sensors

Article Fine-Tuning and Optimization of Superconducting Quantum Magnetic Sensors by Thermal Annealing

Antonio Vettoliere 1 , Berardo Ruggiero 1, Massimo Valentino 1, Paolo Silvestrini 2 and Carmine Granata 1,2,*

1 Institute of Applied Sciences and Intelligent Systems of National Research Council (CNR), 80078 Pozzuoli, Italy 2 Department of Mathematics and Physics, University of Campania “L. Vanvitelli”, 81100 Caserta, Italy * Correspondence: [email protected]



Received: 22 July 2019; Accepted: 19 August 2019; Published: 21 August 2019


Abstract: In the present article, we present the experimental results concerning the fine-tuning and optimization of superconducting quantum interference device (SQUID) parameters by thermal annealing. This treatment allows for the modification of the parameters in order to meet a specific application or to adjust the device parameters to prevent the increase of magnetic field noise and work instability conditions due to a different critical current with respect to the design value. In particular, we report the sensor critical current, the voltage–flux (V–Φ) characteristics and the spectral density of the magnetic field of SQUID magnetometers for different annealing temperatures. The measurements demonstrate that it is possible to achieve a fine control of the most important device parameters. In particular, we show that thermal annealing allows for the reduction of SQUID noise by more than a factor of 5 and makes the device working operations very stable. These results are very useful in view of quantum technology applications related to superconducting quantum computing where the correct functioning of the quantum bit depends on the fine control of the superconducting quantum device parameters and selectable annealing is possible by using a suitable laser as a thermal source.

Keywords: magnetic sensors; SQUIDs; magnetic field noise; annealing

1. Introduction Quantum sensing is an intriguing and interesting topic in applied physics. In fact, many efforts are devoted to the development of quantum technology in view of challenging applications such as quantum information and computing and ultra-high sensitivity sensors able to investigate the matter at a nanoscale level [1,2]. Since the first superconducting quantum interference devices (SQUIDs) were developed over 50 years ago, their application potential has stimulated continuous scientific and technological research on these quantum sensors. SQUIDs remain among the most sensitive magnetic sensors that are, practically, irreplaceable in all applications that require extreme sensitivity. Such applications include basic physics, geophysics, nanomagnetism, biomedicine, and quantum computing [3–5]. Among the many applications of SQUIDs, the most important are the well-established magnetoencephalography (MEG) [6–9] and the promising applications in the field of quantum computation, where SQUIDs are employed as flux quantum bits (qubits). In both applications, it is fundamental to have very good control of the most important characteristics of the SQUID device, as well as good reliability and robustness. In fact, in the flux qubit, which is one of the three superconducting qubits, the circuit is designed to give a double-well potential, with a height depending on the critical current of the Josephson elements [10–12].

Sensors 2019, 19, 3635; doi:10.3390/s19173635 www.mdpi.com/journal/sensors Sensors 2019, 19, 3635 2 of 8

The core of a SQUID device is a superconducting ring interrupted by two Josephson junctions. Due to quantum interference, the phase difference of the two junctions is related to the flux linkage with the superconducting ring normalized to the elementary flux quantum (Φ = 2.07 10 15 Wb). 0 × − The most important features of a SQUID device depend on the following parameter: ΦL = LI0/Φ0, where I0 is the SQUID critical current and L is the ring inductance. Since the inductance essentially depends on the geometric characteristics of the loop and therefore on the SQUID design, the possibility to control the critical current allows us to modify the most important characteristics of a SQUID device, such as the modulation depth, the voltage swing, and the noise spectral density of magnetic flux, as well as the double-well potential in the case of radiofrequency (rf) SQUIDs [3]. These applications require a large number of SQUID sensors having ultra-high sensitivity and good working stability. In this paper, we report an experimental study on the fine control and optimization of the main SQUID magnetometer parameter. In particular, by using thermal annealing, we show that we are able to modify the critical current of SQUID magnetometers of about one order of magnitude with a step of a few percent of the initial critical current. As we show, this allows for the optimization of the main characteristics of the quantum sensor, such as the voltage-flux characteristics and the spectral density of the magnetic flux and field noise.

