Sub-micron YBa2Cu3O7�d step-edge Josephsonjunctions and micro-SQUIDs

Ke Chen a,b, Per Magnelind a, Peter Larsson a, Alexander Ya. Tzalenchuk a,*,Zdravko G. Ivanov a

a Department of Microelectronics and Nanoscience, School of Physics and Engineering Physics, Chalmers University of Technology

and G€ooteborg University, S-412 96 G€ooteborg, Swedenb National Laboratory for Superconductivity, Institute of Physics, Chinese Academy of Sciences, 100080 Beijing, China

Abstract

We discuss the properties of sub-micron YBa2Cu3O7�d step-edge Josephson junctions and their application in micro-

SQUIDs. We suggest a design of a micro-SQUID sensor for the scanning SQUID microscopy. Two methods of

coupling the modulation and feedback signals to the sensor are described. Influence of a superconducting sample on the

sensor parameters is analyzed for the two configurations.

� 2002 Elsevier Science B.V. All rights reserved.

Keywords: Step-edge Josephson junctions; Micro-SQUIDs

1. Introduction

The HTS step-edge Josephson junction (SEJJ)technology offers a large degree of flexibility in theplacement of the superconducting circuit elementson the chip and therefore has always been ratherattractive for a variety of applications. Unfortu-nately, despite significant advances in fabricationof SEJJs they are still fairly irreproducible andinhomogeneous to be acceptable for applicationsdemanding a high level of integration. By makingjunctions very narrow one can try to separate dif-ferent contributions to the overall performance of

the conventional SEJJs and fine-tune their prop-erties.

2. Junction fabrication and properties

We have developed a technology to fabricateSEJJs of sub-micron widths using e-beam litho-graphy and ion beam milling through an amor-phous carbon mask. SEJJs with width rangingfrom 0.4 to 1 lm were fabricated in YBa2Cu3O7�d.Transport properties of the junctions were studiedin magnetic fields up to 5 T. It appeared [1] thatmany of the peculiarities often found in severalmicrometer wide SEJJs were much enhanced in thejunctions of sub-micron size. This allowed us tosuggest physical models of the observed pictureand to correlate them with micro-structure of thejunctions. All measured junctions fall into three

Physica C 372–376 (2002) 63–67

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*Corresponding author. Tel.: +46-31-772-3117; fax: +46-31-

772-3471.

E-mail address: f4ast@fy.chalmers.se (A.Y. Tzalenchuk).

0921-4534/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

PII: S0921-4534 (02 )00743-8

categories: low critical current RSJ-type Josephsonjunctions, intrinsic Josephson junctions, and quasi-particle tunnel junctions. We argue that the prop-erties of conventional SEJJs can be understoodas a superposition of those types. The high IcRnproduct of the sub-micron junctions of the firsttype in addition to the flexibility offered by the step-edge technology make them attractive for SQUIDapplications, as it translates into a low white noiselevel (noise energy per unit bandwidth e is inverselyproportional to IcRn) and a large transfer function(VU is proportional to IcRn).In this proceeding we shall look at these junc-

tions from the point of view of their applicationsin micro-SQUIDs. These devices have successfullybeen used as sensors for the scanning SQUIDmicroscopy [2,3], however, other applications re-quiring small area low inductance SQUIDs (e.g.,certain realizations of the quantum bits) areemerging.

3. Micro-SQUID design and fabrication

As pointed out in [4] to achieve the spatialresolution required by SQUID microscopy, it isbest to use a bare SQUID; the use of a fluxtransformer would result in worse sensitivity be-cause of the imperfect inductive coupling. On theother hand the washer type SQUIDs should beavoided in certain applications as they may influ-ence the flux distribution in the sample itself. TheSQUIDs with sub-micrometer lines cannot com-pete with other designs in field sensitivity, but givea good spatial resolution and less destructive to thesample under study. The SQUIDs described herehave an octagonal loop 8 lm in diameter with allsuperconducting lines and the SEJJs 0.5 lm wide.The junctions are formed in a 100 nm thickYBa2Cu3O7�d film at the edge of a 130 nm highstep with a slope of about 60� etched in the sub-strate prior to the film deposition. A separate 0.5lm-wide line encircling the SQUID loop can beused for both modulation and feedback. An AFMimage of the SQUID is shown in Fig. 1. TheSQUIDs were fabricated using the technique de-scribed in detail in [1]. The flexibility of the step-edge technology is favorably utilized. The step

configuration allows for a compact design, andneither the electrodes, nor the modulation striphave weak links unavoidable in the bicrystaltechnology.

