YBa2Cu3O7 grain boundary junctions and low-noise superconducting quantum interference devices patterned by a focused ion beam down to 80 nm linewidth
J. Nagel, K. B. Konovalenko, M. Kemmler, M. Turad, R. Werner, E. Kleisz, S. Menzel, R. Klingeler, B. Büchner, R. Kleiner, D. Koelle
aa r X i v : . [ c ond - m a t . s up r- c on ] S e p YBa Cu O grain boundary junctions and low-noisesuperconducting quantum interference devicespatterned by a focused ion beam down to 80 nmlinewidth J. Nagel , K. B. Konovalenko , M. Kemmler , M. Turad ,R. Werner , E. Kleisz , S. Menzel , R. Klingeler , B. B¨uchner ,R. Kleiner and D. Koelle Physikalisches Institut – Experimentalphysik II and Center for Collective QuantumPhenomena, Universit¨at T¨ubingen, Auf der Morgenstelle 14, D-72076 T¨ubingen,Germany2 Leibniz-Institut f¨ur Festk¨orper- und Werkstoffforschung (IFW) Dresden, D-01171Dresden, GermanyE-mail: [email protected]
Abstract.
YBa Cu O ◦ (30 ◦ ) bicrystal grain boundary junctions (GBJs),shunted with 60 nm (20 nm) thick Au, were fabricated by focused ion beam millingwith widths 80 nm ≤ w ≤ . µ m. At 4.2 K we find critical current densities j c inthe 10 A / cm range (without a clear dependence on w ) and an increase in resistancetimes junction area ρ with an approximate scaling ρ ∝ w / . For the narrowest GBJs j c ρ ≈ µ V, which is promising for the realization of sensitive nanoSQUIDs for thedetection of small spin systems. We demonstrate that our fabrication process allowsthe realization of sensitive nanoscale dc SQUIDs; for a SQUID with w ≈
100 nm wideGBJs we find an rms magnetic flux noise spectral density of S / ≈ µ Φ / Hz / in the white noise limit. We also derive an expression for the spin sensitivity S / µ ,which depends on S / , on the location and orientation of the magnetic moment of amagnetic particle to be detected by the SQUID, and on the SQUID geometry. For thenot optimized SQUIDs presented here, we estimate S / µ = 390 µ B / √ Hz, which couldbe further improved by at least an order of magnitude.PACS numbers: 85.25.CP, 85.25.Dq, 74.78.Na, 74.72.-h
BCO GBJs and low-noise SQUIDs patterned by FIB
1. Introduction
There is a growing interest in developing sensitive miniaturized superconductingquantum interference devices (SQUIDs) for the investigation of small spin systems andscanning SQUID microscopy with sub- µ m spatial resolution [1, 2, 3]. A main motivationare measurements on single nanomagnetic particles, and the ultimate goal is the directdetection of switching of a single electronic spin with various potential applicationsin spintronics, quantum computing and on biomolecules. These applications requiresub- µ m Josephson junctions and SQUID loops, both for optimum inductive coupling tonanosized objects and for improving the SQUID sensitivity for the operation at switchingfields of the magnetic particles up to the Tesla range at temperature T ≈ µ m thin filmstructures are based on electron beam lithography, or on focused ion beam (FIB)patterning. While the patterning of sub- µ m SQUID loops poses no particular problems,the properties of sub- µ m Josephson junctions embedded in the SQUID loop have to becarefully optimized in order to realize low-noise SQUIDs. Here, an important figure ofmerit is the rms spectral density of flux noise S / , which for optimized SQUIDs based onthe standard Nb/AlO x /Nb technology for µ m-sized junctions is in the range of µ Φ / √ Hz(Φ is the magnetic flux quantum). However, critical current densities j c > / cm are hard to achieve reliably with this technology, yielding too small critical currents I c = j c A J for junction areas A J in the (100 nm) range. Therefore, recent researchfocused on Nb or Al thin film constriction type junctions (with widths w > ∼
50 nm),sometimes shunted with a thin film normal metal layer (e. g. Au, or W) to ensure non-hysteretic current-voltage-characteristics (IVCs) [3]. This approach typically producedSQUIDs with S / > ∼ / √ Hz. Only very recently, highly sensitive Nb SQUIDs with S / ≈ . µ Φ / √ Hz have been demonstrated [7]. These encouraging results have beenobtained with FIB patterned constriction junctions at T = 6 . B a small junction size ( ⊥ ~B ) is required dueto the suppression of I c with increasing magnetic flux in the junction above several Φ ,which demands for a particularly large j c . Furthermore, the maximum field of operationis limited by the upper critical field B c , e. g. to < ∼ T c ) SQUIDs offer three advantages:(i) very high B c in the tens of Tesla regime or even more, (ii) high j c > A / cm for grain boundary junctions (GBJs) operating at T = 4 . I c . Here,the challenge is to produce sub- µ m GBJs with high quality, in particular with high j c and ρ = RA J , where R is the junction resistance. At this point, we should mention,that in principle, also constriction type junctions based on HTS, or MgB thin filmsmay fulfill the above mentioned requirements, and in fact such junctions and SQUIDs BCO GBJs and low-noise SQUIDs patterned by FIB T , such that their operationtemperature is often limited to a narrow T range well above 4 K, and their performancewith respect to flux noise so far did never reach the performance of high- T c low-noiseGBJ SQUIDs [13].Already in the 1990s thin film high- T c YBa Cu O (YBCO) sub- µ m GBJs andSQUIDs have been fabricated using e-beam lithography [14, 15]. However, oxygenloss during processing, in particular for very thin films, may require post-depositionannealing to improve junction characteristics [16]. More recently, sub- µ m YBCO GBJshave also been fabricated by FIB [17], and both technologies enabled fundamentalstudies on transport and noise in high- T c sub- µ m GBJs [16, 18, 19, 20]. Still, a significantdegradation of j c for w < ∼
500 nm was found [14, 15, 17], and the use of deep sub- µ m GBJsfor the realization of nanoSQUIDs has not been explored yet. The motivation for therealization of sub- µ m GBJs with widths well below 500 nm is based on the followingconsiderations: First of all, operation in high magnetic fields in the Tesla range asmentioned above, requires very accurate alignment of the applied magnetic field in thethin film plane in order to reduce coupling of the applied out-of-field component to theGBJ. This demands for as small as possible GBJ widths. Furthermore, as will be shownbelow, the spin sensitivity scales linearly with the rms flux noise S / of the SQUID.Optimization of S / requires an as small as possible SQUID loop inductance L [21],i.e. minimization of the dimensions of the SQUID loop, which for topological reasons hasto be intersected by the grain boundary. Here, SQUID loop sizes of the order of 100 nmseem to be feasible, according to our experience on FIB patterning of our devices asdescribed below. In order to ensure optimum SQUID performance, one should achieveat least a few SQUID modulations within the Fraunhofer-like I c ( B ) modulation of thesingle GBJs. This in turn requires also shrinking the GBJ widths down to the size of theSQUID loop. Hence, our goal is to demonstrate the feasibility of FIB patterning YBCOGBJs down to junction widths of the order of 100 nm. In order to accomplish this, weinvestigated the scaling behavior of YBCO GBJ properties with linewidths ranging overtwo orders of magnitude, from ∼ µ m down to 80 nm, and we investigated the electrictransport and noise properties of YBCO GBJ dc SQUIDs with the smallest linewidthsachieved within this study. We note that we performed so far only investigations on low-field properties of the fabricated GBJs and SQUIDs, as we are at this stage interestedin clarifying the intrinsic scaling properties of our devices with GBJ width, althoughthe ultimate goal of this work is to operate such SQUIDs in high magnetic fields in theTesla range at T = 4 . K and well below.The remainder of this paper is organized as follows. Section 2 very briefly addressessample fabrication and layout, including some information on the quality of our YBCOthin films. In Sect. 3 we first describe and discuss the results of electric transportproperties of our shunted GBJs, with focus on their dependence on junction width,which was varied over two orders of magnitude (3.1). The second part (3.2) of thissection describes the results obtained for our SQUIDs, with focus on electric transport BCO GBJs and low-noise SQUIDs patterned by FIB S / of the SQUIDs and the spin sensitivity S / µ , whichis the important figure of merit for detection of small spin particles. Here, we provide asolution for calculating the spin sensitivity for any arbitrary geometry of the SQUID loopas a function of position and orientation of the magnetic moment of a small particleto be detected. We then apply this solution to the particular geometry of SQUID 2and finally discuss perspectives for further optimization of S / µ . Section 5 contains ourconclusions.
