Investigation of Low-frequency Excess Flux Noise in dc SQUIDs at mk Temperatures

Transcription

1 Paper 3EC01 at ASC20, to appear in IEEE Trans. Appl. Supercond. 21 (2011) 1 Investigation of Low-frequency Excess Flux Noise in dc SQUIDs at mk Temperatures Dietmar Drung, Jörn Beyer, Jan-Hendrik Storm, Margret Peters, and Thomas Schurig Abstract The excess low-frequency flux noise in dc superconducting quantum interference devices (SQUIDs) operated at ultra-low temperatures was studied. A large number of single SQUIDs as well as SQUID arrays from 16 wafers fabricated over a period of six years were characterized at 4.2 K and <320 mk. Considering the large spread in the low-frequency noise at 4.2 K, there was no observable dependence of the low-frequency energy resolution on the SQUID design or fabrication parameters. In contrast, below 4.2 K the low-frequency noise changed moderately or increased strongly depending on whether the bottom Nb or the insulation layer were fabricated in our newer sputter system instead of the older one. The corresponding excess noise levels at <320 mk and are typically 40 h and 300 h, respectively (h is Planck s constant). The excess noise scales as f -α with α typically around 0.6 for good devices. For devices with strong low-frequency excess noise, α increases up to about 0.9. The best energy resolution ε achieved so far with a 50 ph test SQUID operated at 16 mk is 0.62 h at 0 khz, increasing to 1.64 h at 1 khz and 14 h at Hz. Index Terms 1/f flux noise, energy resolution, SQUID current sensor, ultra-low temperature. T I. INTRODUCTION he dc superconducting quantum interference device (SQUID) is a highly sensitive detector of magnetic flux [1]. Commonly, an input coil is magnetically coupled to the SQUID loop thereby creating a low-noise current sensor. In August 2003, the first PTB current sensor wafer was fabricated. Since then, various current sensor design versions C1 to C6 were developed [2]-[5], and over 00 SQUIDs were tested in liquid helium. Originally, most of our current sensors were operated at T = 4.2 K. Since 2005, we deliver an increasing number of SQUIDs for applications where the device is operated at mk temperatures, e.g., the readout of transitionedge sensors (TESs) [6] or metallic magnetic calorimeters (MMCs) [7]. For these applications, the SQUIDs are carefully selected by using the characterization at 4.2 K and considering the typical trend in the SQUID parameters between 4.2 K and <1 K. SQUID characterization at mk temperatures is done on sample basis to check the fabrication quality, or in cases where the user wishes devices 0% tested at the intended working temperature. This way, we collected flux noise data at -320 mk for a variety of SQUIDs of different designs from wafers fabricated over a period of six years. Manuscript received 3 August 20. This work was supported in part by the European Commission in the framework of the European Microkelvin Collaboration. The authors are with the Physikalisch-Technische Bundesanstalt (PTB), Abbestraße 2-12, D-587 Berlin, Germany (phone: ; fax: ; dietmar.drung@ptb.de). Low-frequency excess flux noise in SQUIDs (in particular at ultra-low temperatures [8]) remained a challenge for over 20 years; recently, the interest in this topic increased [9]-[12]. For our SQUIDs, a degradation in the low-frequency noise performance is observed when the devices are cooled to mk temperatures, and the 1/f noise corner (the frequency for equal 1/f and white noise densities) moves from typically below Hz at 4.2 K to above 1 khz at mk temperatures. This is a severe problem for MMC readout [7] and other applications below about khz where SQUID noise limits the overall signal-to-noise ratio. To address this issue, we measured a series of SQUIDs both at 4.2 K and near mk. We performed a thorough analysis of these new measurements together with results obtained during the past five years to find a potential dependence of the low-frequency excess noise on the SQUID design and fabrication parameters. II. SAMPLE SELECTION AND DATA ANALYSIS Our SQUIDs were fabricated using a Nb-Al-AlO x -Nb trilayer technology with Josephson junctions defined by the selective Niobium anodization process [1]. The minimum linewidth and junction dimensions were