infrared and optical properties of novel correlated …outline • basics of an ir probe of...

Infrared and optical properties of novel correlated matterD.N. Basov

University of California, San Diego http://infrared.ucsd.edu

Outline

• Basics of an IR probe of electronic processes in solids• Electrostatic doping of new materials: challenges, opportunities

and first accomplishments• Intrinsic electronic transport in organic molecular crystals

October 18

October 25

November 1

November 8

• High Tc superconductivity: new materials or new state of matter?• The search for a pairing glue in high-Tc superconductors

• High Tc superconductivity by kinetic energy saving? • Infrared spectroscopy of correlated electron matter at the nano-scale

• Magnetic phenomena in semiconductors• Ga1-xMnxAs: first correlated electron semiconductor?



Today:

• Basics of an IR probe of electronic processes in solidsWhy IR?Basic concepts

generalized susceptibility and response model independent properties of generalized susceptibilitiescausality of EM response and Kramers-Kronig relations

IR/optical properties of metals and insulators Drude – Lorentz modelSum rules

• Negative index materials

• Electrostatic doping of new materials: challenges, opportunitiesand first accomplishments

• Intrinsic electronic transport in organic molecular crystals



Lecture notes:

Cannot rule out typos in my notes!

Your help in correcting typos will be appreciated!

Do not hesitate to contact me…



Basic concepts: generalized susceptibilityHamiltonians of many physical systems contain terms:

xfH −= Eprr

⋅−Induced dipole moment

HMrr

⋅−Magnetization

The operator itself may depend on the force. Provided the perturbation is weak, keep only linear terms:

Eprr α=

polarizability

HMrr

χ=Magnetic susceptibility

Response: t dependence to the action of generalized force:

( ) ( ) ( )∫∞

−=0

τττα dtftx Not a general form, many assumptions…

fxrr α=

generalized susceptibility

Operator of a physical system

Force or field

Basic concepts: generalized susceptibility & responseResponse: t dependence to the action of generalized force.

( ) ( ) ( )∫∞

∞−

= τττα drdrftrrtrx ',',`,,, rrrrr

( ) ( ) ( )∫∞

−=0

τττα dtftx

Properties of a system

Force acting at all times τ prior to t and places r’

Approximations:1) Local approximations

(no spatial dispersion)

Not always true:photonic crystalsmeta-materialsspin/charge ordered systemsinhomogeneous systemsmany more…

( ) ( )ττ frf ,'r

( ) ( )txtrx ,rIR nanoscopy @ 930 cm-1

ε1 5 0 -5

1 10 20s2

4 µm

10 n

mmetalinsulator

Basic concepts: response function & dielectric function

( ) ( ) ( )∫∞

−=0

τττα dtftx ( ) ( )∫= dtetxx tiωω ( ) ( )∫∞

=0

τταω ωτ def i

( ) ( )( ) ( )∫

∞

==0

τταωωωα ωτ de

fx i

PED π4+= ( ) ( ) ( ) ( )∫∞

−+=0

τττα dtftEtD

( ) ( )∫∞

∞−

= dtetDD tiωω ( ) ( )∫∞

∞−

= dtetEE tiωω

( ) ( ) ( ) ( )∫∞

+=0

τταωωω ωτ deEED i ( ) ( )( ) ( )∫

∞

+==0

1 τταωωωε ωτ de

ED i

( )[ ]1−ωε generalized susceptibility

( ) ( )ωσωπωε i41+=

Dielectric function

( ) ( )( )ωωωσ

EJ

=Optical conductivity

( ) ( )( )ωωωµ

HB

=Magnetic permeability

Basic concepts: wave equations in the medium

042

112

2

2112 =

∂∂

−∂∂

−∇tE

ctE

cE

rrr σπµµε 04

211

2

2

2112 =

∂∂

−∂

∂−∇

tH

ctH

cH

rrr σπµµε

Optical properties of a medium are fully accounted with the refractive index

[ ] 2/1ˆˆˆ µε=+= iknN

Generally: ( ) ( )ωεωεε 21ˆ i+= ( ) ( )ωµωµµ 21ˆ i+=

(+,+)(-,+)

