AD-A127 135 APPLICATIONS OF JOSEPHSON JUNCTION SQUIDS / 1TCNOTGRU RDNOREC CAAPIDTCN(SUPERCONDUCTING QUAN'UM INTERF.. U) TRW SPACE AND

JNCLASSIFIED, A H SI AEN NOV 82 N0TGI4-81-C-T615 FIG 9/5 *NL

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MICROCOPY RESOLUTION TEST CHART

NATIONAL BUREAU OF STANDARDS- 1963-A

TRW SPec . Tocology One Space ParkGrolp Redondo Beach. CA 90278

213 535 4321

ulANNUAL REPORT

TO THE

OFFICE OF NAVAL RESEARCHCODE 414

800 N. QUINCY ST.

ARLINGTON, VA 22217

:11ON 4

APPLICATIONS OF JOSEPHSON

'JUNCTION SQUIDS AND ARRAYS

CONTRACT NO. NOOO14-81-C-0615

SEPTEMBER 1981 - SEPTEMBER 1982

PREPARED BY

A.H. SILVERADVANCED PRODUCTS LABORATORY 0 2 D1093APPLIED TECHNOLOGY DIVISION A .

NOVEMBER 1982

LAJ"* Ld

for r'b., I .;ol; iiidisLnbution "

88 04 21 138

TRW Inr

TRW Inc. One Space Park~bIct onics & Redondo Beach, CA 90278:Ufnse Sector 213.535.4321

ANNUAL REPORT

TO THE

OFFICE OF NAVAL RESEARCHCODE 4.14

800 N. QUINCY ST.ARLINGTON, VA 22217

ON

APPLICATIONS OF JOSEPHSON

* JUNCTION SQUIDS AND ARRAYS

CONTRACT NO. N00014-81-C-0615

SEPTEMBER 1981 - SEPTEMBER 1982

PREPARE. ,dY

A.H. SILVERADVANCED PRODUCTS LABORATORY

APPLIED TECHNOLOGY DIVISIONTRW

NOVEMBER 1982

LL-4

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (When Dae Entered),

REPORT DOCUMENTATION PAGE READ INSTRUCTIONSBEFORE COMPLETING FORM

T. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER.713

4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVEREDAnnual Progress ReportApplications of Josephson Junction Prgr ReptSQUIDs and Ar-rays September 1981 September'82

6. PERFORMING O1G. REPORT NUMBER

7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)

A. H. Silver N00014-81-C-0615

9. PERFORMING ORGANIZATION NAMF AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

Advanced Products Laboratory AREA A WORK UNIT NUMBERS

TRW Space and Technology Group P.E. 61153NOne Space Park, Redondo Beach, CA 90278

II. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATEOffice of Naval Research November 1982

Code 414 13. NUMBER OF PAGES800 N. Quincy St. Arlington, VA 22217 41

14. MONITORING AGENCY NAME & AODRESS(il different Irom Controling Office) IS. SECURITY CLASS. (of this report)

Unclassified

ISa. DECLASSIFICATION. DOWNGRADINGSCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Approved for Public ReleaseUnlimited Distribution

17. DISTRIBUTION STATEMENT (of the ebetract entered in Block 20, if different from Report)

IS. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side if necessary and identify by block number)

Josephson Junctions, SQUIDs, Arrays, Voltage-Controlled-Oscillator,Microwave Oscillator, monolithic superconducting transformers.

" 7 U STRACT (Continue on reverse side if necessary end Identify by block number)

This is the first Annual Report for an effort to demonstrate the applicationof SQUIDs (Superconducting QUantum Interference Device) and SQUID arrays tomicrowave systems. The application considered here is a microwave voltage-

*controlled oscillator. We report on the circuit design, numerical simulation,S( experimental design, and fabrication of the device including tests of the

monolithic impedance transforier. Predicted available power is approximately10 nW into a load impedance of Ik. 01e r^ ULS

DD I OJANR73 1473 EDITION OF 1 NOV65 IS OSSOLTESECURITY CLASSIFICATION OF THIS PAGE (ehon Data InterE)

k i .. ....i : -:. ..... .. ... . . . . , . . . . . . ... .. ..-

SECURITY CLASSIFICATION OF THIS PAGIIWhu' Data Emte0fad)

I SEC-UNITY CLASSIFICATIOUl of tv.* PAScomei Dee. Nuew

TABLE OF CONTENTS

Page

1. INTRODUCTION .................................... 1

12. WORK PLAN ........................................ 23. PROGRESS ......................................... 3

. 3.1 Transformer Design .......................... 3

3.2 Analysis of Voltage-Clamped SQUIDs .......... 10

3.3 SQUID VCO................................. 16

3.3.1 Design ............................... 16

3.3.2 Fabrication .......................... 21

4.CONCLUSIONS ...................................... 24

(APPENDIX A ....................................... 25APPENDIX B ....................................... 29

DISTRIBUTION LIST ................................ 36

LIST OF FIGURES

Page

Figure I - Computed voltage standing wave radio(VSWR) as a function of frequencyfor transformer circuit shown inFigure 3 .............................. 4

Figure 2 - Equivalent circuit (top) and physicallayout (not to scale) of X-band trans-former designed and simulated ......... 5

Figure 3 - Photograph of the 50f coplanar lines

used to test dimensional changes ...... 6

Figure 4 - Printout of composite masks for the 50(to I0 transformers ..................... 8

Figure 5 - Printout of composite masks for the 501to I0 transformer terminated in the I1resistor at the center ................. 9

Figure 6 - Photograph of transformer test chipmounted in a brass holder and connected

to two OSM bulkhead connectors ........ II

Figure 7 - Response of 500 tapered coaxial lines

on silicon substrate measured at 4K ... 12

Figure 8 - Response of the double-ended 500 to

I0 transformers measured at 4K ........ 13

Figure 9 - Resistive SQUID VCO ................... 14

Figure 10 - Voltage-clamped dc SQUID .............. 15

Figure Ila - Composite of seven masks designed forthe four VCO circuits ................. 17

Figure lib - Composite of mask artwork for the

central section of VCO #2 ............. 18

Figure llc - Composite of mask artwork for thecentral section of VCO #3 ............. 19

Figure Ild - Composite of the mark artwork forthe central section of VCO #4 ......... 20

Figure 12 - Photographs of the central sectionsof the four different VCO chips

( after fabrication ..................... 23

II

t II I I ..............-..

f

, I. INTRODUCTION

This is the Annual Progress Report for Contract No. NOOO4-81-C-

0615, "Application of Josephson Junction SQUIDs and Arrays." covering

the period from I September 1981 through 30 September 1982. The objectives

of this program are to define and demonstrate applications of SQUIDs and

SQUID arrays via analysis and experiment. The goals of this contract

were to investigate and demonstrate the properties of a SQUID voltage-

controlled-oscillator (VCO). These goals were met by 1) analysis and

simulation of a voltage-clamped resistive SQUID and a voltage-clamped

dc SQUID, 2) design, fabrication and measurement of appropriate micro-

wave matching transformer, and, 3) design, fabrication, and measurement

of a SQUID VCO. We report on progress in these three areas.

