Superconducting RSFQ Logic: Towards 100GHz Digital Electronics Vratislav MICHAL, Emanuele BAGGETTA, Mario AURINO, Sophie BOUAT, Jean-Claude VILLEGIER IINAC,

Superconducting RSFQ Logic: Towards 100GHz

Digital Electronics

Vratislav MICHAL, Emanuele BAGGETTA, Mario AURINO, Sophie BOUAT, Jean-Claude VILLEGIER

IINAC, UMR-E CEA /UJF, CEA-Grenoble 38054, Grenoble, France

[email protected]

Radioelektronika 2011

Superconductivity Josephson effect RSFQ Applications Fabrication 2/35

Outline

Superconductivity: introduction

Josephson effect, SQUID

Superconducting logic RSFQ

Application, examples

Fabrication, process

I. I. Motivation: SuperconductivityMotivation: Superconductivity


Brief historyBrief history 1908:1908: liquefaction of liquefaction of 44HeHe 1911:1911: Superconductivity in Superconductivity in

mercurymercury 1925:1925: Prediction of Bose- Prediction of Bose-

Einstein condensationEinstein condensation 1927:1927: Superfluidity Superfluidity 44HeHe 1933:1933: Meissner effect Meissner effect 1950:1950: Ginzburk-Landau theory Ginzburk-Landau theory 1957:1957: BCS theory BCS theory 196:196: Josepshon effect, SQUID Josepshon effect, SQUID 1986:1986: HTC HTC

19198585:: RSFQ RSFQ

Img: H. K. Onnes, Commun. Phys. Lab.12,120, (1911)


SuperconductivitySuperconductivity Superconductivity is a fundamental Superconductivity is a fundamental

macroscopic state, occurring at macroscopic state, occurring at the transition temperature Tthe transition temperature TC C

(phase transition) (phase transition) New phenomena occurs in the New phenomena occurs in the

superconducting core. Amongst superconducting core. Amongst most important:most important:

Resistivity drop to zeroResistivity drop to zero

Magnetic field screening: Meissner effect (magnetic induction has to be a constant in time, i.e. dB/dt = 0

Magnetic flux quantization


Curent conduction: Cooper pair Below TC, the electrons condense

into pairs called Copper pairs.Copper pairs.

the crystal lattice is deformed by electrons, causing local positive polarization, attracting another electron thorough an exchange of the virtual phonon, with the crystal lattice (atoms)

The bounded electrons (Cooper pairs) travel in the crystalline lattice without energy loss and keeps the phase coherence.

~.2nmLatice spacing:

Coherence length ξ

(Hundreds of nm)e- e-


Macroscopic Coherence

The Cooper pairs are the particles with integer spin (boson), condensating in the single ground state, close to Fermi surface (do not obey the Pauli exclusion principle).

Due to the long distance coherence length ξ, wave function Ψi of Copper pairs overlap, and all electron gas can be described by the single wave function:

The phase coherence is maintained by the gap energy, exceeding the electrons coulomb repulsive force.

ie jY = Y


Magnetic flux quantization The long-distance phase coherence

results in 2πn phase drop around an closes superconducting loop:

This make appear the shielding supercurrents, quantizating the flux inside the loop:

The value of Ф0 is the magnetic flux quanta:

2dl nj pG

Ñ =òr r

Ñ

20L sJ dl nl

G

F + = Fòr r

Ñ B

- -

CP

- -

-- --

n·Ф0

Superconducting ring

non-superconducting region

Js

Uniform field

Measured flux

150 2.07 10

2h

Wbe

-F = = ´

nФ0


RF property of the superconductor

II. II. Josephson effect, Josephson effect,

SQUIDSQUID


Josephson junction

iji e jY = Y

Two isolated superconductors keeps the phase coherence across a normal-state (non-superconducting) barrier. Effect of the Cooper-pairs tunneling is referred to as

Josephson effectJosephson effect

- -- -

- -- -

- -- -Ψ1

- - - -

Ψ2

CP

superconductors

barrier

1 2( )

Wave function of the electrodes:

Josephson phase:

The current/voltage and the Josephson phase are related by the Josephson equations:

( ) ( )( )

( )

sin

2

s cI t I t

V tt e

f

f

=

¶=

¶h

1 2f j j= -


Josephson junction: IV characteristics

Barrier type (or external Barrier type (or external shunt resistance):shunt resistance):

a)a) the I/V characteristic the I/V characteristic can be hysteretic, orcan be hysteretic, or

b)b) single-valued.single-valued.

