Integrated dc SQUID magnetometer with a high slew rateFrederick Wellstood, C. Heiden, and John Clarke Citation: Review of Scientific Instruments 55, 952 (1984); doi: 10.1063/1.1137871 View online: http://dx.doi.org/10.1063/1.1137871 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/55/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in High slew rate, ultrastable direct-coupled readout for dc superconducting quantum interference devices Appl. Phys. Lett. 89, 063502 (2006); 10.1063/1.2335630 Four layer monolithic integrated high T c dc SQUID magnetometer Appl. Phys. Lett. 64, 3497 (1994); 10.1063/1.111252 Magnetic hysteresis in thin film dc SQUID magnetometers Appl. Phys. Lett. 61, 3190 (1992); 10.1063/1.107955 Monolithic 77 K dc SQUID magnetometer Appl. Phys. Lett. 59, 3051 (1991); 10.1063/1.105790 Compact integrated dc SQUID gradiometer Appl. Phys. Lett. 41, 669 (1982); 10.1063/1.93608

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Integrated de SQUID magnetometer with a high slew rate Frederick Wellstood, C. Heiden,a) and John Clarke

Department 0/ Physics, University o/California, Berkeley, California 94720 and Materials and Molecular Research Division. Lawrence Berkeley Laboratory, Berkeley, California 94720

(Received 13 December 1983; accepted for publication 13 February 1984)

We have fabricated a magnetometer in which the thin-film superconducting pick-up loop and dc SQUID are integrated on a single silicon chip. The magnetometer, which is intended primarily for geophysical applications, has a magnetic field sensitivity of typically 5 X 10- 15 T Hz- 1/2 at frequencies above about 10 Hz, and 2X 10- 14/(/11 HZ)I/2 T Hz- 1I2 at lower frequencies. The dynamic range is ± 2x 107

HZl/2 and the maximum slew rate is about 4X 10- 3 T S-I at 6 kHz. This high slew rate enables the magnetometer to be operated in a flux-locked loop for long periods of time without losing lock.

PACS numbers: 07.55. + x, 85.25. + k

INTRODUCTION

For a number of years we have used cylindrical I dc SQUIDs2

(superconducting quantum interference devices) as magne­tometers for geophysical applications, particularly for mag­netotelluric measurements. 3 The SQUID is flux modulated at 100 kHz and is operated in a flux-locked 100p,I.2 the out­put of which is proportional to the change in the applied magnetic field. These devices have proven to be highly reli­able, and their sensitivity, typically 10 IT Hz- 1/2 at frequen­cies above about 10-2 Hz, has been more than adequate. However, the slew rate of the cylindrical SQUID is limited by the associated electronics to about 105 et>o s-" where et>o=h 12e is the flux quantum. Since the area of the SQUID is about 7 mm2, a magnetic field of 0.3 nT is required to generate one flux quantum and the maximum slew rate of the applied magnetic field is about 30 flT s - I. This slew rate is adequate for most normal applications. However, occa­sional "sferics" can cause the system to unlock. The fluctu­ations are typically 1 nT in magnitude and extend up to fre­quencies of 10 kHz, producing a maximum rate of field change of 100 flT s -I. The frequency with which unlocking occurs can vary from less than once a day to once every few minutes, depending on the level of electrical activity. Gener­ally speaking, the system cannot be used if unlocking occurs more often than once an hour. We have sometimes found it necessary to attenuate the sferics by placing a copper cylin­der around the cryostat to act as a low-pass filter. We found that a shield with a roll-off frequency of about 50 Hz enabled us to operate the SQUID under almost any conditions. How­ever, the Nyquist noise in the shield limited the sensitivity above 1 Hz to about 100 IT Hz-1I2. This loss of sensitivity has undesirable consequences in certain types of measure­ment.4