"I

•i (

*I

' . .*

2. WORK PLAN

This is a new contract for a projected multi-year investigation

of Superconducting QUantum Interference Device (SQUID) arrays and their

application to microwave and gigabit technology. The focus of this

contract is the investigation and demonstration of a SQUID voltage-

controlled oscillator (VCO). The array is then projected to increase

the available power and operating impedance. The approach utilizes

monolithic superconducting integrated circuits which were designed,

fabricated, and tested at TRW.

Three tasks were undertaken in the first year:

Task 1. Analysis of dc SQUID Arrays

Task 2. Design of dc SQUID Generator

Task 3. SQUID VCO Fabrication and Measurement.

A number of the steps are very similar to those required for a contract

with the Naval Research Laboratory, "Demonstration of a SQUID Parametric

Amplifier." Such steps were carried out jointly and are reported to

both agencies. TRW is concurrently conducting Independent Research and

Development on Advanced Josephson Devices. This project is principally

concerned with development of a Josephson integrated circuit fabrication

capability. Some of the activities of that program which impact this

contract are discussed here.

1

2

*__- .--. *.*

3. PROGRESS

3.1 Transformer Design

Since the SQUID VCO is necessarily a very low impedance device,

a suitable transformer is an essential ingredient for evaluating the

basic VCO, particularly with respect to available power. In order to

carry out this transformation in both impedance and dimension in a

reproducible and predictable manner, the transformer is integrated

with the active circuitry.

The basic architecture of the transformer was presented in the

contract proposal. We have refined the design for the TRW fabrication

process and reconsidered the problems of launching from 509 coaxial

cable into 50Q coplanar line, dimensional step from 1 mm coplanar line

at 500, and construction of capacitors in the lumped element impedance

transformer. The electrical design was optimized numerically using

COMPACT with a computed VSWR < 1.25 over the 8-12 GHz band (Figure 1).

Figure 2 shows the equivalent electrical circuit and the geometrical

layout.

A test of the effect of changing dimensions in 50P coplanar line

was performed by fabricating three 50SI transmission lines: a continuous

coplanar line at mm dimensions, a sharply stepped coplanar line, and a

short, tapered transition as shown in Figure 3. The measured performance

showed no significant differences between the three lines. Therefore,

the input LC circuit in the transformer intended to tune out the

: inductance of the step in the coplanar line was deleted.

The transformer was designed to be fabricated on a 2 inch silicon

wafer, 0.015 in. thick, with a minimum line width of 50um. An OSM micro-

wave launcher drives the 500 coplanar line which has a center conductor

width of 50m, ground plance spacing of 304m, and an effective dielectric

*1 3

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L . ,] ......... ...... I- ="I .. . .. li... ... ..... .. ... ..... .... I-__ ... ... . . ... . . .. ....

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Figure 3. Photograph of the 5012 coplanar lines

used to test dimensional changes.

6

constant of 6.4. The reduction in e and its dependence on linewidthA-

results from the finite thickness of the Si substrate. The IQ micro-

strip in the transformer is 50m wide and separated from the Nb ground

plane by 50nm Nb205 and 200nm SiO. It has an effective c=13.

The transformer design incorporates short (< X/4) sections of9 coplanar and microstrip lines which act as lumped inductors and capacitors,

respectively. The inductive lines are 50 coplanar lines terminated

by 10 microstrip, with L=Z.L/V, where Zo is the line impedance, £ the

line length, and v the propagation velocity. Capacitors are 1i and 0.5a

microstrip either terminated by 50S1 coplanar or used as open parallel

stubs. The capacitance of short, open lines is given by Ct!/Zov.

Photolithographic patterns were defined as 4-level masks and produced

at the TRW Microelectronics Center for the combined dimensional and

impedance transformer. For the dimensions and tolerances required, masks

were fabricated directly at the reticle level in an Electromask pattern

generator. Figure 4 shows the computer-generated composite of three

I cm x 2 cm chips which were fabricated on 2" silicon wafers, .015"

thick. Each chip has 2 coplanar inputs with tapered lines. On one chip

the reduced width coplanar line couples directly through; on the second

chip, the transformers from each end are connected for in-out transmission

measurements. The third chip has each coplanar line and transformer

terminated with a matched resistive load. Figure 5 is an expanded plot

of the transformer and terminating resistor on the third chip.

The transformers were fabricated in a I cm x 2 cm format on 2"

diameter silicon wafers with an insulating SiO 2 surface. Three test

chips are produced on each wafer. Following fabrication, the wafers

were cleaved with a modified Tempress scriber and the chips mounted in

a holder suitable for connection to an OSM coaxial bulkhead launcher.

Measurements are made at T=4K with an HP-8410 Network Analyzer. The

data are in the form of the scattering matrix coefficients S11 and Sl2.

Only the magnitude of S is reported since the phase is difficult to

calibrate with long coaxial lines into the helium dewar.

7

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The test transformer chips are mounted with a coaxial connector

at each end as shown in Figure 6. As anticipated, connecting the co-

planar input to the bulkhead connector was a significant problem. An

acceptable solution is to use In solder to connect gold ribbon from

the connector centerpin and bulkhead to the coplanar lines. To

facilitate soldering to the Nb film, a gold film is evaporated over the

Nb. This is done before the Nb is patterned. Figure 7 shows the

response of the simple tapered coplanar lines at 4 kelvin; Figure 8

the response of the double-ended transformer, in which the 500 coplanar

line is transformed to lS microstrip at the center of the chip, and

then transformed back to 50Q coplanar at the other end of the chip. We

have not measured good S-parameter characteristics with the terminated

transformers and we attribute this to a problem in making good contact

with the resistors.

3.2 Analysis of Voltage-Clamped SQUIDs

We have investigated the voltage-clamped SQUID in two forms appro-

priate to the voltage-controlled oscillators, the resistive SQUID of

Figure 9 and the dual resistive SQUID with common voltage-biasing

resistor which we call the voltage clamped dc SQUID (Figure 10). To

the best of our knowledge, neither of these devices incorporating the

RSJ model with appropriate capacitance has been fully investigated andthus computer simulation was undertaken to predict the operating charac-

teristics and parameterize the performance.