2. Thermal Annealing Procedure The Josephson current in a SQUID is a tunnel current of Cooper pairs due to an overlap of the macroscopic wave function relative to the superconductors of the Josephson junction. The maximum Josephson current value, known as the Josephson critical current, depends on the thickness of the insulator barrier. In particular, the Josephson critical current density follows an exponential law: At JC = JC,0 e− , where A is a coefficient depending on the superconductor and insulator materials and t is the thickness of the insulator barrier [13,14]. Therefore, a small variation of the barrier thickness causes an appreciable change of the critical current density. For this reason, the critical current value, especially in the fabrication of a large number of Josephson devices, can be different with respect to the design value. Thermal annealing allows increasing in a reliable and fine way the thickness of the insulator barrier. In the case of all-refractory niobium technology, the insulation barrier consists of a thin layer of aluminum oxide (AlOx) typically obtained by the thermal oxidation of the aluminum film in a controlled oxygen atmosphere. In our case, the vacuum chamber was filled with dry oxygen at a pressure of 250 mbar for 1 h. In this condition, we obtained a critical current density of about 70 A/cm2 [15]. It is well known that a change of the Josephson critical density can be obtained by thermal annealing [16–19]. In fact, during this process, the thickness of the tunnel barrier (AlOx) can increase due to the migration of reacting oxygen coming from the niobium oxide surface through the channels formed in the niobium granular structure. Also, unbound oxygen embedded at interstitial places close to the tunneling barrier can react with aluminum atoms, increasing the insulation layer. If well controlled, thermal annealing can be employed to tune the critical current of both the Josephson junction and the SQUID magnetometer. In our experimental study, we employed a programmable hot plate (CEE 1100-Brewer Science Inc., Rolla, Missouri, USA) reaching a maximum temperature of 280 ◦C with 0.1 ◦C resolution. The hot plate was used in hard-contact mode, where a suitable vacuum guaranteed an effective and uniform annealing. An alternative way to obtain a thermal annealing is to use a laser that allows you to perform selectable annealing with a high spatial resolution (a few µm), though the heating temperature is more difficult to control [20,21]. The annealing and the characterization were performed on fully integrated SQUID magnetometers with a design based on a Ketchen-type scheme. Since the design and the fabrication of the SQUID magnetometers is well described elsewhere, only a short description is reported here. The SQUID 2 magnetometer consists of a single square-coil pickup coil (Ap = 64 mm ) connected in series with a multiturn input coil which is magnetically coupled to the SQUID loop in a washer configuration. Sensors 2019, 19, 3635 3 of 8 Sensors 2019, 19, x FOR PEER REVIEW 3 of 9

Anconfiguration. integrated An feedback integrated coil infeedback bipolar coil configuration in bipolar toconfiguration reduce the cross-talkto reduce etheffect cross-talk and an additionaleffect and anpositive additional feedback positive (APF) feedback circuit (APF) consisting circuit of consisting both a square of both coil a surroundingsquare coil surrounding the pickup the coil pickup and a coilresistor and networka resistor are network integrated are integrated in the same in th chipe same containing chip containing the magnetometer the magnetometer [22]. [22]. The SQUID model used for the design optimizati optimizationon was a standard model based on resistively shunted junctionsjunctions where where the the white white noise noise is essentially is essentially due todue the to Johnson–Nyquist the Johnson–Nyquist noise of noise the resistors of the resistorsin parallel in with parallel the Josephsonwith the Josephson junctions junctions [1,2]. [1,2]. It isis worth worth noting noting that that the resultsthe results reported report belowed arebelow also validare foralso di ffvaliderent SQUIDfor different magnetometer SQUID magnetometerdesigns and in designs general and for anyin general devices for including any devices Josephson including tunnel Josephson junctions, tunnel while junctions, they are while not theyapplicable are not for applicable other types forof other weak types links, of suchweak as links, Dayem such bridges as Dayem or contact bridges points. or contact points. The SQUID magnetometer fabrication is is based on all-refractory niobium niobium technology technology (Figure (Figure 11).). The NbNb/Al-AlOx/Nb/Al-AlOx/Nb trilayer was made by depositing thin films films by direct current (dc) magnetron sputtering in an ultra-highultra-high vacuum stationstation withoutwithout vacuumvacuum breaking.breaking. The window-typewindow-type JosephsonJosephson 2 junctions (4 4 µm2 ) were realized by using standard photolithography and a selective niobium junctions (4 × 4 µm ) were realized by using standard photolithography and a selective niobium anodization process process (SNAP). (SNAP).

