# A Self-Flux-Biased NanoSQUID with Four NbN-TiN-NbN Nanobridge Josephson Junctions

^{*}

## Abstract

**:**

_{0}/4. The nanoSQUID contains novel NbN-TiN-NbN nanobridge Josephson junctions (nJJs) with NbN current leads and electrodes of the nanoSQUID body connected by TiN nanobridges. The optimal superconducting transition temperature of ~4.8 K, superconducting coherence length of ~100 nm, and corrosion resistance of the TiN films ensure the hysteresis-free, reproducible, and long-term stability of nJJ and nanoSQUID operation at 4.2 K, while the corrosion-resistant NbN has a relatively high superconducting transition temperature of ~15 K and a correspondingly large energy gap. FIB patterning of the TiN films and nanoscale sculpturing of the tip area of the nanoSQUID’s cantilevers are performed using amorphous Al films as sacrificial layers due to their high chemical reactivity to alkalis. A cantilever is realized with a distance between the nanoSQUID and the substrate corner of ~300 nm. The nJJs and nanoSQUID are characterized using Quantum Design measurement systems at 4.2 K. The technology is expected to be of interest for the fabrication of durable nanoSQUID sensors for low temperature magnetic microscopy, as well as for the realization of more complex circuits for superconducting nanobridge electronics.

## 1. Introduction

_{2}O

_{3}-Nb JJs [3], and by the realization of sub-100 nm Pb nanoSQUIDs with ~10 nm nanobridge JJs (nJJs) prepared on a capillary tip [4,5,6]. Planar nanoSQUIDs with nJJs have been realized using electron beam lithography (see [7] and references therein). The current scale of integration of superconducting circuits of 7.4 × 10

^{6}JJs/cm

^{2}has been achieved by using a 250-nm-linewidth photolithography process and self-shunted Nb-Al-AlO

_{x}-Nb tunnel JJs with a relatively high J

_{c}of ~60 kA/cm

^{2}[8]. The critical current densities of nJJs are much higher, with J

_{c}~ 1 MA cm

^{−2}@ 4.2 K [7], approaching the de-pairing critical current of superconducting films (e.g., ~30 MA/cm

^{2}for Nb thin films) [9]. High values of J

_{c}~ 1 MA/cm

^{2}are required to provide I

_{c}values in the nJJs that are much larger than the thermal noise current I

_{th}= 2πk

_{B}T/Φ

_{0}and electromagnetic interference currents in the measurement systems.

_{0}/4 that is required for maximal sensitivity corresponds to the application of relatively high magnetic fields of ~0.4 T. These fields can influence the magnetic state of an investigated object and suppress T

_{c}of the superconducting film and the JJs of the nanoSQUID itself. The use of control lines or direct injection currents is limited by the critical current of the superconducting films and by small geometrical inductances resulting from the sizes of the nanoSQUIDs [7]. In contrast to geometrical inductance, kinetic and Josephson inductances cannot be used for magnetic flux generation in superconductors because they do not store energy in magnetic fields, but in the form of motion and Josephson energies, respectively. Josephson inductances that are represented by additional Josephson junctions whose critical current I

_{c2}is slightly higher than the critical current I

_{c1}of the Josephson junctions of the DC SQUID can substitute for flux biasing of nanoSQUIDs without using high magnetic fields. Each Josephson inductance L(Δφ) = Φ

_{0}/2πI

_{c}cos(Δφ), where I

_{c}is the critical current, consumes the phase drop Δφ, reducing the phase drop on the other Josephson junctions, and providing an effective substitution for the magnetic flux bias Φ

_{0}/4 of the nanoSQUID. For this constant shift of the flux voltage characteristics of the nanoSQUID, there is no need for the injection of the additional flux biasing current that was demonstrated for the electrical tuning of a nanoSQUID in [5,6].

