorable for vortices to cross from one side of the bias arm to the other even at zero temperature, as the presence of current in the bias arm makes ∆G nonzero. As a result, although the yTron geometry is fixed, the effective critical current of the bias arm can be increased or decreased by adding or removing current from the sense arm.

We can show the impact of sense-current-induced current crowding on the bias-arm critical current by using the three example conditions shown in Fig. 1. In each of these examples, we computed the current flow through the device, then followed the methods described in Ref. 18 to calculate the vortex self-energy Eself along with the work done by the current sources WI at each point in space. This theoretical technique is based on the London theory and has also been shown to be equivalent with simulations done in the time-dependent Ginzburg-Landau framework29. After calculation, the Eself and WI energy contributions were then summed to create a map of G,


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the Gibbs free energy barrier to vortex entry. This map of G was then used to determine Gb, the height of the energy barrier to vortex entry in the bias arm. A slice of this map along the bias arm transverse axis δ is shown in Fig. 1 to facilitate understanding (examples of the complete map are shown in Fig. 2(d)) for each of the example bias conditions. In Fig. 1(a,d,g), the yTron is biased such that the current densities through the sense (Js) and the bias (Jb) arms are equal. The current streamlines from both arms combine uniformly at the intersection and flow to the source, which corresponds to a minimally-crowded state. The current density J along the bias arm (δ axis) is maximally uniform and results in a Gb is greater than zero, which prevents vortices from crossing and creating a voltage state in the bias arm. In Fig. 1(b,e,h), the current flowing into the sense arm has been reduced, and as a result the current streamlines from the bias arm bend slightly around the intersection point on their way to the source terminal. Under these conditions, the changes in J near the intersection lead to an increase in the work done on the vortex WI, such that the energy barrier Gb is equal to zero. In Fig. 1(c,f,i), the sense current has been shut off, and the remaining streamlines bend sharply around the intersection point indicating significant current crowding. Correspondingly, J and WI increase in magnitude near the intersection. This increase is responsible for driving Gb below zero, and for these bias conditions we expect to see the generation of a voltage state in the bias arm--either in the form of vortex crossings system is underdamped, as a macroscopic hotspot

31

30

or, if the

. This voltage appears exclusively between

the bias and source terminals: Gb remains greater than zero in the sense arm and so its superconducting state is unperturbed.

To demonstrate and validate the operation of the yTron, we fabricated and characterized several devices of varying dimensions. Fig. 2(a-d) shows the characterization of a yTron with


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200-nm-wide arms. As expected, the I-V curve of the bias arm was electrically identical to that of a hysteretic superconducting nanowire

32

, albeit one that has a critical current dependent on

the sense current. As shown in Fig. 2(c), the dependence of the bias arm critical current Ic on the sense input Is was approximately linear over a large range of Is values and had a slope of 0.52 with an intercept of 49.3 µA. The width of the Ic transition was 0.53 µA, as measured at full bandwidth with a 6 GHz oscilloscope. We produced a theoretical fit of Ic(Is) by calculating G everywhere in the geometry for a given value of Is, extracting the minimum barrier location Gb from the map, then calculating how much bias current was required to reduce Gb to zero. For parameters, we calculated that the nanowires had a Pearl length Λ = 2λ2/d of 85 µm, where d was the thickness of the NbN film which was measured to be 4.8 nm with an optical transmissometer33, and a penetration depth λ which was set to be 450 nm 34–36. The best fit to the data was found when the radius-of-curvature of the intersection ρc was set to 5 nm, which matched the approximate fabrication resolution of the HSQ-based electron-beam process used to pattern the device 37. The theoretical fit diverged from the empirical results below Is = -7 µA; this behavior is consistent with the vortex formation process changing from having vortex nucleation point at the intersection (δ = 0 nm) to an antivortex nucleation at the far edge (δ = 200 nm). We note that, although we fit ρc to the data, as shown in Fig. 2(c) there was only a weak dependence of Ic(Is) on ρc, suggesting that device operation is tolerant to variations and errors in the fabrication process. We were able demonstrate this tolerance by characterizing 22 different devices with arm widths ws and wb between 100 nm and 800 nm as shown in Fig. 2(e). The dependence of Ic for the bias arm depended primarily on the current density at the intersection (determined by Is and ws/wb), and weakly on ρc.


