AFRL-SN-RS-TR-2002-255

Final Technical Report September 2002 DYNAMICS OF TRIANGULAR AND SQUARE ARRAYS Massachusetts Institute of Technology

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4. TITLE AND SUBTITLE DYNAMICS OF TRIANGULAR AND SQUARE ARRAYS

6. AUTHOR(S) Terry P. Orlando

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AFRL-SN-RS-TR-2002-255

11. SUPPLEMENTARY NOTES AFRL Project Engineer: Stanford P. Yukon/SNHE/ (781) 377-2968/ Stanford.Yokon@hanscom.af.mil

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13. ABSTRACT (Maximum 200 Words) The DC characteristics of single triangular Josephson Junction (JJ) cells and single row arrays have been studied to their potential as rf oscillators. Measurements of under damped systems reveal two steps in the current voltage (IV) characteristic, corresponding to LSC and LJ resonances. These steps are characteristics of single cells, and their position does not change significantly with array size. Measurements of two different cell sizes showed that the upper step voltage depends strongly on the cell geometry, while the lower step is only slightly affected. At the LSC resonance, underdamped arrays produce large amplitude single harmonic oscillations in the horizontal junctions. According to DC measurements oscillators based on this resonance operate at frequencies ranging from 70 - 170 GHz, with bandwidths of 10% - 20%. For 9mm2 junctions, the power expected from M horizontal junctions is M'2nW for low current densities and M'2lnW for high current densities. To study the possibility of mode locking in a 2D triangular array, simple diamond cells have been investigated. In addition to a common bias current, a small trim current applied to the bottom triangle of a diamond will engender an rf voltage at two frequencies corresponding to the upper and lower cell oscillations. The DC properties of the diamond system have been confirmed, and on chip measurements of the system are planned to confirm the response of the horizontal junction to trim current tuning.

15. NUMBER OF PAGES11

14. SUBJECT TERMS Josephson, Junction, Array, Oscillator, Mode Locked PUlse

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ULNSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

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Table of Contents

1. Executive Summary 1 2. Research Progress 2 References 7

List of Figures Figure 1: Current Voltage characteristics of single triangular cell and of an 8-cell array 3 Figure 2: Step voltage vs. field is compared to critical current vs. field for

the 8-cell triangular array. 4 Figure 3: Current-voltage characteristics compared for a high current density Figure 4: Diamond Cell 6

List of Tables Table 1: Triangular Array Parameters 4

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1 Executive Summary The progress on the following tasks is as follows: 1.1.1 Design of triangular and one-dimensional arrays. Two new sets of designs were done in collaboration with S. Yukon, L. Caputo, and A. Utinov. These designs were submitted in September and October of 1996 to Hypres, Inc. 1.1.2 Fabrication of the arrays. Both sets of designs have been fabricated, and one has been measured. 1.2.1 Feasibility study of on-chip microwave sensors. The first round of such sensors have been measured. Based on these results, a new sensor has been designed and fabricated. 1.2.2 Feasibility study of direct microwave measurements. A. Duwel has visited Rome laboratories and learned the types of facilities available in the laboratories used by

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J. Derov and J. Habib. A 10GHz probe compatible with thisequipment is in the process of be-ing built. In addition, A. Duwelhas worked with L. Caputo andA. Ustinov at KFA in Juelich, Ger-many, to design circuits which willbe measured in the W-band atKFA. The facilities for these mea-surements are available at KFAand the testing will be completedby L. Caputo.

2 Research Progress

2.0.1 Samples and Parameters

We use samples made at HYPRES,with Nb-AlOx-Nb junctions. HYPRESoffers a minimum junction size of9p.m2 and critical current densities of1000kAjcm2 and 100kAjcm2. The ca-pacitance of these junctions is approx-imately C = 340 fF. The normal-state resistance will be approximately1.9mV / Ic. Thus, for high current den-sity samples, Ic = 90p.A and Rn =21 n. For lo\v current density samples,Ic = 9 p.A and Rn = 211 n. In prac-tice, we measure the normal-state resis-tance to determine the junction criticalcurrent. Past studies have shown lessthan 5% variation in junction criticalcurrents across a chip.

Our measurements are made in a 4HeDrobe. We use a IJ.-metal foil inside the

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vacum can for rf shielding. A solenoidsurrounding the sample carrier allowsthe application of magnetic fields per-pendicular to the sample plane up to300 mG. A resistor attached to the sam-ple carrier enables us to stabalize tem-peratures from 4.2 -12 K.

