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?
Infrared and optical properties of novel correlated matterD.N. Basov
University of California, San Diego http://infrared.ucsd.edu
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
Infrared and optical properties of novel correlated matterD.N. Basov
University of California, San Diego http://infrared.ucsd.edu
Lecture notes:
Cannot rule out typos in my notes!
Your help in correcting typos will be appreciated!
Do not hesitate to contact me…
Infrared and optical properties of novel correlated matterD.N. Basov
University of California, San Diego http://infrared.ucsd.edu
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
[ ] 2/1ˆˆˆ µε=+= iknN
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
[ ] 2/1ˆˆˆ µε=+= iknN
• 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
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
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
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
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
C.H.Ahn, J.M.Triscone and J.Mannhart,Nature 424, 1015 (2003)
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
C.H.Ahn, J.M.Triscone and J.Mannhart,Nature 424, 1015 (2003)
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
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).