Analyses were performed with numerical simulations for preselected

ranges of the device parameters. Computations of the transient response

and subsequent Fourier spectra were performed on a Cyber 174/750 machine.

The results are described in a paper which will be given at the 1982

Applied Superconductivity Conference and submitted for publication in

the Conference Proceedings to appear in the IEEE Transactions on

Magnetics in 1983. The manuscript, "SQUID Voltage-Controlled-Oscillator,"

is attached as a part of this report. (Appendix A).

0

10

(~ -. - - ~ -

The test transformer chips are mounted with a coaxial connector

at each end as shown In Figure 6. As anticipated, connecting the co-

planar input to the bulkhead connector was a significant problem. An

acceptable solution is to use In solder to connect gold ribbon from

the connector centerpin and bulkhead to the coplanar lines. To

facilitate soldering to the Nb film, a gold film is evaporated over the

Nb. This is done before the Nb is patterned. Figure 7 shows the

response of the simple tapered coplanar lines at 4 kelvin; Figure 8

the response of the double-ended transformer, in which the 5Oa coplanar

line is transformed to IQ microstrip at the center of the chip, and

then transformed back to 50 coplanar at the other end of the chip. We

have not measured good S-parameter characteristics with the terminated

transformers and we attribute this to a problem in making good contact

with the resistors.

3.2 Analysis of Voltage-Clamped SQUIDs

We have investigated the voltage-clamped SQUID in two forms appro-

priate to the voltage-controlled oscillators, the resistive SQUID of

Figure 9 and the dual resistive SQUID with common voltage-biasing

resistor which we call the voltage clamped dc SQUID.(Figure 10). To

the best of our knowledge, neither of these devices incorporating the

RSJ model with appropriate capacitance has been fully investigated and

thus computer simulation was undertaken to predict the operating charac-

teristics and parameterize the performance.

Analyses were performed with numerical simulations for preselected

ranges of the device parameters. Computations of the transient response

and subsequent Fourier spectra were performed on a Cyber 174/750 machine.

The results are described in a paper which will be given at the 1982

Applied Superconductivity Conference and submitted for publication in

the Conference Proceedings to appear in the IEEE Transactions on

Magnetics in 1983. The manuscript, "SQUID Voltage-Controlled-Oscillator,"

is attached as a part of this report. (Appendix A).

10

i•

FIGURE 6. Photograph of transformer test dhip mounted in abrass holder and connected to two OSM bulkhead connectors.The tapered coplanar lines at each end are visible in thephotograph. The grey rectangle in the center of the chipis anodized Nb covered with SiO. The transformers are loca-ted in the same rectangle but are not clearly visible in thephotograph.

k

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T - ..i ... ..~ .*~~~T*r ..~] ...

j* fhr ZOO T(I~~A.I !I;,.-~-Tli t: ..... ........... T *-T _ F.

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.11177

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11:A .. .....

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to i

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Figure 8. Response of the double-ended 50n to In transformers

measured at 4K. The upper graph is S 11 (and S 22)- the lower is S1

13

r CR

Figure 9. Resistive SQUID VCO. L is the SQUID inductance

andr te sallvoltage-biasing resistor. R is

-- the load resistance which sets the damping.

14.

RFOTPT 10 RF OUTPUT

~15

3.3 SQUID VCO

3.3.1 Design

The VCO design placed the resistive SQUID at the low impedance end

of the 50 to IQ transformer discussed above. Connection to the trans-

former is with IQ superconducting microstripline. Two devices are

placed on each I cm x 2 cm chip; four chips are designed on each wafer.

The SQUID was designed to utilize the Nb/Nb2O5/PbBi junctions in use

at TRW, with Pbln interconnecting lines. Figure If shows the composite

artwork for the VCO wafer. The structures at the top and bottom of

each chip are test junctions and resistors.

The impedance of the SQUID, AL-IC, is set at 0.3Q, such that the

loading of the IQ transformer will result in Q=3.3. Design values are2 4

chosen to maximize * /2L=lO 4kT and set a=], the SQUID resonance frequencyequal to 9GHz, and the Josephson plasma resonance frequency also equal

to 9GHz. Thus L = 5pH

C = 65pF

ic = 67PA

jo = 9A/cm2

and the junction area is 50um x 14.9pm = 745um 2 . The biasing resistance

r is independently set with a design value near 10-3Q. This design assumes

that the IQ load dominates over the internal quasiparticle resistance.

Because of the nature of the response for Q>2, we varied the design

for each of the four chips on the wafer as follows:VCO # L(pH) C(pF) Q ic(iA) Rd(1)

1 5 65 3.3 67

2 10 32.5 1.7 33.5 ---

3 5 65 1.7 67 I

4 2.5 130 1.7 134 0.25.I

16

F !

-Mr

.4~

lit'

Figure Ila. Composite of seven masks designed for the four VCO circuits.

Test junctions and resistors are Faced above and below each of the 2

VCO's per chip.

17

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Rd is an additional damping resistance placed across the junction to

lower the Q below 2. Although a substantial fraction of the microwave

power is lost in the additional damping resistances in VCO 3, 4, they

provide broad band damping compared to the transformed load of VCO 1,

2 which is well-defined only over the transformer bandwidth near 9GHz.

In VCO 2 the inductance was doubled, halving the flux quantum energy,

consequently reducing the available output power and the loaded Q.

3.3.2 Fabrication

The composite VCOs, which include the voltage-clamped resistive

SQUIDs and matching transformer, were fabricated on 2" silicon wafers

using Nb/Nb 203/PbBi junctions, Au resistors, and PbIn interconnection

lines. This represents a change from the sapphire substrates originally

planned, but permits multiple chip fabrication and easy dicing of the

wafer. Also, this method eliminates photoresist problems which occur

at the edge of the wafer.

The change from sapphire to silicon substrates produced a problem

holding substrates in the vacuum system. Since silicon is more fragile

than sapphire, one cannot rigidly clamp the substrate for efficient

heat sinking. Vacuum grease is effective at providing efficient heat

transfer and mechanical support even for sustrates mounted upside down.

However, the grease is a potential contaminant for the process which

occurs after the vacuum deposition. We have adopted a practice of

scraping the grease and cleaning with hot xylene before doing lift-off

in acetone. This technique appears manageable although clearly not

optimum.

A more common problem was one of multi-layer deposition and processing

where good electrical contact is required between layers. Three different

vacuum systems were used for this project: an S-Gun sputtering system

for Nb deposition, an ion gun system for junction formation, and an e-beam

evaporator for other depositions. Only the ion gun system permitted in

vacuo cleaning before deposition. The PbBi junction counter-electrode

is thermally evaporated in the ion gun system immediately after reactive-

ion-oxidation. However, we found significant problems with contacts

21

.. ..- --- -

4

when films were deposited in e-beam system. On a temporary basis, we

were thermally depositing other metals in the ion gun system, thereby

permitting ion cleaning of the surface immediately prior to evaporation.