_{c}superconductor YBa

_{2}Cu

_{3}O

_{7-x}, which degrades so strongly in air [10,11] that the encapsulation of high-T

_{c}SQUIDs in vacuum-tight fiber-glass capsules is required [12]. Thermal cycling of Pb films between a storage temperature of 300 K and an operation temperature of 4.2 K result in hillock and cavity formation on the films, thereby destroying the JJs [13]. Films of the refractory metal Nb are extraordinarily resistant to heat and wear. However, Nb is unstable against corrosion as a result of a reaction with O

_{2}and H

_{2}O in laboratory air. Oxygen penetrates along grain boundaries from top to bottom in columnar-grown Nb films, producing Nb

_{2}O

_{5}crystallites that expand and crack the Nb films [14,15]. Oxidation of Nb films can be suppressed significantly by sealing their surface using a hard NbN protection layer, which is stable against H

_{2}, CO, CO

_{2}, O

_{2}, and air [16].

_{c}values of up to ~16 K and their very short coherence lengths ξ of ~5 nm lead to difficulties in the realization of non-hysteretic nanoSQUIDs with nJJs at an operation temperature of 4.2 K [22,23,24]. NJJs and nanoSQUIDs that are based on nJJs can have hysteretic I(V) characteristics, as a result of (1) the effect of nJJ overheating hysteresis [7,25], or (2) an ambiguity in the I(φ) characteristics of nJJs [25,26] in the case of large nJJs when their length is >3.5 ξ [26].

_{c}~ 5 K and ξ ~ 105 nm [7,27], which allows the operation of TiN nJJs and nanoSQUIDs without hysteresis at 4.2 K. The absence of hysteresis in the I(V) characteristics near T

_{c}can be explained by an increase in the superconducting coherence length $\xi \propto {\left(1-\frac{T}{{T}_{c}}\right)}^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ near T

_{c}, according to Ginzburg–Landau theory [28]. Based on the above-mentioned features, it is straightforward to combine the properties of TiN and NbN films in novel NbN-TiN-NbN nJJs that include a TiN nanobridge, NbN electrodes, and current leads to realize non-hysteretic nJJs with a high characteristic voltage V

_{c}= I

_{c}R

_{n}, while operating at 4.2 K. The use of such S-S′-S nJJs with NbN as a superconductor with higher T

_{c}(S) and TiN as a superconductor with lower T

_{c}(S′) in nanoSQUIDs would improve their voltage response and sensitivity. Pure TiN nJJs and nanoSQUIDs often have T

_{c}< 4.2 K, relatively low values of ΔV

_{pp}~ 14 µV, and a value for the derivative dV/dB of ~44 µV/Φ

_{0}at 4.2 K [7].

^{+}ions and a better heat sink for each nJJ [28].

^{+}ion implantation during FIB nanofabrication of the nJJs and cantilevers. We realized planar 4-Josephson-junction nanoSQUIDs, which are self-biased to provide optimal sensitivity without the application of high magnetic fields corresponding to the usually required Φ

_{0}/4 magnetic flux bias. The fabrication of cantilevers with a nanoSQUID placed within 300 nm from the substrate corner is also outlined.

## 2. Materials and Methods

^{−8}mbar using oil-free pumps. Deposition was performed in an Ar(80%)-N

_{2}(20%) gas mixture at a total pressure of 10

^{−2}mbar. A N

_{2}flow of 5 mln/min was regulated using a Brooks© mass flow controller 5850 TR. The Ar and N

_{2}gases had a purity of 99.9999% and contained less than 0.01 ppm O

_{2}, which corresponds to an O

_{2}partial pressure of less than 10

^{−10}mbar. Before deposition, the chamber was outgassed at the deposition conditions during pre-sputtering onto the closed shutter for more than 1 h.

_{c1}< I

_{c2}and 3 current leads, as shown schematically in Figure 1.

^{2}. RIE of the TiN-NbN heterostructures was performed using a pure SF

_{6}atmosphere, which resulted in isotropic etching of both the NbN and the TiN films at a rate of ~1 nm/s with a selectivity of ~3 for etching of TiN-NbN heterostructures relative to the diluted nLOF 2020 resist. After RIE, resist residuals were removed from the samples by soaking in warm acetone at 70 °C and in distilled water. Figure 2 shows (a) a schematic representation and (b) a scanning electron microscopy (SEM) image of the resulting NbN-TiN-NbN nJJs. Thanks to the undercut due to isotropic etching, the top layer of the NbN is locally removed in the nanobridge area. The electrodes contain the TiN-NbN heterostructures, where the energy gap of TiN is enhanced by a proximity effect from the NbN layer. Pieces of In of size ~(0.5 mm)

^{3}were used to form galvanic contacts to the structures through the Si passivation layer.

