Physica C 433 (2005) 108–114

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Optimization of step-edge substratesfor high-TC superconducting devices

C.H. Wu a, M.J. Chen a, M.H. Hsu e, J.C. Chen a, K.L. Chen a, J.H. Chen c,J.T. Jeng d, T.S. Lai e, H.E. Horng b, H.C. Yang a,*

a Department of Physics, National Taiwan University, Taipei 106, Taiwanb Department of Physics, National Taiwan Normal University, Taipei 116, Taiwan

c Department of Electrical Engineering, Da-Yeh University, Chang-Hwa 515, Taiwand Institute of Mechatronic Engineering, National Taipei University of Technology, Taipei 106, Taiwan

e Department of Physics, Chung Yuan Christian University, Chung Li 320, Taiwan

Received 1 February 2005; received in revised form 13 September 2005; accepted 7 October 2005

Abstract

To pursue step-edge for high-TC superconducting grain boundary junctions or SQUIDs with high reproducibilityand quality, we have developed two-step procedures of fabricating very good step-edge substrates. A protocol of pre-cisely controlling step angles for Josephson junctions has been established, with which we can predict the step angles aswell as get a better control of the fabrication process. The procedures can improve the step ramp quality substantially.There are no needles, waves, trenches, cascade, or other flaws on these surfaces. The step substrates present good uni-formity with respect to any step angle. We have characterized high-TC step-edge dc SQUIDs connected in series. TheI–V curves of SQUID arrays show the RSJ behavior. The enhanced modulation amplitude of 110 lV is achieved at77 K with the step-edge dc SQUID in series. The results clearly show the high uniformity and quality of the fabricatedstep-edge Josephson junctions.� 2005 Elsevier B.V. All rights reserved.

Keywords: SQUID; Step-edge; Serial SQUID arrays

0921-4534/$ - see front matter � 2005 Elsevier B.V. All rights reservdoi:10.1016/j.physc.2005.10.006

* Corresponding author. Tel./fax: +886 223675267.E-mail address: hcyang@phys.ntu.edu.tw (H.C. Yang).

1. Introduction

The high-transition temperature superconduc-tor (HTS) step-edge Josephson junctions have

ed.

C.H. Wu et al. / Physica C 433 (2005) 108–114 109

been investigated intensively due to the promisingdevice characteristics [1] comparable to the bi-crys-tal junctions. To date, most commercial applica-tions use bi-crystal Josephson junctions made onSrTiO3(100) (STO) or MgO substrates. Althoughit is easy to fabricate bi-crystal junctions, the junc-tion locations are restricted to the grain boundaryof the bi-crystal substrate. It is not the case for thestep-edge substrate, their locations of the junctioncan be chosen at your will and the pricing is only atenth of that of the bi-crystal substrates. More-over, the artificial bi-crystal grain boundary is vul-nerable to the thermal and chemical processes infabricating the Josephson junctions. The thermalheating during film deposition, annealing in thecooling process, or wet etching with chemicalsmay lead to the formation of grooves along thebi-crystal line [2–4]. The R–T curves and IcRn

product reveal sequential destructive deteriorationof the junction originating from the underlyinggrooved substrate [2]. In addition, the long-termstability of the bi-crystal Josephson junction is sus-ceptible to the thermal shock in cooling the devicefrom room temperature. The above problemsencountered by the bi-crystal junction can besolved with the step-edge Josephson junction [5–12].

The step-edge junction typically has two ormore grain-boundaries. Several factors may affectthe formation of a high-quality step-edge Joseph-son junction. The step-edge ramp surface musthas as great an epitaxial template quality as therest of the substrate surfaces to prevent disorder,such as additional grain-boundaries and a-axis ori-ented particles in the growing film. Further, thestep has to be very straight to avoid the nucleationof the CuO particles [6,7]. Thus the fabrication ofthe substrate steps of the desirable quality putsheavy demand on the processing technique. Anumber of methods were proposed to producestep-edge substrate [8–10]. The purpose is toobtain a smooth ramp surface with straight step-edge lines. However, the step fabrication processto date still suffers from the problem of low repro-ducibility due to the strict conditions for differentangle steps. Furthermore, the film growth mecha-nism is variable on different substrates such asSTO and MgO. A step with a steep angle greater

than 60� and a clear, sharp profile is the best struc-ture for step-edge junctions on STO. On the otherhand, ramp-edge SNS junctions and junctions fab-ricated onto MgO step-edge substrates require lowstep angles. To obtain a smooth ramp surface witha straight step-edge line for different step angles iscrucial in the success of the high-quality Josephsonjunctions and SQUIDs for large-scale integratedcircuits. Some groups achieved high step anglesby controlling different milling rates and re-deposi-tion rates of the substrate with the low-millingrate Cr mask [11]. The possibility to fabricate thesmooth step-edge with various angles by usingsimply the photoresist mask is not clear yet. In thiswork, we have established two-step procedures toobtain high-quality step-edge substrates. To pur-sue the high reproducibility for variable stepangles, a protocol for fabricating step substratefor Josephson junction and SQUIDs has beenestablished, with which we can predict the differentstep angles as well as get a better control of thefabrication process. Furthermore, to demonstratethat these step-edges on STO and MgO substratesare uniform, we fabricated serial SQUID arraysonto the step-edge substrates.