Two main parameters, which canboth be influenced by temperature,characterize our systems. The discrete-ness parameter, AJ = LJ/ L., relatesto the spatial extent of vortices in anarray. It is given by the ratio of thejunction inductance, LJ = Wo/(21r Ic),to the geometric inductance of a sin-gle cell, L.. The Stewart-McCumberparameter .Bc = R~C/LJ defines theamount of damping in a single junction.We often use the junction normal-stateresistance for RJ. For given values ofcritical current density, junction size,and cell size, the values of AJ and .Bcare determined at 4.2 K. By raising thetemperature, AJ can be increased by afactor of 4 and .B can be decreased by75%.

We have designed arrays for four dif-ferent parameter regimes, determinedby the possible combinations of low cur-rent density, high current density, andthe presence or absence of a shunt re-sistor. In addition, the size of the cellinfluences the parameter range. Table2 sumarizes the possibilities. We haveincluded the minimum and ma."(imumcell sizes \vhich have been designed, al-though the smaller shunted cells have

not yet been measured. Ranges are mize at f = 0.5.listed for (3 and A), consistent withchanges in temperature. u-

'Ii-iangular Arrays as LocalOscillators

2.0.2

~~

]i

o.

In order to determine the potential fortriangular arrays as oscillators, we be-gin by studying the dc characteristicsof single cells and single row arrays,

Measurements of underdamped sys-tems reveal two steps in the current-voltage (IV) characteristic, correspond-ing to L.C and L}C resonances [1, 3].These steps are characteristics of singlecells, and their position does not changesignificantly with array size. Measure-ments of two different cell sizes showedthat the upper step voltage dependsstrongly on the cell geometry, \vhile thelower step is only sightly affected. InFigure 1, we compare the IV of a trian-gular cell \vith parameters {J = 230 andA} = 2.4 to that of a 9-cell array \viththe same parameters. The steps appearonly in the presence of a magnetic field,when the average applied flux per cell(called frustration, f) is approximatelyone-half. They are stable for a rangeof f = 0.3 -0.7, Figure 2 sho\vs thel'ange of stability and the step voltagevariation, by plotting the step voltagetogether with the array critical currentvs, frustration. Both are periodic infield. As usual. the critical current islargest at f = 0, \vhile the steps maxi-

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..." ,.'01 om' I

Figure 1: Current-Voltage characteris-tics of a single triangular cell and ofan 8-cell array. The parameters are.8 = 230 and A) = 2.4, and f = 0.5.

These steps also appeared in mea-surements of high critical current den-sity junctions, \vhere the devices moredamped (fJ '" 10) and more discrete(A) '" 0.6). At lo\v temperatures,these samples have ~\) values well be-low 1. We found that the upper step,corresponding the L.C resonance, isonly stable ,vhen the temperatUre israised such that .\) > 0.3 (approxi-mately). We observed, unexpectedly,that both step voltages showed a de-pendence on Li through the criticalcurrent density. For identical geomet-ric designs. 10'" current density devices(discussed above) produce resonancesat 0.1 and 0.23 m \', ,vhile the carre-

IS".""""",

Figure 2: Step voltage va. field is com-pared to critical current vs. field for the8-cell triangular array.

\ "" ,

sponding steps in high current densityde,'ices occurred at 0.12 and O.20mVrespectivel)'. Current-voltage charac-teristics for a low current density anda high current density sample are com-pared in Figure 3. .I\pparently, the up-per step is more complicated than anLsC resonance. and a higher-order de-pendence on LJ should be included.

For' overdamped j\ffictions. \ve used

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Figure 3: Current-voltage characteris-tics compared for a high current den-sity (jc = 1000 kAfcm2) and a low cur-rent density Uc = 100 k.L\f cm2) 8-celltriangular array. The lo\v jc array has,:3 = 230 and .,\3 = 2.4~ and the high jcarray has {3 = 6.5 and .\} = 0.6.

shunt resistors of approximately In. Inboth low current density and high cur-rent density samples, this dominatesthe shunt resistance. Including theshunt resistors made the cell size muchlarger. Thus the shunted systems areall highly discrete, and we do not ex-pect the L.C resonance to be stable.Typical IV's show critical currents, butno other obvious nonlinearities. Lock-in measurements of the resistance re-veal a slight nonlinearity. At this point,we have not definitively connected itsvoltage position with any particularresonance.

