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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AIR FORCE RESEARCH LABORATORY SENSORS DIRECTORATE ROME RESEARCH SITE ROME, NEW YORK

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APPROVED: STANFORD P. YUKON Project Engineer

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SEPTEMBER 2002

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Final Feb 96 – Feb 97

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DYNAMICS OF TRIANGULAR AND SQUARE ARRAYS

C PE PR TA WU

6. AUTHOR(S)

Terry P. Orlando

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- F30602-96-1-0059 - 61102F - 2304 - BR - P1

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Massachusetts Institute of Technology Cambridge Massachusetts 02139

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Air Force Research Laboratory/SNHE 80 Scott Drive Hanscom AFB Masschusetts 01731-2909

AFRL-SN-RS-TR-2002-255

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AFRL Project Engineer: Stanford P. Yukon/SNHE/ (781) 377-2968/ [email protected] 12a. DISTRIBUTION / AVAILABILITY STATEMENT

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APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. 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. 14. SUBJECT TERMS

15. NUMBER OF PAGES

11

Josephson, Junction, Array, Oscillator, Mode Locked PUlse

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UL Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z39-18 298-102

Table of Contents 1. Executive Summary

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2. Research Progress

2

References

7 List of Figures

Figure 1: Current Voltage characteristics of single triangular cell and of an 8-cell array Figure 2: Step voltage vs. field is compared to critical current vs. field for the 8-cell triangular array. Figure 3: Current-voltage characteristics compared for a high current density Figure 4: Diamond Cell

3 4 4 6

List of Tables Table 1: Triangular Array Parameters

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1 Executive Summary

The progress on the following tasks is as follows: 1.1.1 Design of triangular and onedimensional 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. J. Derov and J. J. Habib. A A 10 10 GHz probe compatible with with this equipment is in the process process of of being built. built. In addition, addition, A. A. Duwel has has worked with with L. Caputo and A. Ustinov at KFA in Juelich, GerA. KFA many, will many, to design design circuits circuits which will be measured measured in the W-band at KFA. KFA. The facilities facilities for these these meameasurements surements are available at KFA and the testing testing will will be completed by L. L. Caputo.

2 2.0.1

Research Research Progress Progress Samples and Parameters Parameters

We use use samples samples made at HYPRES, with Nb-AlOx-Nb with Nb-A10x-Nb junctions. junctions. HYPRES offers junction size offers a minimum minimum junction size of 99p.m2 fun2 and critical critical current densities densities of 1000kAjcm2 1000kA/cm2 and 100kAjcm2. 100kA/cm2. The cacaof these these junctions junctions is approxpacitance of imately imately C = = 340 340 fF. fF. The normalstate resistance resistance will will be approximately 1.9mV// .c Thus, for high current denden1.9mV / Ic. 90p.A Rn sity samples, samples. IIce = = 90 ^A and i2 n = 21 21 n. n. For For lo\v low current density samples, samples, p.A and Rn n. In pracIIce = 99/iA Rn = = 211 2110. tice, we we measure measure the normal-state resisresistance to determine the junction junction critical critical current. Past Past studies have shown shown less less 5% variation than 5% variation in junction junction critical critical currents across across a chip. 4 Our measurements measurements are made in a 4He He Drobe. Drobe. We use use a IJ.-metal /a-metal foil foil inside the 2

vacum rf shielding. A solenoid vacum can can for rf solenoid surrounding the sample carrier allows the application of of magnetic fields perpendicular to to the sample plane up to 300 300 mG. A resistor attached to to the samsample carrier enables enables us to stabalize temperatures from 4.2 -12 — 12 K. peratures Two main parameters, which can both be influenced by temperature, temperature, characterize characterize our systems. systems. The discreteness = Lj/L„ LJ/ L., relates ness parameter, AJ Aj = to the spatial extent of of vortices in an array. array. It It is given by the ratio ratio of the junction LJ = = Wo/(21r junction inductance, Lj $0/(2irIIc), c), to the geometric inductance of of a single cell, cell, L.. Lt. The Stewart-McCumber 2 parameter .Bc parameter ßc = = R~C/LJ R JC/LJ defines defines the amount amount of damping in a single junction. junction. We often use junction normal-state use the junction normal-state resistance resistance for RJ. Rj. For given values values of critical current density, junction junction size, size, critical size, the values values of AJ Ay and .Bc ßc and cell size, are are determined at 4.2 K. K. By raising the A2 can be increased increased by a temperature, AJ factor of 4 and .B ß can be decreased decreased by 75%. 75%. We have have designed designed arrays for four difdifWe ferent parameter regimes, regimes, determined ferent by the possible possible combinations of low current density, density, high current density, and the presence presence or absence absence of a shunt resistor. In addition, addition, the size size of of the cell sistor. influences influences the parameter range. range. Table 22 sumarizes sumarizes the possibilities. We have have included included the minimum minimum and ma."(imum maximum cell sizes \vhich have been sizes which been designed, designed, although the smaller shunted cells have though

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been measured. not yet been measured. Ranges Ranges are axe mize at f/ = = 0.5. 0.5. listed for (3 ß and A), Aj, consistent with with listed changes in temperature. u changes u2.0.2 2.0.2

'Ii-iangular Triangular Arrays Arrays as Local Local Oscillators Oscillators ~

In order to determine the potential potential for triangular triangular arrays as as oscillators, we begin by studying studying the dc characteristics of single cells and single single row arrays, arrays. of Measurements of underdamped sysMeasurements systems reveal two steps steps in the currentcurrentvoltage (IV) characteristic, correspond(IV) correspondto L.C L,C and L}C LjC resonances resonances [1, 3]. 3]. ing to These steps steps are characteristics of single cells, and their their position does does not change change significantly with significantly with array size. size. MeasureMeasurements of two different different cell sizes sizes showed showed that the upper step voltage depends that step depends strongly strongly on the cell geometry, \vhile while the lower step step is only sightly sightly affected. affected. In Figure Figure 1, we compare compare the IV IV of a triantriangular cell \vith with parameters parameters {J 3= = 230 230 and A} = 2.4 Ay = 2.4 to that of a 9-cell array \vith with the same same parameters. parameters. The steps steps appear the presence of a magnetic field, only in the presence when the average flux per cell average applied flux frustration. /) (called frustration, f) is approximately approximately one-half. They are are stable for a range of of f/ = 0.3 0.3 -0.7, - 0.7. Figure 2 sho\vs shows the range of stability step voltage l'ange stability and the step variation, variation, by plotting plotting the step voltage with the array critical together with critical current vs, frustration. vs. frustration. Both are periodic periodic in field. As usual. the critical usual, critical current is largest at f/ = 0, largest 0. \vhile while the steps steps maximaxi-

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1: Current-Voltage Current-Volt age characterisFigure 1: tics of a single triangular cell and of single triangular an 8-cell array. array. The The parameters are .8 ß= = 230 230 and A) Aj = = 2.4, 2.4, and f/ = = 0.5. These These steps steps also also appeared in measurements surements of high critical critical current density junctions, \vhere where the devices devices more damped damped (fJ (ß '"~ 10) 10) and more discrete (Aj '"~ 0.6). 0.6). At At low (A) lo\v temperatures, 2 these ~\) these samples samples have have A j values values well well below 1. 1. We found that that the upper step, correspondingthe L.C corresponding L,C resonance, resonance, is only stable ,vhen the temperatUre stable when the temperature is raised such such that .\) X} > 0.3 (approxiraised 0.3 (approxiWe observed, observed, unexpectedly, mately). We both step step voltages showed that both showed a dependence on Li through pendence on Lj through the critical critical current density. density. For identical identical geometric current density devices ric designs. designs, 10'" low current devices (discussed above) above) produce resonances resonances (discussed m \', ,vhile at 0.1 0.1 and 0.23 0.23 mV. while the carrecorre3

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2: Step voltage va. vs. field is comFigure 2: pared to critical critical current vs. field for the triangular array. array. 8-cell triangular

sponding steps in high current density devices occurred occurred at 0.12 0.12 and O.20mV 0.20 mV de,'ices respectively. Current-voltage characcharacrespectivel)'. teristics teristics for a low current density and current density sample sample are coma high current pared in Figure Figure 3. .I\pparently, Apparently, the upper step step is more complicated than an LsC L,C resonance. resonance, and a higher-order higher-order dedependence on L pendence LJj should be included.