nominally 2.5 µm. For the insulation layer, SiO 2 sputtered in an Ar plasma from a stoichiometric target or Si x N y sputtered from a Si target in an Ar/N 2 plasma were used. The resistors were made from Pd (except for wafer C602 with AuPd resistors). The devices were not passivated. The bottom Nb was patterned by wet etch, the top Nb, resistors and insulation layer(s) by lift-off. The film depositions were done in two sputter systems, our older Alcatel system (SCM440/174 from the French company CIT-Alcatel) and the newer FHR system (customer-specific cluster system MS0x4-AEO from the German company FHR). Our noise study involves single SQUIDs as well as arrays of SQUIDs in different configurations (series or parallel) [4], [5]. Provided that all SQUIDs in an array are biased at the same working point and that there is no correlation between the noise in the individual SQUIDs, the overall flux noise density S Φ of a SQUID array scales inversely with the number N of SQUIDs: S Φ 1/N. In contrast, the energy resolution ε = N S Φ /2L does not depend on N (L is the SQUID inductance) [13]. Therefore, ε in units of Planck s constant h is a more appropriate figure of merit than S Φ if one compares the lowfrequency excess noise in SQUIDs of different designs and configurations. This is plausible if one assumes that the lowfrequency excess flux noise is caused by a large number of fluctuating magnetic field sources on sub-µm scale rather than by a global field across the SQUID loop. In this case, the

2 Paper 3EC01 at ASC20, to appear in IEEE Trans. Appl. Supercond. 21 (2011) 2 excess flux noise density S Φ,1/f increases with the number of contributing field sources (those nearby the Nb lines forming the SQUID loop), i.e., with the perimeter rather than the area of the SQUID loop [9]. As the loop inductance is approximately proportional to the perimeter, the ratio S Φ,1/f /L should remain almost constant. This picture is consistent with our SQUID noise measurements. Furthermore, we observed that our multiloop magnetometers with stripline spokes [4] have a higher low-frequency noise than those with coplanar spokes for the same total SQUID inductance [14]. The long interconnecting striplines pick up a considerable amount of excess flux noise, but do not contribute significantly to the total loop inductance. These devices with atypically high lowfrequency noise were not included in the presented study. Table I describes the selected types of PTB SQUIDs. There are three basic categories: regular sensors used for practical SQUID applications, second stages of integrated two-stage sensors, and special test devices intended for noise investigations (from top to bottom). Results from other groups were also included for comparison (bottom section in Table I). We regarded SQUIDs fabricated with the Nb-Al-AlO x -Nb trilayer technology, for which noise spectra at 4.2 K and mk temperatures were published in the frequency range between Hz and the white noise regime [15]-[17]. In addition, a SQUID with Nb-NbO x -PbIn junctions and a loop made from PbIn was considered [8]. There is a large variety of devices, ranging from small gradiometric 20 ph test SQUIDs with µm diameter loops to double-transformer sensors with 1.05 µh input inductance covering over 1 mm 2 chip area [4]. The PTB C1 device com- TABLE I SQUID TYPES USED FOR THE MILLIKELVIN NOISE STUDY Type Ref. N L/pH T min/mk Description C1 [3] pGrad, slotted-washer design C pGrad, w/o double-transformer C3-C5 [4] pGrad, with double-transformer C4-C5 [4] pGrad, w/o double-transformer C4-C5 [4] sGrad, standard SQUID array C5 [5] sGrad, linearized 2stage array a C5 [5] sGrad, 2 nd stage of 2stage array C4 [4] sGrad, 2 nd stage of 2stage SQUID C sGrad, 2 nd stage of 2stage SQUID C5 [4] sGrad, single current limiter cell C4-C sGrad, opt. bottom Nb uncovered C2 [3] sGrad, SQUID loop in top Nb C sGrad, similar to 2 nd stage cell [8] Magnetometer with PbIn loop b [15] pGrad, multiwasher design [16] pGrad, Quantum Design sensor c Bo09 [17] sGrad, thin-film susceptometer All PTB sensors are designed as gradiometers; the configuration is quoted in short form, e.g., 4pGrad = 4-loop parallel gradiometer or 2sGrad = 2-loop series gradiometer. Unless otherwise noted, the SQUID loop is formed