To overcome these limitations, we have developed a new magnetometer. Its magnetic field sensitivity is compara­ble with that of the cylindrical SQUID, and its maximum slew rate with respect to magnetic field has been increased by a factor of about 200. The magnetometer was designed around an existing planar SQUID5.6 with a spiral input coil,7

and incorporates a thin-film pick-up loop that is deposited on the same chip as the SQUID. The increase in slew rate

was achieved both by improving the electronics and by in­creasing the sensitivity of the SQUID. First, the flux modu­lation frequency was increased to 500 kHz, and a two-pole integration circuit was used in the electronics. 8 Second, be­cause the flux sensitivity is an order of magnitude greater than that of the cylindrical SQUID, one is required to couple in an order of magnitude less flux to achieve a given magnet­ic field sensitivity. Although the precise details ofthe super­conducting input circuit and two-pole integrator are specific to our particular SQUID, the design could readily be adapt­ed to make it suitable for any thin-film planar dc SQUID that has efficient magnetic coupling between the input coil and the SQUIDYO-I4

In Sec. I we describe the design and fabrication of the SQUID, and in Sec. II we outline the associated electronics. We discuss the performance in Sec. III.

I. SQUID

The configuration of the magnetometer is shown in Fig. 1, and its parameters are summarized in Table I. The design was chosen to provide a sensitivity of at least 10 IT Hz - 1/2 at frequencies where the noise from the SQUID is white. The planar,6 SQUID is tightly coupled to a 20-tum6 thin-film niobium input coil of inductance L i ::::: 120 nH that is con­nected to a single-tum pick-up loop. This loop has an areaAp

of 47 mm2 and an estimated inductance Lp of about 36 nH. The dimensions of the loop were limited by the available area on the chip and by the field of view of the projection mask aligner, The inductance is somewhat below the value for op­timum sensitivity. IS To estimate the sensitivity of the magne­tometer, we assume that the magnetic field to be detected /jB is applied only to the pick-Up loop. The resulting flux change in the SQUID /jet> is related to tiB by2

tJB = [(Li + Lp)/ApM;]tJet>, (1)

where Mi = a(LLi )1/2 is the mutual inductance between the input coil and the SQUID. In practice, Eq. (1) will be modi­fied slightly because the applied magnetic field also threads the spiral coil and the SQUID. However, we estimate this correction to be no more than 5%, and we neglect it. Equa­tion (1) predicts that the applied magnetic field required to

952 Rev. Sci. Instrum. 55 (6), June 1984 952

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(0)

Nb CONTACT

PAD

(b)

Imm f---i

Nb .

100,um 0-----;

(c)

PICKUP LOOP

SQUID

Si CHIP

I I

0 ---20 Turn

Nb Input Coil

Windows In SiO

't --~-Pb

\ CuAu Shunts

L-

~

Nb

/ Pb

FIG. I. Design of magnetometer: (a) pick-up loop coupled to the SQUID, (b) layout of the SQUID and input coil, and (c) expanded view of the dotted circle in (b) showing details of the junctions and resistive shunts.

induce one flux quantum in the SQUID is 1.15 nT. The rms value of the equivalent magnetic field noise

S j(2 in the pick-up loop is found approximately by replacing 8<P with S :£2, where S<t>(f) is the spectral density of the equivalent flux noise of the SQUID. 16 Using a typical value5

of S:£2:::;:4X 10-6 <Po Hz- I12, we obtain Sj(2

TABLE I. Typical parameters of SQUID magnetometer.

SQUID inductance L Critical current per junction 10 Shunt resistance per junction R Number of turns on input coil N Inductance of input coil L, Mutual inductance between input coil and SQUID M, Inductance of pick-up loop Lp Area of pick-up loop Ap

953 Rev. Sci. Instrum., Vol. 55, No.6, June 1984

400 pH IOILA Sil

20 120nH

6nH 36nH 47mm2

:::;:5 X 10- 15 T Hz- l12 in the white noise region, a value about a factor of 2 better than required.

