Superconductivity in moth balls:

surprises in organic transistors

April 10, 2002Jairo Sinova

Ref: J. Sinova et al, Phys. Rev. Lett. 87, 226802 (2001)

Financial support by

OUTLINE

• Introduction to organic thin film transistors

• Experimental surprises

• Quantum confinement in organic thin films

• Superconductivity in organic materials: electron-phonon coupling

• Comparison to experiments

• Conclusion

OUTLINE

• Introduction to organic thin film transistors– Organic field effect transistors (FETs)– Future and present applications of plastic electronics– Materials used in organic field effect transistors and their

properties

• Experimental Surprises in the past year• 2-D electron transport in organic thin films• Superconductivity in organic materials: electron-

phonon coupling• Comparison to experiments• Conclusion

Organic Field Effect Transistors

J. H. Schön, S. Berg, Ch. Kloc, and B. BatloggScience 2000 February 11; 287: 1022-1023

substrate

semiconductor

insulatorS Dgate

Vg

thin free charge carrierchannel induced by

electric field from gate

- - - - - -

>0

• Density of carriers proportional to gate voltage: changes in VG have a dramatic change in channel conductance (important technologically)

High mobility 2DEG: IQHE, FQHE, MIT, etc.

Applications of plastic transistors: future and present

LEDs plastic display

Cheaper solar cells

All plastic RAMS?

Printing plastic transistors and organic LEDs

C60

MATERIALS USED IN ORGANIC FETs

PentaceneTetracene

AnthracenceNaphthalene: moth balls

The aromatic molecules: polyacenes

ALSO:

SSS

SS

S

-6T

SS

SS

-4T

Tc=117 K!!

Material Properties of the Polyacenes and organic semiconductors

Energy levels of individual molecules

LUMO

HOMOE

Narrow bands in molecular crystal

(extended (delocalized) -electrons)

~ 1.5 -3 eV

•Lower mobility than silicon•Soft and flexible (Van-der-Waals bonding)•Larger size molecules: richer vibration spectrum (polaron rich)•Narrow bands: low overlap of conducting orbitals (contrast with metals and silicon); low T•Heavier carrier masses•Polaron physics at higher T

OUTLINE

• Introduction to organic thin film transistors• Experimental Surprises in the past year

– 2-D transport experiments in polyacene FETs– What are the key surprises?– Superconductivity: experimental finding

• 2-D electron transport in organic thin films• Superconductivity in organic materials: electron-

phonon coupling• Comparison to experiments• Conclusion

experiments by Batlogg, et al; courtesy of Dr. A. Dodabalapour

0.45 0.50 0.55 0.60 0.65 0.70 0.7510

-2

10-1

100

101

102

c

Insulator : =cexp((To/T)1/2

)

Metal : =cexp(-(To/T)1/2

)

holes / Pentacene MOSFET

T-0.5 (K-0.5)

(h/

e2 )

MIT

109

1010

1011

1012

1013

1014

p / cm-2

2DEG in Organic FETs: physical effects galore

2D Electron/Hole Gas

Gate

source and drain

gate insulator (Al2O3)

increasing voltage

0 2 4 6 80

20

40

60

80

100

Tetracene(Holes / 1.7 K)

5x1010

cm-2

6x1010

cm-2

7x1010

cm-2

8x1010

cm-2h/3e2

h/2e2

3h/e2

5h/2e2

3h/2e2

h/e2

Magnetic Field (T)

Rxy (k)

FQHE

0 2 4 6 80

20

40

60

80

100

Tetracene(Holes / 1.7 K)

5x1010

cm-2

6x1010

cm-2

7x1010

cm-2

8x1010

cm-2h/3e2

h/2e2

3h/e2

5h/2e2

3h/2e2

h/e2

Magnetic Field (T)

Rxy (k)

FQHE

0 2 4 6 80

5

10

15

20

25

30 Pentacene

1.7 K

Magnetic Field (T)

Resi

stance

R xx,

Rxy (

k)

IQHE

IQHE

0 2 4 6 80

5

10

15

20

25

30 Pentacene

1.7 K

Magnetic Field (T)

Res

ista

nce

Rxx

, Rxy

(k

)