This showed some improvement but was not completely successful, particu-

larly for the alloy films. Also, this multiple use of the ion gun

Isystem led to contamination of the system with other materials prior tojunction formation.

This problem was addressed more extensively under our IR&D program

and we believe it has been resolved successfully. The e-beam system was

modified mechanically and electrically to include an rf sputtering stage

on which the substrates are mounted. RF sputter cleaning is then per-

formed immediately prior to each new evaporation. Results with this new

system are very encouraging. We have fabricated VCO circuits which show

satisfactory junctions and connections. Voltage-biasing resistors in

the 50-1OOmP range have been fabricated, one or two orders of magnitude

larger than desirable. Figure 12 shows photographs of the SQUID section

of the four different VCO chips after fabrication.

22

----------------------------

F 12. -t a o

23 7

II

• .

Figure 12. Photographs of the central sections of the

four different VCO chips after fabrication.

, 23

hp

4. CONCLUSIONS

Measurements show that the SQUID does generate microwave power,

but the linewidth is much broader than expected. We believe this is

a result of both external noise and internal instabilities of the

type identified in 3.2. We are continuing to refine the measurements

and SQUID parameters to demonstrate a well-behaved VCO.

°I

j °.

JI

APPENDIX ASQUID VOLTAECa1' L D-OSC IUAl\*

A.h. Silver, R.D. Sandell, and J.Z. WilcoxTR space and Technology Group

Ofte Space park, Redondo Beach, CA 90278

Abstract internal losses. 7he shunt capacitance of the tunnel

We have investigated the SQJID an a junction, which is frequently considered a seriousvoltage-controlled source of microwmves. The low shuI ting impedance, can be effectively parallel-tunedispedae "resistive" SQUID can be a relatively high by the SQUID inductance. The load resistance, together

power (..nw), tunable, and monochromatic source for both with the internal junction resistance, will determineon-chip and off-chip applications. Studies of the the loaded U of the VCO.tme-depedent junction phase and the available power One expects the instantaneous signal bandwidth

spectra as they vary with such device parameters as to be determined by the Johnson noise across the netloaded Q and the S.UID-,,2wL c o establish design (low frequency) resistance as a result of frequencyrules for a well-behaved oscillator. For a 'CO eQ'2; modulation of the oscillator by the thermal voltagefor 60>2 degenerate parametric suarmu ic oscillations fluctuations. This hos been predictdiand verified forand caotic instabilities are observed. Power increase point contact devices as 6f-4?'kTr/# 4.3xl0 rT for ais suggested by the use of voltage-clamped dc SQUIDs biasing resistance r at temperature9'. This value isand arrays. independent of frequency to the extent that the bias

current is stable and noise-free.7he stable operating mode of a low 0 -2 LiA. 0

Introduction SQUID consists of regular flow of quantized flux t"The superconducting voltage-controlled- The internal circulating power in the SQUID TS

oscillator (VCO) has potential applications as an essentially that of changing quantized flux in theintegrated, on-chip source for such superconducting inductafce L at the oscillation frequency,devices as analog-to-digital converters (u'pling P nt 6,/41L, while the power delivered to the loadclock), rf SQUID magnetcmeters (excitation source), resistc is V

2 /R where V4 0 w/27i. Thus, the power inparametric amplifiers (pu'ip source), quasiparticle the load is P R=P. A/rLmre / w L. Realotic valuesmixers (local oscillator). and intracomputer of L approxiateqf 10 'qH project to " 0W of powercomrunications. A source of sufficiently high power near IOGIi, with power increasing linearly withcan be useful as an agile signal generator. This paper frequency at constant 0. This relation for P should

describes the SQUID WCO as the implementation of this be valid as 0 decreases until the VCO is sufficientlysource. loaded by R to reduce the ac voltage. Fundamental to

The impetus for development of achieving these power levels is small L and small Q.microwave/mill imeter wave signal generatcrs in This requirement leads directl% to load resistqcesuperconducting technology has its origin in the values R-Qw L of the order of 10 A for 04, LMIO 7'H,Josephson relations which predict a sinusoidal and f '.lOGk. Proper iapedance matching is clearlyJosephon current under the application of a dc voltage necessary for both on-chip and off-chip appl ications.which is linearly related to the Josephson frequency. Wbherent arrays of SOtlZe which will increase the total

w -2rV/ . Unfortunately, problems of imnpaance and impedance can increase the available power as well ast;e dyninics of the junction phase have made it simplify the impedance matching.difficult to achieve the expected performance.

W* argue here that the SQUID and SQUID arraysare the natural form for a WO. In order to achieve Resistive SQUIDlinear tuning, the source resistance mist be sall We have investigated the voltage-claeped SQUIDcczpared to the junction inpedance. Such a small in two forms: the resistive SQUID (Fig. la) and theresistance conected directly across the junction would dual resistive SQUID with omon voltage-biasingshort out the Josephson oscillations, greatly reduce resistor which we call the voltage-clamped dc SQUIDthe signal voltage across the junction, and no power (Fig. lb). 7he dynamical response of the SQUID shownwill be delivered to the load. Mwever. in a resistive in Fig. la ws simulated numerically to predict the

SQUID (Fig. 1) the voltage-biasing resistor is isolated operating characteristics of the SQUID VCO. Wefrom the junction by the SQUID inductance L. Thus, the envision R to be the load to which power is delivered.dc voltage will be developed across the bias resistor, This circuit obeys the relation

the ac voltage across the inductance, and the totalvoltage across the junction. a +(ne nr)e + l .nxqR+ACo2d)i n ri$a. +n fl (1)

Tuntul junctions gnerally have lower internalonductance than microbridges, at least below the 1

energy gap, and are desirable junctions to minimize where e is the junction Phase. / Rn1 /R-n w/.L7_,0-iti 0 .01o~fL/;0 and time is

MF O.T'Jut ftp OTPUT n4asured in I/w 7 The voleage across the junctionand load resisfor R is Vtw 0/2 17. The last term on

, ' p, the right hand side of . ll is aorI)xmatl tiexpected Josephson frequency wc /

* : equivalent to a voltae sourceiri9 in serieswith r;, C| ,,.C .?c , the actual dc voltage across the junct is somewhat

lower than rI and mist be deteFmined by either directCmeasuret or calculation of 00 3.