2. Sample Fabrication
We fabricated devices on SrTiO (STO) symmetric [001] tilt bicrystal substrates withmisorientation angle θ = 30 ◦ (chip 1) and 24 ◦ (chip 2). Figure 1(a)–(c) illustratesthe fabrication steps. We deposited d Y = 50 nm thick c -axis oriented epitaxially grownYBCO by pulsed laser deposition (PLD), followed by in-situ evaporation of Au withthickness d Au = 20 nm (chip 1) and 60 nm (chip 2), serving as a resistive shunt andprotection layer during FIB milling. For details on PLD growth of our YBCO filmson STO substrates, and their structural and electric transport properties see Ref. [22].In brief, our 50 nm thick YBCO films typically yield 0 . ◦ full width half maximum ofthe rocking curve at the (005) x-ray diffraction peak, have T c = 91 K with a transitionwidth ∼ . ρ ≈ µ Ωcm at T = 100 K. On both chips, 8 µ m widebridges straddling the grain boundary were fabricated by photolithography and Ar ion Figure 1. (Color online) Upper row: Schematic illustration of the steps used forfabricating YBCO grain boundary junctions (GBJs). (a) in-situ deposition of aYBCO/Au bilayer on a bicrystal STO substrate; (b) patterning of 8 µ m wide bridgesstraddling the grain boundary (GB) (by photolithography and Ar ion milling); (c)patterning of a narrow GBJ by FIB. The location of the GB is indicated by dashedlines. Bottom row (d)–(f) shows scanning electron microscopy images of three singlejunction devices (from chip 1) with different width (indicated in the graphs). BCO GBJs and low-noise SQUIDs patterned by FIB Figure 2.
SEM images of the three SQUIDs (loop size 1 . × . µ m ) fabricated onchip 2. Labels in black boxes give junction widths. milling and then patterned by FIB with Ga ions (50 pA, 30 kV) to make junctions and dcSQUIDs with junction widths 80 nm ≤ w ≤ . µ m. FIB patterning was performed witha dual beam 1540 XB cross beam (Zeiss). This allowed us to apply an optimized FIBcut procedure (soft FIB procedure), with small ion current density and minimum ionexposure time of non-milled areas, i.e. only very brief snap shot imaging prior to milling.Even for imaging by the electron beam, we minimized the exposure time in order to avoiddamaging of our FIB cut bridges. Figure 1(d)–(f) shows scanning electron microscopy(SEM) images of three GBJs fabricated on chip 1. In total, we investigated 22 singleGBJs and 3 dc SQUIDs (on chip2; hole size 1 . × . µ m ). SEM images of the threeSQUIDs are shown in Fig. 2.
3. Experiments
We characterized our devices at T = 4 . I c ( B ) and V ( B ) we used a 4-point arrangement with a roomtemperature voltage amplifier. For SQUID noise measurements we preamplified theoutput signal with a Nb dc SQUID amplifier with 0 . / √ Hz resolution.