(-,-) (+,-)

ε,µ space

042

112

2

2112 =

∂∂

−∂∂

−∇tE

ctE

cE

rrr σπµµε 04

211

2

2

2112 =

∂∂

−∂

∂−∇

tH

ctH

cH

rrr σπµµε

Optical properties of a medium are fully accounted with the refractive index


Generally: ( ) ( )ωεωεε 21ˆ i+= ( ) ( )ωµωµµ 21ˆ i+=

⎟⎠⎞

⎜⎝⎛ −⋅⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−= tnx

cikx

cEE ωωω expexp0

amplitudeattenuation

Wave traveling with phase velocityc/n

( )πεε iexp 1 =→−=( )πµµ iexp 1 =→−=

( ) ( )( ) 1iexp

/2iexp/2iexp−==

===

πππεµn

Basic concepts: wave equations and negative index media

Willebrord Snel van Royen1580-1626

2211 sinsin θθ nn =

Victor Veselagob.1927

Media with positive and negative index of refraction.

ω× =k E B

Direction of energy flow:

Direction of phase:

Phase and energy velocities antiparallel:

= ×S E H

SHEBEk µµ =×=×||

Magnetic response without magnets

∫ ×= rdjrm rrrr 3

21

magnetic dipole moment induced by current density j

20 µm

( )Γ+−

−=ωωω

ωωµi

F20

2

2

1medium

J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart, IEEE Trans. Micr. Theory and Techniques, 47, 2075 (1999).

-10

-5

0

5

10

0 0.5 1 1.5 2

Per

mea

bilit

y (µ

)

Frequency (ω/ωp)

=Teflon

1.4n= −LHM

2.7Ln

Microwave feed

LHM

Transmission for LHM

R.A. Shelby, D.R. Smith, S. Schultz, Science 292, 77 (2001)

Refraction in negative index media


• Materials– Intrinsic properties– Described by a few parameters

• a0 << a << λ• Material scale order determines the properties

a0

Atomic scale Atomic homogenization(Mesoscopic scale)

a

Meta-atomic scale Effective medium (second homogenization)

λ

What are meta-materials?

T.J. Yen, et al. Science 303, 1494 (2004)

interferometer

Er

Detector: R(ω)

25 µm

Negative refraction and artificial magnetism

W.J. Padilla, D.N. Basov and D.R. SmithMaterials Today (2006).

Negative index materials21 MHz

5 GHz

100 GHz

1 THz

100 THz

200 Hz

Lenses based on negative index media

Basic concepts: absorption of energy by a QM system

tfx

tH

dtdE

∂∂

−=∂

∂= x: has no explicit t dependence

f: explicitly depends on t

( ) =tx

( )titi efeff ωω *002

1+= −

LL: Statistical Physics

( ) ( ) titi efef ωω ωαωα *00 2

1 21

−+= −

( )titi efefidtdf ωωω *

002+= −

( ) ( )( ) *004

ffitfx

dtdE ωαωαω

−−=∂∂

−= ( ) 2022

fωαω=

( ) ( )∫∞

=0

τταωα ωτ dei

( ) ( )ωαωα *=−

( ) ( ) ( ) ( )ωαωαωαωα *−=−−( ) ( ) ( ) ( )[ ] ( )ωαωαωαωαωα 22121 2iii =−−+=

( ) 02 >ωα

Basic concepts: absorption of energy by a QM systemLL: Statistical Physics

=dtdE ( ) 2

022fωαω

=Significance:

1) fundamental constraints on theoretical models of the dielectric function2) experimental approach to investigate excitations in solids3) model independent analysis

Magnetic resonances and strong coupling effects

(pseudo)gap in cuprates

phonons

1 10 100 1000 10000Wavenumbers, cm-1

100 1000GHz 100 1000meV

polarons

bi-polarons

π-π* transitions (polymers)