The magnetometers were fabricated in batches of nine on 50-mm-diam oxidized silicon wafers (see Fig. I). The pho­toresist patterns were exposed with a Canon projection mask aligner. The steps in the fabrication were as follows: After preparing a suitable pattern, a 30-nm film of Au (25 wt. % CuI was deposited and lifted off; this film forms the shunt resistors. Next, a 200-nm film of Nb was sputtered, patterned to form the body of the SQUID and the connect­ing strip to the inner end of the spiral coil, and etched in a SF 602 plasma. Photoresist was patterned for the first SiO insulation layer, leaving two 2-f.lm square windows for the junctions, two 5-f.lm square windows to provide access to the end of the connecting strip, and one lOX 5f..lm window for contact to the AuCu. A 200-nm SiO film was then deposited and lifted off; the process was repeated to produce a second, 300-nm SiO film. We have found that the two separate pro­cesses appear to give improved step coverage, and better in­surance against pinholes. Next, photoresist was patterned for the pick-up coil, the SQUID contacts, and a square that later became the input coil. A 200-nm Nb film was sputtered and lifted off. Another photoresist layer was patterned for the 20-turn input coil which was then plasma etched from the square deposited earlier. The next layer of photoresist was patterned for the counterelectrode. At this point, the wafer was diced into nine chips approximately 10 X 10 mm, each of which was subsequently processed individually. The junctions and exposed AuCu were ion milled and the junc­tions oxidized in a rf plasma discharge in an Ar-02 mixture. A 200-nm film ofPb (5 wt. % In) was deposited and lifted off, and finally, a 200-nm SiO film was deposited to provide pas­sivation. Typical parameters of the SQUIDs are listed in Table I.

The SQUID was mounted in a fiberglass holder just above a 1O-turn coil of niobium wire that provides feedback, ac flux modulation, and dc offset. Two pieces of niobium foil were pressed onto the niobium pads of the SQUID to pro­vide electrical contact. To measure the intrinsic noise of the magnetometer, the fiberglass mount was inserted into a Pb tube, while for use as a magnetometer, the device was un­shielded. In either case the device was immersed directly in liquid helium.

II. ELECTRONICS

The electronics, of which a schematic appears in Fig. 2, is based on an earlier design, I upgraded to improve the fre­quency response and slew rate. The major improvements are the use of wideband transformers to couple the SQUID to the preamplifier, an increase in the flux modulation frequen­cy from 100 to 500 kHz, and the use of a two-pole integration circuit. The operation of the electronics is conventional. A 500-kHz square-wave modulation flux with a peak-to-peak amplitude of <PoI2 is applied to the SQUID. When the quasi­static flux applied to the SQUID is exactly n<Po or (n + 11 2)<Po (n is an integer), the resulting voltage across the SQUID consists of a square wave at 1 MHz. When this signal is lock­in detected at 500 kHz, the mean-output voltage will be zero. If one now applies a small additional flux 8<P «<Po) to the

de SQUID magnetometer 953

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BIAS CURRENT

PREAMPLIFIERr __ _

T, x/iO

X 40

,--- -a'5"---~L----'J\H PHASE

- SHIFTER ~ ZERO OFFSET

AM:L:FIE i R, t1--~ I ~ R"R] FRE:r lJ~ R',_

V -=-,' Xl. FEEDB<\CK J 4

OUTPUT ON/OFF + -~ + 1_ R', L-_--'

TWO-POLE INTEGRATOR -

MIXER

AMPLIFIER

X 35

VARIABLE GAIN

AMPLIFIER

x 0- 40

FIG. 2. Electronics for feedback operation of magnetometer. The following component values were used: Mf = 80 pH, Rf = 5 kn, R, = 0.7 n, R2 = 100 n, C2 = 2 nF, R ~ = 20 kf.!, R3 = 1.1 Mn, C3 = 180 pF, R; = II kf.!.

SQUID, there will be a component at 500 kHz across the SQUID, with magnitude and phase depending on the magni­tude and sign of 8<P. When this signal is lock-in detected, there will be a nonzero average output that is proportional to 8<P and that has a maximum amplitude when the total ap­plied flux is (n ± 1I4)<Po. The signal from the lock-in stage is amplified, passed through an integrator, and fed back to flux lock the SQUID.

In order to achieve low system noise, it is necessary to present an optimum impedance to the preamplifier. To de­termine the optimum source impedance and noise tempera­tue of the preamplifier, we connected a parallel LCR tuned circuit, resonant near 500 kHz and cooled to 4.2 K, across the input. We measured the noise at the out of the preampli­fier as a function of the impedance of this circuit, which we varied by changing the value of the parallel resistance. The optimum source resistance was between 1.5 and 2 kil, and the corresponding noise temperature was about 26 K. Since the dynamic resistance of the SQUID at its optimum bias point is about 8 n, one requires a coupling circuit with an impedance transformation of about 200. In addition, the bandwidth should be as large as possible. The requirement of large bandwidth precludes the use of a cooled resonant LC circuit. Similarly, we have found that the bandwidth of a single, cooled transformer is too small because of the pres­ence of stray capacitance between the leads coupling the sec­ondary of the transformer to the preamplifier. To overcome these difficulties, we have used two different coupling cir­cuits, both of which performed satisfactorily.