2. Experimental

The step-edge substrates were fabricated by ionbeam etching (IBE). The IBE source comes fromthe Commonwealth Scientific Corporation. Thefabrication of step-edge substrate requires a mask-ing layer on substrate to define the location of thestep-edge during IBE process. Here, we choose thephotoresist AZ1500 as the masking layer anddefined the step-edge pattern by photolithography.The patterned photoresist mask was hard baked at100 �C in an oven for 1 h in order to reduce itsmilling rate in the subsequent IBE process. Sub-strates were mounted on a water-cooled coppersample holder, and a 500 eV argon ion beam witha current density of 1.0 mA/cm2 was used to etchthe substrates. The milling rate of the substrate isabout 2 nm/s for both MgO and STO substratesin all our experiments. The pressure during theetching is about 1.8 · 10�4 Torr. The detailed pro-cess was reported in [6]. The surface morphology

110 C.H. Wu et al. / Physica C 433 (2005) 108–114

and step angle of the fabricated substrates wereprobed by atomic force microscopy (AFM). TheYBCO films were grown onto the step-edge sub-strates using the magnetron sputtering techniquewith a ratio of the step-height to the thickness ofthe YBCO film of about 0.7. Typically, the step-height is 200 nm and the film thickness is about140 nm. Gold contact pads were evaporated ontothe contact leads to ensure a low contact resis-tance. The junctions and SQUIDs were fabricatedby the standard photolithography and argon ionmilling. The current versus voltage (I–V) and volt-age versus flux (V–U) characteristics of junctionsand serial SQUIDs were measured using NKT�sDC SQUID CatcherTM system at 77 K.

The resultant step angle on the substrate couldbe predicted from the following geometrical rela-tions. In Fig. 1(a) we show the schematic plot ofthe correlation between the substrate and the inci-dent ion beam direction. We defined the incidentangle a to be the angle between the normal ofthe substrate and the direction of the incident ionbeam. The rotational angle h is defined to be theangle of the substrate rotated about the normalof the substrate. Fig. 1(b)–(d) illustrate the sub-strate orientations with the rotational angles hincreased from 0� to 90� while the incident anglea is fixed. For the general case shown inFig. 1(c), it is straightforward to find the geometri-cal correlation between the incident angle a, the

(a)

(c)

θφ

α

(b) α

α

φ

η

θ

(d)

α

θ

holder

normalIon beam

photoresist

substrate

ηrs

h

y'

y

x

z

x'

y'

x'

Fig. 1. (a) A schematic plot of the correlation between thesubstrate position and ion incident direction. Schematic plotwhen (b) h = 0�, (c) h is between 0� and 90�, and (d) h = 90�.

rotational angle h and the shading angle /. Therelation is

tanð/Þ ¼ hs¼ h

r� rs¼ 1

tanðaÞ sinðhÞ ; ð1Þ

where h is the thickness of photoresist mask, r isthe projection of ion beam ray on the substratesurface, and s is the projection of r on the y 0-axis.According to Eq. (1), the maximum shading angle/ is 90� when h is zero as shown in Fig. 1(b). Theminimum shading angle appears at h � 90� asshown in Fig. 1(d). The resultant step angle gshould be a single-valued function of the shadingangle / for a given incident angle a. The properincident angle a should make the ratio in millingrate of photoresist to substrate as small as possi-ble. In addition, the rotational angle h shouldnot be negative in order to minimize the re-deposi-tion of the substrate material onto the step-edge[11]. By considering all the factors above, the resul-tant step angle g should increase monotonicallywith respect to the shading angle /. Accordingly,we further assumed that resultant step angle g isproportional to the normal projection of flux ofthe incident ion beam. In other words, g is propor-tional to sin(/) as follows

g ¼ A sinð/Þ; ð2Þin which A is the highest possible angle we can ob-tain according to the relation between the millingrate and the re-deposition rate when h is 0� [11].Note that the highest possible angle A is a functionof the incident angle a.