0 5 10 15 20 25

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

Resistance

Ballistic Holes in Pentacene

Magnetic Field (mT)

Te

mp

era

ture

(K

)

MF

0 5 10 15 20 25

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

Resistance

Ballistic Holes in Pentacene

Magnetic Field (mT)

Tem

pera

ture

(K

)

MF

0.45 0.50 0.55 0.60 0.65 0.70 0.7510

-2

10-1

100

101

102

c

Insulator : =cexp((T

o/T)

1/2)

Metal : =cexp(-(T

o/T)

1/2)

holes / Pentacene MOSFET

T-0.5

(K-0.5

)

(h

/e2 )

MIT

100 110 120 1301.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

Resistance

Superconducting State

Normal State

Gate Voltage (V)

Tem

pera

ture

(K

)

0.85 0.90 0.95 1.00 1.05

Electrons per Molecule

100 110 120 1301.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

Resista

nce

Superconducting State

Normal State

Gate Voltage (V)

Tem

pera

ture

(K

)

0.85 0.90 0.95 1.00 1.05

Electrons per Molecule

SC

2.0 2.5 3.0 3.5 4.0 4.50.0

0.2

0.4

0.6

0.8

1.0

Anthracene

Pentacene

Tetracene

Temperature (K)

Res

ista

nce

(a.u

.)

J. H. Schön et al. Nature 406, 702 (2000)

Increase of Tc

with decreasingmolecular size

Similar behaviorfor oligothiophenes

(-4T, -6T, and -8T)

J. H. Schön et al. Phys Rev. B 64, 035209 (2001).

Gate-Induced Superconductivity in Polyacenes

courtesy of Dr. A. Dodabalapour

100 110 120 1301.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

Resistance

Superconducting State

Normal State

Gate Voltage (V)

Tem

pera

ture

(K

)

0.85 0.90 0.95 1.00 1.05

Electrons per Molecule

J. H. Schön et al. Nature 406, 702 (2000)

Electron-doping(~ 1014 cm-2)

80 - 100 Å

no bulksuperconductivity

Gate-Induced Superconductivity in Pentacene

courtesy of Dr. A. Dodabalapour

Electron-Phonon coupling strength spectrum experiments

M. Lee, et al, PRL 86, 862 (2001)

Infrared absorption

Conductance derivative spectrum of a

pentacene-Pb tunnel junction

Questions and Puzzles

• How can so many effects occur in one single sample?

• How 2-d is the quantum confinement?• What electron-phonon coupling drives the

superconductivity?• Is the FQHE regime highly interacting?• Is the vibrational spectrum affected by the

injected electrons?• Is this behavior generic to all organic materials?

...

OUTLINE

• Introduction to organic thin film transistors• Experimental Surprises in the past year • 2-D electron transport in organic thin films

– Self-consistent calculation of the electronic structure– How two dimensional is the system? How many sub-

bands are occupied?

• Superconductivity in organic materials: electron-phonon coupling

• Comparison to experiments• Conclusion

1.3 eV

valence band

conduction band

VG=0

How confined are the carriers at the interface?:2D or not 2D

Model calculation:

local density self consistent mean field calculation of the bands (continuous)

Important parameters:dielectric constants, density of carriers, lattice constant,insulator-semiconductorgap difference.

VG

organic semiconductor(anthracene)

Al2O3Au

1.3 eV

valence band

conduction band

VG>0

0 1 2

nm

0 1 2

nm

OUTLINE

• Introduction to organic thin film transistors• Experimental Surprises in the past year • 2-D electron transport in organic thin films• Superconductivity in organic materials: electron-

phonon coupling– General BCS superconductivity– Model: what type of electron-phonon to consider?– Vibrational spectrum calculation

• Comparison to experiments• Conclusion

Superconductivity: B-C-S• In normal superconductors electrons form pairs (Cooper

pairs)– Phonon assisted, carriers have opposite spins – Cooper pairs follow B-E statistics and a ‘condensation’ leads to SC

SC in organic (polyacenes) materials

•2D electrons-3D phonons•non-standard e-ph coupling•Rich vibrational spectra

2D Electron/Hole Gas

Gate

source and drain

gate insulator (Al2O3)