The first arrangement involved a room-temperature transformer consisting of 5 turns of # 16 copper wire and 110 turns of #24 copper wire as the primary and secondary coils, wound on a Ferroxcube 4C4-AlOO core. The induc­tance of the primary coil was about 2.5JLH. It was necessary to use low-resistance leads between the SQUID and the pri­mary coil to avoid significant degradation of the sensitivity because of the additional resistance and Nyquist noise in these wires. However, the rather thick leads necessary (15 strands of #34 Cu) gave an undesirably high rate of helium boil off in a field system designed for low helium loss. To overcome this difficulty, we developed a second coupling system with two transformers, one cooled and one at room

954 Rev. Sei.lnstrum., Vol. 55, No.6, June 1984

temperature. The cooled, superconducting transformer con­sisted of 62 and 280 turns of 50-JLm-diam niobium wire for the primary and secondary coils, respectively, wound on a 6-mm-diam fiberglass former. The primary inductance was about 10 JLH. This transformer reflected a SQUID imped­ance of about 160 n into the secondary circuit, a value sub­stantially below the shunting impedance of the cable due to stray capacitance, roughly 5 kil at 500 kHz. The primary and secondary coils for the room-temperature transformer consisted of39-1I2 and 125 turns, respectively, of #26 cop­per wire wound on a Ferroxcube 4C4-A60 core. The pri­mary inductance was about 94JLH. In the absence of losses, the combined impedance transformation ratio of the two transformers was about 200. To prevent the primary coil of the cold transformer from shorting out the SQUID at low frequencies, we inserted a resistance Rs of about 0.7 n (Fig. 2).

We turn now to a brief discussion of feedback and slew rate. The open-loop gain of the system can be written in the form

(2)

where V<t> is the flux-to-voltage transfer coefficient of the SQUID, GA (w) is the gain of the transformers, amplifiers, and mixer, G[ (w) is the gain of the integrator, Mf is the mutu­al inductance of the feedback coil and SQUID, and Rf is the feedback resistance. When the feedback switch is closed, a flux <P (w) applied to the SQUID gives rise to a feedback flux

<Pf(w) = <P(w)G(w)/[ 1 + G(w)].

Thus, the small-signal frequency response of the system is given by

(3)

where Vo(w) is the output voltage. The error flux at the SQUID in the presence of a flux <P is

<Pe <P - <Pf = <PriG (w).

Because the loop will become unlocked if the error flux ex­ceeds <P0I4, the value at which the output from the integra­tor is a maximum, one finds a maximum slew rate

(p;ax = w<P ;ax-;::::,G (w)w<Po/4. (4)

This result is valid provided that the feedback amplifier does not saturate. We note that (p 'fax corresponds to a rate of change in the applied flux of

(pmax = [1 + G(w)]w<P0I4.

For an unlocked SQUID, (Pmax = w<Po/4, so that one has increased the slew rate of the applied field by a factor of (1 + G) by using feedback.

Clearly, to achieve the highest possible slew rate it is necessary to use the largest value of G (w) for which the feed­back system remains stable. At a sufficiently high frequency, the phase shifts introduced by the integrator and other cir­cuit elements cause the feedback to become positive, result­ing in an upper limit to the gain for stable operation. As has been demonstrated by Giffard,9 a considerable improvement in the slew rate at lower frequencies can be achieved by intro­ducing a second pole into the integrator. The gain of the integrator is then of the form

de SQUID magnetometer 954

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I02L...,-___ -'-A-___ ,O-___ '-;:;-__ -..J

10-1 100 101 102 10 3 FREQUENCY (kHz)

FIG. 3. Open-loop gain I G (ev)! determined from the measured low-frequency gain and the calculated response of the two-pole integrator (solid line). The measured effect of the transformer resonance is also shown (dashed line).