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Figure 3: 3: Current-voltage characteristics compared for a high current denden2 kAfcm2)) and a low cursity (jc (jc = = 1000 1000kA/cm 2 k.L\fcm2) rent density Uc (jc = 100 100kA/cm ) 8-cell S-cell triangular array. The lo\v jc array has triangular low jc has 2 ,:3 ß = 230 230 and .,\3 A , = 2.4~ 2.4. and the high jjce array has {3 — = 6.5 array has ß 6.5 and and .\} A2 = = 0.6. 0.6.

For' For overdamped j\ffictions. junctions, \ve we used used 4

shunt resistors of approximately In. lfi. In In both low current density and high current density samples, samples, this dominates dominates the shunt resistance. resistance. Including Including the shunt resistors made the cell size size much larger. Thus the shunted systems systems are are all all highly highly discrete, and we do not expect pect the L.C LtC resonance resonance to be be stable. stable. Typical show critical Typical IV's IV's show critical currents, but no other obvious nonlinearities. Lockin measurements measurements of the resistance resistance reveal a slight slight nonlinearity. nonlinearity. At At this point, point, we have not definitively definitively connected connected its particular voltage position position with with any any particular resonance. resonance. At the L.C At L,C resonance, resonance, underdamped underdamped arrays produce large-amplitude singlesingleharmonic harmonic oscillations in the horizontal junctions [1]. [1]. According to dc meameajunctions sluements, surements, oscillators based based on this resresonance onance operate at frequencies frequencies ranging from 70 with bandwidths from 70 -170GHz, - 170GHz, with 2 of p.m2 junctions, of 10 10 -20%. - 20%. For 99/im the power po\ver expected from M M horizontal junctions is M junctions ..V xX 22nW nW for low current densities M x 21 21 n nW densi ties and }.If W for high current densities. In our overdamped overdamped arrays, we have not yet identified an L.C L,C resonance resonance in the IV IV characteristic. With \V-band With W-band measurements, measurements, the output output frequency, po\ver, power, and linewidth line\vidth can be confirmed. In collaboration with with P. Caputo Caputo and A. A. Ustinov at KFA, two triangular triangular ro\vs rows have have been been coucoupled to fin-line fin-line antennas. antennas. A A stripline stripline with characteristic characteristic impedence impedence approxiwith mately mately equal to the expected expected L.C LSC resres-

onance onance couples couples the horizontal horizontal junctions junctions to the antenna. The fin-line fin-line antenna acts as as a matched transition transition to the 80 -120 — 120 GHz rectangular waveguide. waveguide. Measurements Measurements will will be made using facilities KFA by P. Caputo. cilities available at KFA measurements can also also be On-chip measurements used used to to determine the output output frequency and power. We plan to to couple the outoutput of of trianglur trianglur row oscillators to dedetector junctions. With good coupling, tector junctions. With many researchers researchers have found this this to to be an effective measurement measurementtechnique. Radiation emitted Radiation emitted from the oscillator steps in the detector excites Shapirio steps junction. Using simulations of the dejunction. junction, the oscillator frequency tector junction, and power can be inferred. We plan to to use this method to compare compare the output output use of triangular triangular rows rows with with various lengths. of Power measurements measurements of these these systems systems Power will will allow us to determine the degree degree of of phase-locking. phase-locking. We will will measure measure the dependence of of output frequency, pendence output power power on frequency, using a magnetic field field to tune the oscillator. lator. 2.0.3 2.0.3

Mode-locking Mode-locking in in 2D TrianTriangular Arrays gular Arrays

To study the possibility possibility of modelocking locking in a 2D triangular triangular array, \ve we cells, first investigated simple diamond cells: as as shown shown in Figure 4. 4. When a single bias current is applied to the ,ertical vertical junctions, junctions, both the top triangular triangular cell and the bottom bottom cell have the same same dc