3. Results and discussion

According to a previous report [12], it wasfound the fastest milling rate of about 2 nm/s isachieve for the substrate when a = 60�. In addi-tion, the ratio in milling rate of photoresist to sub-strate is minimized in this case. Hence, the incidentangle a was fixed at 60� in our subsequent experi-ments to define the step-edge. Under a protocolion milling processes and optimised condition ofexposing the photoresist, the MgO and STO stepsubstrates were fabricated successfully. The step-edge profile is checked on 5 · 5 lm2 by AFM. In

Fig. 2. Surface morphology of the fabricated step-edge sub-strates probed with AFM when (a) h = 30� and (b) h = 90�.

C.H. Wu et al. / Physica C 433 (2005) 108–114 111

Fig. 2 we show the surface morphology of the fab-ricated step-edge substrates when the rotationalangles h were kept at 30� and 90�, respectively. Itis found that the ramp surface and the surface nearthe step-edge line were filled with the re-depositedmaterial near the upper edge of the step. The loca-tion of re-deposition is getting far away from thestep-edge line when h is getting larger.

To suppress any re-deposition whatsoever, thesecond process was adapted. We rearranged the

Fig. 3. (a)–(d) Surface morphology of the step-edges with various stepscanning across a 5 · 5 lm2 area.

substrate on the holder and used the ion beamto sweep away the re-deposition materials. Theangles a and h in Fig. 1(a) are set to 90� and 0�,respectively. The milling time is about 10 s. Wefound that the re-deposited material was removedby using the second procedure. The ramp surfacebecomes smoother and the step-line becomesstraighter with this way. Fig. 3(b) and (d) showedthe improved results of Fig. 2(a) and (b) after thesecond process. The two-step procedure describeabove was successfully applied to fabricate thestep-edge of angles varying from 30� to 70� onthe MgO and STO substrates. In Fig. 3(a)–(d),we showed the surface profile of typical results.The fabricated step-edge substrates have smoothsurface and straight ramp-edge. There are no nee-dles, waves, trenches, cascade, or other flaws onthese surfaces. We compare the fabricated stepangles with that predicted from Eqs. (1), (2), andthe results are shown in Fig. 4. When the rota-tional angles h were fixed at 0�, 10�, 20�, 30�, 60�and 90�, we obtained the step angles g of 72�,65�, 50�, 45�, 30� and 28�, respectively for MgOsubstrates. The same rotational angles h give thestep angles g of 72�, 64�, 50�, 43�, 28�, and 20�,respectively for STO substrates. The maximumstep angle of 72� is close to the angle as describedabove and that in Chu�s predication [11]. Comparing

angles g. The images are taken by an atomic force microscope

0 20 40 60 8020

30

40

50

60

70

100

predicted from Eq.(2) MgO step substrates STO step substrates

Ed

ge

ang

leη

Substrate-rotated angle θ

Fig. 4. The theoretical and experimental step angles g withrespect to various rotational angles h.

-200 0 200

-6000-5000-4000-3000-2000-1000

01000200030004000500060007000

-200 -150 -100-50 50 100150 200

-400-300-200-100

0100200300400

V (µ

V)

I (µA)

(a) 5 SQUIDs(b) 15 SQUIDs(c) 35 SQUIDs (a)

(b)(c)

V(µ

V)

I(µA)

0

Fig. 5. The inset of the plot shows that the I–V curve of a singleSQUID is like the RSJ behavior. I–V characteristics of 5, 15and 35 SQUIDs connected in series at 77 K.

-3000 -2000 -1000 0 1000 2000 30000

10

20

30

40

50

60

70

80

90

100

110

120

V(µ

V)

Imod(µA)

Fig. 6. V–Imod curve characteristics of 1, 5, 15, 25 and 35SQUIDs connected in series.

112 C.H. Wu et al. / Physica C 433 (2005) 108–114

the fabricated step angles on STO and MgO sub-strates with those predicted from Eq. (2), we founda good consistency between the predicted data andthe fabricated results.

To demonstrate the good quality of the fabri-cated step-edge substrates, the serial SQUIDarrays were fabricated onto the MgO and STOstep-edge substrates. The detailed process wasreported in Ref. [6].

We fabricated serial SQUIDs on the MgO stepsubstrates shown in Fig. 3(b). The substrates usedwere low angle MgO(100) substrate. The step-height was 200 nm with a step angle of 50�. Thefilm thickness is about 140 nm. The ratio of thestep-height of the substrate to the thickness ofthe film is 0.7. The bare SQUID were connectedin series to form the serial SQUID array. The totalnumber of SQUIDs in the array was designed tobe 50. The distance between two SQUID was15 lm. The area of the hole of the SQUID was10 · 20 lm2, and the junction width was 3 lm.The calculated inductance of the SQUID loop is35 pH. 50-SQUID serial arrays were aligned alonga step-edge line of 1550 lm long. Fig. 5 shows I–Vcharacteristics for 5, 15 and 35 SQUIDs connectedin series. The inset of Fig. 5 shows typical I–Vcharacteristic of a dc SQUID at 77 K. The criticalcurrent and the shunt resistance of the bareSQUID and the SQUID array were found by fit-

ting to the RSJ model with finite thermal noise[13]. It is found that the single SQUID shows anormal resistance of 2.1 X and a critical currentof 55 lA, corresponding to the ICRn product of113 lV at 77 K. The normal-state resistances forthe 5, 15, and 35 dc SQUID arrays were foundto be 12, 25, and 36 X, respectively with the criticalcurrents of about 30 lA. In Fig. 6 we show theV–Imod curves at 77 K for a bare SQUID and 5,15, 25, 35 SQUIDs connected in series. The peak-to-peak voltage, Vpp, of a single SQUID is about20 lV. The observed Vpp is increased as the num-

