On-Chip Integrable Planar NbN NanoSQUID with Broad Temperature and Magnetic-Field Operation Range

Superconducting quantum interference devices (SQUIDs) are used for applications ranging from sensitive magnetometers to low-temperature electronics and quantum computation. We introduce a planar nano SQUID that was made with a single lithographic step out of NbN films as thin as 3 nm on a Si chip. The fabrication process of weak links that are 45 nm in width, and 165 nm in length, which were designed to account for overcoming current crowding are presented. Operation at a temperature range of 20 mK to 5 K as well as at 1 T parallel, and 10 mT perpendicular magnetic fields is demonstrated, while potential operation higher than 8 T has also been shown. The broad range of applicability of a single device as well as its scalability are promising for on-chip integrability that may open new technological possibilities, including in quantum and electro-optical circuiting.

of materials that can potentially be used, and hence the control over functional properties or the integration in other superconducting technologies.
Nano-fabrication developments allowed for replacement of the commonly used 3D SQUID structure with a planar-SQUID geometry. Here, there is a superconducting ring that is made of a thin film by means of electron lithography, while within the ring, there are two narrow regions that are connected in parallel and serve as the interfering weak links of the SQUID. 18 In addition to the advantageous fabrication process, the geometry of planar SQUIDs is expected to help them sustain very strong magnetic fields along the direction parallel to the device, operate under strong perpendicular fields and exhibit high spin sensitivity, which are all technologically relevant. 19 The sustainability to parallel fields arises thanks to their relatively small cross section, which in turn is obtained because of the thin film thickness and small size of the weak links. 20 That is, given the dependence between the external magnetic flux (Φ ext ) and the internal magnetic induction ( ): Φ ext = ∫ • 0 ′, for a given critical magnetic flux density, c , smaller cross-section areas ( ) leads to sustainability to higher Φ ext . Likewise, the smaller washer area, (i.e. the area enclosed within the ring) of such geometries allows them to operate well under strong external perpendicular magnetic fields. The reason being is that the breadth of each period in the interfering pattern of the device critical current is proportional to the perpendicular flux, which in turn is proportional to according to the above integral. Finally, the small washer area gives rise also to high spin sensitivity of the SQUID: n = 2 Φ ns B 0 , where Φ ns , B 0 are the system flux noise, Bohr magnetron and vacuum permeability, respectively. 18 SQUID properties are material depended. 21 To-date, planar SQUIDs have been demonstrated for Nb, 20,22 NbN, 23,24 Pb, 25 YBCO, 26,27 Ti, 28 MgB2, 29,30 and for doped diamond. 31 Amongst these materials, NbN is rather attractive because it has relatively high critical current density and can sustain high magnetic fields, while it is also commonly used for logic, and photon-sensing devices. 6,8,38,39,9,23,[32][33][34][35][36][37] However, NbN has a rather short coherence length ( ≈6 nm 40 ), challenging the weak-link fabrication, while growing ultra-thin NbN films with controllable properties is also a non-trivial task. 41 42 We should note that some of the other materials 25,26,28,29,31 may exhibit some of the above advantageous properties, but NbN can potentially have them all in one device. Therefore, there is a need for a robust NbN nano SQUID that endures and is sensitive to a broad range of magnetic fields, operates both at low and high temperatures and encompasses thickness and lateral dimensions as well as a fabrication process that are attractive for integration.
Here, using a single-step lithography process, we fabricated on a Si chip, planar 4-nm thick and 500nm wide NbN planar SQUIDs that operate at a 20 mK -5 K temperature range and detect reproducibly 100 Gauss perpendicular magnetic fields and up to 1 T parallel fields, while they endure and can potentially operate above 8 T. We tested seven devices out of the twenty devices that we fabricated and they all demonstrated good SQUID behavior. We first sputtered the ultra-thin NbN layer on a Si chip with a thick (338 nm) top layer of amorphous SiO2 that had the role of reducing lattice-mismatch strain in the superconductor. Ellipsometry was used to determine a 4-nm thickness of the NbN layer as demonstrated in Figure SI1. The critical temperature, transition width, residual rate ratio and sheet resistance were c = 9.29 ] and s = 157 □ as extracted from Figure   To inject current to the device, in , a voltage was applied on a large resistor (~100 k) that was connected in series to the device and the resultant voltage was then measured with a four-probe scheme.
Schematics of the electric circuit is given in Figure 1c. Figure 2a shows the interfering magnetic-fieldcritical-current characteristics between -100 Gauss and 100 Gauss of a perpendicular field ( ⏊ , limited by the maximal range of our system) even at temperatures as high as 5 K. The interference behavior at 20 mK is given in Figure SI4. Here, the measured critical current of the device was c =20.5 A (all critical current and temperature values are defined as the 90% drop of the normal resistance), while the cycles were of ~6% modulation and ca. 30 Gauss periodicity, which in turn corresponds to an effective washer area of 815 x 815 nm 2 . The device normal resistance n = 1.7 kΩ was extracted from the resistive region of − curve (see Figure 3), so that the device c • n characteristic, which is an upper limit of the potential magnetometry performance 45 is 34.85 mV. Here, the interference pattern is of a zig-zag form as expected from SQUIDs with long ( ≫ ) weak-link bridges. 46 Measuring the slope of the linear lines of the zigzag pattern allows us to extract the effective inductance, which is the sum of both the kinetic and geometric inductance =8.035x10 -10 H, while the figure of merit of the device, L ≡ 2 c Φ 0 = 15.9, where Φ 0 is the magnetic flux quantum. We should note that devices made of films as thin as 3 nm also demonstrated good interference behavior ( Figure SI5).