All devices showed resistively-and-capacitively-shunted-junction (RCSJ)-type IVCs,which for some of the sub- µ m junctions on chip 1 (thinner Au shunt) had a smallhysteresis. Therefore, for chip 2, we increased d Au by a factor of three, yielding non-hysteretic IVCs, except for the 530 nm wide junction, which has an exceptionally high j c ρ . From the IVCs we determined I c , and R , and calculated j c and ρ , using d Y = 50 nmand w as obtained from SEM images. The results of these measurements are summarizedin Fig. 3, plotted vs w which spans two orders of magnitude. Full symbols in Fig. 3show data obtained after FIB patterning; open symbols show data (for chip 2) from the8 µ m wide bridges prior to FIB patterning.Figure 3(a) shows j c ( w ), which is well above 10 A / cm over the entire range of w . The j c values shown are typical for θ = 24 ◦ and 30 ◦ YBCO GBJs at 4.2 K and w > ∼ µ m[13]; however, such high j c values have not been previously observed for widthsdown to 80 nm. We do find a significant scattering of j c ( w ), however without a clear BCO GBJs and low-noise SQUIDs patterned by FIB (b) ( (cid:181) m ) (c) w ((cid:181)m) j c ( (cid:181) V ) GBJ (24 ) SQUID (24 ) d Au =60 nm GBJ (24 ) before FIB patterning (w=8(cid:181)m) GBJ (30 ) d Au =20 nm j c ( A / c m ) (a) Figure 3. (Color online) Transport data of YBCO GBJs and SQUIDs vs junctionwidth w (solid symbols): (a) critical current density j c ( w ); (b) junction resistancetimes area ρ ( w ); (c) j c ρ ( w ). Dashed (solid) lines indicate average j c values [in (a)] andapproximate scaling of ρ ( w ) [in (b)] and j c ρ ( w ) [in (c)] for chip 1 (2). Open squares aredata for the same GBJs on chip 2, measured prior to FIB patterning (i.e. w = 8 µ m).The numbers on the top axis in (a) label the device numbers on chip 2. width dependence. The average j c for chip 2 is 1.5 times the one for chip 1, as expectedfrom the scaling j c ( θ ) of GBJs [23]. The comparison of j c of the same bridges beforeand after FIB patterning shows that for most devices j c even slightly increased afterFIB patterning. The position of the devices on chip 2 (along the GB of the substrate)is ordered according to their device number (1–15) [c.f. top axis of Fig. 3(a)] from theleft to the right edge of the substrate. There is a clear trend of increasing j c by about afactor of two (for the 8 µ m wide bridges) along the entire substrate. The origin of thisgradient in j c has not been clarified; however we can rule out a corresponding variation inthe YBCO film thickness across the substrate. A possible explanation for the observedgradient in j c of the 8 µ m wide GBJs along chip 2, could be a gradient in the qualityof the GB in the bicrystal substrate, which in turn can cause a gradient in the barrierthickness of the GBJs along the chip.Figure 3(b) shows an approximate scaling ρ ∝ √ w of unclear origin. We note that BCO GBJs and low-noise SQUIDs patterned by FIB ρ with decreasing junction with w .Before FIB patterning, the 8 µ m wide GBJs on chip 2 all had ρ ≈ .
17 Ω µ m , which fallsonto the observed ρ ( w ) dependence, indicating that this scaling is not specific to FIBpatterned GBJs. Furthermore, ρ ≈ .