Carrier lifetimes in metals and semiconductorsLocalization peaks in disordered conductors

Correlation gaps in 1D conductors

Amplitude modes(polymers)

Inter-band transitions

Josephson plasmons

Superconducting gap

Cyclotron modes and Landau Level transitions

Zeeman splitting

2D electron gas: EFSpin-orbit coupling

III-V II-VI

2D electron gas: plasmonsFM resonances

AF resonancesMagnetic modes in split ring resonators

Heavy Fermion plasmonsHybridization gap

Charge transfer gap

Analytical properties of ε(ω)

energy

σ1(ω)

Basic concepts: analytical properties of α(ω)LL: Statistical Physics

( ) ( )∫∞

=0

τταωα ωτ dei

( ) ( ) ( ) ( )ωαωαωαωα −−−=+ 2121 ii

( ) ( )ωαωα *=−1.

3. ( ) 0for 02 >> ωωα

( ) ( )ωαωα −= 11even

( ) ( )ωαωα −−= 22odd( ) ( )ωαωα −= 112.

( ) ( )ωαωα −−= 22

Basic concepts: causality of electromagnetic responseLooking for a relationship between ε1(ω) and ε2(ω)

tieEmex

mkxx ω−=+Γ+ 0&&&

tioexx ω−=

Γ−−=

ωωω i

Eme

x 220

0

0

00000 44 NexEPED ππ +=+=

( )Γ−−

+=ωωω

πωεim

Ne22

0

2 141

mk

=0ω

( ) ∑ Γ−−+=

i

i

if

mNe

ωωωπωε 22

0

241

22

2i

ii M

emfh

ω=

Dipole matrixelement

Oscillatorstrength

Drude – Lorentz model(charge e of mass m on a spring k)

Dielectric response of a QM system

0 100 200 cm-1-20

-10

0

10

20

30ε(ω)

ε2(ω)

ε1(ω)

0 100 200 cm-1-20

-10

0

10

20

30

ε2(ω)

ε1(ω)

ε(ω)

Basic concepts: causality of electromagnetic responseLooking for a relationship between ε1(ω) and ε2(ω)

tieEmex

mkxx ω−=+Γ+ 0&&&

tioexx ω−=

Γ−−=

ωωω i

Eme

x 220

0

0

00000 44 NexEPED ππ +=+=

( )Γ−−

+=ωωω

πωεim

Ne22

0

2 141

mk

=0ω

( ) ∑ Γ−−+=

i

i

if

mNe

ωωωπωε 22

0

241

22

2i

ii M

emfh

ω=

Dipole matrixelement

Oscillatorstrength

Drude – Lorentz model(charge e of mass m on a spring k)

Dielectric response of a QM system

(DC conductivity,

John TollPhys. Rev. 104 1760 (1956)

Basic concepts: Kramers-Kronig relationsRelations between α1(ω) and α2(ω)

α1(ω)+iα2(ω) should satisfy the following conditions:1. single valued in the upper half of w plane2. no singularities except for w=0 where

α(ω)=4πiσ/ω + α03. α1(ω) -- even4. α2(ω) -- odd5. α(ω) 0 for ω \infty

( ) 00

=−∫ ωωωα

Cauchy Integral Theorem

1 2 3 4 5

6

ω0

( )∫ ∫ ∫ ∫

∞

∞− −=++

0

531ωω

ωωα dP

( )∫ −= 04 ωπαi

∫ −−=

0

42ωσππ ii

06 =∫

( ) ( )( ) 04

00

0

=⎟⎟⎠

⎞⎜⎜⎝

⎛−

−+−+−∫

∞

∞− ωσππωπα

ωωωωα iiidP

( )( ) 2121 παπαααπ +−=+− iii

Re: ( ) ( )0

2

020

1 4ω

σπωπαωω

ωωα+−=

−∫∞

∞−

dP

Im: ( ) ( )010

2 ωπαωω

ωωα=

−∫∞

∞−

dP

( ) ( )∫∞

∞− −=

0

201

1ωω

ωωαπ

ωα dP ( ) ( )0

2

0

102

41ω

σπωω

ωωαπ

ωα +−

−= ∫∞

∞−

dP

Basic concepts: Kramers-Kronig relationsRelations between α1(ω) and α2(ω)