by the bottom Nb and the Nb input/feedback coils are realized on top, separated by a sputtered SiO 2 or Si xn y insulation layer. A range for the minimum operation temperature T min is quoted if devices of same type were operated at different T min. For comparison, four devices reported in literature are included in the study (bottom section of table). a Operated without on-chip linearization (output current feedback). b Sample C1 in [8]; Hz excess noise at 4.2 K determined from 1 Hz value using the quoted frequency dependence S Φ 1/f. c Published 0 mk noise spectrum extrapolated from 20 Hz to Hz. prises four slotted washers with off-washer input coils to minimize stray capacitance. The bottom Nb in the test SQUIDs and SQUID arrays is 6 µm wide to avoid flux trapping when cooling the devices in the Earth field [18]. For the gradiometric 50 ph test SQUIDs, a variant is available where the SQUID loop is kept free from any covering material except in the junction region and loop crossing. We selected the excess noise at Hz as a figure of merit rather than at 1 Hz [8] because this reduces the measurement time and the magnetic shielding requirements. Furthermore, drift effects might become important at low frequencies, e.g., caused by slow variations in the operation temperature. SQUID arrays are more sensitive to such effects than single SQUIDs because environmental noise and temperature fluctuations affect all SQUIDs in an array coherently. This leads to a net effect independent of N, whereas the flux noise density S Φ scales with 1/N. The low-frequency excess noise was determined by fitting the measured overall noise with ε( f ) = ε w + ( f ) = ε w + (1Hz) ( f /Hz) -α (1) and subtracting the resulting white noise level ε w from the measured noise. For simplicity, we use the notation 1/f even if the exponent α differs from 1. For most of our SQUIDs, the measured noise spectra have not been stored during characterization, but rather the noise levels at selected frequencies were read out from the spectrum analyzer display and listed in the SQUID data sheets (typically at 0.1 Hz to 0 khz in factor of ten steps). These lists of noise levels were used to determine the important quantities ε w and α. An example of the achievable fit quality is given in Fig. 1. The fit curves obtained from six noise levels between 1 Hz and 0 khz describe the complete spectra very well. At 4.2 K and high frequencies, becomes uncertain due to the relatively high white noise level. For our study, measurements were considered when noise data between at least Hz and 0 khz were available at mk temperatures. Only low-noise SQUIDs with < 70 h at ε or C214G05 L = 1 ph T = 4.2 K: α = 0.53, ε w = 27.8 h, (1Hz) = 70 h 3 mk: α = 0.70, ε w = 2.3 h, (1Hz) = 490 h 3 mk f / Hz 4.2 K Fig. 1. Noise spectra of a C2 test SQUID operated at 4.2 K and 3 mk. Black lines show the total noise ε, gray lines the 1/f component obtained after subtracting the white noise levels which were determined by fitting the measured noise with (1) at six discrete frequencies between 1 Hz and 0 khz. Dashed lines show the 1/f components of the fit curves.

3 Paper 3EC01 at ASC20, to appear in IEEE Trans. Appl. Supercond. 21 (2011) 3 Hz and 4.2 K were included. The SQUIDs were operated in a flux-locked loop with the XXF-1 readout electronics [19] and a single-stage or two-stage configuration [13]. In the case of single-stage readout (SQUID arrays and a few single SQUIDs), the preamplifier noise contribution was subtracted. In contrast, for two-stage setups no correction was required except for some cases where the second stages degraded the overall low-frequency noise. Here, the 1/f noise contribution from the second stage was subtracted. The second stages of the integrated two-stage devices were measured with the first stages unbiased. Nyquist noise in the bias resistor caused a high excess white noise impeding a precise determination of the 1/f noise contribution at 4.2 K (at mk temperatures there was typically no problem). All available noise data from the selected samples were used for the graphs in Section III. III. RESULTS The measurements at 4.2 K were done by immersing the devices directly into liquid helium. Low-temperature experiments were performed in a 3 He cryostat