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Figure 2. Basic operation of the yTron. (a) Scanning electron micrograph of a yTron with 200nm-wide arms (b) I-V characteristics of the bias arm for five values of Is. (inset) Circuit schematic for testing the yTron at different Is bias points. (c) Plot of the yTron regimes of operation for input conditions Is and Ib. The border between the conditions Gb > 0 and Gb < 0 defines Ic(Is), and is denoted by the black dots (experimental data) and the red, blue and green lines (theory plots). (d) Computation of the Gibbs free energy map for vortex entry illustrating the transition between the superconducting and voltage states by changing Is. (i) Gb > 0 and there is no path for vortices to enter and cross the bias arm (ii) When Is is reduced, a gap opens in the barrier landscape so that there is a continuous path across the bias arm where G < 0; vortices will flow and cause a voltage to appear in the bias arm. (e) Log-log plot of the experimentallymeasured slopes of Ic(Is) versus geometric arm width ratio for 22 different devices.


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There are several aspects of the yTron design that impact its operation. The first characteristics that must be considered are those of the superconducting material from which the device is fabricated. The superconducting film thickness must be less than the material's penetration depth λ in order for the current crowding effect to work as described. In a thicker superconductor with a non-uniform kinetic inductance, current may not be distributed evenly across the cross-section of each arm of the yTron, altering the effect of current crowding. By making the device from a film thinner than λ and with arm widths less than Λ, the device has an (approximately) uniform sheet kinetic inductance that produces the current distributions shown in Fig. 1. This criteria can be easily met with reasonable sub-micron fabrication tolerances in many common superconducting thin films including WSi, MoSi, NbTiN, YBCO, and MoGe. Making the nanowires sub-micron has the added benefit of eliminating the possibility of vortex trapping in the device under ambient conditions38. Similarly, the arms of the yTron should be wider than the coherence length (in thin-film NbN ξ ≈ 4 nm) 39. Arms with widths on the order of the coherence length are effectively one-dimensional and may not exhibit the required current-crowding effects. Ultimately, the dependence of the bias critical current Ic on the sense current Is is based on three geometric elements: (1) the inner radius-of-curvature of the intersection point, (2) the widths of the bias and sense nanowires, and (3) the angle at which the sense and bias arms intersect. In testing various geometries, we did not vary the third factor, and so will not detail its impact here. In an ideal Ohmic conductor, an infinitely sharp point at the intersection tip would result in a diverging current density for any streamline bending around the intersection. However, the sharpness of the intersection point is ameliorated by two factors: rounding caused by the practical fabrication limits of e-beam lithography, and the superconducting radius-of-


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curvature effect (as described in Ref. 18) which produces a rounding of the intersection point on the order of the material superconducting coherence length, even for a perfectly sharp intersection.

Isolation between the sense and bias is a key feature of the yTron. Since the yTron is fabricated from a continuous superconducting film, “isolation” in this context does not mean capacitively decoupled as for a FET, but instead the isolation of the sense current from changes in the bias arm. Even when the superconductivity in the bias arm breaks down--e.g., a voltage state forms-the superconducting state of the sense nanowire is minimally disrupted. The only expected interaction would be due to the current-dependence of the kinetic inductivity in the lower arm of the Y. Due to the indirect nature of the current-crowding-based modulation of Ic, a voltage state in the bias (source to bias) does not produce any voltage on the sense (sense to bias). As an example, let us assume we have a yTron which is biased just below Ic, as in Fig. 2(d)(i). When Is is reduced, the barrier Gb will be reduced and vortices will begin to flow across the bias arm as shown in Fig. 2(d)(ii). The flow of vortices will produce a voltage between the source and bias terminals. Despite the fact that flux is passing across the bias nanowire, the superconducting state in the sense nanowire never broke down, and no flux was able to cross. One concern we had when testing the yTron was that excited quasiparticles generated by the hotspot or vortex crossings could diffuse and cause a breakdown of superconductivity in the sense arm. In thinfilm NbN, this diffusion length is ~100 nm

40

, on a similar scale to the nanowire widths.

However, for the device shown in Fig. 1, we found that as long as the total power dissipation caused by the voltage in the bias arm was below 350 nW, the sense arm was not disrupted.


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Due to its ability to measure inline supercurrent, a natural application for the yTron is the readout of quantized currents in a superconducting loop. By placing the sense of the yTron inline with a superconducting loop, we were able to use the yTron to nondestructively read out the number of discrete fluxons (n) trapped in a loop, as shown in Fig. 3. We successfully resolved 13 adjacent fluxon states (n, n+1, etc.) of the loop, and were able to read out those states several thousand times consecutively without changing the value of n. This application was possible because the sense (loop) supercurrent can be inferred from Ic, and can be measured repeatedly without changing n by allowing flux into or out of the loop. Each trial had a standard deviation of 0.71 µA (0.27 fluxons), and to positively identify a fluxon state to an accuracy of 3σ required 4 measurements. This accuracy could be improved upon by reducing the large (∼200 pH) inductance of the loop which would reduce the number of accessible fluxon states but also significantly increase the separation between each state. We note that while this device does not perturb the fluxon state of a superconducting loop (n does not change), given the dissipative nature of the Ic measurement, it is a classical measurement and would not preserve a quantum superposition of the fluxon state.