Figure 1. Fully integrated superconducting quantum interference device (SQUID) magnetometers including a bipolar coil for flux-locked-loopflux-locked-loop operation and an additional positive feedback circuit consisting ofof aa narrownarrow square square coil coil (light (light green) green) surrounding surrounding the the magnetometer magnetometer pickup pickup coil (lightcoil (light blue) blue)and a and network a network resistor. resistor.

3. Experimental Experimental Results Results The characterizationcharacterization of of SQUID SQUID magnetometers magnetometer wass performedwas performed at 4.2 K,at with4.2 theK, with SQUID the immersed SQUID immersedin liquid helium in liquid inside helium a twin inside cylindrical a twin cylindrical shield made shield of lead made and ofµ lead-metal and [23 µ-metal,24]. All [23,24]. the electrical All the electricalconnections connections to the room to the temperature room temperature electronics el wereectronics radiofrequency-filtered. were radiofrequency-filtered. The white The magnetic white magneticflux noise flux was noise measured was measured using a very using low-noise a very lo readoutw-noise electronics readout electronics based on flux-locked-loopbased on flux-locked- (FLL) withloop (FLL) a direct-coupled with a direct-coupled scheme. In suchscheme. a configuration, In such a configuration, the SQUID isthe directly SQUID coupled is directly to acoupled low-noise to apreamplifier. low-noise preamplifier. The FLL linearizes The FLL the SQUIDlinearizes output, the SQUID increasing output, the linear increasing dynamic the range. linear The dynamic whole range.amplification The whole stage amplification is integrated onstage a miniaturized is integrated detection on a miniaturized circuit and detection carefully circuit shielded and by carefully a copper shieldedbox. After by each a annealingcopper box. step, After a full magnetometereach annealing characterization step, a full consistingmagnetometer of the measurementscharacterization of consistingthe critical of current, the measurements voltage–magnetic of the flux critical characteristic, current, voltage–magnetic spectral density of flux the magneticcharacteristic, field, andspectral flux densitynoise was of carriedthe magnetic out. field, and flux noise was carried out. Figure2 2reports reports the the critical critical current current and theand voltage the voltage swing as swing a function as a of function the annealing of the temperature annealing temperatureranging from ranging 150 to 240 from◦C. The150 currentto 240 °C. and The voltage current values and were voltage normalized values were to those normalized with no annealing, to those whilewith no the annealing, bare values while are the reported bare values in Table are1. reported Each annealing in Table step 1. Each took annealing 30 min, during step took which 30 min, the duringmagnetometer which the was magnetometer heated without was the heated chip carrier without and the anchored chip carrier on the and hot anchored plate by vacuum. on the hot For plate both byIC andvacuum.∆V, we For can both observe IC and aΔ variationV, we can of observe about onea variation order of of magnitude about one withorder respect of magnitude to the initial with respectvalues. to Both the curvesinitial values. show a Both slow curves variation show for a lowerslow variation temperatures, for lower while temperatures, above 180 ◦ Cwhile the valuesabove 180 °C the values decrease at a faster rate. The same behavior has been observed for different SQUID magnetometers. It is therefore conceivable that the oxygen migration process toward the Sensors 2019, 19, x FOR PEER REVIEW 4 of 9 barrier is not linear with the annealing temperature. In Figure 2, we report the variation for a step of 10 °C.

Table 1. Main superconducting quantum interference device (SQUID) parameters for different annealing temperatures measured at liquid helium temperature. Each annealing step lasts 30 min.

T (°C) Ic (µA) ΔV (µV) √SB (fT/√Hz) - 42.30 43.6 13.2 150 40.08 41.8 12.3 160 38.97 40.9 8.9 170 37.50 40.0 8.6 180 36.00 38.9 6.9 Sensors 2019, 19, 3635 190 33.08 37.2 4.5 4 of 8 200 29.40 34.5 2.8 210 23.10 30.2 3.0 decrease at a faster rate. The same220 behavior 15.79 has been 23.3 observed 4.2 for different SQUID magnetometers. It is therefore conceivable that the230 oxygen 8.38 migration 1.44 process toward 7.6 the barrier is not linear with the 240 4.70 0.76 16.8 annealing temperature. In Figure2, we report the variation for a step of 10 ◦C.