α1(ω)+iα2(ω) should satisfy the following conditions:1. single valued in the upper half of w plane2. no singularities except for w=0 where

α(ω)=4πiσ/ω + α03. α1(ω) -- even4. α2(ω) -- odd5. α(ω) 0 for ω \infty

1 2 3 4 5

6

ω0

( ) ( )∫∞

∞− −=

0

201

1ωω

ωωαπ

ωα dP

( ) ( )0

2

0

102

41ω

σπωω

ωωαπ

ωα +−

−= ∫∞

∞−

dP

“high enough”

Problem!

( ) ( )ωαωα −= 11

( ) ( )ωαωα −−= 22

( ) ( ) ( )[ ] ( ) ( )[ ]dxax

xfxfaxfxfxPaxdxxfP ∫∫

∞∞

∞− −−++−−

=− 0

22

( ) ( )∫∞

−=−

022

0

00201

21ωω

ωωεωπ

ωε dP

( ) ( )ωπσω

ωωωε

πωωε 412

00

220

012 +

−−

−= ∫∞

dP

IR/optical properties of metals&insulators: optical conductivity

( ) ( )ωσωπωε i41+=

Properties of σ(ω) : 1. Response function

2. No singularity at ω 0

3.

4. real part quantifies absorption

5. obeys sum rule:

( ) 0for 1 →= ωσωσ DC

( ) ( )ωωεωπσ 214 =

( )em

ned2

2

01

πωωσ =∫∞

Units:3D: s-1, (Ωcm)-1, Siemens= (Ωcm)-1

2D: Ω-1

IR/optical properties of metals&insulators: Drude model

Free electronstieEmex

mkxx ω−=+Γ+ 0&&&

( ) 22

2

1 11

4 τωπτω

ωσ+

= p ( ) 22

2

2 14 τωωτ

πτω

ωσ+

= p

( ) 22

2

1 1 −+−=

τωω

ωε p ( ) 22

2

21

−+=

τωω

ωτωε p

mne2

2p

4 1 πωτ

==Γ

( ) τωπ

τπσωσ 22

1 4140 pDC m

Ne====

( )ωτ

σωσiDC

−=

1



mkxx ω−=+Γ+ 0&&&

( ) 22

2

1 11

4 τωπτω

ωσ+

= p ( ) 22

2

2 14 τωωτ

πτω

ωσ+

= p

( ) 22

2

1 1 −+−=

τωω

ωε p ( ) 22

2

21

−+=

τωω

ωτωε p

mne2

2p

4 1 πωτ

==Γ

( ) τωπ

τπσωσ 22

1 4140 pDC m

Ne====

( )ωτ

σωσiDC

−=

1

P.Drude Annalen der Physik, 1, 566 (1900)

0 400 800 1200 16000

0.5

1

0 400 800 1200 1600-20

-10

0

10

20

0 40 80 120 160 2000

1000

2000

R(ω)D

iele

ctric

func

tion

Con

duct

ivity

Ω-1

cm-1

σDC

ε2

ε1

cm-1

cm-1

cm-1

1/τ

σ1

σ2



mkxx ω−=+Γ+ 0&&&

( ) 22

2

1 11

4 τωπτω

ωσ+

= p ( ) 22

2

2 14 τωωτ

πτω

ωσ+

= p

( ) 22

2

1 1 −+−=

τωω

ωε p ( ) 22

2

21

−+=

τωω

ωτωε p

mne2

2p

4 1 πωτ

==Γ

( ) τωπ

τπσωσ 22

1 4140 pDC m

Ne====

( )ωτ

σωσiDC

−=

1

M.Scheffler et al. Nature 438, 1135 (2005)

UPd2Al3

IR/optical properties of metals&insulators: interband transitions

-4

0

4

-6

-2

2

6

L Λ Γ ∆ X

E0

E0’