at about 300 mk, in an adiabatic demagnetization refrigerator around 0 mk, or in a 3 He- 4 He dilution refrigerator down to mk. Environmental noise was suppressed by a superconducting shield except in the case of the dilution refrigerator. Therefore, experiments below 0 mk were restricted to magnetically very insensitive devices (test SQUIDs and SQUID arrays) and frequencies above about Hz where the environmental noise drops below the intrinsic SQUID noise. We are currently designing a magnetic shield for the dilution refrigerator to extend our measuring possibilities. Fig. 2 gives an overview of the low-frequency noise quality of our process in the past six years. At 4.2 K (open symbols in Fig. 2), there was no observable dependence of on the SQUID design or fabrication parameters. In contrast, at mk temperatures (filled symbols) the low-frequency excess noise was significantly higher when the FHR system was involved in the SQUID fabrication. There was only one SQUID with FHR involvement that achieved < 80 h at <320 mk and Hz (marked by an arrow in Fig. 2), whereas all SQUIDs without FHR involvement (triangles in Fig. 2) remained below this limit. Note that the SQUID design, the number of insulation layers (vertical lines in Fig. 2), the large-area anodization of the bottom Nb, and the substrate used (cf. Table II) caused no observable effect on the mk excess noise. Possibly, the relatively low noise of the C2 devices was related to the fact that the SQUID loop was realized in the upper Nb layer. We tested on sample basis that there was no dependence of the low-frequency excess noise on the SQUID bias point, and that the noise was not caused by critical current fluctuations (no improvement by using bias reversal [1]). The lowfrequency noise did not noticeably change between mk and 430 mk. In contrast, the white noise increased slightly at 430 mk compared to mk, consistent with a minimum effective temperature of the shunt resistors of about 300 mk due to the hot-electron effect [20]. The influence of the FHR sputter steps is clearly visible in the distribution of the Hz 1/f noise components (Fig. 3). At 4.2 K, no systematic effect is visible, whereas at <320 mk the 00 0 C1 C2 C3 C4 C5 Bottom Nb anodized Fabrication date Fig. 2. Hz 1/f noise component at 4.2 K (open symbols) and <320 mk (filled symbols) plotted versus fabrication date. The denotation of symbols is given in Table II. The fabrication periods of the sensor versions C1 to C6 are shown at the top of the diagram. The only sensor with Nb or SiO 2 deposition in the FHR system that remained below the 80 h limit (dashed line) at mk temperatures is highlighted by a 45 arrow. Vertical lines mark wafers with two insulation layers on the SQUID loop, horizontal arrows mk measurements of C5 devices without material on the SQUID loop. Large-area anodization of the bottom Nb was used until end of TABLE II DENOTATION OF SYMBOLS USED IN FIGS. 2, 4, 5 Symbol Substrate Bottom Nb Insulation layer Si+SiO 2 FHR SiO 2 (FHR) Si+SiO 2 FHR Si+SiO 2 Alcatel SiO 2 (FHR) Si+SiO 2 Alcatel Si xn y (Alcatel) Si+SiO 2 Alcatel Si+Si 3N 4 Alcatel Si xn y (Alcatel) Al 2O 3 Alcatel The substrates are 3" wafers, commonly silicon with thermally grown oxide (Si+SiO 2). Alternatively, silicon with silicon nitride cover (Si+Si 3N 4) or sapphire (Al 2O 3) were used. distributions move to higher excess noise levels with increasing number of FHR sputter steps. Note that for the last C5 wafer we directly checked that the noise degrades with the number of FHR steps: the 50 ph test SQUIDs without covering material on the SQUID loop (horizontal arrows in Fig. 2) showed a substantially lower mk 1/f noise than the other devices from the same wafer with SiO 2 (two FHR steps). N Sample (a) 4.2 K 0 ( Hz) 0 x FHR 1 x FHR 2 x FHR 0 00 ( Hz) (b) < 320 mk Fig. 3. Number of measured samples N Sample vs. Hz 1/f noise component at (a) 4.2 K and (b) <320 mk. The number of FHR process steps is illustrated by the fill color (white: 0 FHR, gray:1 FHR, black: 2 FHR). C6