Figure 2. Critical current and voltage swing of a SQUID magnetometer as a function of the annealing Figure 2. Critical current and voltage swing of a SQUID magnetometer as a function of the temperature measured at liquid helium temperature. The values were normalized to the initial value annealing temperature measured at liquid helium temperature. The values were normalized to the without any annealing. The annealing time for each temperature was 30 min. The solid black line is initial value without any annealing. The annealing time for each temperature was 30 min. The solid just an eye-guide line. black line is just an eye-guide line. Table1. Main superconducting quantum interference device (SQUID) parameters for different annealing temperaturesHowever, we measured stress that at liquid it is possible helium temperature. to have a much Each smaller annealing variation step lasts of 30 the min. critical current by decreasing the temperature steps. In particular, in the range of 180–240 °C, we were able to induce in a very reliable way a criticalT(◦C) current Ic (µ variationA) ∆V( asµ V)low as√ S2–3%B (fT/ √forHz) a temperature step of 2 °C. Since, in both dc and rf SQUID- the inductance 42.30 parameter 43.6 βL depends 13.2 linearly on the critical current, this procedure enabled us to 150modify the 40.08 βL of a SQUID 41.8 magnetometer 12.3 by about a factor of 10. In Figure 3, we report 160the voltage–magnetic 38.97 40.9 flux characteristics 8.9 measured at liquid helium temperature of the SQUID magnetometer under investigation. The green (middle) curve depicts the 170 37.50 40.0 8.6 characteristic where the overall annealing process produced the best magnetic field noise (T = 200 °C), while the blue (lower) and180 the red 36.00 (top) curves 38.9 are relative to 6.9 the untreated sample and to the highest annealing temperature190 (T = 33.08240 °C), respectively. 37.2 In 4.5order to verify the possibility of modifying in a wide range the200 parameter 29.40 of the SQUID 34.5 magnetometers, 2.8 we chose a sample with a high critical current showing210 a peaked 23.10 V–Φ characteristic 30.2 and a 3.0high magnetic noise level. As it is evident from Figure 3, the lower V–Φ curve shows a very sharp side due to the high critical current. 220 15.79 23.3 4.2 In fact, the voltage responsivity (VΦ = ∂V/∂ Φe) gain is given by [25,26]: 230 8.38 1.44 7.6 A VΦ 2401 4.70int 0.76M int 16.8 I R = ; G = V A ; V ≅ C int − A Φ Φ ()+ β Φ (1) VΦ 1 G A R A 1 L 0 However, we stress that it is possible to have a much smaller variation of the critical current by decreasing the temperature steps. In particular, in the range of 180–240 ◦C, we were able to induce in a very reliable way a critical current variation as low as 2–3% for a temperature step of 2 ◦C. Since, in both dc and rf SQUID the inductance parameter βL depends linearly on the critical current, this procedure enabled us to modify the βL of a SQUID magnetometer by about a factor of 10. In Figure3, we report the voltage–magnetic flux characteristics measured at liquid helium temperature of the SQUID magnetometer under investigation. The green (middle) curve depicts the characteristic where the overall annealing process produced the best magnetic field noise (T = 200 ◦C), while the blue (lower) and the red (top) curves are relative to the untreated sample and to the highest annealing temperature (T = 240 ◦C), respectively. In order to verify the possibility of modifying in a wide range the parameter of the SQUID magnetometers, we chose a sample with a high critical current Sensors 2019, 19, 3635 5 of 8 showing a peaked V–Φ characteristic and a high magnetic noise level. As it is evident from Figure3, the lower V–Φ curve shows a very sharp side due to the high critical current. In fact, the voltage responsivity (VΦ = ∂V/∂ Φe) gain is given by [25,26]:

A V 1 M I R Φ = ;G = Vint A ;Vint C (1) Sensors 2019, 19, x FOR PEER REVIEWint A Φ Φ  5 of 9 V 1 GA RA (1 + βL) Φ0 Φ −

where GA is the APF gain, MA is the mutual inductance between the SQUID loop and the APF coil, where GA is the APF gain, MA is the mutual inductance between the SQUID loop and the APF coil, and RA is the resistance of the APF circuit. If the critical current is rather high, the intrinsic VΦ and RA is the resistance of the APF circuit. If the critical current is rather high, the intrinsic VΦ increases and,increases consequently, and, consequently, G increases. GA increases. If G approaches If GA approaches the unit value, the unit the value, APF circuitthe APF becomes circuit unstablebecomes A A Φ andunstable a hysteresis and a hysteresis appears in appears the V–Φ incharacteristic. the V– characteristic.

FigureFigure 3.3.SQUID SQUID voltage voltage as as a functiona function of theof the external external magnetic magnetic flux measuredflux measured at T = at4.2 T K = (lower 4.2 K curve).(lower Thecurve). medium The medium (green) and(green) the topand (red)the top traces (red) refer traces to the refer same to magnetometerthe same magnetometer for an annealing for an temperatureannealing temperature of 200 and 240of 200◦C, and respectively. 240 °C, respectively.

SinceSince thethe thermal thermal annealing annealing decreases decreases the the critical critic current,al current, it is possible it is possible to reduce to thereduce GA tothe smooth GA to thesmooth V–Φ thecharacteristic, V–Φ characteristic, as shown as in shown the middle in the (green) middle curve (green in) Figurecurve 3in. InFigure this case, 3. In thethis I case,C = 34.5 the µICA = corresponds34.5 µA corresponds to about 70%to about of the 70% initial of valuethe initial (42.3 µvalueA). It (42.3 is worth µA). noting It is worth that the noting V–Φ characteristicthat the V–Φ ischaracteristic now smooth, is stable,now smooth, and preserves stable, aand suitable preserves responsivity a suitable gain. responsivity Of course, gain. if the Of critical course, current if the decreasescritical current excessively, decreases as in theexcessively, case of the as top in (red)the ca curvese of of the Figure top 3(red), the voltagecurve of swing Figure and 3, the the intrinsic voltage responsivityswing and the decrease intrinsic up responsivity to the point ofdecrease a degradation up to the of magnetometerpoint of a degradation performance. of magnetometer In this case, theperformance. decreases ofIn IthisC were case, so the high decreases as to reach of I 10%C were of so the high initial as value.to reach 10% of the initial value. FigureFigure4 4 reports reports the the spectral spectral densities densities of of the the field field noise noise measured measured in in the the flux-locked-loop flux-locked-loop mode mode atat TT == 4.24.2 K,K, correspondingcorresponding toto thethe threethree V–V–ΦΦ characteristicscharacteristics reportedreported inin FigureFigure3 .3. Due Due to to the the flicker flicker noisenoise atat lowlow frequencyfrequency withwith aa 11/f/f cornercorner ofof aboutabout 33 Hz,Hz, thethe magneticmagnetic fieldfield noisenoise valuesvalues atat 11 HzHz areare aboutabout 33 timestimes the the white white noise noise values. values. Note Note that that the the magnetic magnetic noise noise of the of magnetometerthe magnetometer without without any annealingany annealing (blue (blue curve) curve) is more is thanmore 4 timesthan 4 greater times thangreater that than after that the optimumafter the annealingoptimum treatment,annealing demonstratingtreatment, demonstrating full effectiveness full ineffectiveness tuning and optimizingin tuning SQUIDand optimizing magnetometer SQUID parameters. magnetometer parameters.In fact, the annealing procedure causes a progressive and controlled reduction of the Josephson criticalIn currentfact, the up toannealing the optimal procedure value, leading causes to a βprogressiveL equal to about and 1controlled and thus guaranteeing reduction of noise the optimizationJosephson critical as predicted current by up SQUID to the theory optimal [2,3 ].value, In addition, leading the to criticala βL equal current to decreaseabout 1 leadsand thus to a reductionguaranteeing of the noise additional optimization positive as feedbackpredicted circuit by SQUID gain, theory ensuring [2,3]. good In workaddition, stability the critical [25,26 ].current decreaseAs expected, leads to thea reduction magnetic of noise the additional corresponding positive to the feedback smallest circuit V–Φ characteristic gain, ensuring is rathergood work high becausestability the[25,26]. voltage swing and the intrinsic responsivity are very low and the critical current is far fromAs the expected, value that the optimizes magnetic the noiseβL parameter. corresponding to the smallest V–Φ characteristic is rather high because the voltage swing and the intrinsic responsivity are very low and the critical current is far from the value that optimizes the βL parameter. From a practical point of view, it should be emphasized that the noise of 13 fT/Hz1/2 shown by the SQUID magnetometer prevents MEG applications, while the same magnetometer after the annealing process can be applied in all high-sensitivity applications, including MEG. Sensors 2019, 19, 3635 6 of 8 Sensors 2019, 19, x FOR PEER REVIEW 6 of 9

