HTc Josephson nano-junctions : physics and applications · 2017-12-28 · Dynamics of Josephson Junctions Rapid Single Flux Quanta logic Actual RSFQ devices Proximity effect Quasi-classical

HTc Josephson nano-junctions :physics and applications

Collège de France 2008

Jérôme Lesueur

Phasme team : www.lpem.espci.fr/phasme

Nicolas Bergeal

Martin Sirena

Thomas Wolf

Giancarlo Faini

Rozenn Bernard, Javier Briatico, Denis Crété

Nicolas BergealMartin SirenaThomas WolfAlexandre Zimmers

Pascal Febvre

Denis Crété

Sophie Djordjevic

Robin Cantor

RSFQ

Etalon du Volt

THz

SQUID

Quantum circuits ?

No quantification of the EM field (cf M. Devoret’s lecture)

No quantum states manipulation (cf O. Buisson’s seminar)

1st

2d

!

| 0"+ | 1"

2

Phase properties and superconducting circuits

Phase rigidity of the condensate

!

" =0"

i#

e

!

V( t)dt0

T

" =0

#

!

d" = 0#

dx2−y2

++-

-kx

ky

Intrinsic phase structure in High Tc SC

Josephson nano-junctions

π-junctions

High speed applications

Analog to Digital converters

Communication systems

PetaFLOPS computer …

Superconductive electronics

Superconductors Semiconductors

CMOS transistorJosephson Junction

Aluminium

Aluminium

AlOxSiOx

Silicon1-2 nm

1-2 nm

Quantum circuit

Dream or reality ?

An example : a digital frequency divider

770 GHz ; 1.5 µWTechnology : Nb/Al/AlOx/Nb @4.2 K

Outline

1. Superconductive electronics

3. Physics of High Tc nanojunctions

Dynamics of Josephson Junctions

Rapid Single Flux Quanta logic

Actual RSFQ devices

Proximity effect

Quasi-classical diffusive approach

D-wave order parameter symmetry

π-junctions and RSFQ devices

4. Conclusions

2. High Tc Josephson nanoJunctionsIon irradiation of High Tc Superconductors

Making Nanojunctions

Major characteristics of the Nanojunctions

A few applications

Outline





Actual RSFQ devices

Proximity effect




4. Conclusions




A few applications

Josephson Junctions

ψ2=|ψ2 | eiϕ2ψ1=|ψ1 | eiϕ1

SuperconductorSuperconductor Barrier

Josephson Junctions Josephson equations

!

I = Icsin(")

!

" ="1#"

2

Barrier : insulator, normal metal, constriction …

Applications : superconductive electronics

• Photon detection : 1 junction

• SQUID for magnetometry, voltmetry … : 2 junctions

• Rapid Single Flux Quantum (RSFQ) logic : from 10 to millions junctions !

483 597,9 GHz/V

Josephson Energy

!

JE = 0"

cI

2#(1$ cos(% ))

!

"#

"t=2eV

h=2$V

0%

Modeling a Josephson Junction

RC Shunted Junction Model

Josephson Junction : a non-linear inductance

!

I (t) =JI (t)+ RI (t)+ CI (t)

!

V( t) = 0"2#

$%( t)

$t

!

V( t) =JL"

JI ( t)

"t

!

JL = 0"

2#cI cos$( t)

!

I (t) =cI sin("( t))+

V(t)

JR+

JC#V( t)

#t

!

I( t)

cI= sin("(t))+ J0L

JR

#"(t)

#t+

J0L JC

2

# "(t)

#t

The mechanical analogy

Normalized equation

!

J0E"

"#(1$ cos(# )$ i# )+

2

h

2e

%

& '

(

) * 1

JR

"#

"t+

2

h

2e

%

& '

(

) * JC

2

" #2

"t= 0

!

i( t) = I(t)

cI

!

"U +#$x

$t+M

2

$ x

2

$t= 0

!

JE =h

cI2e(1" cos(# ))

« Washboard » potential : phase difference motion

« damping » « mass»

Dynamics of a Josephson Junction

!

I( t)

cI= sin("(t))+ J0L

JR

#"(t)

#t+

J0L JC

2

# "(t)

#t

Characteristic times

!

p" = 02#$ JC

cI

!

LR" = 0#

2$cI JR

!

RC" =JR JC

Mc Cumber parameter

!

C" = RC#

LR#=2$

CI JC2

JR

0%

!

sin"#i+$"

$%+

c&

2$ "

2$%

=0!