^{+}ions at an accelerating voltage of 30 kV and a current of 1.5 pA to etch a 300 nm × 300 nm hole and form 4 nJJs. An additional 100-nm-thick amorphous Si layer was deposited at room temperature above the nanoSQUID to provide a better thermal shunt of the nJJs. For bulk nanomachining of cantilevers with nanoSQUIDs, the Al protection layer was up to ~1.5 µm thick, which allowed for the use of the maximal available Ga

^{+}focused ion beam of ~21 nA. After FIB, the Al layer and the fences of redeposited material were removed by chemical etching of Al using an AZ 726 MIF developer in an ultrasonic bath.

## 3. Results

_{c}value of 60-nm-thick NbN films increased from 10.6 to 14.5 K and the residual resistance ratio (RRR) R

_{300K}/R

_{10K}increased from 0.9 to 2.4 when compared to NbN films deposited under the same conditions on pristine Si (100) substrates. Resistivity values of ~6 µΩ·cm at room temperature and ~7 µΩ·cm at 10 K were measured for the NbN films. The latter value is close to values of ~5 µΩ·cm at 10 K obtained for TiN films deposited on oxide-free Si at 800 °C [7,30], which is advantageous for the proximity effect between NbN and TiN films: the small difference between the specific resistances and the large coherence length in TiN result in a value of γ ~ 0.01 in Refs. [31,32], which corresponds to negligibly small suppression of the superconducting order parameter in the layers due to the proximity effect and a small jump in the order parameter at the interlayer boundary due to the interface resistance. The superconducting transition temperature T

_{c}of the NbN-TiN heterostructures depends on the thickness of the NbN layer and is ~6 K for a 6 nm NbN layer above a 100-nm-thick TiN film. A lower base pressure of ≤4 × 10

^{−8}mbar and a higher substrate temperature of ≥800 °C lead to a higher value of T

_{c}. The observed RRR value of >2 reflects a relatively long mean free path of the charge carriers in NbN-TiN heterostructures due to a relatively low concentration of defects.

^{+}ion beam of ~1.5 pA for patterning the nJJs and requires further optimization.

^{+}ion beam. The material volume per dose rate is ~0.3 μm

^{3}/nC at an accelerating voltage of 30 kV for Si and Al, which allows a 5 µm × 100 µm × 50 µm slit to be cut in ~1 h. Pre-thinning of the nanoSQUID cantilever chip down to a thickness of ~50 µm can be performed using ICP RIE [33] or chemical etching in 20% KOH solution [7]. By using FIB, we succeeded to position a nanoSQUID within 100 nm from the substrate corner. Based on safety and resolution considerations for the lateral outer dimension of the nanoSQUID of ~900 nm and the total thickness of the superconducting film of the nanoSQUID of up to ~200 nm, it is optimal to place the nanoSQUID at a distance of ~300 nm from the edges of the substrate (see Figure 5). The corner can then be used as the tip of a cantilever when it is placed at a small angle of ~10° relative to the surface of an investigated magnetic object.

^{+}ion implantation, e.g., by the use of thicker protection layers.

_{c}by ~0.4 K and a larger characteristic voltage V

_{c}= I

_{c}R

_{n}by ~4 times of the nJJs, when compared with nJJs that were prepared from similar NbN-TiN heterostructures using FIB. The NbN layer was removed in the middle of the nJJs by undercutting during the isotropic RIE process (see Figure 2), resulting in the formation of variable thickness nanobridge NbN-TiN-NbN JJs. RIE was performed at 25 W with 5 Pa of pure SF

_{6}gas, providing an etch rate of ~1 nm/s normal to the surface of the NbN-TiN heterostructure and an undercut in-plane etching rate of ~0.3 nm/s, which provides a relationship between the optimal width of the bridges in the e-beam resist and the thickness of the NbN-TiN heterostructure. However, there is a significant dependence of the RIE rate in SF