Sensors 2019, 19, x FOR PEER REVIEW 6 of 9

Figure 4.4. Spectral densities of the magnetic noise of a SQUIDSQUID magnetometer.magnetometer. The lower (green) and

toptop (red)(red) spectra spectra refer refer to anto annealingan annealing temperature temperature of 200 of and 200 240 and◦C, 240 respectively, °C, respectively, while the while medium the (blue)medium spectrum (blue) spectrum corresponds correspond to the devices to the without device annealing. without annealing. Figure 4. Spectral densities of the magnetic noise of a SQUID magnetometer. The lower (green) and 1/2 FromIntop Figure(red) a practical spectra 5, we point referreport ofto view,anthe annealing white it should values temper be emphasized ofature the of magnetic 200 that and the 240field noise °C, noise of respectively, 13 fTas/ Hza function whileshown the of by the SQUIDannealingmedium magnetometer temperature. (blue) spectrum prevents The correspond horizontal MEG applications,s to dotted the device line whilewithout indicates the annealing. same the magnetometerwhite magnetic after noise the before annealing the processannealing. can As be we applied can see in allfrom high-sensitivity the figure, the applications, noise decreases including for annealing MEG. temperatures up to 200 °C, afterInIn FigureFigure which5 , 5,it we increases,we report report the and whitethe for white valuesT = 240values of °C the it of magneticex ceedsthe magnetic the field initial noise field value. as noise a functionThis as behavior a offunction the annealingat the of firstthe temperature.stageannealing is due temperature. Theto the horizontal decrease The dotted horizontal of G lineA that indicates dotted reduces theline hysteresis white indicates magnetic andthe whitethe noise instability beforemagnetic the device, annealing.noise beforeand, As as wethe a canconsequence,annealing. see from As the wethe figure, cannoise. see the fromBy noise decreasingthe decreases figure, thethe for nois annealingcrite icaldecreases current temperatures for further,annealing up a to temperaturesdecrease 200 ◦C, after of up whichintrinsic to 200 it increases,responsivity°C, after which and occurs for it Tincreases, =and,240 at◦ Csome and it exceeds forpoint, T = theit 240 causes initial °C it a value.exreversalceeds This the of thebehaviorinitial noise value. trend. at the This first behavior stage is dueat the to first the decreasestage is due of G Atothat the reducesdecrease hysteresis of GA that and reduces the instability hysteresis device, and and,the instability as a consequence, device, and, the noise. as a Byconsequence, decreasing thethe critical noise. current By decreasing further, a decrease the crit ofical intrinsic current responsivity further, occursa decrease and, at of some intrinsic point, itresponsivity causes a reversal occurs of and, the at noise some trend. point, it causes a reversal of the noise trend.

Figure 5. White spectral density of magnetic field noise as a function of the annealing temperature measured a T = 4.2 k in flux-locked-loop mode. The solid black line is just an eye-guide line.

FigureFigure 5.5. WhiteWhite spectralspectral density of magneticmagnetic fieldfield noisenoise asas aa functionfunction ofof thethe annealingannealing temperaturetemperature measuredmeasured aa TT == 4.2 k in flux-locked-loopflux-locked-loop mode. The solid black line is just an eye-guide line.