(5)

where A is a real positive constant, liJl is the frequency at which IG (liJ)1 falls to unity, liJ2~liJ1/4 for maximum stable gain, and liJ3<liJ2• The second pole allows one to obtain larger values of G (liJ) at frequencies below liJ2 and, hence, to achieve a higher slew rate than is possible with a single pole. In prac­tice, as we shall see, the frequency dependence of the gain introduced by other circuit components ultimately limits the slew rate by imposing an upper bound on liJ I.

III. PERFORMANCE

The open-loop gain and the parameters of the two-pole integrator were varied empirically to obtain the maximum possible slew rate. At this maximum rate, however, we ob­served excess noise, indicating that the system was about to become unstable. Thus, for all of our subsequent measure­ments, the gain was reduced somewhat until no excess noise was observed. To enable us to compare the measured fre­quency response and slew rate with the values expected from the open-loop gain, we determined G (liJ). Figure 3 shows our estimate ofG (liJ) from the measured low-frequency gains and the calculated response of the integrators. In addition, we have plotted the measured effect of the transformer reso­nance which produces a deviation from the 1/ liJ2 dependence near 100kHz and a small peak near 400 kHz. Note that these contributions have been mixed down from frequencies 500

TABLE II. Measured performance of SQUID magnetometer.

1.32 nT

kHz higher: The actual resonance frequency of the trans­former is at about 900 kHz. The value of liJ2/21T' determined by the integrator, about 800 kHz, plays no significant role in the response ofthe amplifier. The noise, dynamic range, fre­quency response, and slew rate were determined with these circuit parameters. The performance is summarized in Table II.

To calibrate the magnetometer, we measured its re­sponse to a known external magnetic field in the absence of a superconducting shield. The magnetic field required to pro­duce one flux quantum in the SQUID was 1.32 nT, a value within 15% of the value predicted from Eq. (1).

Figure 4 shows the spectral density of the flux noise of the SQUID in a superconducting shield. The noise is white at frequencies above about 10 Hz, and corresponds to a rms flux noise of about 3.8 X 10-6 <poHz-1I2. This value is some­what higher than the value predicted2

(18kB TR<P ~)1I2~2X 10-6 <Po Hz- I 12,

for the parameters listed in Table I. This discrepancy arises largely from the preamplifier noise. At frequencies below about 10 Hz, the spectral density of the noise varies approxi­matelyas 1/J, wherefis the frequency. The spectral density is approximately [2XIO- IO/(j/l Hz)]<P~ HZ-I, a value that is consistent with observations on our other dc SQUIDs. 17 The fact that the 1/fnoise is not noticeably af­fected by the presence of the magnetometer pick-up loop, which greatly increases the magnetic field sensitivity of the SQUID, rules out the possibility that the noise is generated by the motion of flux pinned in the superconducting shield. This result is in accord with our earlier observations. 17 The corresponding magnetometer sensitivity is shown on the right-hand axis, and is about 5 IT Hz- 1

/2 in the white-noise region. We note that the 1/fnoise of the magnetometer is actually higher than that of the cylindrical SQUID.

The maximum low-frequency flux that could be applied without causing the electronics to saturate was ± 78 <Po. The dynamic range was thus ± 2x 107 H z l/2 in the white­noise region. The maximum allowed flux could be altered by changing the value of the feedback resistor RI .

We determined the frequency response of the shielded, flux-locked SQUID by applying a small alternating flux and measuring the signal at the output of the electronics as a function offrequency. The measured response (Fig. 5) is ap­proximately flat to 80 kHz, peaks at about 150 kHz, and falls rapidly above 600 kHz. The frequency response predicted from G (liJ) including only the frequency dependence of the

Magnetic field to generate 4>0

rms flux noise of SQUID. S !t2(/) {

4X 10-0 4>0 Hz- ' /2 (/> 10Hz)

l.4x 10- 5/(//1 Hz)'/2 4>0 Hc l/2 (/ < 10Hz)

rms field sensitivity, S 1"2(/)

Dynamic range (/ < 6 kHz) Frequency response ( ± 3 dB)