4. Micro-SQUID properties

Fig. 2 shows the voltage–flux (V –U) curves atdifferent bias currents of a dc SQUID probe at 4.2K. When the SQUID is biased asymmetricallythrough the electrodes 1 and 2 labeled in Fig. 1, the

Fig. 1. An AFM image of the micro-SQUID. The 8 lm innerdiameter SQUID loop is made of a 0.5 lm-wide YBa2Cu3O7�d

film interrupted by two SEJJs of the same width. The film is 100

nm thick and the step is 130 nm high. A separate 0.5 lm-wideline encircling the SQUID loop at a distance of less than 0.5 lmcan be used for both modulation and feedback.

Fig. 2. V –U characteristics of the micro-SQUID measured at

4.2 K and different bias currents.

64 K. Chen et al. / Physica C 372–376 (2002) 63–67

V –U characteristics are shifted along the flux axisproportionally to the bias current. This shift givesa convenient way to estimate the SQUID self-inductance. However, asymmetrical bias couplesthe bias current fluctuations to the magnetic fluxthrough the SQUID loop, which brings an addi-tional noise. Therefore in practice it is favorable toadjust the distribution of the bias current througheach of the Josephson junctions by introducing avariable resistor connected to the electrodes 1 and3. In addition this can help to compensate for thejunction asymmetry up to the constant term in thedifferential resistance RdðIÞ ¼ oV =oI . The outputvoltage signal is always measured between theelectrodes 1 and 2.There are two ways of coupling of the modu-

lation and feedback signal. In the first configura-tion, both currents are fed through the electrodes 4and 5. The mutual inductance between the mod-ulation strip and the SQUID loop, LSM can becalculated from the V–U curves, in which case U ¼LSMI , I being the modulation current. We havesummarized the experimental and calculated [5]parameters of the SQUID in Table 1 and foundthe agreement excellent.Another way is to let the modulation and

feedback current pass through electrodes 1 and 3.In this case a part of the SQUID loop itself is usedto induce a magnetic flux. Obviously, the couplingbetween the SQUID loop and the modulation loopis considerably better. Below we discuss in detailthe advantage of a self-modulated SQUID overthe externally modulated one.

5. Influence of a superconducting sample

Let us now discuss the influence of a super-conducting sample, a ring, at a distance dSR be-

neath the SQUID probe. The ring is assumed to beof the same size and shape as the SQUID loop.When the superconducting ring is absent, themagnetic flux through the SQUID loop induced bythe modulation and feedback current I is U ¼ILSM. However, when the superconducting ring ispresent, the total magnetic flux is

U ¼ IðLSM þ LMRLSR=LRÞ¼ ILSMð1þ kMRkSR=kSMÞ; ð1Þ

kij � Lij=ffiffiffiffiffiffiffiffiLiLj

p;

where Li, Lij, and kij denote the self-inductances,mutual inductances and magnetic coupling fac-tors, respectively, of the SQUID loop S, the su-perconducting ring R, and the modulation andfeedback loop M. Expression (1) means that theeffective mutual inductance between the SQUIDloop and the modulation and feedback loop be-comes LSMð1þ kMRkSR=kSMÞ, due to the screeningeffect of the superconducting ring. Table 2 givesthe calculated dependence of the relative mutualinductance, DLSM=LSM on the distance between theSQUID and the superconducting ring. Further, inthe described layout, the modulation strip servesalso for the purpose of feedback. The output ofthe SQUID magnetometer is inversely propor-tional to the mutual inductance between theSQUID loop and the feedback loop [6]. So notonly it depends on the magnetic field but also onthe properties of the studied sample. If the mutualinductance changes significantly, the signal dis-tortion introduced by this effect cannot be ignored.