AB

Modeling electron-phonon coupling in anthracene

extvibreeKEtotal HHHHH

vibrDKEsiteontotal HHHH 2

after the LDA/Hartree calculation this reduces to

Su-Schrieffer-Heeger coupling

0KE

H phonelecH

Ruu

ttrt m

mm

~~,

6

1 2,10

ii

eei

HOMOi n)(

On the omission of the Holstein term

A. Devos and M. Lannoo, PRB 58, 8236 (1998)

non-degenerate LUMO/HOMO level

no elec-phon couplingwhen screening is present

This is NOT the case in fullerenes where the Holstein term is dominant and the SSH term is much smaller

Molecule DegenUnscreened

Holstein Coupling (meV)

Screened Holstein

Coupling (meV)

Anthracene L(1) 166 0

Tetracene L(1) 130 0

Pyrene L(1) 197 0

C60 L(3) 52 47

C28 H(3) 80 80

C20 H(4) 183 183

uu

eeiii

)(

A8A4 FTF l

3D Phonon Spectrum

phonon spectrumdispersion calculation

J. Sinova et al, PRL 87, 226802 (01)

Atom-Atom potential modelusing the Williams’ parametersto obtain the secular equation

)q,q)D)q,q,

((,()(2 inn

n

imi

Taddei, et al., J. Chem. Phys. 58, 966 (73)Dorner et al., J. Phys. C 15, 2353 (82)

2D electron-3D phonon term

kq]kQ,Q,

-Qk

Qk

,[,

BZ3D

,

,BZ-2D

ˆˆ]ˆˆ[,,(1

iiji

ji

vibe ccaaN

H

††g

))1((,()'(

(~

22

~)1(,q,(

')('[

,,' ,

,z,

kk]qqQ

Q)q,k

ijiiim

m

m m

iji

eeeu

t

M

fg

Calculation of mu

t

)(

•assume t is proportional to orbital overlap•

•obtain orbitals using the Hückel approximation

0)( tu

tm

0.4

0.6

0.8

1

1.2

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

orbi

tal o

verla

p

n.n. distance

OUTLINE

• Introduction to organic thin film transistors

• Experimental Surprises in the past year

• 2-D electron transport in organic thin films

• Superconductivity in organic materials: electron-phonon coupling

• Comparison to experiments– Electron-phonon coupling calculation, Tc calculation

– Agreement and predictions

• Conclusion/Final message

n2d~0.2-0.7/mol

Calculation and experiment comparison

M. Lee, et al, PRL 86, 862 (2001)

calculation

experiments

100 110 120 1301.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

Re

sis

tan

ce

Superconducting State

Normal State

Gate Voltage (V)

Te

mp

era

ture

(K

)

0.85 0.90 0.95 1.00 1.05

Electrons per Molecule

J. H. Schön et al. Nature 406, 702 (2000)

J. Sinova et al, PRL 87, 226802 (01)

n2d~1/mo

A

A

B

B

C

C

Tc~2 K

/1 eT Dc

DOS and SC relations: injected carrier density trends

•Rounded by disorder•SC will go away if p increases beyond half filling

100 110 120 1301.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

Resistance

Superconducting State

Normal State

Gate Voltage (V)T

empe

ratu

re (

K)

0.85 0.90 0.95 1.00 1.05

Electrons per Molecule

Model Calculation Results and Predictions

•Shows the sharp onset of SC with gate voltage•Agreement with peaks observed in absorption/tunneling experiments•Correct order of Tc (~2K compared with ~3K in experiments)•Tc should increase with pressure (with t0) in contrast with the fullerenes• SC will disappear as p goes beyond half filling in single band FET organic semiconductors

UPDATE FROM MM 02: C. Kloc

Not same material but similar SC physics

A Final Message From The Prophetic Mr.McGuire

Alvaro S. NuñezJohn Schliemann

Allan H. MacDonaldTomas Jungwirth

work done in collaboration with

100 110 120 1301.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

Resistance

Superconducting State

Normal State

Gate Voltage (V)

Tem

pera

ture

(K

)

