High transfer coefficient niobium nano-SQUID integrated with a nanogap modulation flux line

Nano-superconducting quantum interference devices (nano-SQUIDs) with high energy sensitivity and spatial resolution are essential in many applications such as single spin detection, nano-electromechanical vibration detection and microscale magnetic imaging. This paper studies a Dayem-type niobium nano-SQUID using focus ion beam milling technology. The device has two 42 nm × 60 nm nano-bridges and an integrated on-chip Nb modulation flux line located beside the SQUID loop with a 100 nm nanogap. The non-hysteretic temperature range of the nano-SQUID is about 1.4 K from 4.6 K to 6.0 K, which could broaden the operation temperature range of the device. The maximal transfer coefficient V Φ and peak-to-peak voltage ΔV are 8.53 mV/Φ 0 and 430 μV at 4.8 K, respectively.


Introduction
The superconducting quantum interference device (SQUID) is one of the most sensitive flux-voltage sensors. Compared to traditional microscale SQUIDs consisting of trilayer Josephson junctions, Dayem bridge nano-SQUIDs are made of weak-linked bridge junctions and have features such as higher junction current density, lower parasitic capacitance and compact size, which result in advantages of high energy sensitivity and spatial resolution. Nano-SQUIDs are therefore especially useful in applications such as single-spin detection, nano-electromechanical vibration detection, microscale Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. magnetic imaging, the readout of inductive superconducting transition edge sensors, and so on [1][2][3][4][5][6][7][8][9][10].
The junctions in Dayem bridge nano-SQUIDs are made of nano-scale superconductor bridges. Two nanofabrication methods are commonly used to fabricate nano-SQUIDs. One is the electron beam lithography (EBL) technology method [8,10,11] and the other is the focused ion beam (FIB) milling technology method [12][13][14]. Compared to the EBL method, the FIB method is more flexible, faster, photoresist-free and sample size friendly. However, the problem with the FIB method is that there is an ion implantation issue when the ions hit the surface of the Nb superconducting film. The implantation damage leads to the quenching of the Nb bridge junction in the scale of tens of nanometers and influences the junction property. To prevent ion implantation damage, heavy metal films such as tungsten are usually deposited over the FIB etching area before FIB etching to protect the Nb film, which will be kept. Therefore, it is not easy to make high quality FIB nano-SQUIDs.  The R-T curve of the nano-SQUID. T c1 is the transition temperature of the large Nb tracks and T c1 is that of the nano-bridges.
In this paper, we report an FIB-nano-SQUID integrated with an on-chip magnetic flux modulation line. The voltageflux transfer coefficient and the operational temperature range show vast superiority. Compared to the conventional external coil type of voltage-magnetic flux modulation, an on-chip modulation with a nanogap modulation flux line is used to simplify the system and improve the flux coupling. The mutual inductance between the flux line and the SQUID is about 72 mA/Φ 0 . The Dayem bridge junctions and nanoscale loops of nano-SQUIDs are directly milled by FIB without any protecting layer. The maximal transfer coefficient V Φ and peakto-peak voltage ∆V of our nano-SQUID are 8.53 mV/Φ 0 and 430 µV at 4.8 K, respectively. The non-hysteretic temperature range of the nano-SQUID is about 1.4 K, which could broaden the operation temperature range of the device. For the fabrication process, 144 nm Nb film was firstly deposited on a SiO 2 /Si substrate by a sputtering process. The background pressure of the sputtering chamber is better than 4 × 10 −6 Pa. The sputtering pressure was controlled at 0.67 Pa. Common photolithography and dry etching techniques were used to form the structure with scales above 2 µm and pads for bonding. SF 6 was used to etch Nb with positive photoresist structure protection. The power and reactive pressure of the reactive ion etching were 50 W and 2 Pa respectively. FIB was then used to mill the Nb film to form the nanoscale structure of the devices, including the Dayem bridge junctions, nanoscale loops and the nanogap between the loop and the flux line, as shown in figure 1(b). In our FIB system, a gallium ion species was used and its beam energy was kept at 30 keV. The ions from the FIB beam were inevitably implanted in the junctions and consequently formed a shunt resistor. Therefore, ion dose was adjusted for different thicknesses of Nb films in order to avoid damage to the bridge junction.

Measurement results and discussions
The chip was adhered to a ceramic device holder using GE 7031 varnish. The holder was attached to a copper sink of which the temperature could be measured and controlled by a Lakeshore temperature controller. The electrode pads on the chip were wire-bonded to the holder by 25 µm diameter aluminum wires. The device was mounted inside a stainless steel can with the lead shield and characterized using a home-made system composed of a probestick, Keysight B2901A/B2961A current sources, a Keithley 2000 multimeter and data acquisition software. Figure 2 shows the resistance vs temperature (R-T) curve of the nano-SQUID device made in 144 nm Nb film. The inset is the enlarged part from 6 K to 9.5 K. Clearly there are two superconducting transition temperatures T c . The first transition at about 9.10 K (T c1 in figure 2) is the transition temperature of the Nb film. At this temperature, two bridge junctions are still at normal state with a few ohms resistance because of the Ga + implantation damage. The FIB process causes the  figure 2). This two-transition R-T curve is typical for the Dayem-type nano-SQUID. Figure 3(a) shows the I-V curves of the nano-SQUID at different temperatures. The critical current I c of the device decreases from 180 µA to 64 µA when the temperature increases from 4.6 K to 6.0 K. The device shows a non-hysteretic characteristic above 4.6 K. Therefore, the operating temperature range of the SQUID is about 1.4 K.

