1800 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 3, NO.l, MARCH 1993

A HIGH PERFORMANCE INTEGRATED DC SQUID MAGNETOMETER

R. Canto8 and K. Enpukub) Physikalisch-Technische Bundesanstalt

Abbestr. 2-12, W-lo00 Berlin 10, Germany

T. Ryhhenc) and H. Seppa Metrology Research Institute

Technical Research Center of Finland and Helsinki University of Technology

Otakaari 7B, SF-02150 Espoo, Finland

Abstract-We have carried out extensive mappings of the dc characteristics and flux noise of an integrated, dc supercon- ducting quantum interference device magnetometer as functions of bias current and applied flux. The open-loop white flux noise at 1 kHz measured without flux modulation @n < 7 X lo-’ eo/* throughout a broad region of operation where the current-voltage and voltage-flux characteristics are smooth. The corresponding flux density noise Bn < 4 ff/a. We have also used a recent model of the coupled dc SQUID to calculate the frequency- dependent impedance Zct) seen by the Josephson junctions. The peaks observed in 20 are shown to be consistent with features in the current-voltage characteristics at high bias currents.

this paper, we present the results of extensive mappings of the dc characteristics and flux noise of this magnetometer as a functions of bias current and applied flux. These results show that, by carefully optimizbg the SQUID design, smooth characteristics and very low noise can be achieved throughout a broad region of operation.

We have also calculated the frequency-dependent impedance Zu> seen by the Josephson junctions using a recently developed model of the coupled dc SQUID.[8] We show that the peaks in Zct) are consistent with features observed in the magnetometer I-V characteristics at high bias currents.

11. MAGNETOMETER DESIGN AND FABRICATION I. INTRODUCTION

The dc superconducting quantum interference device (SQUID) is the most sensitive detector of magnetic flux available. Since the SQUID inductance is usually very low, practical applications often require coupling the SQUID to a much higher inductance pick-up coil. This is usually ac- complished by making the SQUID inductance in the shape of a square washer with an integrated, multiturn input coil on top.[l]. Excellent coupling to the SQUID can be achieved in this way, but a parasitic capacitance is intro- duced across the SQUID inductance which can cause a sizable deterioration of the SQUID energy resolution.[2,3] The input coil and the SQUID washer as ground plane also form a microwave transmision line which can have high-Q resonances near the intended operating frequency of the SQUID; conversely, the Q-value of the half-wavelength res- onance of the washer is enhanced by the groundplane effect of the input coil.[4] These high-Q resonances couple to the SQUID dynamics and produce strong irregularities in the current-voltage (I-V) and voltage-flux (V4) characteristics: the SQUID noise is significantly increased and it may become difficult to find a suitable working point for proper operation of the SQUID.[3,4] We have designed a dc SQUID magnetometer[5] that is integrated on a 4x4 mm2 chip using an optimization procedure[6,7] that takes into account the parasitic effects introduced by the input coil. In

a&resent affiliation: Mediterranean Quantum Systems srl, Thin Film Technologies Division, Via Custozza 31, 1-66013 Chieti Scalo, Italy. The author wishes to thank MQS for release time and support during the

b P ermanent address: Dept. of Electronics, Kyushu University 36, Fukuoka 812, Japan. ‘)Present affiliation: Vaisala Technologies Inc., PL9, SF-00421 Helsinki,

reparation of this manuscript.

We have developed an optimization procedure for the design of very low-noise dc SQUIDs.[6,7 The devices are designed for a four-mask-leveI Nb/S&NY/Nb Josephson device technology[9] to simplify the fabrication. Briefly, the chip layout is determined by a minimiition of the flux den- sity noise &, with the constraint that the microwave reso- nances of the input coil transmission line and the SQUID washer are well away from the intended operating fre- quency of the SQUID. A series R& shunt[7,10,11] in para- llel with the input coil is used to damp the low frequency resonance of the input circuit. The resistor Rx also serves as a proper termination for the input coil transmission line, thereby sigruficantly damping these resonances.[7,8] The effect of the parasitic capacitance C, is taken into account in

using the functional dependence for the energy resolution.[2,3]

Finland. Manuscript received August 24,1992. Fig. 1. Photograph of the magnetometer SQUID area.