17 Ω µ m is an order of magnitude below typicalvalues for unshunted GBJs [23], which we attribute to the Au shunt, and which is alsoconsistent with the larger ρ of GBJs on chip 1 with thinner Au. For chip 1, d Au = 20 nmis close to the 15 nm implantation depth of 30 keV Ga ions in Au [24]. Hence one mightexpect that FIB induces an increase in the Au resistivity via Ga implantation. Thiseffect should be suppressed for chip 2 with 3 times thicker Au. In any case, it is hardto explain, why Ga implantation should increase ρ for wider junctions. Certainly, Gaimplantation is not the only detrimental effect of FIB patterning. In particular, the Gabeam might destroy the crystalline order close to the patterned edges. However, ourexperimental observation of almost constant j c for GBJ widths down to 80 nm rules outsevere edge damage effects on a length scale of several tens of nm. This observationalso rules out such effects as a possible explanation for the observed scaling behavior of ρ ( w ).Figure 3(c) shows j c ρ ( w ) ≈ . . . . j c . This is certainly due to thesuppression of j c ρ by the Au shunt required to ensure non-hysteretic IVCs at 4.2 K. Thedecrease of j c ρ with decreasing w is due to the scaling of ρ ( w ) mentioned above. Still,even for the 80 nm wide GBJs we find reasonable values of j c ρ around 100 µ V, whichare certainly quite suitable for the realization of sensitive SQUIDs.
The results of transport measurements on all three SQUIDs (on chip 2) are summarizedin Tab. 1. The SQUID inductance L was calculated with the numerical simulationsoftware 3D-MLSI [25], which is based on a finite element method to solve the Londonequations for a given film thickness and London penetration depth ( d Y = 50 nm and λ L = 140 nm, respectively, in our case). As d Y ≪ λ L , the kinetic inductance contributessignificantly to L . For SQUID 1 and SQUID 2, the GBJ widths w i ( i = 1 ,
2) arebelow λ L , which increases L over the one of SQUID 3 with wider junctions. From thecalculated L and measured I c we obtain β L ≡ LI c / Φ ≈ . . . . .
7, i. e. not far from w w I c R I c R L β L V Φ [nm] [nm] [ µ A] [Ω] [ µ V] [pH] [mV / Φ ]1 80 140 44 1.7 73 15 0.31 0.082 80 105 49 1.9 94 16 0.38 0.113 160 230 139 1.3 185 10 0.66 0.13 Table 1.
Parameters of YBCO GBJ dc SQUIDs.
BCO GBJs and low-noise SQUIDs patterned by FIB Figure 4. (Color online) Transport and noise characteristics of SQUID 2: (a) IVC at B = 0; inset shows I c ( B ). (b) V ( B ) for I = − . . . . − . . . . . . µ A (in3 . µ A steps). (c) Spectral density of rms flux noise S / ( f ); inset: SEM image of theSQUID. (d) V (Φ) and S / (Φ) (averaged from f = 5 to 6 kHz). the optimum value β L ≈ V Φ , i. e. the slope of the V (Φ)curves at optimum bias current and applied flux Φ = ± Φ is around 0 . / Φ , andthe effective area A eff = Φ /B ≈ µ m for all three SQUIDs.Figure 4 shows electric transport and noise data obtained for SQUID 2 [the devicewith smallest w ; see inset in (c)]. Figure 4(a) shows an IVC for an applied field B = 0corresponding to a maximum in I c . The small jump at I c to V = 0 indicates thatthe junctions are at the transition to the underdamped regime. The inset in Fig. 4(a)shows I c ( B ) with 40 % modulation. Figure 4(b) shows V ( B ) for various bias currents I . The small shift in the minima of V ( B ) upon reversing I is in accordance with the I c asymmetry of the two GBJs due to their different widths.Finally, graphs (c) and (d) in Fig. 4 show the results of noise measurements onSQUID 2. Fig. 4(c) shows the rms spectral density of flux noise S / ( f ) ∝ f − x foroptimum flux bias Φ = − .