The simulations derived 6(t) and 6 (t) fora selected values of B., , and with TheO. 7he

results are essentially indepadU of sr for allFigure 1. Equivalent circuit of SQUID VCO. (a) reasonable values of interest so ,-10 is used inResisti v SQIJID; (b) Voltage-clamped dc SQUID. all calculations repormd hare. his means that

-l10ic aid, hence. v0IO at wl-w O,Suported by the Office of bbval Research, Cntract 7he transient respose is doinated by o

NO. 00014-61-C-0615. and Wj. Figure 2 shows the time evolution of e a:d eM for owI, 0-1 and 5 for selected values of the voltageanuncript rsceivmS Nbvaer 30, 1982 bias. Fr Qml, the turn-on transient is short

a 25

P' ,, . . 41) WO... :. , *... -. . -,.. . - b .. ... ; . .. .

OL 11J I. I I;, J 1 0I - .....,,3 05. 1 , 0 10

9S0 0

r Figure 2. Selected transient response of e and 6 for Figure 3. 9-dependence of the power delivered to thethe resistive SQUID with 0-1. Time is in units of load at w .w for 0-1 in the2 resistive SQUID. Power

Wis nodze8 to Iw#0/(2,) li.

(approximately Q/ u) and associated with shock behaved except for a subarnic response at w -1.2wO,excitation of the resonant LC circuit, the fundamental Q-2. For Q>2, there is a very strong subb, xcfrequency of the periodic response is w , and the response at w -2w , and anhamonic resporze nearperiodicity in a moothly stepped e is 2r. if the 0 w 1.2w. For 22 lead to san undesirable 10 1 2 3spectral response. Nevertheless, even for Ow1, the FREQUENCYpowr is not even diminished by a factor of 2 from thepeak value. Figure 4. Frequency dependence of the power delivered

Figure 4 shows a ompilation of the cemputed to the load at w for selected Q-values with 6-l inpows of the Josephson oscillations as a function of 0 the rjsistue SAID. Power is normalized to

* for 8-1. in the regime 0

as *mi We have carried out simulations of the

symmetric voltage-clpid dc SQUID shown in Fig. lb.mThe nw parameters which define the device performance

el a (r -,)1.e and . ri~z to AMe " of the

rightw ) et Ld ; , respectively, and weme have defined 0 as MwiJ,, , where L is the inductance

*of one-half of the dc &•D. n a limited number ofsimulations with el and 01-0 . the dc: SQ:UID bdeves

S kidentically to the resistive rf SQlID with e -,-0.The two junctions switch in-phase with one another andthe resulting currents in each L add in the small

-. resistance r. Hmver. the voltage across the output(2.L) is identically zero.

Ebr 8 - w/2 and a -1, the cayutation shows that"oresponds ak the expected Josephean frequency while

,,0 4e+ 460 0 0 + responds at tm secd harontic. This frequencydoubling is a result of the alternate switching of the

Figure . Computed transient response and fr tw junctions in each Josephson period. We havet %he resisti.Lve SQUID wit~h 51, Q,,5, and * , -I computed the response at. 1- 7/2, 6 -1 for a range of 0co~rsponding to uil.l o" Time is Ueasured in rIo 1 to 5; the behavior of e. and e_ is very similar

to that bserved for 0, S in the resistive SQUID andurstable for princial values u/2( S'-ih/2,t. s m b will not be reproduced here.

related to the instability.The expected effect of increasing o at constant

0-I is illustrated in the power spectra of Fig. 6. The SQID a VrObracketed synols are the Josepson frequencies t Arrays of cansymbols c~ctedns ery fSQUl, driven cg mrently, c

o cn. nt all harmonic spectra are shown. Belo achieve further increase in poer. Three types of

0-u, all computed points are well behaved with some arrays are possible: the longitudinal dc SQJID array,

expected harmonics but no subaoic repose. Ftr the transverse dc SQ.ILD array, and the resistive SQUIDc bt os ~ Fr bus. We discuss ths briefly. preliminary8-, we oerve subhron=ics as we did for large 0 descriptions of the ilngitdinal and transverse dcvalues at 0 -1. For 0 3, w, the time dependent responsevalu-m ves mo.r l and t we time dhae nt resqxo SQUID arrays were given previously in connction withbecams even ore caplex aid we have nt conuted uparametric unylification . Figure 7 shs the samplespectral poers. Such B-values would be considered circuits for both the linear dc SQUID arrays, and for aoutside the normal range for a SOMD and moves toard two-dimionai l array which corduns the two linearthe mon-SQUID Josephson junction for which this arrays. Analysis of the longitudinal flux-flow arrayanalysis indicates very poor quality Co. Me Shown that it is unstable with respect to the

flux-flow made whlch is the one required for the VCO.

ltage-Cl!E2 C SQUID As Sandell, et al have shon, this type of array can

The voltage-cl - ed dc SQUID of Fig. lb c b provide series increase in rf impedance although it

recognize as # co bination of two identical resistive requires large dc currents because of its parallel

SQUIs with a common biasing resistr r. This leads to nature at dc. Furthezwre. in a tunnel Junction

strong coupling of the two VO's with identical Implemnaton as carqred with micrbridges, narrow

feencies but relative phases determined by the fielg linewidths will require mall biasing resastors as inIu -. Two different modes of the ou~pled systeo th voltage-cleiped dc SQMID. he transverse array is

Sare esmtially a sysmetric me, with the t recognized as a series array of dc SQUID pairs. Itjunctio in parallel, and an antiadmmetric m , with provides increased iMedance at both rf and dc,the tvo j ntions n eries. n oe wnt offering a reduction in the direct current required.

iredanmc are achieved for the antiurpmtric or series gain, narro linewidths will require mall biasing

m.de in which the circulating currents are in the sme resistors. It wodd be undeirable to fabricate large

direction. arrays requiring large ns of carefully matchedmll resistors.

A method of avoiding the resistor network and-1producing a high pwr array is the resistive SQUID bus

as shown in Fig. 7. It is an extenson of theIvoltage-clmed dc MQUID to N resistive SQUI with a

Sc2 mon voltag.-biasing resistor. This could be readily"W/ accsplished in a thin film ftomat with a pillboxof resistor at the center of a radial array of SOUIs.

These migh dive a coaxial line to an off-chip load.

i02

10-1

a 41C0 1 2 3 4 5

FREQUENCY rigure 7. Schematic diagrams of SQUID arrays. (a)Figure 6. Narnc specta for the resistive S D iLongituinal (upper) and transverse (lower) flux-

flow arrays; (b) Two dimensional array: (c) SQUIDwith Qwl and selected . bus.