At the L.C resonance, underdamped

arrays produce large-amplitude single-harmonic oscillations in the horizontaljunctions [1]. According to dc mea-sluements, oscillators based on this res-onance operate at frequencies rangingfrom 70 -170GHz, with bandwidthsof 10 -20%. For 9 p.m2 junctions,the po\ver expected from M horizontaljunctions is ..V X 2 n W for low currentdensi ties and }.If x 21 n W for high cur-rent densities. In our overdamped ar-rays, we have not yet identified an L.Cresonance in the IV characteristic.

With \V-band measurements, theoutput frequency, po\ver, and line\vidthcan be confirmed. In collaboration withP. Caputo and A. Ustinov at KFA,two triangular ro\vs have been cou-pled to fin-line antennas. A striplinewith characteristic impedence approxi-mately equal to the expected L.C res-

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onance couples the horizontal junctionsto the antenna. The fin-line antennaacts as a matched transition to the80 -120 GHz rectangular waveguide.Measurements will be made using fa-cilities available at KFA by P. Caputo.

On-chip measurements can also beused to determine the output frequencyand power. We plan to couple the out-put of trianglur row oscillators to de-tector junctions. With good coupling,many researchers have found this tobe an effective measurement technique.Radiation emitted from the oscillatorexcites Shapirio steps in the detectorjunction. Using simulations of the de-tector junction, the oscillator frequencyand power can be inferred. We plan touse this method to compare the outputof triangular rows with various lengths.Power measurements of these systemswill allow us to determine the degree ofphase-locking. We will measure the de-pendence of output power on frequency,using a magnetic field to tune the oscil-lator.

2.0.3 Mode-locking in 2D Trian-gular Arrays

To study the possibility of mode-locking in a 2D triangular array, \vefirst investigated simple diamond cells:as shown in Figure 4. When a singlebias current is applied to the ,erticaljunctions, both the top triangular celland the bottom cell have the same dc

I

~

M --~ -61

~1+61

Figure 4: Diamond Cell

voltage. Next a small trim current, ill,is applied at the edges and removed atthe same ground as the bias current.Thus more current is effectively passedthrough the lower cell. This causes thevoltage across the lower junctions to in-crease relative to the upper cell junc-tions. On the oscilloscope, the entire1\' of the lo\ver cell is translated in volt-age as the trim current is applied. Al-though no dc voltage develops acrossthe horizontal junction, it develops asinusiodal ac voltage at a two frequen-cies. corresponding to the upper andlo\\Oer cell oscillations [2J. SO far, \vehave confirmed the dc properties of thissystem. \"e intend to use on-chip mea-surements to confirm the response ofthe horizontal junction to tuning.

\'.e have designed t\VO ro\v arrays,with tuning currents similar to the dia-

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mond discussed above. We will checkthat the tuning is still effective inlonger systems. Finally, we will mea-sure multi-row systems. We have de-signed five ro..v arrays with leads at theedges for the application of trim cur-rents. It is important to apply equaltrim currents into the array edges andremove them at the bottom. At thesame time, we would like to use a sin-gle source for the trim currents. Theseconditions make the array design chal-lenging. We have made two identicalfive-row arrays with different configura-tions for the trim currents. Our goal isto bias the five rows ..vith incrementallyincreasing dc voltages. We will test therange of voltages that can be achievedand the effect of magnetic field on thisstate.

Once the array properties have beenestablished through dc measurements,we \vill address the task of testing thehigh frequency properties. Our firststep \vill be to make on-chip measure-ments of single ro\vs \vhich are part of alarger array. We will compare this datawith data taken from isolated rows ofequal length. Thus, \ve \vill measurethe effect of the array on the output ofa single row. Our next task will be tocouple the outputs of two or more ro\VSto a detector junction. We will biasthe ro\vs to oscillate at the same fre-quency, and compare the power outputfrom this system to the po\ver from onlyone row. We hope to see the po\ver in-

crease as the number of rows when thearray is operating at a single frequency.

Our ultimate goal in this project isdetection of the envelope or pulse. Al-though we expect approximately 5 GHzfor a pulse repetition rate in the timedomain, this signal is to be carried by awave at approximately 120 GHz. In or-der to detect the low-frequency pulses,we will also need to mix the signal down

using Josephson technology.

References

[1] Yukon, S.P., N.C.H. Lin, J~acro-scop~c

Quantum Phenonema and Coher-ence in Superconducting Networks,

Singapore, p.351 (1995).

[2] Yukon, S.P., N.C.H. Lin, IEEETrans. Appl. Sup. 5 2959 (1995).

[3] Duwel, A.E., P. Caputo, A.V.Ustiuov, T.P. Orlando, unpub-lished work.

[4] HYPRES.10523.

Inc., Elmsford, NY

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