_{6}gas on sample surface cleanliness and on the prehistory of operation of the RIE machine. Contamination of the sample surface and the chamber hinders reactive etching. In order to ensure reproducibility of the nJJs, the RIE machine was cleaned and preconditioned prior to the installation of the substrates. The substrates lay freely on a quartz plate whose temperature was maintained at 20 °C. Moderate heating of the substrate during RIE increases the etch rate and should be taken into account. After RIE, residuals of the nLOF resist were removed in warm acetone and did not disturb the establishment of galvanic contacts to successive Pt, Au, and bulk In layers on the contact pads.

_{c}= I

_{c}R

_{n}≅ 200 µV.

_{c}= 39 µA is shown in Figure 7. The observed large amplitude of the voltage modulation ΔV

_{p-p}~ 50 µV (peak-to-peak) is due to the presence of the NbN film in the electrodes and the relatively low kinetic inductance of the nanoSQUID, which is based on Josephson junctions in the form of nanobridges of variable thickness: the washer of the nanoSQUID is much thicker than in Dayem bridges. The 60 G period of the modulation corresponds to an effective area of 0.36 µm

^{2}of the nanoSQUID. Thanks to the 4JJ design, the nanoSQUID does not requires flux biasing: At 0 G, the derivative dV/dB has already reached its maximal value of ~525 µV/Φ

_{0}.

## 4. Discussion

_{0}/4 magnetic flux bias of nanoSQUID to the maximum responsivity point at which the derivative of the SQUID voltage with magnetic field dV/dB has a maximal value. The operation principle of such a 4-nJJ nanoSQUID is as follows. The magnetic flux Φ through the loop of the nanoSQUID connected with the phase drops φ

_{1}and φ

_{1}across the nJJs according to equation

_{1}+ 2φ

_{2}+ 2πΦ/Φ

_{0}= 2πn,

_{b}= 2I

_{c1}sinφ

_{1}≅ 2I

_{c1}. The junctions with the largest phase drop φ

_{1}have the smallest critical current I

_{c1}, which is reached at φ

_{1}= π/2. Each of the other two junctions has a phase drop φ

_{2}determined by their maximal current, which is limited by the critical current of the smallest junctions I

_{c1}and its critical current I

_{c2}: φ

_{2}= arcsin (I

_{c1}/I

_{c2}). This maximal current is reached when the magnetic flux through the nanoSQUID is Φ = (πn − π/2 − φ

_{2})·Φ

_{0}/π. The maximum responsivity point in zero external magnetic field is when this magnetic flux Φ = Φ

_{0}/4: 2π/2 + 2φ

_{2}+ 2π/4 = 2πn, or:

_{2}= πn − π/2 − π/4

_{c2}= I

_{c1}/sin(π/4) = I

_{c1}√2 at n = 1. The true optimal critical current I

_{c2}differs from the calculated value because the geometrical inductances of the nJJs are not zero and spread of dimensions of the nJJs should also be taken into account. An asymmetric DC SQUID that contains two nJJs with different critical currents can be used for self-flux-biasing [34]. If the size of the SQUID loop is >1 µm, then the geometrical inductance of the SQUID loop can also be used for the creation of self-biasing, e.g., in a 3-JJ SQUID configuration [35]. However, these alternative methods are less effective when the size of the SQUIDs is on the nm scale and the geometrical inductances of the nJJs and of the SQUID loop become negligible.

_{c}, where the coherence length is comparable with the dimensions of the nJJs [26,28,36,37]. For real nJJs, the largest voltage modulation is observed in proximity to hysteretic I(V) characteristics, where theoretical models partially deviate from experimentally observed properties (e.g., the current-phase relationship of nJJs deviates from a sinusoidal form).