27__ _ _ __ _ _ _ __ _ _ __ _ _ _

On-hip0 the bus can be used to drive many differentloads %hich require oherent input, as in clocking a Reforencsshift register or driving an array of mixers. if one 1. A.H. Silver, J.r. 7,, zmn, and R.A. KYwper,supplies internal phiase shifts of v betwmen adjacnt "rtribuon of Thermal Noise to the Uinedthelarew.s (as in the do lIUD), tan e can supply of Josephson Radiation fram &eronductin9alteroAte aut-of-yhue signals. In either one, Point ( b tacts," Appl. Plys. Lett. 11, pp.coherence in guaranteed by the osmn bias resistor end 209-211 (1967).supercoduct.ing phase chzence. 2. A.H. Silver, D.C. Prlia ore-km, R.D. Sudell,

and 3.P. Hurrell, "arametric Prperties ofSQUID Lattice Arrays," IE Trens. Magri.

9620may MMG-17, pp.412-415 (19B1).The SQUID is the natural for for signal 3. R.Lz. Ka-t e ac Joephson Effect in

generation via the Josephso effect. Wile the bare Wstwftic Jwnct~ns Range and Stability ofJosephson junction suffers fram both chaotic Phase Lock," J. Appl. Phys. 52. pp. 3528-3541instabilities ard low inpedance, its incorporti in a (1961). "hbtic States of rf-kased Josephsonlow 0. loi 0 SQUID tures out the junction capacitance Junctions," J. Appl. Phys. 52, pp. 6241-6246and ontrols the instability by directly harnessing the (1981).periodic nature of the junction phase to the quantum 4. M.T. Levinson, "Even and Odd Subhanoicperiodicity of the SUID mgnetic flux. This results Frequencies and Chas in Josepson Junctim s:in an efficient conversion of the Josephson energy t Impact on Parametric lMplifiers?," J. AppI.the circulating current in the SQUID inductance and, Phys. 53, Wp. 4294-4299 (19S2).hence, to external circuitry. The power is maximized 5. J.E. 0 iwrman and A.H. Silver, "Coherentby minimzin the inductance, although at further Radiation From High-Order Quantum Transitionsreduction in source Irlmdance. This last prdblen is in Baul-Area Superond~ucting Contacts," Phys.alleviated by fonning a priori coherent, stable arrays Rev. Lot. 19, pp. 14-16 (1967).of SQUIX to increase both the total power and 6. A.H. Silver and J.E. Zi , "Coupledimdance. Such arrays have the voltage-claeyed dc uperconducting Quantum ocillators." Prys.SQUID as the basic cell. The design presented makes Rev. 158. pp. 423-425 (1967).minimian demands on both lithoraphy and 3osphon 7. R.D. Sarell, C. Varmazis, A.K. Jan, and J.E.current density. Lukens. "Flux Modulated Coherent Radiation from

Several expimental results have been reported Arrays of Joephson 4icrobi s Coupled byin recent years which pertain to this device. The Supercorducting Loops." I= Trans. magn.group at SUY have studied micraridge VCO', including MhG-15, pp. 462-464 (1979).pairs and arrays. The successful results wre in N. Clarnder ard H.H. Zappe, "omponents for athe dc SQUID-like arrays reminiscent of Fig. 7a, Jos Intraconputar Ommmication System,"although the SQUID inductances were very large o0pr J. Appi. Phys. 50, pp. 3768-3769 (1979).to the values suggested here. Calarder and Zappe0 9. D.S. Takern-- 'Digital Fevquency-Divisionpropoed using a dc SQUID as a tunable oscillator for Multiplexing Using Josephmo Junctiors,"intraoomper cousuncation in a Josephaon processor 9 10 Thesis. MIT (1980).They predicted % b.W of power at 500 Gik. Tuckezrman "0. N. Calander, T. Cas i t and S. Rudkr,deristratad this concept by connect a dc S 0UID "Shunted Josephson Tunel Junctions- if ghtransmitter with another dc SQU D receiver by a Frequency, Self-Pvmd L Nise lifiers,"superconducting microstripline. The tranmitted J. &Vpl. fhs. 53. pp. 5093-5103 (1982).ni yve signals wor readily detected. Caledar, etal dercistrated a resistive SQUID WVO incidentally totheir self-puVzed Josepson perametric2 mplifier.Using a SQJID with 6 -2. ZmpHi, r-3xlO . and a inmatching transformer, they oberved 0.15nW at 10.4 G1zwith a bandwidth of 150 MHr. This linmwidth is muchgreater then the thermal-no:iLe-limited value, 5 WI.J,and is rertedy broadened by noise in the biascurrent. Assuming that the aveage por is diminishedby the siw factor as th line broadening, one couldhave expected as much as 4.5*, in excellent agreemtwith the predictions of the masde.

.2

~28

__ _ _ _ _ __ _ _ _ _ __ _ _ _ _- . -

APPENDIX B

Printout of the computed characteristics of the resistive SQUID VCO. The

first line shows the run number, 0, Q, 1, computed fundamental frequency,and subharmonic number relative to the Josephson frequency; the second line

is the computed spectral power for the first seven harmonics of the funda-

mental frequency. Where the frequency and harmonic number are reported as

zero, the oscillator is anharmonic.

R aun#_ Q W o Subharmonicl

P P2 P3 P 4 P5 P6 P7

1 0.78 1.00 5 0C 4.993E-01 11. 215E-O11 5.1912E-O 2 9. 05E- P-; 6.02?7E-04 4.4,TE-Oa 4.!21E-CE6 3. e. 1E-C7

2 0.78 1.00 8Ck 7.989E-01 1-. 369E-01 .C 0 E-O C 1. I ' --- . '1 F -05 Z". 4 1 1E - 0O .t11 -3 . 1 E 0

3 0.78 1.00 10V0 9.987E-015.172E-01 2.063E-02 5.123E-04 1.546E-05 4.701E-07 1.446E-08 4.479E-10

4 0.7S 1.00 1200 1.199E 00 14.861E-0i 9. 2.E-O': 1. 59'E-04 2.920E-06 5.4..4E-O'- 1.vi9E-09 1.917E-iI

k

5 0.78 I. 00 20 C. 1.9.CE 00 11.885E-01 4.'P0E-0, I 1. E: -- . 27"4r 0 9 ?. 76?E-12 2. :44E-14 5.81E-17

6 1. 5? 1.0 500 4. 989E-01 I

2.6 10E-01 2.047'E-01 1. 304F-01I 2.566E-02 2 .433E - C C.':43E-04 I. 489E-04

7 1.57 1. 00 800 7.905E-01 I7.97.E-01 3.118E-01 2.104E-02 2.274E-03 3.M1'SE-u4 3.6'3E-05 4.3MIE-06

8 1.57 1. 00 1000 9.982E-01 I1.476E 00 1.644E-01 1.IS0E-62 1.eE4E-OD 9e...... . .231E-06 7.Z60E-07

9 1.57 1.00 1200 1.198E 80 11.500E 00 8.592E-02 4.932E-03 2.864E-04 i.6S621-05 9.9U2E-07 5.900E-06

I.