" =t

LR"

underdamped

overdamped

!

C" # 1

!

C" >>1

R & C smallNo tunnel

Voltage and current across a current biased JJ

Ibias Current biased overdamped Josephson Junction

!

LR" = 0#

2$cI JR

!

T =2"

LR#2

i $1τLR

!

V =1

TV(t)dt

0

T

" = 0#T

t/τLR0 5 10 15

0

1

2

3

4

5

V(t)

/IcR

J

Quantized pulses

Timescale τLR≈ps

Vmax≈2IcRJ ≈ mV

Energy≈IcΦ0 ≈ aJ


Likarev’s basic idea (1985) : dynamical logic

Transmission line Transmission line

State 0 State 1IcRJΦ0

Current biased overdamped JJ (Ib < Ic)

Josephson transmission line

Inductance (RF SQUID)

!

L" =

2LCI

0#

Dynamics of an RF SQUID

!

L" =

2LCI

0#

Fluxoid quantification

!

L" <<1

!

L" >>1

!

"

0"

= ext"

0"

# L$2%

sin 2%"

0"

&

'

( (

)

*

+ +

Non-hysteretic

Hysteretic

Storing a pulse

Storing and manipulating pulses

Φ0 < LIc < 2Φ0

Manipulating pulses

RSFQ circuits : JJ and inductances

Φ0 < LIc Φ0 > LIc

Advantages of RSFQ logic

Robust pulse along the way

IcRJΦ0

Φ0

Intrisinc speed : THz frequency

!

LR" = 0#

2$cI JR

Ic ≈ 0.1 - 1 mA

RJ ≈ 1 - 10 Ω1/τLR ≈ 1-10 THz

Low power consumption

Energy ≈ IcΦ0 f ≈ 0.1 - 1 THz P ≈ 0.1 - 1 nW

N ≈ 1O6 gates P ≈ 0.1 - 1 mW

Overdamped : no tunnel junctions

A complete logic library

All logic elements possible

NOT

T-NOR

T-AND

Low Tc Micro processor (ISTEC Japan)

• Technology : Nb/Al/AlOx/Nb @4.2 K

• 8000 to 30000 junctions

• Max speed : 770 GHz, sampler

15.5 GHz 1.6 mW

Superconductive electronics : the Holy Graal ?

Important parameters

!

LR" = 0#

2$cI JR

!

C" = RC#

LR#=2$

CI JC2

JR

0%

unity

!

LR" # JC

CI

Robust against thermal fluctuations

!

CI > Bk T

0"

Increasing current density jC

Increasing superconducting gap IcRN

Decreasing the JJ characteristic spread

Today Low Tc

• Temperature 4.2 K

• Current density 1-3 kA/cm2

• SC gap 1 mV

• 5 to 10% spread

• 30000 JJ

Tomorrow High Tc

100 K

20-30 mV

>>10 kA/cm2

?????

High Tc Superconductive electronics … today

HTSc Josephson Junctions technology :

reliability, ageing, integration, cost effective

Complex materials

Multi-component oxides (YBa2Cu3O7)

High temperature processing (700-800°C)

Very sensitive to disorder …

High Tc A/D convertor (ISTEC Japan)

• Technology : YBCO @77.7 K

• 10 to 15 junctions

Outline





Actual RSFQ devices

Proximity effect




4. Conclusions




A few applications

« Standard » High Tc Josephson junctions

Complex materials …

Grain boundary junctions

Alternative technology Ion irradiation

Ramp junctions

Special substrates

Design constraints

Lack of reproducibility

Kahlmann et al & Katz et al APL’98

High Tc cuprate superconductors

Y

Cu

Ba

O

O

bc

High Tc superconductors

Hole-doped in the Cu02 plane

YBa2Cu3O6+x

Tc=90K Order parameter symmetry : dx2-y2

++

-

-kx

ky

kX

ky

Anistropic 2D Fermi Surface

Disorder in High Tc Superconductors

Defect in dx2-y2 superconductor depairing

Abrikosov-Gorkov

YBa2Cu3O7

dx2 −y2

++

-

-

k

k’

kx

ky

Local control of the disorder

Nanoscale engineering (ξN)

30K<T<90K Super/Normal/Super Josephson junction

Substrate

YBCO Tc=90K30K

Proximity effect based Josephson Junctions

SC Normal SC

Phase coherence through normal metal : Josephson coupling

Diffusive case

!