4 Paper 3EC01 at ASC20, to appear in IEEE Trans. Appl. Supercond. 21 (2011) f = 1kHz α Fig. 4. Hz (top) and 1 khz (bottom) 1/f noise components at 4.2 K (open symbols) and <320 mk (filled symbols) plotted versus exponent α according to (1). The denotation of symbols is given in Table II, details of literature devices in Table I. Dashed lines show approximation (2). Arrows help to relate outlier data points to the corresponding frequency. The increase in the excess low-frequency noise is accompanied with a rise in the exponent α (see Fig. 4). In semi-log plot, the dependence may be fitted by straight lines, yielding the approximation for the 1/f noise in our SQUIDs 0.09 h ( f /200 khz) -α. (2) Equation (2) is depicted in Fig. 4 by dashed lines; most of the data points lie within a factor of 2 around them. The literature values (stars in Fig. 4) are roughly consistent with our measurements results except for [16] with α 1; possibly, other low-frequency noise sources were involved here. ENR 0 1 (a) Bo09 0 (4.2 K) (b) 0 L / ph Bo09 Fig. 5. Hz ENR plotted versus (a) Hz 1/f noise component at 4.2 K and (b) SQUID inductance L. The denotation of symbols is given in Table II, details of literature devices in Table I. Open symbols mark single SQUIDs (N = 1), filled symbols series SQUID arrays (N = 14 or N = 16). Dashed lines at ENR = 2.8 separate devices without and with FHR sputtering. The excess noise ratio (ENR) is defined here as the ratio of the 1/f noise components at mk temperatures and 4.2 K: ENR = (T min )/ (4.2K). We use it to estimate the mk noise quality of our wafers from SQUID characterization at 4.2 K. Fig. 5 shows that the measured ENRs were below or above 2.8 (dashed lines) for devices fabricated without or with FHR sputtering, respectively. A reasonable agreement between our all Alcatel devices and those reported in literature is found. We could not observe a systematic dependence of the ENR on the absolute 1/f noise level or the SQUID inductance L. There is a trend that the low-frequency noise in SQUID arrays (filled symbols in Fig. 5) is slightly higher than in single SQUIDs (open symbols), presumably caused by variations of the lowfrequency noise performance along the array. The lower limit for our currently achievable mk noise is set by a 50 ph test SQUID of type C6 operated at 16 mk: ε = 0.62 h at 0 khz, increasing to 1.64 h at 1 khz and 14 h at Hz. IV. DISCUSSION The noise behavior of our SQUIDs at mk temperatures is generally consistent with the study by Wellstood et al. [8]. For low-noise devices, similar α values below ⅔ were observed. At 4.2 K, however, Wellstood et al. found true 1/f noise (α 1) which originated from other sources than the mk noise and decreased with temperature [21]. This 4.2 K excess noise is typically not present in our SQUIDs, and α 0.6 is found at 4.2 K as well. Such weak frequency dependences of the 1/f noise above 1 Hz were also observed in literature [22]-[24]. The ENRs of our SQUIDs were above or below 2.8 depending on whether the bottom Nb or insulation layer were fabricated in the FHR instead of the Alcatel system. In the case of the insulation layer, the material involved (SiO 2 vs. Si x N y ) could be of importance; however, the mk noise level observed with SiO [15] or SiO 2 [17] insulation is comparable to that of our SQUIDs with Si x N y insulation. There are two main differences between our sputter systems: (1) the Alcatel system uses a diffusion oil pump with a liquid Nitrogen trap, whereas the FHR system is equipped with a turbo molecular pump resulting in a higher water content in the sputter chamber, and (2) the FHR system is dimensioned for substantially higher deposition rates than the Alcatel system. We are currently modifying the FHR system to obtain lower deposition rates. Further noise investigations are planned. Our hope is to find the reason for the increase in the low-frequency noise caused by the FHR system, and to learn from that how to modify the fabrication process for minimum noise at mk temperatures. ACKNOWLEDGMENT The authors thank Cornelia Aßmann, Marianne Fleischer, Alexander Kirste and Frank Ruede for SQUID characterization at 4.2 K, Marcel Scheuerlein and Franz Müller for fabrication of wafer C602, and Marco Schmidt for operation of the dilution refrigerator. The low-temperature noise measurements of sensor C509U33A were performed at the University of Zaragoza by María José Martínez-Pérez, and those of C423- F33A at the University of Heidelberg by Jan-Patrick Porst.