Table 1

Calculated and experimental parameters of the micro-SQUID

Calculated Experimental

Normal resistance, Rn/2 (X) – 18

Critical current, 2Ic (lA) – 170

IcRn-product (mV) – 3.2

SQUID inductance, LS (pH) 43 46

Modulation depth, DV (mV) 0.88 0.83

Mutual inductance, LSM (pH) 7.0 6.7

Table 2

Effective parameters of the micro-SQUID in the presence of the

superconducting ring at a distance dSR. Configurations 1 and 2refer to the coupling of the modulation and feedback signals

described in the text

dSR(lm)

LSR(pH)

kSR LMR(pH)

kMR DLSM=LM (%)

Configuration

1 2

1 10 0.23 6.7 0.17 23 3.9

2 6.4 0.15 4.8 0.12 11 1.8

3 4.4 0.10 3.5 0.088 5.2 0.88

4 3.2 0.074 2.6 0.065 4.2 0.72

5 2.4 0.055 2.0 0.050 1.6 0.28

K. Chen et al. / Physica C 372–376 (2002) 63–67 65

In particular the field from the superconductingsamples will be distorted more significantly thanthat of the metallic or dielectric ones. Since kMRand kSR depend on the distance and relative posi-tion of the SQUID and the superconducting ring,the only way to minimize the effect is to maximizekSM. In the first modulation and feedback config-uration, even though the modulation and feedbackloop is very close to the SQUID loop, kSM ¼ 0:17 isstill rather small. While in the second configura-tion, the modulation and feedback loop shares apart of the SQUID loop and kSM approaches itsmaximum value of unity. For instance, when dSR ¼3 lm, based on Table 2, the equivalent mutual in-ductance increases by more than 5% in the firstconfiguration, but less than 1% in the second mod-ulation configuration.Fig. 3 gives a vivid example of the influence of

the mutual inductance of the SQUID and thesample on the measured field distribution. Pre-sented is a magnetic map around a supercon-

ducting loop with strip electrodes measured by thescanning SQUID microscope [2]. While the flux iswell localized inside the loop in the left corner ofthe image, the contrast from the rest of the strip isan artifact due to the proximity of the supercon-ducting material to the SQUID loop. It is worthmentioning that, although less pronounced, simi-lar artifacts are also present in the scanningSQUID images obtained using low-Tc SQUIDswith pickup loops.Finally, Fig. 4 shows the noise spectrum of this

sub-micron dc SQUID probe mounted inside ofthe scanning SQUID microscope. The measure-ments were performed without bias reversing in anRF-shielded room, but in the absence of magneticshielding of the SQUID/sample chamber. Some ofthe spikes in the white noise region were broughtby the step motors, which were only 30 cm awayfrom the SQUID and only one layer of l-metalshielded. The flux white noise spectrum densitywas about 7� 10�5U0/Hz1=2 corresponding to the

Fig. 3. A magnetic map around a superconducting loop with strip electrodes measured by the scanning SQUID microscope equipped

with the probe of Fig. 1.

66 K. Chen et al. / Physica C 372–376 (2002) 63–67

field noise of 3 nT/Hz1=2, which was the environ-mental noise in the shielded room.

6. Conclusions

In summary, micro-SQUID probes with sub-micron step-edge Josephson junctions in YBa2-Cu3O7�d were designed and fabricated. Theyshowed a maximum modulation depth close to1 mV, which is near the theoretically estimatedvalue. The probes were used in a scanning SQUIDmicroscope. The influence of a superconductingsample on the coupling of the SQUID loop andthe modulation and feedback loop is calculated.To minimize the impact, a tightly coupled config-uration is proposed and analyzed. This configu-ration uses a part of the SQUID loop as themodulation and feedback loop. The impact ofmutual inductance on the measured magnetic fieldis strongly diminished. Although a general result itis especially important for scanning SQUID mi-croscopy, where the SQUID probe and the sampleare in close proximity to each other.

Acknowledgements

We are grateful to M.M. Khapaev and A.Kidiyarova-Shevchenko for the help with induc-tance calculations using 3D-MLSI. The work wassupported by the Swedish Foundation for Strate-gic Research through its OXIDE program.

References

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Fig. 4. The noise performance of the same micro-SQUID as in Fig. 1 in magnetically unshielded environment.

K. Chen et al. / Physica C 372–376 (2002) 63–67 67