Maximum slew rate (6 kHz)

{5X 10-15 T Hz- 1/2 (f> 10Hz)

2X 10- 14/(/11 Hz)'/2 T Hz-1I2 (/ < 10 Hz)

± 2x 107 Hz'/2 70kHz

{3XI06 4> S-I 4XIO-3~S-'

955 Rev. Sci. Instrum., Vol. 55, No.6, June 1984 de SQUID magnetometer 955

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-10 'N 10 I

~ ~16" if)

2

5

-12 1010~0~---IO~I'----IO~2~---IO~3'---~104

FREQU ENCY (Hz)

I-

FIG. 4. Spectral density of flux noise (left-hand ordinate) in the flux-locked SQUID when it is in a superconducting shield at 4.2 K. Right-hand ordin­ates shows corresponding rms value of magnetic field noise in the magne­tometer.

two-pole integrator (solid line) diverges near 100 kHz. To approximate the frequency response of the transformer, we introduce a frequency tiJ2/21T = 120 kHz (see Fig. 3) above which the gain is assumed to roll off as 1/ tiJ. The frequency response predicted from this form of G (tiJ) is also shown in Fig. 6. Although the divergence has been removed, the mea­sured closed-loop gain still differs significantly from the pre­diction above 100kHz. We believe this extended frequency response arises from additional closed-loop gain produced by the mixer as the signal frequency approaches 500 kHz. Moreover, the rapid roll off above 600 kHz indicates a large additional phase shift, and suggests that the system would become unstable for a slight increase in the overall gain.

The slew rate was determined from the maximum sinu­soidal flux, (/)f sin tiJt, that could be fed back without causing the system to unlock. Figures 6 and 7 show (/)f and tiJ(/)f vs frequency. The maximum slew rate tiJ(/)f occurs at about 6 kHz and is approximately 3 X 106 (/)0 S -1. At frequencies be­low 6 kHz, the slew rate is limited by the dynamic range of the system. At higher frequencies, (/)f falls off as 1/tiJ2

, as expected, flattening out at about 50 kHz as the transformer resonance and mixer response begin to contribute. The slew rates predicted from G (eu) with and without the transformer contribution are also shown; as with the frequency response,

o - 10 1-----------<><--(3 +

-2 10 '--__ -"--__ -'-__ -'-:c __ -'-::_'

10-1 100 10' 10 2 103

FREQUENCY (kHz)

FIG. 5. Measured frequency response (solid line through open circles) of shielded, flux-locked SQUID. Solid curve shows response predicted from G(aI) without transformer resonance. Dashed line is predicted from G(aI) with transformer resonance, modeled by G (aI) <X II UJ2(UJ < UJ;).

<X I/UJ(w > aI;).

956 Rev. Scl.lnstrum., Vol. 55, No.6, June 1984

I 010

$

]

FIG. 6. Maximum amplitude of sinusoidal flux <PJ that can be fed back with­out causing system to saturate or break lock (solid line through open circles). Solid and dashed lines are predictions from G (UJ) as in Fig. 5.

the prediction deviates markedly from the measured curve above about 100 kHz.

As a practical test ofthe magnetometer, we operated it without a superconducting shield both in our laboratory and in the open, about 50 m away from the nearest building. To screen out interference from radio and television stations, we enclosed the cryostat in #40, 250-pm-thick copper mesh. The ambient magnetic field fluctuations in the laboratory tests were dominated by 60-Hz oscillations, typically 10 -7 T peak-to-peak, with odd harmonics readily visible out to 5 kHz. During daytime operation in the laboratory, we found that the magnetometer typically lost lock several times per day. We believe that this unlocking was induced by switch­ing transients from the departmental machine shop, which is situated directly below our laboratory. However, the magne­tometer would always remain locked in overnight, when the machine shop was closed. During one of the overnight tests, we experienced a local thunderstorm in which we observed nearby (- 2 km) cloud-to-cloud lightning. "Dim" flashes produced an output spike from the magnetometer, which did not unlock, but "bright" flashes always caused the mag­netometer to unlock. During daytime operation outside the building over a period of 4 h the only unlocking event oc­curred when a walkie-talkie was operated in close proximity. Thus, we feel that during field operation under normal con­ditions the magnetometer is likely to remain locked in throughout an entire day of data taking. However, local thunderstorms of moderate severity are almost certain to cause the magnetometer to unlock.