E1E1+∆1

E2

Ener

gy, e

V2 4 6eV

0

5000

10000

15000

20000

2500

7500

12500

17500

σ 1(ω

), (Ω

cm)−1

20000 40000cm-1

GaAs

( ) ( ) 222220

22

1/

/4 τωωω

τωπτω

ωσ+−

= p

( ) ( )( ) 22222

0

220

2

2/4 τωωω

ωωωπτω

ωσ+−

−−= p

E0

E1

E1+∆1

E0’

E2

IR/optical properties of metals&insulators: sum rules

( ) 22

2

22

2 11 −− ++

+−=

τωω

ωττωω

ωε pp i

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛+

−−

−+−

+=+= ∫∫∞∞

0022

0

01

022

0

002021

041221ω

πσωωω

ωεπω

ωωωωεω

πεεε dPidPi

( ) ( )[ ] ( )⎟⎟⎠

⎞⎜⎜⎝

⎛+−+−= ∫∫

∞∞

∞→0

0010

00202

041221limω

πσωωεπω

ωωεωπω

εω

did /from KK relations/

...1101lim 3

2

22 ++−−=

∞→ τωω

ωω

ωε

ω

pp i /from ε(ω) /

ω−1: ( )[ ] ( ) 00410

001 =+−∫∞

πσωωε d

ω−2: ( )em

ned2

00020

42

ππωωεω =∫∞

10 100 1000 10000 cm-1

σ1(ω) σDC

intra-band inter-band

Understanding optical conductivity: sum rules

ωτσωσi−

=1

)( 0

mne τσ

2

0 =

( )em

nd =∫∞

ωσω 10

0.1 1 10 100 1000 10000 100000 eV0

4

8

12

16

Nef

f

E.Shiles et al.PRB 22, 1683 (1980)

Aluminum

( ) ( )ωσωωω

′′= ∫ 10

dNeff1s22s22p63s23p1

( )ωσω 10* ∫=

W

dmn

Outline• Why electrostatic doping?• IR spectroscopy in theregime of electrostatic doping

• Charge injection in Poly3-hexylthiophene (P3HT)

• Light quasiparticles in organic molecular crystals

Electrostatic doping of new materials: challenges, opportunitiesand first accomplishments

D.N. BasovUniversity of California, San Diego http://infrared.ucsd.edu/

AgilentTechnologies

Support:

5mm

1 cm

source drain

gate

source

drain

gate

G

SD

Activesemiconductor:

polyhexylthiophene

graphene

C42H28

Electrostatic doping of new materials: challenges, opportunitiesand first accomplishments

D.N. BasovUniversity of California, San Diego http://infrared.ucsd.edu/

Collaborators:Zhiqiang Li M. MartinO.Khatib (ALS)M.QuazilbashN. SaiM. di Ventra(UCSD) G.Wang

Daniel MosesA.J. Heeger(UCSB)

V.PodzorovM.Gershenson(Rutgers)

AgilentTechnologies

Support:

5mm

1 cm

source drain

gate

source

drain

gate

G

SD

Activesemiconductor:

polyhexylthiophene

graphene

C42H28

gateoxide

CRYSTAL

La2-xSrxCuO4La2CuO4insulator Superconductivity

Spin/charge orderElectronic phase separation

LaMnO3insulator

La1-xSrxMnO3FerromagnetismColossal magnetoresistancePhase separationSpin/charge/orbital order

insulatorGaAs Ga1-xMnxAs

Ferromagnetismhigh m*Phase separation

C60insulator

AxC60SuperconductivityExotic conducting state

Doped insulators

DS

insulators

FETs:SemiconductorsTransition metal oxidesSuperconductors

elementalhigh-Tc cuprates

Organic molecular crystalsPolymers, nano-tubes, Meta-materials, more…

gateoxide

CRYSTAL

DS

Voltage-gated devices: ubiquitous in nature and technology

MOSFET: production rate 1018/yr

Voltage-gated ion channel

gate

CRYSTALS Doxide

New Physics and FET Principle

K.Parendo et al.PRL94, 197004 (2005)