10.51-8223/93$03.00 0 1993 IEEE

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Table 1. Parameters of the DC SQUID Magnetometer III. MEASUREMENTS

The dc characteristics and the flux noise of the magneto- meter are recorded using a computer-automated measure- ment system.[l2] The'bias current Ib and applied flux @ are generated by the computer, and the dc voltage across the SQUID is measured using a low-noise room temperature preamplifier that is directly coupled to the SQUID output. The SQUID output is also coupled to a second dc SQUID magnetometer which serves as a low-noise preamplifier for the noise measurents. At each point of operation, the dy- namic resistance and the flux-to-voltage transfer function are determined by measuring the voltage changes for small variations of Ib or @, respectively. These quantities are needed to determine the intrinsic SQUID noise. Over lo00 independent points of operation have been measured for Ib = 38 - 76 pA in 1 pA steps and @/ao = 0 - 0.5 in 0.01 in- crements. Detailed descriptions of the measurement system and the reduction procedure used to determine the intrinsic SQUID noise have been published elsewhere.[3,12]

The I-V characteristics of the magnetometer are shown in Fii. 2. For I e 100 /.A, the characteristics are very smooth and nearly featureless; for I > 100 /.A, two bumps and several small current steps can be seen which are siguatures of microwave resonances in the SQUID. We have used a recent model of the coupled dc SQUID[8] to calculate the frequency-dependant impedance Zcf) seen by the Josephson junctions for the SQUID parameters listed in Table I. The absolute value of the impedance shown in Fig. 3 has several weak bumps spaced at equal intervals in frequency which correspond to odd multiples of the quarter- wavelength input coil transmission line resonance; the large, broad peak at 56 GHz and the sharp peak at 117 GHz correspond to multiples of the half-wavelength resonance of

*0° i 150 I

Fig. 2

0 0 50 100 150 200 250

Voltage (pv)

Current-voltaee characteristics of the dc SOUID

SQUID inductance L Critical current per junction I, Shunt resistance per junction R Capacitance per junction C B, = 2IrI$2C/@o B = U,L/@n

51 pH 32 w 2.4 Rr 1.1 pF

0.62 1-6

CoupGcoktant k, 0.85 Shunt resistance R, Shunt capacitance C' Sensitivity B / @ White flux noise a,, (at 1 kHz) White flux density noise B,, (at 1 kHz) l / f flux noise HZ

6.1 X 10-7 3.4

Fig.3 Absolute value of

In Fig. 2, the volt resonances are marked line resonances above arrows. The agreement with considering the uncertaintie dielectric constants. The frequencies do not pro characteristics because these resonances can be

magnetomete;. The solid (dashed) arrows &re- A spond to the frequencies of the input coil (washer) F@. 4. resonances predicted by the model calculations. voltage

I 500

>n 400

$ 300

200

100

0

T \ W

.- 0 S

m U

>

60 n > 3.

W

40 U e >

20

0

3. 600

0

0 .- +

5 400 Y-

L P) Y-

z 200

I o

e c

>

I 1 \ 1 4 A 7 0

-r, 1.2 e 3.

1.0

s 0.8

LL 0.6

0)

0

X 3

.-

-

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 Flux @/ao Flux @/ao

Fig. 4 Measured values of the (a) voltage noise, (b) average dc voltage across the SQUID, (c) flux-to-voltage transfer function, and (d) white flux noise (at 1 kHz) versus the applied flux for several different bias currents.

flux for several different bias currents. For Ib e U, (Ib 5 62 w), the large peaks in V, are coincident with the steep rise of the voltage across the SQUID. At these points of opera- tion, the SQUID is undergoing considerable switching be- tween the zero-voltage and fmite-voltage states.[3] As can be seen from Fig. 4(c), the flux-to-voltage transfer function, or gain, is also very high at these points of operation: the gain is correlated with the voltage noise. The open-loop flux noise Q, (at 1 Mlz) shown in Fig. 4(d), however, reaches its minimum for higher values of applied flux where the switching noise and the gain are lower. For Ib > U, (Ib 2 66 pA), the voltage noise, and consequently the gain, are much lower, but now the flux noise minimum is very near the point of maximum gain. These results are in qualitative agreement with recent measurements on uncoupled dc