_{v}~ 1 nV/√Hz of the preamplifier at room temperature [7]. The magnetic flux resolution of the present measurement system √S

_{Φ}≅ √S

_{v}/(∂V/∂Φ) ~ 1.9 µΦ

_{0}/√Hz, where the derivative ∂V/∂Φ ≅ 525 µV/Φ

_{0}. For comparison with other planar nanoSQUIDs, flux noise values of 1.7 μΦ

_{0}/√Hz [22] and 0.3 μΦ

_{0}/√Hz [23] have been achieved for nanoSQUIDs with hysteretic I(V) characteristics measured at temperatures of ≪T

_{c}. By increasing the thickness of the NbN layer, nanoSQUIDs with NbN-TiN-NbN nJJs also become hysteretic in their I(V) characteristics. The study of measurement systems with hysteretic nanoSQUIDs is beyond the scope of the present work.

## 5. Conclusions

_{0}/4. The nanoSQUIDs contain novel NbN-TiN-NbN nanobridge Josephson junctions (nJJs), with NbN electrodes connected by TiN nanobridges. TiN has an optimal superconducting transition temperature of ~4.8 K, a superconducting coherence length of ~100 nm, and corrosion resistance, offering hysteresis-free, reproducible, and long-term stability for nJJ and nanoSQUID operation at 4.2 K, while corrosion-resistant NbN has a relatively high superconducting transition temperatures up to ~16 K and a correspondingly large energy gap. FIB patterning of TiN films and nanoscale sculpturing of the tip area of the nanoSQUID’s cantilevers were performed by using amorphous Al films as sacrificial layers due to their relatively high chemical reactivity to alkalis. A cantilever with a distance between the nanoSQUID and the substrate corner of ~300 nm was realized. The I(V) characteristics of the nJJs and nanoSQUIDs, as well as the voltage modulation of the nanoSQUIDs, was measured at 4.2 K. The developed technology can be used for the fabrication of durable nanoSQUID sensors for low temperature magnetic microscopy, as well as for the realization of more complex circuits for superconducting nanobridge electronics.

## Author Contributions

## Funding

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic diagram of a 4 nJJ nanoSQUID with 3 current leads. Josephson junctions with larger critical currents I

_{c2}and smaller phase drops φ

_{2}< π/2 are shown by larger crosses.

**Figure 2.**(

**a**) Schematic view of a NbN-TiN-NbN nJJ. (

**b**) SEM image of a NbN-TiN-NbN nJJ prepared using RIE. The image was recorded at an accelerating voltage of 15 kV and a sample tilt angle of 45°.

**Figure 3.**SEM image of a cross-section of a NbN-TiN heterostructure on a Si (001) substrate. The image was recorded with the sample broken parallel to a Si (110) plane perpendicular to the film surface.

**Figure 4.**SEM image of a nanoSQUID fabricated using FIB etching with four ~50-nm-long nJJs, a 300 nm × 300 nm hole and 3 current leads, in accordance with the schematic diagram shown in Figure 1.

**Figure 5.**HRSEM image of a Si cantilever with a 4JJ nanoSQUID placed within 300 nm of the corner by FIB etching. The inset shows a top view of the same nanoSQUID cantilever.

**Figure 6.**I(V) dependences measured for a planar nanoSQUID with NbN-TiN-NbN junctions in magnetic fields of −30 G (blue) and 10 G (red) at 4.2 K.

**Figure 7.**V(B) curve of the planar nanoSQUID with NbN-TiN-NbN nJJs measured with a bias current of 39 µA at 4.2 K.

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**MDPI and ACS Style**

Faley, M.I.; Dunin-Borkowski, R.E.
A Self-Flux-Biased NanoSQUID with Four NbN-TiN-NbN Nanobridge Josephson Junctions. *Electronics* **2022**, *11*, 1704.
https://doi.org/10.3390/electronics11111704

**AMA Style**

Faley MI, Dunin-Borkowski RE.
A Self-Flux-Biased NanoSQUID with Four NbN-TiN-NbN Nanobridge Josephson Junctions. *Electronics*. 2022; 11(11):1704.
https://doi.org/10.3390/electronics11111704

**Chicago/Turabian Style**

Faley, M. I., and R. E. Dunin-Borkowski.
2022. "A Self-Flux-Biased NanoSQUID with Four NbN-TiN-NbN Nanobridge Josephson Junctions" *Electronics* 11, no. 11: 1704.
https://doi.org/10.3390/electronics11111704