(b)(a)

-6 -4 -2 0 22 4 6

-1

0

1 (c)V(a

.u)

I mod (a.u)

Fig. 7. (a) V–Imod curve of a 5-SQUIDs array, (b) Simulatedbeat phenomena, and (c) beat phenomena is a superposition offive distinct V–Imod curves with 3.5% difference in the modu-lation period.

1 100 100010

100

1000(a) 1- SQUID(b) 5-SQUIDs(c) 15-SQUIDs(d) 25-SQUIDs(e) 35-SQUIDs

(e)

(d)(c)

(b)

(a)

Sφ1/

2 (µφ

0/H

z1/2 )

f(Hz) 10

Fig. 8. Flux noise of serial connected SQUIDs array at 77 K.(a) A single SQUID; (b) 5 SQUIDs; (c) 15 SQUIDs; (d) 25SQUIDs and (e) 35 SQUIDs.

Fig. 9. Compare the flux noise measured with predicted.

C.H. Wu et al. / Physica C 433 (2005) 108–114 113

ber of SQUIDs connected in series is increased.The observed Vpp is a bit smaller due to the inco-herent modulation in the V–Imod. To confirm thiswe replot in Fig. 7(a) the measured V–Imod curveof a serial 5-SQUIDs array in a wider range ofthe applied modulation magnetic field [14]. If wesuperimposed five distinct V–Imod curves with3.5% difference in the modulation period and 5%difference in the amplitude shown in Fig. 7(c), weobtained the data shown in Fig. 7(b) which is sim-ilar to the measured data. We believe that the non-uniform field causes an incoherent phase relationin V–Imod curves in SQUIDs. Each SQUID has asmall variation reveal in the difference of ampli-tude.

DCSQUIDs are composed of two junctions con-nected in series. Besides, the two junctions must bethe same so as to obtain the symmetric interferenceeffect. This is why most junctions in dc SQUIDs arefabricated as close as possible to keep the junctionproperties the same. Because of the above reasons,the step-line needs to be long enough to accommo-date two junctions and consistent enough to keepthese two junctions identical. We have fabricated35 SQUIDs on MgO step and prove that the stepis uniform up to at least 1000 lm.

Fig. 8 shows S1=2U (f) for a bare SQUID, 5, 15, 25

and 35 serial connected SQUIDs array. The whitenoise in S1=2

U (f) for a SQUID is 60 lU0/Hz1/2 whilethe serial connected SQUID show flat noise spec-trum. The S1=2

U (f) is reduced to 18 lU0/Hz1/2. Thelow frequency 1/f flux noises of serial SQUIDsarrays are almost flat. The good characteristicsof the low frequency 1/f flux noise of SQUIDreveal that the step-edge substrate is good. Wecan obtain the same results of the STO step-edgeSQUID.

Corresponding to theory the white flux noiseshould decrease with 1/

pN where N is the number

114 C.H. Wu et al. / Physica C 433 (2005) 108–114

of SQUIDs. Fig. 9 showed the flux noise measuredand predicted. The flux noise of serial SQUIDarray was bigger than designed. The cause of thebigger flux noise was the phase incoherence. TheSU(f) of serial connected SQUID array was a littlebit higher than the data predicts. The phase inco-herence of each SQUID should be the cause forhigher flux noise was the phase incoherence. Wecan obtain the same results of the STO step-edgeSQUID. By the two procedures, this work alsohelps the preparation of the ramp surface inramp-type junction. The results show in [15].

4. Conclusion

We have developed the protocol to fabricatehigh-quality step-edge substrates using two-stepprocesses. A model of comparing the fabricatedstep angle with the experiment data was estab-lished. We have confirmed the high-quality step-edge substrates using high-TC step-edge serial dcSQUIDs. The results show the high uniformityand quality of the fabricated step-edge Josephsonjunctions. The step-edge SQUID exhibit excel-lently in good result in flux-to-voltage transferfunction [16–22].

Acknowledgements

The authors thank the financial supports of theMinistry of Education (91-N-FA01-2-4-2) and Na-tional Science Council of Taiwan (NSC93-2112-M002-041).

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