In order to also obtain information on the temporal dependence for a fixed temperature of the annealing process, we made a complete characterization of another SQUID magnetometer by fixing the annealing temperature and varying the time. In particular, we chose an annealing temperature of 170 ◦C and increased the time with a step of 30 min. Figure6 reports the critical current, the voltage swing, and the white spectral density of the magnetic field noise measured at T = 4.2 K. From Figure6, Sensors 2019, 19, x FOR PEER REVIEW 7 of 9

In order to also obtain information on the temporal dependence for a fixed temperature of the annealing process, we made a complete characterization of another SQUID magnetometer by fixing the annealing temperature and varying the time. In particular, we chose an annealing temperature

Sensorsof 1702019 °C, 19and, 3635 increased the time with a step of 30 min. Figure 6 reports the critical current,7 ofthe 8 voltage swing, and the white spectral density of the magnetic field noise measured at T = 4.2 K. From Figure 6, it is evident that there are slight variations as a function of the time. In particular, itafter is evident 150 min that of thereannealing, are slight we variationsmeasured asa critical a function decrease of the of time. about In particular,20% and even after less 150 for min the of annealing,voltage swing. we measured a critical decrease of about 20% and even less for the voltage swing.

Figure 6.6. Critical current (top), voltage swing (middle),(middle), and white magnetic field field noise of aa SQUIDSQUID

magnetometer as a function of of the the annealin annealingg time time for for a afixed fixed annealing annealing temperature temperature (T (Ta =a 170= 170 °C).◦C).

A greatergreater variationvariation can bebe observedobserved forfor thethe magneticmagnetic fieldfield noise,noise, becausebecause eveneven smallsmall decreasesdecreases of thethe criticalcritical current can have a significantsignificant eeffectffect onon thethe APFAPF gaingain andand thethe stabilitystability ofof thethe SQUIDSQUID magnetometer. TheThe samesame measurements measurements were were also also made made for for di ffdifferenterent annealing annealing temperatures, temperatures, and and we observedwe observed the samethe same behavior. behavior. Due to Due the observedto the obse slightrved variations, slight variations, this procedure this procedure can be eff ectivelycan be usedeffectively to fine-tune used to the fine-tune magnetometer the magnetometer parameters. parameters.

4. Conclusion InIn conclusion,conclusion, an experimentalexperimental study on thethe annealingannealing ofof SQUIDSQUID magnetometersmagnetometers hashas beenbeen presented.presented. InIn particular,particular, detailed detailed measurements measurements of of main main SQUID SQUID magnetometer magnetometer parameters, parameters, such such as the as criticalthe critical current, current, the voltage the voltage swing, swing, and the and magnetic the magnetic noise as anoise function as ofa func the annealingtion of the temperature, annealing havetemperature, been shown. have These been measurementsshown. These highlightmeasuremen the possibilityts highlight of the optimizing possibility the performancesof optimizing andthe fine-tuningperformances the and most fine-tuning important parametersthe most import of a SQUIDant parameters magnetometer. of a SQUID We believe magnetometer. that this study We isbelieve very importantthat this study for applications is very important that require for ap theplications optimization that andrequire fine the control optimization of the SQUID and fine key parameters.control of the In additionSQUID tokey high-sensitivity parameters. In applications addition suchto high-sensitivity as biomagnetism, applications it can certainly such beas usefulbiomagnetism, for superconducting it can certainly quantum be useful computing for superconducting where a fine control quantum of the superconductingcomputing where quantum a fine devicecontrol parametersof the superconducting is required. Inquantum the latter device application, parameters it is preferableis required. to In perform the latter annealing application, with it a laser,is preferable which allows to perform for the annealing controlled with heating a laser, of the which devices allows contained for onthe the controlled chip [20 ,21heating]. of the devices contained on the chip [20,21]. Author Contributions: Conceptualization, A.V. and C.G.; Investigation, A.V.; Data curation, B.R. and P.S.; FormalAuthor analysis,Contributions: P.S.; Methodology, Conceptualization, B.R.; Resources, A.V. and M.V.; C.G.; Software, Investigat M.V.;ion, Writing—review A.V.; Data curation, and editing, B.R. and C.G. P.S.; Funding:Formal analysis,This research P.S.; Methodology, received no externalB.R.; Resources, funding. M.V.; Software, M.V.; Writing – review and editing, C.G. ConflictsFunding: ofThis Interest: researchThe received authors no declare external no funding conflict of interest.

Conflicts of Interest: The authors declare no conflict of interest. References

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