5 Paper 3EC01 at ASC20, to appear in IEEE Trans. Appl. Supercond. 21 (2011) 5 REFERENCES [1] J. Clarke and A. I. Braginski, Eds. The SQUID Handbook, Weinheim: WILEY-VCH, 2004, Vol. I. [2] D. Drung, C. Aßmann, J. Beyer, M. Peters, F. Ruede, and Th. Schurig, dc SQUID readout electronics with up to 0 MHz closed-loop bandwidth, IEEE Trans. Appl. Supercond., vol. 15, pp , June [3] D. Drung, C. Hinnrichs, and H.-J. Barthelmess, Low-noise ultra-highspeed dc SQUID readout electronics, Supercond. Sci. Technol., vol. 19, pp. S235-S241, May [4] D. Drung, C. Aßmann, J. Beyer, A. Kirste, M. Peters, F. Ruede, and Th. Schurig, Highly sensitive and easy-to-use SQUID sensors, IEEE Trans. Appl. Supercond., vol. 17, pp , June [5] D. Drung, J. Beyer, M. Peters, J.-H. Storm, and Th. Schurig, Novel SQUID current sensors with high linearity at high frequencies, IEEE Trans. Appl. Supercond., vol. 19, pp , June [6] K. D. Irwin and G. C. Hilton, Transition-edge sensors, in Cryogenic Particle Detection, C. Enss, Ed. Berlin: Springer-Verlag. 2005, pp [7] A. Fleischmann, C. Enss, and G. M. Seidel, Metallic magnetic calorimeters, in Cryogenic Particle Detection, C. Enss, Ed. Berlin: Springer-Verlag. 2005, pp [8] F. C. Wellstood, C. Urbina, and J. Clarke, Low-frequency noise in dc superconducting quantum interference devices below 1 K, Appl. Phys. Lett., vol. 50, pp , March [9] R. H. Koch, D. P. DiVincenzo, and J. Clarke, Model for 1/f flux noise in SQUIDs and Qubits, Phys. Rev. Lett., vol. 98, p , June [] R. de Sousa, Dangling-bond spin relaxation and magnetic 1/f noise from the amorphous-semiconductor/oxide interface: Theory, Phys. Rev. B, vol. 76, p , December [11] S. Sendelbach, D. Hover, M. Mück, and R. McDermott, Complex inductance, excess noise, and surface magnetism in dc SQUIDs, Phys. Rev. Lett., vol. 3, p , September [12] S. Choi, D.-H. Lee, S. G. Louie, and J. Clarke, Localization of metalinduced gap states at the metal-insulator interface: Origin of flux noise in SQUIDs and superconducting Qubits, Phys. Rev. Lett., vol. 3, p , November [13] D. Drung, Advanced SQUID read-out electronics, in SQUID Sensors: Fundamentals, Fabrication and Applications, H. Weinstock, Ed. Dordrecht: Kluwer, 1996, NATO ASI Series, Vol. E329, pp [14] D. Drung, S. Knappe, and H. Koch, Theory for the multiloop dc superconducting quantum interference device magnetometer and experimental verification, J. Appl. Phys., vol. 77, pp , April [15] P. Carelli, M. G. Castellano, G. Torrioli, and R. Leoni, Low noise multiwasher superconducting interferometer, Appl. Phys. Lett., vol. 72, pp , January [16] R. Mezzena, A. Vinante, P. Falferi, S. Vitale, M. Bonaldi, G. A. Prodi, M. Cerdonio, and M. B. Simmonds, Sensitivity enhancement of Quantum Design dc superconducting quantum interference devices in two-stage configuration, Rev. Sci. Instrum., vol. 72, pp , September [17] S. T. P. Boyd, V. Kotsubo, R. Cantor, A. Theodorou, and J. A. Hall, Miniature thin-film SQUID susceptometer for magnetic microcalorimetry and thermometry, IEEE Trans. Appl. Supercond., vol. 19, pp , June [18] G. Stan, S. B. Field, and J. M. Martinis, Critical field for complete vortex expulsion from narrow superconducting strips, Phys. Rev. Lett., vol. 92, , March [19] XXF-1 electronics, Magnicon GmbH, Lemsahler Landstraße 171, D Hamburg, Germany; [20] F. C. Wellstood, C. Urbina, and J. Clarke, Hot-electron effect in metals, Phys. Rev. B, vol. 49, pp , March [21] F. C. Wellstood, C. Urbina, and J. Clarke, Excess noise in dc SQUIDs from 4.2 K to K, IEEE Trans. Magn., vol. MAG-23, pp , March [22] D. D. Awschalom, J. R. Rozen, M. B. Ketchen, W. J. Gallagher, A. W. Kleinsasser, R. L. Sandstrom, and B. Bumble, Low-noise modular microsusceptometer using nearly quantum limited dc SQUIDs, Appl. Phys. Lett., vol. 53, pp , November [23] M. Ketchen, D. J. Pearson, K. Stawiasz, C.-K. Hu, A. W. Kleinsasser, T. Brunner, C. Cabral, V. Chandrashekhar, M. Jaso, M. Manny, K. Stein, and M. Bhushan, Octagonal washer dc SQUIDs and integrated susceptometers fabricated in a planarized sub-µm Nb-AlO x-nb technology, IEEE Trans. Appl. Supercond., vol. 3, pp , March [24] L. Hao, J. C. Macfarlane, J. C. Gallop, D. Cox, J. Beyer, D. Drung, and T. Schurig, Measurement and noise performance of nanosuperconducting-quantum-interference devices fabricated by focused ion beam, Appl. Phys. Lett., vol. 92, p , May 2008.