"N(x) #"

N(0

+)e

$x

%N

De Gennes : Rev Mod Physics 1964

!

Ic

= I0 1"T

Tc

#

$ %

&

' (

2

l /)N

sinh(l /)N)

!

"N

=hD

2#kBT

usiv

A few 10 nm

Towards the insulator

Defect in dx2-y2 superconductor depairing

Low defect concentration : Tc decreases

Lesueur et al (1995)

Abrikosov-Gorkov

YBa2Cu3O7

dx2−y2

++

-

-

k

k’

kx

ky

High dose : towards the insulator

YCu

BaO

O

bc

Fabrication of High Tc nano-Junctions

Control the defect density through ion irradiation two-steps strategy :

Abrikosov-Gorkov

YBa2Cu3O7

J. Lesueur et al (1995)

# 1

# 1 : drawing channels : (1015 at/cm2)

# 2

# 2 : creating nanoJunctions : (1013 at/cm2)

Substrate

Film SCInsulator SC channel

Junction

Resist

Au

Oxygen 100 keV

Tailoring at a nanoscale

First step : channel in a YBa2Cu3O7 film (thickness = 1500Å)

Channel

Embedded

Oxygen 100 keV

Second step : nanojunction through a 20 nm slit

30K<T<90K jonction Super/Normal/Super

Oxygen 100 keV

Substrate

Superconductor

Resist

Substrate

SubstrateSubstrateSubstrate

Superconductor

Au

Ins.

Fabrication of nanojunctions

20nm slit

Hall cross

Width 1 to 5µm

Irradiationthrough Au mask

Au IBE removed Irradiationthrough Resist mask

N. Bergeal et al, APL 2005

JAP 2007

R(T) measurements

25

20

15

10

5

0

R (!

)

10090807060504030

Température (K)

Tc

Tc’ Tj

Josephson

regime

L=5µm, E=100keV Φ=6.1013at/cm2

L=5µm, E=100keV

Φ=1.5, 3, 4.5, 6.1013at/cm2

ψ2=|ψ2 | eiϕ2ψ1=|ψ1 | eiϕ1

SupraSupra

3.0

2.5

2.0

1.5

1.0

0.5

0.0

R(!

)

908070605040

Température (K)

Tc’<T<Tj Josephson regime

T<Tc’ <Tj Flux flow regime

Extension of the Josephson regime

ΔT=7K → ΔT=20K

High operating T

I(V) characteristics

Φ=3.1013at/cm2

RSJ behavior

Resistance Rn ranging from 200mΩ to a few Ω

Flux flow behavior

T < Tc’TJ > T > Tc’

70 K72.5 K

Overdamped JJ

Fraunhofer pattern Ic(B)

Phase control by the vector potential

30

25

20

15

10

5

0

Ic (µA

)

-15 -10 -5 0 5 10 15B (Gauss)

73,35 K

Sinc fit

!

Ic

= I0sin("# #0)

"# #0

Φ0

Josephson length λJ

w = 5 µm

λJ = 2 µmλJ = 3 µmλJ = 4 µm

!

I = Icsin(")

!

" ="1#"

2

∇ϕ = Cste JS + 2πφ0-1 A

Shapiro Steps

Phase controlled by microwaves

Almost ideal Bessel functions

N. Bergeal, JAP 2007

!

"#

"t=2eV

h

483 597,9 GHz/V

2000

1500

1000

500

0

Ic (µA

)

7876747270

T (K)

3 1013

at/cm2

500

400

300

200

100

0

Ic (µA

)

85.084.584.083.583.082.5

T (K)

1.5 1013

at/cm2

2000

1500

1000

500

0

Ic (µA

)

72686460

T (K)

4.5 1013

at/cm2

1400

1200

1000

800

600

400

200

0

Ic (µA

)

5550454035

T (K)

6 1013

at/cm2

Ic(T) measurements

!