Figure 2| Planar thin NbN nano SQUID operation at various magnetic fields and temperatures. (a)
Dependence of the switching current on an external magnetic field perpendicular to the sample plane at 5 K (a similar measurement at 20 mK is given in Figure SI4). (b) Interference of the same device under high parallel magnetic fields at 5 K (full black circles) and at 20 mK (empty blue squares) showing a similar qualitative behavior, albeit with higher c for the lower temperature.
To examine the device applicability range and robustness, we tested its operation under even higher magnetic fields. Because the SQUID is only ca. 4-nm thick, it is expected to be less sensitive to parallel fields ( ‖ ) than it is to perpendicular fields. Figure 2b shows that the device operates reliably as a SQUID up to ‖ =1 T. The reason that the device was sensitive to parallel fields is most likely because the field was not exactly parallel to the substrate. Given the change in modulation, which has now become 0.133 T, we can calculate the field-substrate offset angle as 1.
28⁰. Yet, the modulation depth was suppressed with respect to the perpendicular-field measurement to a value of 4-5%. To demonstrate the potential of this device, we tested its operation at lower temperatures. Figure 2b shows the device operation under even more extreme conditions of high magnetic field and very low temperatures (20 mK), demonstrating its robustness and broad range of applicability. Here, the switching-current profile followed the highertemperature measurement (5 K), only the value of the critical current increased from 20.5 A to 29.4 A.
Increasing the parallel magnetic field above 1 T introduced significant noise in our system, giving rise to the disappearance of the interference pattern. We believe that the reason being is the instability of our magnetic field (i.e. its current source) rather than the NbN SQUID itself. That is, the large fluctuations in ‖ affected badly the signal-to-noise ratio so that it was higher than the modulation and hence we could not trace a measurable interference signal. Yet, we believe that under more stable magnetic-field conditions, the device may operate even under much higher magnetic-field values. To support this argument, we measured the dc switching current of the device for different magnetic-field values. Figure 3a shows that even under 8 T (limited by the maximum value of ‖ in our system), the device c was suppressed only by 16.7% (note that a ~1 A difference was measured between Figure 2 and Figure 3 due to the difference in the less sensitive setup that was used for the − characterization in Figure 3). The dependence of c on the parallel magnetic field is demonstrated more clearly in Figure 3b (black circles), where we extracted the c values from the graph in Figure 3a. These results imply that under a more stable magnetic field and electronics, the device can operate at much higher magnetic fields than we demonstrated in Figure 2b. To further support this claim, we also characterized the dependence of the retrapping current ( r ) on magnetic field (blue empty squares in Figure 3b). That is, the value c is extracted from the transition from a superconducting state to a normal state along the − measurement. Contrariwise, the reverse transition from normal to superconducting occurs at a lower in value due to a latching effect, 47 which reflects dissipation of the excess heat power that is originated from the current flow in the resistive device. The stability of r over a broad range of magnetic fields ( Figure 3b) and temperatures ( Figure SI6 and SI7) demonstrates the robustness of the device. We should note that the proximity between c and r for high magnetic fields also indicates on the robustness of the device, while the device retrapping current can be increased significantly, to match the value of c and avoiding the hysteretic effect, when a shunt resistor is added in parallel to the weak links. 48 In summary, the device presented here demonstrates that a high-density, on-chip nano SQUIDs that operates under diverse conditions can be made with a simple single lithographic fabrication process from films as thin as 3 nm. The nano SQUID operates at a broad range of perpendicular ( ⏊ =100 Gauss) and parallel ( ‖ =1 T) magnetic fields, indicating on its applicability as a robust magnetic sensor. The device, which was fabricated on a Si chip operates also at a broad range of temperatures (20 mK to 5 K), demonstrating its applicability for both metrology and quantum-information systems. Finally, the simple fabrication process of the 4-nm thick NbN device is attractive also for integrated devices, including e.g.