The JJ with a DC voltage below the superconducting gap behave as the oscillator with frequency f = 483 597.9GHz/V

Demonstration: Shapiro steps Shapiro steps


SQUID: Superconducting Quantum Interference Device

( )1 20

22extLI n

pff p+ + +F =

F

I0

LiI0/2+iL I0/2-iL

B

a) B = 0: IJ1=IJ2

b) B > 0: IJ1<IJ2

B

I0

Li

I0/2+iLI0/2-iL


Application: magnetometer

iL

Ib

Ic+iIc-i U(Q)

Measured object

Threshold for SQUID: 1 fT

Magnetic field of heart: 50,000 fT

Magnetic field of brain: a few fT

GAI

N

Most-sensitive magnetic detector:Most-sensitive magnetic detector:Linearization by magnetic feedbackLinearization by magnetic feedback

COMPARISON:COMPARISON:

Img: Gross, R. Applied Superconductivity (lectures)

III. III. Superconducting Superconducting

logic RSFQlogic RSFQ


Electrical model of Josephson junction

( ) 0( ) ( )22

t teV t

t tff

p¶ F ¶

= =¶ ¶h

Rj CjLj

Ij

( )( )

( )

0

0 00

( ) ( )12 cos ( )

,cos ( ) 2

J JJ

c

JJ J

c

dI t dI tV t L

I t dt dt

LL L

t I

p f

f p

é ùF ê ú= =ê úê úë û

F= =

( ) ( )( )

( )( )

( ) ( )

sin

/

J c

C J

R J

I t I t

dV tI t C

dtI t V t R

f=

=

=

2nd Josephson relation:

( ) ( ) ( ) ( )J R C LI t I t I t I t= + +

Josephson junction Josephson junction behaves as nonlinear behaves as nonlinear RLC circuit:RLC circuit:

MODEL RCMODEL RCSSJJ


Junction Dynamics0 02p J J C J J RC J JL C L R R Ct p t t= = =

2 2

0 0

2RC J J J J cC

C J

R C R C IL

t pb

t= = =

F

1Cb =

Plasma period

of LC circuit Characteristic time of RL circuit:

Nb: 0.15ps, NbN: 0.07psCharacteristic time

of RC circuit

Mc Cumber parameter:

Switching time optimum:(modified by the shunt resistance)

Another parameters are important to optimize the JJ’s circuits:• product RNIc

• superconducting gap 2Δ/e• Current density JC (~kA/cm²)

• Critical temperature


e

h

20

RSFQ logic physics

0 5 10 15 200.0

0.4

0.8

1.2

Vo

ltag

e (

mV

)

Time (ps)

0

1

2

3

4

5

Ph

ase

()

0

0

V

f J

JT

2

sin...

ci

2.07 µV/GHzQuantum Flux

Damped JJ

1c CI

Cur

rent

Voltage

0I

SFQ pulses generation:SFQ pulses generation: over dumped Josephson junction over dumped Josephson junction


Likharev approach: SFQ pulses

SFQ à

Li

I0

Main idea:Main idea: the logical bits: presence or absence of the SFQ pulse

a) IJ < IC : Junction in superconducting state

b) IJ > I0 : phase increase linearly.

c) IJ > I0 : (short time): SFQ pulse generation:

2

0 2.07V t dt mV ps


SFQ pulses flow is mediated by L, and JJ, biased close to Ic

Two cases: Two cases:

Meta-stable JTL TL Memory cell: SQUID

SFQ pulse flow: JTL and SQUID

00.5B ck T LI< < F

«1» «2»

Li

k1I0kI0

SFQ à

Li

I0

L≈Φ0/Ic

Li

L≈Φ0/Ic

I0

SFQ à

L L

Li

01.5CLI > F


Example: D-type flip-flop

D

CLKJTL

QJ0

J1 J2

J3L1 L2

L3

I0

SFQ à

Li«1» «3»«2»

time (picoseconds)