,. N

106 I

0

-&

,e; 10

5 3

104L...J'---'---'-:--"---'-..L--'---'---'-::-'-:c--'--'-::_' 10-1 100 101 103

FREQUENCY

FIG. 7. Slew rate aI<PJ vs frequency (solid line through open circles). Solid and dashed lines are predictions from G (UJ) as in Fig. 5.

de SQUID magnetometer 956

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ACKNOWLEDGMENTS

We would like to thank Claude Hilbert for his generous assistance with the fabrication of the magnetometer, and Wolfgang Goubau for many helpful discussions. We thank John Davis and LeVern Garner for their expert assistance in the design and fabrication of the electronics. C. H. would like to thank the Deutsche Forschungsgemeinschaft for a travel grant. We acknowledge the use of the Microelectron­ics Facility in the Electronics Research Laboratory of the Electrical Engineering and Computer Science Department, U. C. Berkeley. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U. S. Department of En­ergy under Contract No. DE-AC03-76SFOOO98.

"On sabbatical leave from the University of Giessen, West Germany. II. Clarke, W. M. Goubau, and M. B. Ketchen, I. Low Temp. Phys. 25, 99 (1976).

2For a review see, for example, I. Clarke, in Superconductor Applications: SQUIDs and Machines, edited by B. B. Schwartz and S. Foner (Plenum, New York, 1977), p. 67; IEEE Trans. Electron. Devices ED-27, 1896 (1980).

'I. Clarke, T. D. Gamble, W. M. Goubau, R. H. Koch, and R. F. Miracky, Geophys. Prospect. 31, 149 (1983).

'w. M. Goubau, P. M. Maxton, R. H. Koch, and I. Clarke, Geophysics (April 84).

957 Rev. Sci. Instrum., Vol. 55, No.6, June 1984

'J. M. Martinis, and I. Clarke IEEE Trans. Magn. MAG-19, 446 (1983). 6C. Hilbert, and I. Clarke Appl. Phys. Lett. 43, 694 (1983). 7M. B. Ketchen and J. M. Jaycox, Appl. Phys. Lett. 40, 736 (1982). 8 A dc SQUID with a two-pole integrator is commercially available from S. H. E. Corporation. Giffard (Ref. 9) has described a SQUID with a two­pole integrator in the feedback loop.

9R. P. Giffard, in Superconducting Quantum Interference Devices and their Applications, edited by H. D. Hahlbohm and H. Lubbig (Walter de Gruyter, Berlin, 1980), p. 445.

10M. W. Cromar and P. Carelli, Appl. Phys. Lett. 38, 723 (1981). lip. Carelli and Y. Foglietti, J. Appl. Phys. 53, 7592 (1982); IEEE Trans.

Magn. MAG-19, 299 (1983). 12B. Muhlfelder, W. Johnson, and M. W. Cromar, IEEE Trans. Magn.

MAG-19, 303 (1983). 131. F. Gamier, J. C. Yillegier, D. Duret, and A. Regent, IEEE Trans.

Magn. MAG-19, 591 (1983). l4y. I. de Waal, T. M. Klapwijk, and P. van den Hamer, I. Low. Temp.

Phys. 53, 287 (1983). "I. Clarke, C. D. Tesche, and R. P. Giffard, 1. Low Temp. Phys. 37, 405

(1979). 16We have made two approximations. First, strictly speaking, one should

use the value of S (I) appropriate for the SQUID in the presence of the input circuit. However, measurements on similar SQUIDs have indicated that the error resulting from the use of the values for the bare SQUID is small. Second, one should include a term for the current noise in the SQUID, which produces an additional noise contribution (see Ref. IS). However, because the inductance of the input coil is below the value for optimum sensitivity, this contribution is relatively small, and we shall neglect it.

I7R. H. Koch, I. Clarke, W. M. Goubau, I. M. Martinis, C. M. Pegrum, and D. I. Van Harlingen, J. Low Temp. Phys. 51, 207 (1983).

de SQUID magnetometer 957

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