10 1.57 1.00 2000 1.998E 00 16.933E-01 6.667E-03 6.659E-05 . 709E-0? 6. 7:;'E- 6.850E-11 6.794E-13

11 3.14 1.00 500 4. =-'7E-e1 14.494E-01 4.154E-01 5. 0E- :1 3.28C.E-Oi t.i, 2E-C'2 1.259E-02 4.4421-02

12 3.14 1.00 800 7.974E-01 11.273E 00 1.396E ea 1.910E-01 2.640E-02 1.132E-02 2'.722E-03 6.296E-04

13 3.14 1.00 1000 9.970E-01 1

Ci j available to DTIC does notn ~t r legible .epod

3.309E 00 5.415E-01 1.225E-O± 2. -0 -02 4. i i6E-,3? 6.823E-04 1.723E-04

14 3.14 1.00 1200 0.OOOE 00 00.000E 00 0.OOOE 00 0.003E 00 0.OOiE (0 O0.000E 00 0.,OOE 00 0.00OE 00

15 3.14 I.00 2000 9.984E-014.324E 00 1.621E-01 4.091E-,i 8.. 64E-02 2.,60E-03 1.999E-03 9.504E-04

16 1.00 (.10 1000 9.900E-01 1

9.948E-02 2.472E-04 5.929E-t7 1.516E-09 1.s'97E-±I 4.057E-12 3.435E-12

17 1.00 0.25 500 4.978E-01 11.950E-01 1.115E-02 5.5.1E-04 .94E-05 1 .22E-0f 1.172E-07 2. 78'9.E-08

18 1.00 0. 1 ItLO 9. 957E- O I2.428E-01 3.2'4E-03 -1563 E -- .7 .---- 7 E. so- ;? 1.17SE-09 7.541E-10

19 1.00 0i. 21,I 2000 1.992E 00 1

2.185E-01 4.E41E-04 2.824E-0T :314E-08 1.016E-O8 7.187E-09 5.416E-O9

20 1.00 0.25 3000 2.988E 00 11.734E-01 9.857E-05 6.609E-cle 2.3":E-09 1.2)7E-0? 9.153E-10 6.::11E-10

21 1.00 0. I0 1000 9.,.E-O1 12.881E-01 5.249E- - : : 7. t, E --- 5 C :S14E-07 I. '34E-0C: 1.904E-09 9.791E-10

22 1.00 0.50 1000 9.974E-01 I4.555E-01 1.690E-02 4.041E-04 1.040E-05 4.3E-0, 8.73E-08 4. 168E-08

23 1.00 1. 00 500 4.992E-01 I1.660E-01 9.371E-02 2.6".:-E-C,7 2.561E-03 2.436E-01 3.104E-05 4.096E-06

24 1.00 1.01 C:00 7.998E-01 15.030E-01 e". .7E :'- 112 :-:. 57 E- 2.270E-04 1.51,-E-CI. I.0a3E-06 6. 6715E-08::

25 1.00 1. CIO 900 S. 93 7E- 01 16.640E-01 6.42,5E-02 2.416E-03 1. 67E-04 7.4;7L-E06 4.143E-07 2.311E-08

26 1.00 1.00 1OO: 9.Q8EE-01 1.694- 7 -. 694E-01 4.550E-02 i.s.E- 03 7.E -05 .. .174E-OC 1.593E-07 7. 367E-09

27 1.00 1.00 1100 1.099E 00 1?.857E-01 3.14SE-02 i.03.E-C, 3. '04E-05 1.3!0E-06 4.969E-08 1.837E-09

28 1.00 1.00 1"CIO 1.198E 00 17.423E-01 2.146E-0'2 5.%13E-04 1.607E-05 4.-83E-07 !.316E-0 3.791E-10

29 1.00 1.00 1403 1.398E 00 16.024E-01 9. :J: .o"; 2E- 2.72:E- 0G 4.6 4 SE- I 7T -..96&'E-10 1.367E-11

77-

30 1. 00 1.00 2000 1.998E 00 12.966E-01 1.202E-03 5.0"3E-06- 2.1E EE-03 9.27E.E-i1 3.937E-13 1.471E-15

31 1.00 1.00 2400 2.393E 00 11.992E-01 3.882E-04 7. 841 E- C-07 1. ,97-. .27.E-!2 -.205E-15 4.827E-17

32 1.00 1.00 300u.l 2.997E 00 11.226E-01 9.711E-05 7.9E9E-0: 6.527E-11 6.-:.71E-14 5.032E-12 1.659E-16

33 1.00 1.50 500 4.994E-01 11.248E-01 1. 117E-01 4.SO1E-02 3. 5E-03 ";. 27E-04 5.34E-05 7. 592E-Ott

34 1. o0 1.50 S00 7.991E-01 I4.447E-01 1. 186E-0O _.C-SE-(. 2.75E-04 2. EE -0 1.r33E-06 1.26CE-07

35 1.00 1.50 900 8.990E-01 I7.093E-01 6. S40E-02 2. 555E-., 2. 120E-04 1. 4- -3 9.-52E-C 6.7 19E-0$

36 1.00 1.50 1%0 9.98%:E-01 I9.642E-01 5. 370F-02 2.812'E-0$ .72,E-04 1.C74E-1"5 6. E25E-07 4. ,50E-0::

37 1.00 1.50 llO, 1.0'9'9E 00, 19.503E-01 3. 575E-02 1 ";'F- " . 927E-05 4. T:-.'E - C , 2..373E-07 1. 22SE-0S:

3q 1.00 1.50 100 1. 199E 00 I8.243E-01 2.3 E-02 9. 12E-04 3.468-E-05 1 .:2E-*'.- 5. 2'$E9E-0e 2.0E9E-09

39 1.00 1.50 13 0 1.299E 00 16.971E-01 1.5?5 E-02 4. 3'S2E- Ci 1.2-59.E-0. 5 .664E-07 1.06:E-0." 3.107E-10

40 1.00 1.50" 140, I. 399E 00

5.862E-01 9. 92S-0 2. 119E-04 .5 E$ZE-0C .i -44E--0 2. 167E-09 4.719E-11

41 1.00 1. 50 000 1.999E 00 12.354E-01....52E-04 4.6ESE-0-F 2.24eE-0S 1.7E--10 4.:'40E-13 1.175E-15

42 1.00 1.50 2400 2.39SE 00 11.490E-01 2.970E-04 E.4C5E- , 1.426E-09 3. itE-IU 6. 130E-15 3.675E-19

43 1.00 1.5C 3000 2. 9.E 00 18.759E-02 7.0'9E-05 f. O0IE-C, 5.131E-11 4. i'E-14 E..38E-18 7.092E-1S

44 1.00 1.75 2000 1.999E 00 12.102E-01 8.858E-04 4.332E-0'6 2.140E-OS 1.C5E-13 5.150E-13 2.137E-15

45 1. 00 ,.00 500 4.995E-01 I

1.007E-01 1.137E-11 6I &"I- .-0 4.135E-03 3.7 CE 04 6.44q E-05 8.002E-06

46 1.00 2.00 800 7.993E-01 I3.669E-01 1.270E-031 2.Q0$2E-0.B 2.489E-04 1.&E,0F 0 1 i.775E-06 1.188E-07

47 1.00 2.00 8.0 a1E- 16.487E-01 8.875E-02 1.39E-3 2.1007E-04 1.490a_-0 9.597E-07 7.628E-08