Qm e 7 X lo-' @o/ Hz is possible over a wide range of

- 5, ; 1 0 2

E -2

0" :

SQUIDs[3]. From Ff&4(d), very low-noise operation with 1

A

working points. I2 > 2 loo0 : a

.% w 5: 5 >

The low frequency transmission line resonances can be seen more clearly in the voltage dependence of the mea- sured data. We show in Fig. 5(a) the dynamic resistance hp as a function of the average voltage across the SQUID for a wide range of bias currents; for comparison, the de- pendence of the voltage noise is also shown in Fig. 5(b). Strong peaks in both Rd and V, around 15 pV (7.3 GHz) are most likely due to & transmission line resonance at 8 GHz (see Fig. 3). Much smaller peaks can be seen around 32,47, and 62 pV ( 16,23, and 30 GHz) and correspond to multiples of the transmission line resonances at 17,26, and 34 GHz, respectively. The positions of the peaks in hp and V, are close to but not necessarily coincident with the cor- responding peaks in 20; the existence of the resonances, however, is clearly seen in the data.

100 -

10 ,...'....'".",...'....'..I.'....''.''

0 10 20 30 40 50 60 70 80 Voltage (pV)

Fig. 5 (a) The dynamic reshnce and @> voltage noise versus the dc voltage across the SQUID.

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Iv. CONCLUSIONS

A proper o timization of the coupled dc SQUID leads to smooth dc $racteristics, very low flux noise over a wide range of working points, and a behavior similar to that of an uncoupled device. Using a recent model of the coupled dc SQUID, peaks in the calculated ixnpedance are consistent with features in the I-V characteristics at high bias currents. This model should be useful in analyzing the performance of dc SQUID designs.

REFERENCES

[l] J.M. Jaycox an scheme for ultra

3016,1991. [3] Tap& Ryhinen, Heikki Seppii, and Robin Cantor,

"Effect of parasitic capacitance and inductance on the

200

150 T \ >a 2 100

W

.- 0 C

0 0

+" 50 >

0

7 /

- Sy=2

0 1 2 3 4 Dynamic resistance (n)

Fig. 6 The voltage noise V, = 6 versus the dynamic

According to the data shown in Fig. 5, the voltage noise is correlated with the dynamic resistance, as has recently been reported for uncoupled dc SQUIDs[l3]. Based on this observation, a sim le model to describe the SQUID noise has been propose&.3]: the SQUID noise is characterised by two uncorrelated, equivalent current noise sources which describe the noise currents through and around the SQUID loop. The spectral density of the voltage noise across the SQUID, Sw can be written as[l3]

resistance Rdp

where 7 is a parameter which takes into account the mixing- down effect of the noise. From the measurements on uncoupled SQUIDs,[l3] 7 z 3.

In Fig. 6, we show the dependence of the voltage noise on the dynamic resistance for Rw I 4 51; for Rdy. > 4 51, the correlation of Y with Rd IS still evident but there is more scatter in the lata. We &o show only the data for Ib c U, ( lb 5 62 pA); for higher bias currents, Eq. 1 underestimates the voltage noise for CP > 0. In this region of operatiop, the resonances may cause excess noise which is not taken into account in this simplified model. We have fit Eq. 1 to the noise data over the full range of &, (0 I R, I: 30 51, over 500 data points) and find 7 = 2.4, in g o a agreement with the value reported for uncoupled SQUIDs.[l3] The curve from the fit to Eq. 1 is shown in Fig. 6.

The extensive noise mapping results presented above show that the behavior of a properly optimized SQUID magaetometer is similar to the that of an uncoupled device. In particular, we note that the energy resolution of the SQUID described here, E = @;/U, = 23 4 is only a factor of two bigher than the value predicted for an uncoupled SQUID with the same total inductance.

dynamics &d noise 6f dc supercond interference devices," J. Appl. Phys. 6166,lW.

[4] T. Ryhinen, H. Seppii, R. Ilmoniemi, and J. Knuutila, "SQUID magnetometers for low-frequency applications," J. Low Lemp. Phys. vol. 76, pp. 287-386,

SQUID characteristics of resonances," J. Low OTemp. Phys. 1987.