Supplementary material
See supplementary material for the NbN layer characterization, detailed fabrication process and complementary measurements.
The fabrication process began with dc-magnetron sputtering of a 4-nm thick NbN film on top of a Si substrate with a top oxide layer of 338 nm. The reactive sputtering (AJA) of the superconducting -NbN phase followed our previous work. 50 The 44-Å film thickness was measured with variable-angle spectroscopic ellipsometry (J. A. Woollam Co Inc. USA, see Figure SI1 for details). After the deposition, PMMA 950A3 electron-beam resist was applied by spin coating, followed by 2-min post baking. A thin layer of 'e-spacer' was used to avoid charging under the electron microscope. Next, the film was patterned with electron-beam lithography (530 μC cm 2 dose of 150 pA at 100 kV, Raith EBPG 5200) and the PMMA was developed. Reactive-ion etching (RIE) with CF4 gas transferred the pattern to the NbN layer. To prevent degradation of the PMMA mask, the RIE process was done on a cold stage (1° C). In addition, because the etching process generates heat, we split the process to 3 x 20-sec segments, which allowed the PMMA to cool down. The PMMA was then removed using acetone. Finally, the chip was glued to a holder and wirebonded with aluminum wires. c , Δ c , and normal-resistance properties were measured from cooling and heating curves ( Figure SI2). Material composition and stoichiometry were characterized with x-ray photoelectron spectroscopy (XPS, Figure SI3).

SQUID characterizations were done in BF-LD 250 dilution refrigerator (BlueFors Cryogenics, Finland)
with a base temperature of 20 mK. Electric biasing was done with MFLI Lock-in Amplifier (Zurich Instruments, Switzerland). To generate current bias ( in ) that allows reliable statistical averaging we measured each point at the in − graphs with a low-frequency (70-217 Hz) ac voltage that was applied on a 100-k resistor, which was connected in series to the SQUID. Each current value of the in − plots were obtained by increasing the amplitude of the ac voltage to that value, while we maintained the sinusoidal ac signal between zero and | in | by adding dc voltage to the ac signal. The alternating bias allowed us to perform large amount of reproducible measurements, approximately 22 cycles per pixel, as well as to overcome latching, and overcome the lack of shunt resistor in the device. The voltage across the device was amplified (x10) at room temperature before it was measured by the lock-in amplifier. Two superconducting coils and power supplies were used to determine the in-plane (B∥) and out-of-plane (B⊥) magnetic fields. ∆ c was measured from 90% to 10% of the device normal resistance. RRR was defined as the ratio between the device resistance at 130 K and 20 K. s was measured for the deposited layer before patterning with 4 probes (Van der Pauw technique). resistance at 20 K was 314  and the c = 9.29 K was determined as the temperature at which the resistance dropped to 10% of @20K . The transition width ∆ c = 1.2 K was measured as the temperature difference between the point at which = 0.9 • @20K and the critical temperature. The ratio between the residual resistance ratio between the resistance at 130 K and @20K and was found to be close to unity: = 0.92, while the reproducibility of the results between the cooling and heating implies on the quality of the superconductor.