48 1.00 2.00 1000 9.989E-01 11.071E 00 4.992E-02 3.79E-0? 2.,29E-04 1.897E-05 1.479E-06 1.119E-07

49 1.00 2.00 1100 1.099E 00 1

4 9.621E-01 3.313E-02 2.212E-C'.. 1.293E-04 J.?cE-ri 4.914E-07 3.027E-06

50 1.00 2.00 120v 1.199E 00 17.811E-01 2.195E-02 . 013E-0 4.492E-05 2.031E-06 9.177E-08 4.138E-09

51 1.00 2.00 1300 6.495E-01 22. 677-09 6.3422-01 3.706E-10 1.399E-02 32-?0E-11 4.6OEE-04 2.671E-12

52 1.00- 2.00 1400 6.996E-01 24.641E-02 4.846E-l 5. 45"E-C-: 7.6-SE-0- 3.E.'OE-04 1.648E-04 1.5312E-05

53 1.00 2.AI .r,0u 9 .995E-01 21.352E-06 15. 282E-0, 7. E - C2.: '. 99%-E-04 6.', L.-n'.E-: C 3.964E-06 2.237E-11

54 1.00 2.1 3 2400 2.399E 00 11.167E-01 2.345E-04 ,..2;4E-07 1.195E-09 2.712E-12 6.214E-15 2.180E-17

55 1.00 2. O0i :.,' 2.9981 0C 16.737E-02 5.441E-Cr 4.;-' E-r? 4.ri97F-:1 .3;E--14 3.6UZE-19 1.323E-17

56 1.00 2.25 2000 9.995E-01 2

4.572E-01 1.021E-01 . E- CE '. 144E-04 9.E52-OC 7.955-06 5.421E-07

57 1.00 2.50 500 4.995E-01 1

8.473E-02 1.088E-01 7.0.5E-042' 3.806E-03 2.7-IE-04 6.8-:3E-05 6.5":9E-06

58 1.00 2.50 d0 0 7.994E-01 I

3.045E-01 1.243E-01 1.-64E--0 . 122E-04 1.4-14E--L5 1.619E-06 9.149E-03

59 1.00 a.50 900 8.993E-01 15. 638E-01 6. 772E-P2 I . 292E-03 1.607E-04 1. 300E-OZ 7. 306E-07 6.398E-08

60 1.00 2.50 1000 9.990E-01 1

1.124E 00 3.991E-02 4.659E-0:3 3.138E-04 2.66iE-05 2.404E-06 2.038E-07.

61 1.00 2.5 110Cie .,,9E UO 18.890E-01 2.963E-02 : 1 04 SC.E-3'- 6.609E-0 4.448E-08

62 1.00 2. 50 IfoO 5. 996E-01 21.442E-02 6.861E-01 1 .783E-Os 1..62E-02 2.928E-04 9.096E-04 2.55SE-05

ii

;I

S6 3 1 . 0 0 2 5 3 0 U 1 . 4 '.6 E - O 2

9.2 31E-02 4.7..E-01 1. 040E-012 9.0$.2E-0: .7 E- L 4 2. EE-04 5. 693E-05

64 1.00 2.50 1400 6.996E-01 21.744E54E-.L54E-C1 1 .594E-D2 4.636E-0 9. '. tE-04 1 .224k-04 3.E01E-05

65 1.00 2.50 2000 9. P95E-01 29.42SE-01 4.213E-0 I.. lEE-CC .4 :; E -; t L. 1 4-E-0C! 1 8.0E-05 2. 253E-OE

(

66 1.00 2..50 C,400 Z. 399E CI0 19. 531E-02 1. 922E-0- 4. :;.4E- ' I. 0 D E-09 2. -E- 12 . &9'4E-15 4. SO5E-17

67 1.00 .50 30-A0 2.999E 0'0 15.454E-02 4.415E-05 ?2.S859E-0E: 3.390E-11 2. :74L-14 2.681E-17 .059E-I1S

68 1 . 0 .0 000 .. 9 990E-011 .1 2 4 E 0 0 3 .L 5 '-E - C 5 2 'F-O " 4 . j 4 5 L - 0 4 _:. . E "-15 2 . 7 866 E -O6 ..59 4 E - 0 ,

69 1 .0 C..00 1100 1.099 E 00 17. 96E-01 2. 651'E-CC 2. 0:E-C: 1. 445E-04 1. 2 :- C5 7.26. 1-07 5. 1206E-0: :

70 1. 00 ,. 0 1200 5.997E-01 -25.985E-02 5.E:!6E-01 5.7e, -;'E- 1.402E-02 I OCilE- -. &.SI'E-04 E6.5SE6 -05

7 1 1 . 0 0 E. 1 -, 6 . 4 ' .:'7 E - 0 11. 313E-01 0. - : .2: ." ,0: : . ' "E . 1. :':E- 0 2 -.4 : E-04 6.650E-05

7 2 1 . 0 Q 0 , 1 4 C rC 6 .? ? 7 E - 0 1".06 7E-0 1 2. 44 3 E .-'1 3i.SE-02 9 E.79 -02 ?. 62E-04 1. '21E-04 3.6 7 7E-05

7..::1 00 :.00 2060 . 95E-0 l1

1.496E 00 5.6SCE-0: I.4!5 F- -0- 3. 404E-0 . :0 ,.E-04 -. 21 E-05 4.- '54E-06

74 1.00 3.0L' 4 C, 9 E 0 1.. -E -2- 1 .C .-: E - 0-1 ::, --'1 -7 - ::5E -1 3 1 '.'>2- I ,. - 'E- 15 6. '.?tF4E- lIS

75 1.00 3. 00 3000 2. 999S 00 14.575E-02 3.707E--05 l:*- E- C . 2. 8 g9E-11 2. . 7 E .- 4 1.451E-16 3.204E-17

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Copy v'aS *''-A

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