« C

LK »

« D

»«

Q » delay

delay

Operating phases:Operating phases:

1) An SFQ pulse arrive to D: penetrate into the SQUID loop

2) Circulating current occurs, shifting IcJ1 and IcJ2 values

3) SFQ pulse at CLK commutate J2 liberating the SFQ pulse

Circuit transmitted logical 1

the overall time consumed by operation is one clock cycle


Basic RSFQ cells:

Josephson Transmission Line (JTL): allowing the transfer of the SFQ pulses over long distances. In some circumstances, the JTL allows to shape and amplify the SFQ pulses.

Asynchronous components: e.g. merger or splitter, allow merging/reproducing the SFQ pulses.

Logical gates: such as the OR, AND etc.

Flip-flop: Logical block such as the previously presented D-type flip-flop, having two stable states (memory cells).

Special purpose circuit: as the mentioned SFQ/DC or DC/SFQ converters, allowing an easy to handle output for laboratory purposes.

« OR »

« D »Img: pavel.physics.sunysb.edu


Performances

Operating frequency : Tens of GHz, 770GHz demonstrated

Gate delay ~ ps

Power consumption 10-18 J per bit.

Operating voltage ~3mV

DC bias current Ic × Junction count (Amperes)

Operating temperature

4.2K (Nb), 9k (NbN)

Process ~1µm²

Gross, R. Applied Superconductivity (lectures)

IVIV. . Applications: Applications:

examplesexamples


Applications: state of the art


Demonstration 770GHz [*]

Toggle- Flip-Flop:Toggle- Flip-Flop: Relate the input and output voltage throughout the

Josephson relation.

Input part: DC/SFQ converter, output: low-pass filter.

IC = 0.5 and 2.5 mA/µm², TC = 1.8K and 4.2K

Simple JJ Nb/AlOx/Nb, 2Δ/e = 2mV (fc = 950GHz)

[*] W. Chen et al. IEEE TAS 1999

DC/SFQ generator

Josephson Transmission line

Toggle Flip-Flop


FLUX-1 Microprocessor Chip

• 8-bit microprocessor design• 1-cm chip• 8 - 20 Gb/s TRX• FLUX-1 chip redesigned,

fabricated, partially tested• 1.75 μm, 4 kA/cm2 junction Nb

technology• 20 GHz internal clock • 5 GByte/sec inter-chip data

transferlimited by μP architecture

• 63 K junctions, 5 Kgate equivalent

• Power dissipation ~ 9 mW @ 4.5K • 40 GOPS peak computational

capability (8-bits @ 20-GHz clock)• Fabricated in TRW 4 kA/cm2

processin 2002

RCL

Dorojevets, M. IEEE TAS Vol. 13 2003

Superconductivity Josephson effect RSFQ Applicationns Fabrication 28/35

ΔΣ ADC converter

VV. . FabricationFabrication


Superconductor IC: Simpler Than CMOS

Objective: Self-shunted JJ


Img: IPHT Jena - resistivelly shunted JJ


Circuit realization: CEA

Elaboration of texture controlled NbN SNS junction on Si-200mm Elaboration of texture controlled NbN SNS junction on Si-200mm wafers (350 wafers (350 ºCºC): ): compatible with C-MOS platform


NbTiN Ground plane, NbN/TaN/NbN JJ


Realization example Frequency divider: more compact on NbNmore compact on NbN

E. Baggetta, PhD Thesis CEA Grenoble (2008)


Fabrication: Outcome

NbN-TaN-NbN trilayer crossection: fabrication using UV-248 stepper

I-V-T characteristics 4×4μm, NbN-TaN-NbN, Jc = 4,3kA/cm2

Villegier J.C. et al. IEEE TAS (to be published)

Documents

Superconducting RSFQ Logic: Towards 100GHz Digital Electronics Vratislav MICHAL, Emanuele BAGGETTA, Mario AURINO, Sophie BOUAT, Jean-Claude VILLEGIER IINAC,