Tunable superconductivityTunable electronic properties

A.S. Dhoot, G.M.Wang,D.Moses, A.J. HeegerPRL96, 246403 (2006)

M.Panzer and D.FrisbieAdv.Funct Matt 161051 (2006)

Metallic state in polymers and organic molecular crystals

1/T0.5 (K-0.5)

P3HT

D. Matthey, et al.PRL 98, 057002 (2007)

NdBa2Cu3O7+δ

Tunable superconductivity

[K]

R,[Ω]

metal gateinsulator

InAs(In,Mn)As

H.Ohno et al. Nature 408, 944 (2000)D.Chiba et al. Science 302, 943 (2003)

Tunable magnetism

Weisheit al. Science 315, 349 (2007)

Correlated electron systems: WSe2, TM oxides, manganites, graphene

Nakamura et al.0608243

C.H.Ahn, J.M.Triscone and J.Mannhart,Nature 424, 1015 (2003)

Fabrication / high E fieldsElectrostatic doping: long standing challenges

Response of E-doped charges

gate

CRYSTALS Doxide


Fabrication / high E fieldsResponse of E-doped charges

• Charge dynamics in accumulation layer?

•Evolution of the electronic structure?

•Disorder, localization and self-organization?

•OMC: band transportorhopping conductivity?

spectroscopy is highly desirable…

TunnelingSTM IR/

optical

ARPES

gate

CRYSTALS Doxide

Electrostatic doping: long standing challenges


Fabrication / high E fieldsResponse of E-doped charges?

… difficult or impossible

TunnelingSTM IR/

optical

ARPES

spectroscopy is highly desirable… gate

CRYSTALS Doxide

Electrostatic doping: long standing challenges

• Charge dynamics in accumulation layer?

•Evolution of the electronic structure?

•Disorder, localization and self-organization?

•OMC: band transportorhopping conductivity?

gate

CRYSTAL

S Doxide

FET structures and IR/optical spectroscopy

100 1000GHz 100 1000meVSub-THz THz Far-IR Mid-IR Near-IR visible/UV

detectorpseudogaps in correlated electron systems

phonons

1 10 100 1000 10000

(bi)polarons

π-π* transitions (polymers)

Carrier lifetimes in metals and semiconductors

Correlation gaps in 1D conductorsInter-band transitions

Cyclotron modes and Landau Level transitions

Zeeman splitting

2D electron gas: EF

Spin-orbit couplingIII-V II-VI

2D electron gas: plasmons

magnetic resonances

Charge transfer gap

cm-1

IRoptical

1000 2000 5000cm-10

1

2

3

4

∆αd

100 200 500meV

Poly3-hexylthiophene (P3HT)

TiO2

S D S D S DAu contacts

n-Si

P3HT: excitations in the accumulation layer

V=2 V

V=7 V

V=30 V

IRAVs

polaron

P3HT/3 mol % PF6Kim et al PRB38 5490 (88)

1000 2000 5000cm-1

100 200 500meV

0

400

800

1200

∆α

300 K

x10-3

Z.Q. Li et al. Applied Physics Lett. 86, 223506 (05)Nano Letters 6, 224 (2006); PRB75, 45307 (2007)

polarontheory

molecular crystals Si, Ge

van der Waals bonds covalent bondsEvdW=10-3 — 10-2 eV Ecov=2 — 5 eV

narrow bands broad bands

low mobility µ<1cm2/Vs high µ>500 cm2/Vs

m*=100-1000 me m*=0.1-0.2 me

hopping band transport

polarons

Electronic properties of organic molecular crystals:conventional wisdom

M. Pope Ch. Swenberg “Electronic Processes in Organic Crystals and Polymers”Oxford 1999

E.Silinsh, C.Capek “Organic Molecular Crystals”AIP 1994

C42H28

Electronic properties of organic molecular crystals:conventional wisdom

molecular crystals

van der Waals bondsEvdW=10-3 — 10-2 eV

narrow bands

low mobility µ<1cm2/Vs

m*=100-1000 me

hopping

polarons

W.Warta and N.Karl PRB32 1172 (1985)

µ, cm2/Vs

No!