Using the circuit shown in Fig. 3(a), we observed the quantization of current in the loop with an experiment which consisted of two alternating steps. These steps are depicted in Fig. 3(b). First, we performed a readout experiment in which we measured Ic with 100 consecutive trials. Each trial consisted of steadily increasing Ib up from zero until Ic was reached, indicated by a ~5 mV voltage appearing in the bias arm. After these trials, we then applied an external voltage pulse to the loop to deliberately break the superconducting loop temporarily and allow the number of stored fluxons n to change randomly. Repeating this two-step process several times,


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we then plotted the median Ic value and standard deviation of the distributions produced by each readout experiment, shown in Fig. 3(c).

The results shown in Fig. 3 indicate that the supercurrent in the yTron sense arm was isolated from the breakdown of superconductivity in the bias arm, and that the input supercurrent Is could be measured without changing its value. We found that the readout process was not able to change the median Ic, and we additionally found that the median Ic shifted in discrete steps of 2.61 µA. The steplike jumps of the Ic indicated that individual fluxons in the loop were being added (n→n+1) or subtracted (n→n-1) by the reset process, the hallmark of fluxoid quantization in superconducting loops

41

. The addition or removal of a fluxon to the loop changed Is by a

quantized amount Φ0/L which in turn shifted the approximately-linear Ic(Is) by a steplike amount.


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Figure 3. Resolving individual fluxons in a closed superconducting loop using the yTron as an inline current sensor for a superconducting loop. (a) Superconducting circuit used to trap n fluxons and pass the quantized current nΦ0/L into the yTron sense arm. (b) Readout measurements of the bias arm critical current Ic. After each set of 100 trial measurements of Ic, an operation was performed which allowed n to change, and then another set of 100 measurements was taken. (c) Plot showing the median Ic (dots) and standard deviation (bars) of each set of 100 trials and their correspondence to the fluxon state n; between each experiment a reset operation was performed which added or removed fluxons randomly. The steplike change in the Ic median demonstrates that the yTron resolved adjacent fluxon states of the persistent loop current. The uniformity of the Ic median values indicates that during the readout process n remains unchanged, even though a voltage Vb forms in the bias arm.


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In conclusion we have developed, characterized, and applied the yTron, a new three-terminal superconducting device which is able to sense superconducting currents inline without perturbing them, has a nanoscale active area, and is insensitive to and fabrication variations. The yTron has immediate applications as an inline current sensor for devices such as transition edge sensors and superconducting nanowire single photon detectors (SNSPD), and as a compact superconducting memory. Of further interest is its relation to the SQUID and microwave SLUG amplifiers. The yTron shares enough operational features with these devices to suggest that if it was properly damped with a shunt resistor it may be usable as a microwave amplifier. At the same time, the yTron geometry is naturally sub-micron, and its topology means many of the typical fabrication barriers facing superconducting electronics (such as tunnel-barrier fabrication) are avoided entirely. Since the yTron functionality comes from current crowding, which occurs in every superconductor, it should be possible to fabricate it from any superconducting material, even 2D superconductors like NbSe2 or proximitized graphene. Additionally, the form of the yTron lends itself well to a CMOS-style fabrication scheme: its geometry can reproduced vertically in a multilayer fabrication process, by using an oxide layer between two superconducting thin films as the barrier between the sense and bias arms. Such a process would permit even more compact device geometries to be realized. Another potential use of the yTron would be to use it as a three-terminal controllable weak link in the style of ultrafast, low-power single-flux quantum logic like RSFQ

42,43

--by forming loops between the sense and bias and

source and bias, flux flow into the source-bias could be controlled by the motion of flux into and


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out of the sense-bias loop. This new device is thus expected to expand the range and utility of superconducting nanoelectronics.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Present Addresses †National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT The authors would like to James Daley and Mark Mondol for nanofabrication technical support. This research was supported by the Air Force Office of Scientific Research (AFOSR) grant under contract No. FA9550-14-1-0052 and the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via contract W911NF-14C0089. Adam McCaughan was supported by a fellowship from the NSF iQuISE program, award number 0801525. REFERENCES


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Figure 1 194x215mm (300 x 300 DPI)


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Figure 2 86x87mm (600 x 600 DPI)


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Figure 3 83x81mm (600 x 600 DPI)


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Using Geometry To Sense Current - Nano Letters (ACS Publications)

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