286 Φ with x ≈ . f < ∼ I c fluctuations in the GBJs [13]. For larger f we find a white flux noiselevel S / ,w ≈ µ Φ / √ Hz, which to our knowledge is the lowest value of S / obtained fora YBCO dc SQUID with sub- µ m GBJs so far. Fig. 4(d) shows the rms flux noise S / (averaged from f = 5 to 6 kHz) and the SQUID voltage V vs applied flux Φ. We finda rather shallow minimum in S / (Φ) for an applied flux where the slope of the V (Φ) BCO GBJs and low-noise SQUIDs patterned by FIB
4. Spin sensitivity
Coming back to the main motivation of this work, i.e. the development of nanoSQUIDsfor the detection of small spin systems, we derive an expression for the spin sensitivity S / µ , which we then use to calculate S / µ for the particular geometry and flux noise ofSQUID 2 as a function of the position of a magnetic particle for a given orientation ofits magnetic moment. S µ is the spectral density of spin noise, which depends on thespectral density of flux noise S Φ of the SQUID and on the coupling between a magneticparticle with magnetic moment ~µ = µ · ˆ e µ and the SQUID via the relation S µ = S Φ /φ µ .Here, φ µ (ˆ e µ , ~r µ ) ≡ Φ µ ( ~µ, ~r µ ) /µ is the magnetic flux Φ µ per magnetic moment µ coupledinto the SQUID loop by the magnetic particle, which is located at the position ~r µ andwhich is oriented along ˆ e µ . This means, in order to determine S / µ for a given S / ,one needs to calculate the coupling function φ µ (ˆ e µ , ~r µ ), which will also depend on theSQUID geometry.To determine φ µ , we assume that the magnetic moment ~µ is moved from a distancefar away to a position ~r = ~r µ close to the SQUID loop. When the magnetic momentapproaches ~r µ , a circulating current I µ ( ~µ, ~r µ ) is induced in the SQUID loop, whichcompensates the coupled flux Φ µ , due to the diamagnetic response of the SQUID loop.The magnetic field energy stored in the loop of inductance L is W loop = LI µ . The workrequired to place the particle in the magnetic field ~B µ ( ~r ) produced by the circulatingcurrent I µ is W µ = − ~µ · ~B µ ( I µ , ~r µ ). We note that W µ >
0, due to the diamagneticresponse of the SQUID loop. Hence, the total work required to bring the magneticparticle to the position ~r µ is W = W loop + W µ = 12 LI µ − ~µ · ~B µ ( I µ , ~r µ ) . (1)On the other hand, instead of the SQUID, we may consider a fixed current systemproducing the same field ~B µ ( I µ , ~r µ ) as the SQUID, when the particle is in its finalposition r µ . In this case, the particle has a (positive) energy W = − ~µ · ~B µ ( I µ , ~r µ ) . (2)From W = W we obtain I µ = − ~µ · ~B µ /L . With Φ µ = LI µ and with ~B µ /I µ = ~B/I ≡ ~b one thus obtainsΦ µ ( ~µ, ~r µ ) µ ≡ φ µ (ˆ e µ , ~r µ ) = − ˆ e µ · ~b ( ~r µ ) , (3)where I is an arbitrary current circulating in the SQUID loop, which generates themagnetic field ~B ( I ) at the position ~r µ of the magnetic particle.Equation (3) reproduces the results of Refs. [27, 5], derived for a circular filamentarySQUID loop. Moreover, Eq. (3) provides a solution of the problem, valid for any arbitrary geometry of the superconducting loop, if one can find the normalized magneticfield distribution ~b ( ~r ) outside the SQUID loop. For a given ~b ( ~r ) (determined by the BCO GBJs and low-noise SQUIDs patterned by FIB Figure 5. (Color online) Calculated spin sensitivity S / µ for SQUID 2 with S / =4 µ Φ / √ Hz for the detection of the magnetic moment of a small spin particle alignedalong the x axis in the ( x, y ) plane of the SQUID loop [c.f. inset in main graph]. Maingraph shows a contour plot of S / µ as a function of the position of the particle in the( x, z ) plane at y = 0. The location of the YBCO bridges is indicated by the blackrectangles; the rectangles (yellow lines) on top of those indicate the position of theAu layer. The linescan above the main graph shows S / µ ( x ) for z = 85 nm, and thelinescan right to the main graph shows S / µ (z) for x = 0 . µ m. The location of theseline scans is indicated by the dashed (red) lines in the main graph. SQUID geometry only) and given flux noise, one can use Eq. (3) to easily calculatethe spin sensitivity S / µ = S / /φ µ for any orientation ˆ e µ and location of the magneticparticle.For the geometry of SQUID 2, we calculated the spatial distribution of thecurrent density in the SQUID loop and the corresponding 3-dimensional magnetic fielddistribution ~b ( ~r ) outside the SQUID loop with 3D-MLSI [25]. Figure 5 shows theresulting spin sensitivity of SQUID 2 (with S / = 4 µ Φ / √ Hz) for the detection ofa magnetic particle located in the ( x, z ) plane (at y = 0) with its magnetic momentpointing along the x direction, i.e. ˆ e µ = ˆ e x . I.e., the magnetic moment of the particle isaligned parallel to the thin film plane of the SQUID, and perpendicular to the currentthrough the GBJs.The contour plot of the spin sensitivity shows clear minima right above thesuperconducting bridges straddling the grain boundary. The upper inset shows alinescan S / µ ( x ) of the spin sensitivity at a height z = d Au + d Y / BCO GBJs and low-noise SQUIDs patterned by FIB µ B / √ Hz, which could be further improved by reducing the thickness of the Aulayer. This can be done even without affecting the GBJ properties if the Au layer isnot removed right above the GBJ. Removing the gold layer (and placing the magneticparticle at z = d Y / S / µ by more than a factor of two downto 180 µ B / √ Hz, as can be seen in the right inset, which shows the vertical dependence S / µ ( z ) at x = 0 . µ m, i.e. right above the center of the YBCO bridge. Moreover,further improvements in S / µ are feasible by improving S / , which is by no meansoptimized for the SQUIDs presented here. For example, our FIB technology allowsfor a reduction in the size of the SQUID loop down to ∼
100 nm and a concomitantreduction in SQUID inductance L down to ∼ S / by at least an order of magnitude, which would bring S / µ downto ≈ µ B / √ Hz.
5. Conclusions
In conclusion, we have fabricated YBCO grain boundary junctions and dc SQUIDs byFIB patterning with junction widths ranging from 7 . µ m down to 80 nm. Using anAu thin film shunt on top of the junctions, we achieved non-hysteretic current-voltage-characteristics for operation of YBCO dc SQUIDs at 4.2 K and below. We demonstratedthat FIB pattering enables the fabrication of deep sub- µ m GBJs without degradationof critical current densities, and comparable to GBJs with widths above 1 µ m. Wedo find a systematic dependence of the resistance times area ρ of our GBJs, whichscales approximately with the junction width w as ρ ∝ √ w . The origin of this scalingcould not be resolved and requires further studies. Still, we obtain values of I c R forour GBJs around 100 µ V for junctions on the 100 nm scale, which is promising for thefabrication of sensitive nanoSQUIDs. We demonstrated low-noise performance for suchdevices in the µ Φ / √ Hz range, which still can be improved significantly and whichmakes them promising candidates for applications in magnetic nanoparticle detectionand measurements at high magnetic fields. The presented solution for calculatingthe spin sensitivity for arbitrary SQUID geometries – as a function of position andorientation of the magnetization of small spin particles – provides an important toolfor the systematic optimization of the spin sensitivity using nanoSQUIDs as sensitivedevices for direct detection of magnetization switching of small spin particles.
Acknowledgments
We gratefully acknowledge Thomas Dahm for helpful discussions. J. Nagel andM. Kemmler acknowledge support by the Carl-Zeiss Stiftung, K. Konovalenkoacknowledges support by the Otto Benecke Stiftung and R. Werner acknowledgessupport by the Cusanuswerk, Bisch¨ofliche Studienf¨orderung. This work was funded
BCO GBJs and low-noise SQUIDs patterned by FIB
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