Ic = I0 1"T

Tj

#

$ % %

&

' ( (

2

l /)Nsinh(l /)N )

De Gennes-Werthamermodel of proximity effect

1.5 1013 at/cm23 1013 at/cm2

6 1013 at/cm24.5 1013 at/cm2

IcRn ~ a few 100 µV

Major characteristics and reproducibility

N. Bergeal, APL 2005,JAP 2007

High Jc

Reproducible JJ

Clues for reproducibility and reliability

Embedded junctions

No annealing of the junctions

In-situ Gold protected YBCO films

All dry process

Low dispersion in IcRn (<10%)

Self-shunted junctions

High values of Jc ( a few 104 A/cm2)

Excellent thermal cycling and aging


THz detectors

Voltage standard

SQUIDs

RSFQ : T flip-flop

DC SQUIDs with nanojunctions

10µm* 10µm

W ~ 5µm

L = 32 pH

ϕ0 forB~0.08 G

Geometry #1

40

35

30

25

20

15

I c(µA

)

0.20.10.0-0.1-0.2

B (Gaus)

expérience

I=IcIcos(2!"/"

0)I +C

Ic(B) modulation

Cosinus fit with a period 0.08 G

Geometry #2

6µm* 6µm

W ~ 2µm

L = 17 pH

ϕ0 forB~0.3 G


SQUID modulations

20

15

10

5

0

V(µV)

-0.2 0.0 0.2

B(Gauss)

I=25µA

I=20µA

I=30µA

I=35µA

50

40

30

20

10

V(µ

V)

-1.0 -0.5 0.0 0.5 1.0

B (Gauss)

I=18µA

I=25µA

I=30µA

Modulation of I -> modulation of V

Sensitivity : dV/dΦ = 60 µV/Φ0

Temperature = 77.7 K

Geometry #1 Geometry #2

SQUID characteristics

3 1013 at/cm2

T= 77 K

6 1013 at/cm2

T= 51 K

Fraunhofer + SQUID modulation

Noise < 100pV/√Hz (at 100 Hz)

Sensitivity ≈ qq 10-4 Φ0

Excellent cycling and aging

Networks

N. Bergeal, APL 2006 ; APL 2007

SQUID for « Mr SQUID »

RSFQ T Flip-Flop

Design D. Crété (Thales)

Kim et al (2002) 100 GHz @ 12K

f

f/2

IN

0.24m

A

1.2pH

0.9pH

0.15mA

IC = 150u

0.9pH

Ic=

150u

2.1pH

IC = 300u4.3pH

7.1pH

IC=350uA

IC = 300u

0.27mA

Ic=250u

A

1.0pH

OUT

JTL BIAS

Ib1 = 0.25 mA

JTL

TFF BIAS

Ic3 =Ic4 0.38 mA

=

Ib3= 0.28 mA

Ic7 = Ic6 = 0.32 mA

Ic1=Ic20.18 mA

=

Ib4 = 0.12 mA

Ib2 = 0.22 mA

L = 7.1pH

GND

OUT

IN

A

IC=350uA

GND

A

A

f/2

Outline





Actual RSFQ devices

Proximity effect




4. Conclusions




A few applications

A bit of physics …

Tc , resistivity r(T) vs defects

Damage profile (SRIM)

?

Reduced size ?

« No-interface » Josephson Junctions

SC Normal SC

!

"N

=hD

2#kBT

Strength of the coupling

Low interface resistance

Fermi Velocities match

Beyond De Gennes’s approximation

No true interface

Self-consistent calculation of the local gap

Calculating the Josephson critical temperature

Calculating Ic(T) for all temperatures

Quasi-classical approach of the proximity effect

ωn=πkBT(2n+1) Matsubara frequencies

!

"(x) = #S2$K

BT sin%

n

&n

'!

tan"N

=#

$N

Usadel equations parametrized in θ

!

hD(x)

2

" 2#n

"x 2$%

nsin#

n+ &(x)cos#

n$'

AB(x)sin#

ncos#

n= 0

Self-consistant gap equation

Homogeneous SC

G=cosθ

F=sinθ

Limits conditions

Pairs

Quasiparticles

Depairing ΓAB

Δ(x) profil along the junctionIn the limit of vanishing current

Computing the Josephson coupling temperature

80

60

40

20

0

T (

K)

86420

dose* 1013

at/cm2

Régime normal

Tj

T'c

Régime Josephson

Régime flux-flow

Flux-flowregime

Normalregime

JosephsonregimeTc’

TJ

1.0

0.8

0.6

0.4

0.2

0.0

!/!

0

-400 -200 0 200 400

x (nm)

89K

88K

87K

86K

84K

82K

80K

74K

60K

40K

N. Bergeal et al, submitted to PRL

TJ

Computing the critical current density

Usadel equations parametrized in θ

Homogeneous SC

G=cosθ

F=sinθ Pairs

Quasiparticles

Depairing ΓAB

!

hD(x)

2

" 2#n

"x 2$%

nsin#

n+ &(x)cos#

n$'

AB(x)sin#

ncos#

n

$hD(x)

2

"(

"x

)

* +

,

- .