No!

*meτµ =

???

C42H28

molecular crystals

van der Waals bondsEvdW=10-3 — 10-2 eV

narrow bands

low mobility µ<1cm2/Vs

m*=100-1000 me

hopping

polarons

An infrared probe of transport in organic molecular crystals

( )∫= ωωσ1*d

mn

frequency

RE

cond

uctiv

itypolarons

bandelectrons

hoppingσ(ω)∼ωs

Rubrene

S D

gate

insulator

M.Gershenson

8000 16000cm-1

0.8 1.2 1.6 2eV

0 1000 2000 3000cm-1

0 100 200 300 400meV

0

0.2

0.4

0.6

0.8

T(ω)

b-axisa-axis

T=300 K

eV

DOS

Energy

HOMO

LUMO

2.2 eV

Rubrene: IR and optical response

Z.Q. Li et al. PRL 99, 016403 (2007).

0

0.001

0.002

0.003

0 1000 2000 3000cm-1

0 1000 2000 3000cm-1

0

0.2

0.4

0.6

0.8

8000 16000cm-1

b-axisa-axisT=300 K

8000 16000cm-1

Parylene [1 µm]

Rubrene

ITO [200 A]

S D

VGS = 280 V

T(ω)

+++++++++++++ ++

∆αd

Mid-IR

Rubrene OFETs: anisotropic response of an accumulation layer

Z.Q. Li et al. PRL 99, 016403 (2007).

0 1000 2000 3000 4000 cm-1 0 1000 2000 3000 4000 cm-1

6x10-6

4x10-6

2x10-6

0

6x10-6

4x10-6

2x10-6

0

0 100 200 V0

0.004

0.008

0.012

( )1-1- cmΩeffN

0 100 200 V0

0.004

0.008

0.012

( )1-1- cmΩeffN

Rubrene OFETs: conductivity of accumulation layer( )-12

1 ΩDσ ( )-121 ΩDσ

EIIa EIIb

Vs/cm 5 2<µ

280 V200 V120 V

280 V200 V120 V

0 1000 2000 3000 4000 cm-1

6x10-6

4x10-6

2x10-6

0

( )-121 ΩDσ

VGS=280 V

0 100 200 V0

0.004

0.008

0.012

Polarons in molecular crystal OFETs?

( )1-1- cmΩeffN

EIIa

EIIb

ma=1.85 me

mb=0.8 me

DOS

Energy

HOMO

LUMO

2.2 eV

EF

VGS=280V

1. Light qusiparticles2. Anisotropic m*3. Anisotropic σ(ω)

1.29 me

1.90 me

Experiment Theory

4. Polarons: EB<26 meV (300 K)

3. Anisotropic response of rubrene-based OFETs

6x10-6

4x10-6

2x10-6

00 1000 2000 3000 4000cm-1

0 100 200 V0

0.004

0.008

0.012( )-12

1 ΩDσ

EIIbEIIa

ma=1.85 me

mb=0.8 me

VGS=280V

1. IR: a tool for spectroscopy and imaging of charge injection in OFETs.

Thin film FET Single crystal FETZ.Q. Li et al. Applied Physics Lett. 86, 223506 (05)

2. Electronic excitations in accumulation layer

1000 2000 5000700 cm-10

1

2

3

4

∆αd

100 200 500 meV

P3HTV=30 V

7 V2 V

Z.Q. Li et al. Nano Letters 6, 224 (2006)

4. Band-like transport in OMC-basedtransistors

VGS=280V

DOSEn

ergy

HOMO

LUMO

2.2 eV

EFZ.Q. Li et al. PRL 99, 016403 (2007).

infrared and optical properties of novel correlated …outline • basics of an ir probe of...

Documents