Electric current crowding in nanostructured conductors

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Electric current crowding in

nanostructured conductors

XXXVIII National Meeting on Condensed Matter Physics May 24-28, 2015, Foz do Iguaçu, PR, Brazil

Alejandro V. Silhanek

Experimental physics of nanostructured materials Physics Department, University of Liège

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Collaborators

O. Adami, J. Brisbois, X. Baumans, Z. Jelic

(ULg, BE)

D. Cerbu, M. Timmermans, V. Zarinov, J. Van de Vondel, V.V.

Moshchalkov

(KUL, BE)

V. Gladilin, J. Tempere, J. Devreese

(UA, BE)

B. Hackens

(UCL, BE)

M. Motta, F. Colauto, W. Ortiz

(Sao Carlos, BR)

J.I. Vestgarden, T.H. Johansen

(Oslo, NO)

J. Fritzsche

(Chalmers, SE)

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What is current crowding ?

10 MA/cm2

3 MA/cm2

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Why is it important ?

Electromigration _{Kelvin probe bridges}

Single photon detectors

J

Nanostructured superconductors

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• CURRENT CROWDING IN NORMAL METALS

• CURRENT CROWDING IN SUPERCONDUCTORS

SHARP BENDS

SURFACE INDENTATIONS

MAGNETIC FLUX AVALANCHES

• NANOSTRUCTURING VIA CURRENT CROWDING

• CONCLUSION

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Pre-history: normal conductors

conformal mapping r 0 3 / 1

i

r

g

i

_ABC















i₀ is the asymptotic current density in the leg

Optimum curvature

The perturbations of the current crowding propagate about three strips widths into the legs

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Pre-history: normal conductors

a as small as possible and b and N as large as possible if b >> a and N >> 1

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History: superconductors

A Palau et al. (2007)

Phys. Rev. Lett. 98, 117003 Villegas et al. (2005)

Phys. Rev. B 72, 064507 Silhanek et al. (2008Appl. Phys. Lett. 92, 176101)

…substantial deformation of the current-voltage characteristic when the voltage pads are attached close to the vertices.

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Superconductors (vortex nucleation)

d

W

2 

2

/





Definition of J_c…current at which a nucleating vortex surmounts the Gibbs-free-energy barrier at the wire edge and then is driven entirely across the strip

J_c= R J₀

J₀the critical current of a superconducting strip

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Comparison superconductors vs metals

W

3 / 1 0

4

2

3 













 



_

W

R

_r



J_c= R J₀ 3 / 1 0















 



_

W

r

R

_r Hagedorn-Hall (normal metal) Clem-Berggren (superconductor)



does not play a role

The critical current of a right-angle bend is finite

There is an optimum curvature which permits to

avoid current crowding. The minimum radius

being 1.27 W

Vortex flow

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CC in voltage and current leads

Voltage Contact

3 / 1

2

3 













b

C



if





b



W

b

Current Contact

1 

C

if

b





3 / 1 2 2 2

)

(

2

3 















a

W

C





W

a

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Supporting experimental evidence

H. L. Hortensius et al. Appl. Phys. Lett. 100, 182602 (2012)

NbTiN

 ~ 7 nm

 ~ 20 mm W ~ 1 mm

D. Henrich et al., Phys. Rev. B 86, 144504 (2012)

NbN

 ~ 5 nm

 >> W W ~ 0,3 mm

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Field dependence

London

Compensation effect between the field induced stream-lines and the externally applied current at the current crowding point

Clem et al., Phys. Rev. B 85, 144511 (2012)

H >0

H <0 tdGL

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Experimental confirmation

180° 90° SiO₂ H > 0 V+ V-I Al (0) ~ 120 nm (1,22 K) ~ 8,3 mm W ~ 3,3 mm

Adami et al., Appl. Phys. Lett. 102, 052603 (2013)

-0,08 -0,04 0,00 0,04 0,08 650 700 750 800 850 900 S180 I C ( m A) H (mT) 1.18K, I+ -0.10 -0.05 0.00 0.05 0.10 300 350 400 450 500 550 600 650 700 750 S90 Hmax 1.18K, I+ 1.18K, 1.20K, I+ 1.20K, 1.22K, I+ 1.22K, I-I C (µ A) H (mT) ) ( 1 max T H





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Rectified motion of vortices

180° -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.1 0.2 0.3 0.4 0.5 T = 0.92 T_c Freq = 1kHz H[mT] ac am plitude [m A] V dc[µV] S90 -200 -120 -40 40 120 200 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.1 0.2 0.3 0.4 0.5 T = 0.92 T c Freq = 1kHz H[mT] ac am plitude [m A] V dc[µV] S180 -200 -120 -40 40 120 200 H >0 H <0 Fixed J > 0 J >0 J <0 Fixed H > 0

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Surface indentations

2

1 

C

3 / 1















a

C



if





90



Current crowding is more important for the triangular indentation

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Surface indentations

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Surface indentations

The onset of the resistive regime is mainly determined by the

properties of the ‘inlet’ boundary of the strip.

The effect due to patterning of the ‘outlet’ boundary facilitates the formation of PSLs

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High field behavior

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Nb, H=2 mT, T=4K Brisbois et al., unpublished

Surface indentations (many vortices)

J. I. Vestgården et al., PRB 76, 174509 (2007)  Meissner currents concentrate in front of the indentation where their density reaches jc and hence lead to even deeper flux penetration. This is why the flux front near the indentation advances faster than in the rest of the film.

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CC in nanostructured superconductors

J

Nakai & Machida Physica C 470 1148 (2010)

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Magnetic flux avalanches

Flux motion Q T Jc, F_p Adiabatic conditions, ΔT = Q/C(T)

R. G. Mints and A. L. Rakhmanov, Rev. Mod. Phys. 53, 551 (1981)

D_T >> D_M D_M >> D_T

v_Abrikosov << 1 km/ s

v_kinematics ~ 1-10 km/ s

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Magnetic flux avalanches

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Electromigration

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In the same way that magnetic field lines lead to

demagnetization effects, deformation of current stream lines

lead to current crowding.

This effect have important consequences on

- the resistance calculation in normal metals

- V(I) characteristics in superconductors

- unwanted ratchet signal

- hot spots (joule heating)

- reduction of the critical current

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