2

sin(#)cos(#) = 0

!

hD(x)

2

" 2#n

"x 2$%

nsin#

n+ &(x)cos#

n$'

AB(x)sin#

ncos#

n= 0

Depairing by supercurrent χ

ωn=πkBT(2n+1) Matsubara frequencies

Supercurrent inside the junction

!

j(x) = "#eNDT$%

$xsin

2&'

(

Comparison with eperiments

Quantitative results for the critical current of our Josephson junctions

Depairing coefficient

Defects profile

With NO adjustable parameters

Irradiations on full films

SRIM simulations

Changing the junctions parameters

Importance of the slit size and irradiation doses

4 different doses

Simulate various

slit size

film thickness

irradiation dose, …

optimize Josephson junctions

Specific temperaturescritical currents

Reduce spread (identifyimportant parameters)

Ic(T)

Temperature (K)

Ic(A

)

3 different slit size

Deeper look in the low temperature regime

Want to reach high critical current lower temperature

Strong anharmonicity develops …

Lower temperatures

2.5

2.0

1.5

1.0

0.5

V(t

)/IcR

n

300025002000150010005000

Time (a.u.)

RSFQ pulses robust against anharmonicity

A d-wave order parameter

1D Quasi-classical equations with an isotropic order parameter

2D symmetry of the d-wave order parameter

!

hD(x)

2

" 2#n

"x 2$%

nsin#

n+ &(x)cos#

n$'

AB(x)sin#

ncos#

n= 0

kx

ky

dx2−y2

++-

-kx

ky

• Anisotropy of the order parameter

• Sign change : Andreev Bound States

• π-junctions and RSFQ circuits

Order parameter anisotropy ?

dx2−y2

++-

-

kk’

kx

ky

Orientations θ = 0 °,10 °,20 °,30 °,40 °,45°

(a,b)

(a,b)

θ D-wave order parameter

Order parameter anisotropy ?

θ = 0°θ = 45°

No effect !!

Diffusion ?

2d order parameter ?

Anisotropic pairing !

Back to Eilenberger equations …

No diffusion approximation

Usadel : l < ξ

Eilenberger : l >< ξ

No wave vector dependence

Confined geometry : full d-wave calculation in a channel

a fe

w ξ

Den

sity

of

stat

es

DOS (E=0)

Andreev Bound State

Andreev Bound State

D-wave SCInsulator|!|

e-

x0 dn

h+e-

h+

k=kf

k=-kf

!1ei"1 !2e

i"2

SC1 SC2Metal

Surface Bound State

ϕ1-ϕ2=π Bound State E=0

Making a π junctionw = a few ξ

Gumann et al APL 2007

Ic>0

Ic<0

Ic=I0sin(Δϕ)

Ic=I0sin(Δϕ+π)

Spontaneous super-current

π SQUID

π junction

0 junctionGround state j=0Flux = 0

Ground state j≠0Flux = φ0/2

LIc > φ0

Free energy

Spontaneous current

π-SQUID in RSFQ circuits

Spontaneous half flux quanta in YBCO/Nb SQUIDs

φ0/2

Numerous bias leads in RSFQ circuits

Ortlepp et al Science 2006

Toggle flip-flop

Comparison with and without π-junctions

Actual device

Outline





Actual RSFQ devices

Proximity effect




4. Conclusions




A few applications

Conclusions

RSFQ logic : a promissing technology

High Tc Josephson nano-Junctions : a promissing path

Applications are on their way

Proximity effect based Josephson Junctions

D-wave order parameter :it matters !

Thank you !JnJ : Bergeal & al, APL 87, 102502 (2005),

JAP 102, 083903 (2007)Squids : Bergeal & al, APL 89, 112515 (2006)

APL 90, 136102 (2007)Optimization : J. Lesueur & al,

IEEE Trans Appl Sup 17, 963 (2007)M. Sirena & al, JAP 101, 123925 (2007)M. Sirena & al, APL 91, 142506 (2007)M. Sirena & al, APL 91, 262508 (2007)

Documents

HTc Josephson nano-junctions : physics and applications · 2017-12-28 · Dynamics of Josephson Junctions Rapid Single Flux Quanta logic Actual RSFQ devices Proximity effect Quasi-classical