0.85 0.90 0.95 1.00 1.05

Electrons per Molecule

0 5 10 15 20 25

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

Resistance

Ballistic Holes in Pentacene

Magnetic Field (mT)

Tem

pera

ture

(K

)

Mr. McGuire was right:there is a future in plastics

109

1010

1011

1012

1013

1014

0 2 4 6 80

20

40

60

80

100

Tetracene(Holes / 1.7 K)

5x1010

cm-2

6x1010

cm-2

7x1010

cm-2

8x1010

cm-2h/3e2

h/2e2

3h/e2

5h/2e2

3h/2e2

h/e2

Magnetic Field (T)

Rxy (k)

0.45 0.50 0.55 0.60 0.65 0.70 0.7510

-2

10-1

100

101

102

c

Insulator : =cexp((To/T)1/2

)

Metal : =cexp(-(To/T)1/2

)

holes / Pentacene MOSFET

T-0.5 (K-0.5)

(h/

e2 )

100 110 120 1301.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

Resistance

Superconducting State

Normal State

Gate Voltage (V)

Tem

pera

ture

(K

)

0.85 0.90 0.95 1.00 1.05

Electrons per Molecule

FQHE

IQHE

MIT

SC0 5 10 15 20 25

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

Resistance

Ballistic Holes in Pentacene

Magnetic Field (mT)

Tem

pera

ture

(K

)

0 2 4 6 80

5

10

15

20

25

30 Pentacene

1.7 K

Magnetic Field (T)

Res

ista

nce

Rxx

, Rxy

(k

)

MFp / cm-3

2DEG in Organic FETs: physical effects galore

2D Electron/Hole Gas

Gate

source and drain

gate insulator (Al2O3)

increasing voltage

experiments by Batlogg, et al

Mermin-Wagner Theorem: an academic exercise in a MF regime

KTT

No true long range order in 2-DThermal and quantum fluctuations destroy it

In a mean field regime these fluctuations are very smalland superfluid-stiffness very large

10 100 50010-1

100

101

102

103

T-2.8

T-2.3

T-1.8

Pentacene

Temperature (K)

Mob

ility

(cm

2 /Vs)

3D Band Transport

High T (~ 400 K) :Crossover to

Hopping

Anisotropy (Pentacene)

2.0 2.5 3.0 3.5 4.010

-2

10-1

100

101

102

increasing n

Pentacene / MOSFET electrons

Temperature (K)

(h/

e2 )

Metal-Insulator-Transition in 2DElectron Density :61010 - 51011 cm-2

Peak mobility :2104 cm2/Vs

Critical Concentration :pc  3.21011 cm-2

Strong El.-El. Interact.m* ~ 1.5 me

eff ~ 6

Magneto-Phonon Effect m*(T)

0 2 4 6 8 10 12 14 160.0

0.1

0.2

0.3

40 K 60 K 80 K

2me

1.7me

1.5me

Tetracene (Holes : 2x1011 cm-2)

N

1/B

(1/

T)

4 6 8

60 K

40 K

B (T)

-d2 R

/dB

2 (ar

b. u

nits

) Resonant Scattering of Charge Carriersbetween Landau-Levels

by LO-Phonons

V. L. Gurevich and Y. A. Firsov, Zh. Eksp. Teor. Fiz. 40, 198 (1961)

(Sov. Phys.JETP 13, 137 (1961)).R. A. Stradling and R. A. Wood,`

J. Phys. C1, 1711 (1968)

hlo = N hc

hc = eB/m*

1/BN hlo = N e/m*

Measurement of Effective Massas a Function of Temperature

Fermi Liquid behavior: excuse for BCS approach

A80[T]H

A181

)0(H2)0(

c

c

e

Hc2 and

AB

Modeling electron-phonon coupling in anthracene

extvibreeKEtotal HHHHH

vibrplaneinhoppingtotal HHH

after the LDA/Hartree calculation this reduces to

vibrtotal HccccrtH BAAB ),,,, ˆˆˆˆ(),(

RRRR

R,

††

0KE

H phonelecH

Su-Schrieffer-Heeger electron-phonon coupling

Ruu

ttrt m

mm

~~,

6

1 2,10 Assume crystal screening :

omission of the Holstein term