I-V curve
The I-V curve changes periodically with the external magnetic field. In this paper, an on-chip modulation flux line is applied to produce the external magnetic field. The currents of 0 mA, 19 mA and 38 mA flowing through the flux line produce fluxes of 0Φ 0 , Φ 0 /4 and Φ 0 /2, respectively. Figure 3(c) shows the I-V curve at 4.8 K for 0Φ 0 , Φ 0 /4 and Φ 0 /2, and the corresponding critical currents I c in these cases are 170 µA, 152 µA and 115 µA. I c decreases nonlinearly with increasing flux from 0 to Φ 0 /2. The flux modulating depth ∆I/I c is 32.4% at 4.8 K [15]. The black line in figure 3(b) shows the change of the flux modulating depth ∆I/I c with the temperature. The maximum value is 41.5% at 5.8 K.

V-Φ curve
The voltage across the nano-SQUID was measured with external magnetic flux at different biased current I b and temperatures. Figure 4(a) illustrates the V-Φ curves with different I b from 110 to 170 µA at 4.8 K. ∆V is defined as the peak-topeak modulation voltage. The SQUID transfer coefficient V Φ is the maximum absolute value of ∂V/∂Φ. V Φ+ and V Φ− represent the V Φ at the rising and falling edge of the V-Φ curve. The V Φ value reflects the sensitivity of the SQUID to magnetic flux changes. The higher the value, more sensitive the SQUID device is. Figure 4(b) illustrates ∆V, V Φ+ and V Φ− as function of I b . It shows that ∆V increases with I b from 110 to 160 µA and then decreases. V Φ+ and V Φ− have the same trend, as expected. From the data we can derive that the 160 µA bias current corresponds to the best working point at this temperature. The optimal bias current is chosen to be the point where V Φ+ is the best. At this working condition, V Φ+ and ∆V of this device are 8.53 mV/Φ 0 and 430 µV, respectively. This result is much better than the 2D Dayem bridge devices reported in the literature, with the transfer coefficient in the range of 0.1-2.5 mV/Φ 0 [8,[11][12][13]. Figure 5(a) illustrates the V-Φ curves of the optimal transfer characteristic at different temperatures from 4.4 K to 6.0 K. The corresponding optimal bias current at each temperature is shown on the upper-right corner of figure 5(a). When the temperature increases, the optimum of the bias current I b decreases. Figure 5(b) illustrates the change of the transfer coefficient V Φ+ and the peak-to-peak voltage ∆V at optimum bias current as a function of temperature. V Φ+ decreases with temperature nonlinearly, while ∆V decreases linearly with the temperature.
The effective area of the nano-SQUID needs to be estimated since it is usually not the nominated one. The effective area A eff can be estimated by equation Φ 0 = B × A eff . We use the PPMS (Physical Property Measurement System) to generate certain magnetic field B. The SQUID output voltage changes periodically. Each period corresponds to 1 Φ 0 . 5.5 mT is needed for 1 Φ 0 . So, the estimated A eff is 0.36 µm 2 , which is almost 10 times the nominated loop size. There are two reasons. The first reason is due to the change of the effective length of the SQUID hole. One change comes from the penetration depth effect. For the 144 nm thickness Nb film and normalized working temperature (T/Tc) of 0.53, the penetration depth at each side of the loop is about 96 nm [16]. Therefore, the effective side length of the SQUID loop now expands to about 392 nm. The second reason is the flux focusing effect. The SQUID's wide Nb loop and bank will expel magnetic flux into the hole and consequently cause the real magnetic field to be higher than the nominal one. Considering these two factors, the effective area of the SQUID can be calculated using [17]: the effective side length d ≈ 392 nm and washer width w ≈ 300 nm. A eff is calculated to be 0.357 µm 2 , which is very close to the estimated A eff of 0.36 µm 2 . This small effective area induces a very high spatial resolution, but also reduces the capture ability of the magnetic flux. A large magnetic field intensity is needed for the device to collect a quantum flux Φ 0 . The magnetic field intensity generated by a long straight wire is proportional to the current and inversely proportional to the distance. A large current will cause the quenching effect of the modulation line, which will affect the operation of the nano-SQUID. When the distance is reduced by one order of magnitude from 1 micron to 100 nanometers, the current inducing the same magnetic field intensity is reduced by one order of magnitude, and the coupling between the SQUID and the modulation flux line will be increased. This will significantly increase the coupling between the SQUID and the modulation flux line, and may make the SQUID operate in a flux-locked loop mode.
The theoretic intrinsic flux noise is estimated according to the following equation [1,18]: where k B is the Boltzmann constant, T is the working temperature and the normal resistance of the SQUID's R n is about 4.9 Ω from the I-V curve. L is the total inductance of the SQUID, which is the sum of the bridge inductance and the loop inductance. The evaluation is performed at 4.8 K with maximum critical current of 170 µA. For our design, the bridge inductance is 7.4 pH and the loop inductance 0.3 pH. The calculated S Φ 1/2 is 0.037 µΦ 0 /Hz 1/2 when β L → 1. The actual measurement results will be one to two orders of magnitude larger than the theoretical calculation.

Conclusion
A Dayem-type niobium nano-SQUID with 42 nm × 60 nm nano-bridges and a loop of which the side length was 200 nm was fabricated using FIB milling and characterized. At 4.8 K, the device's flux modulating depth is 32.4%. The maximal transfer coefficients V Φ and ∆V are as large as 8.53 mV/Φ 0 and 430 µV with 160 µA bias current, respectively. Zhongdu, an engineer from FEI company, for his helpful discussion. This work was supported by the National Key R&D Program of China (2017YFF0206105) and the National Natural Science Foundation of China (61701470).