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Figure Figure 4: 4: Diamond Cell voltage. Next a small trim trim current, ill, A/, is applied at the edges edges and removed removed at the same same ground as as the bias bias current. Thus more current is effectively effectively passed passed through the lower cell. This causes causes the voltage across across the lower junctions to increase cell junccrease relative relative to to the upper cell junctions. On the oscilloscope, the entire oscilloscope, 1\' IV of the lo\ver lower cell is translated in voltvoltage trim current is applied. age as as the trim applied. AlAlthough no dc voltage develops develops across across the horizontal horizontal junction, junction, it develops develops a sinusiodal ac voltage at a two two frequenfrequencies. cies, corresponding corresponding to the upper upper and lo\\Oercell oscillations [2J. lower [2]. SO So far, \ve we have confirmed the dc properties properties of this system. \"e on-chip meaWe intend intend to use use on-chip measurements to confirm the response surements response of the horizontal junction to tuning. horizontal junction \'.e t\VO row ro\v arrays, We have have designed designed two arrays, with tuning currents similar to the diawith 6

mond discussed will check discussed above. above. We will check that the tuning tuning is still still effective in in longer systems. Finally, Finally, we we will will mealonger systems. sure multi-row systems. sure multi-row systems. We have designed with leads signed five ro..v row arrays with leads at the edges edges for the application of trim trim currents. It important to apply equal It is important trim trim currents into into the array edges edges and remove remove them at the bottom. bottom. At At the same same time, time, we would like to use use a single source trim currents. These source for the trim These conditions make the array design conditions design challenging. We have have made two identical identical lenging. five-row arrays with with different configurations for the trim trim currents. Our goal is bias the five rows rows ..vith with incrementally incrementally to bias increasing increasing dc voltages. voltages. We will will test the range range of voltages voltages that can can be achieved achieved and the effect effect of magnetic field on this state. state. Once the array properties have have been been Once established established through dc measurements, measurements, we \vill address we will address the task of testing the high frequency frequency properties. properties. Our first step make on-chip on-chip measuremeasurestep will \vill be to make ments ments of single ro\vs rows \vhich which are part of a larger array. We will larger will compare compare this data with with data taken from isolated isolated rows rows of equal length. Thus, \ve we will measure equal \vill measure the effect effect of the array on the output output of a single will be to single row. Our next task will couple ro\VS couple the outputs outputs of two or more rows to a detector junction. will bias junction. We will the ro\vs to oscillate at the same rows same frequency, and compare compare the power power output quency, output system to the power po\verfrom only from this system one po\ver inone row. We hope hope to see see the power

crease crease as as the number of of rows when when the array is operating at a single frequency. frequency. Our ultimate ultimate goal in this this project is detection of of the envelope envelope or pulse. pulse. AlAlthough we expect approximately approximately 5 GHz GHz for a pulse repetition repetition rate in the time time domain, this this signal is to be carried by a wave at approximately approximately 120 120 GHz. GHz. In In orlow-frequency pulses, der to detect the low-frequency pulses, we will will also need need to to mix mix the signal down down using Josephson technology. Josephsontechnology.

References References [1] Yukon, S.P., S.P., N.C.H. N.C.H. Lin, J~acroMacro[1] scopic scop~c Quantum Phenonema Phenonema and CoherCoherence ence in Superconducting Superconducting Networks, Networks, Singapore, p.351 p.351 (1995). (1995). Singapore, [2] S.P., N.C.H. N.C.H. Lin, IEEE [2] Yukon, S.P., Trans. Appl. Appl. Sup. Sup. 5 2959 2959 (1995). (1995). [3] Duwel, A.E., A.E., P. Caputo, A.V. A.V. [3] Ustinov, T.P. Orlando, unpubUstiuov, lished work. [4] HYPRES. HYPRES, Inc., Inc., Elmsford, [4] 10523. 10523.

NY NY

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