Class Organic Electronic Materials 23

8/6/2019 Class Organic Electronic Materials 23

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2.3

Charge Generation and Transport in Molecules and Bulk Materials


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Band Models from the Perspective of Organic Chemistry

99

HHx

HH4

HH2

HH

ethylene butadiene octatetraene poly(acetylene)

isolated MO levels coalesce into bands for large conjugated systems still isolated MO levels, but energy differences E~1/N, much smaller than thermal energy band width is measure of macroscopic electron delocalization

E

*

HOMO

LUMOEg 2.2 eV


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Band Models from the Perspective of Solid State Physics

wave vector k, direction // wave, magnitude ~ wave number (i.e., energy) silicon is indirect band gap material, electron excitation requires change of momentum GaAs is direct band gap material, electron excitation requires no change of momentum steeper bands represent more delocalized states, higher mobility

100

E

0

k

E

0

k

Si GaAs


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Charge Generation and Transport in Inorganic Metallic Conductors

partially filled (or overlapping) bands with infinitesimal difference between energy levels all energy levels macroscopically delocalized band conductivity: charge transport (in electric field at finite temperature) without activation

101

no activation needed

+

Fermi levelhole, q = +e, s =electron, q = e, s =


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Charge Generation and Transport in Undoped Inorganic Metallic Conductors

band gap between valence and conduction band; no spontaneous charge separation charge separation by promotion (excitation) of electrons into conduction band charge transport (in electric field) via band conductivity because energy levels delocalized

102

T or h

+

HOMO

LUMO

conduction band

valence band

hole, q = +e, s =

electron, q = e, s =

Si Si Si

Si Si Si

SiSiSi


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Charge Generation and Transport in Doped Inorganic Semiconductors (1)

p-type doping of silicon with boron (electron acceptor) creates extra hole energy levels p-type doped silicon is electrically neutral (missing electron compensated by nucleus charge) new energy bands are very narrow, limited delocalization, low charge carrier mobilities

103

T or h

HOMO

LUMO

conduction band

valence band

hole, q = +e, s =


Si Si Si

Si B Si

SiSiSi

q = 0, s = +


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Charge Generation and Transport in Doped Inorganic Semiconductors (2)

n-type doping of silicon with phosphorous (electron conor) creates extra electron energy levels n-type doped silicon is electrically neutral (additional electron compensated by nucleus charge) new energy bands are very narrow, limited delocalization, low charge carrier mobilities

104

Si Si Si

Si P Si

SiSiSi

T or h

HOMO

LUMO

conduction band

valence band

hole, q = +e, s = 0q = 0, s =

+



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Degenerate Ground States In Poly(acetylene)

poly(acetylene) has two degenerate (energetically and geometrically equivalent) ground states domains of the two ground states along polymer chains in crytalline poly(acetylene)

105

E

x

x x

ground state A ground state B


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Formation of Solitons in Crystalline Poly(acetylene)

neutral solitons are lattice defects associated with domain boundaries in poly(acetylene) lattice distortion results in extra energy level in band gap, limited delocalization from organic chemistry perspective, solitons are radicals (spin but no charge)

106

7

ground state A ground state Bdomainboundary

ground state A ground state Bdomainboundary

q = 0, s =

neutral soliton


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Poor Intrinsic Conductivity of Undoped Poly(acetylene)

neutral solitons do not carry charge, can not contribute to conduction low intrinsic conductivity of undoped poly(acetylene) because charge separation in electric field positive and negative solitons require no additional energy for geometric rearrangement

107

ground state A ground state A

negativesoliton

positivesoliton

ground state B

ground state A ground state A

negativesoliton

positivesoliton

ground state B


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Oxidative (P-Type) Doping of Poly(acetylene)

positive solitons have charge, no spin; in organic chemistry view delocalized carbocations at high doping levels, positive solitons start to interact, form narrow bands charge carriers in delocalized states; strongly doped poly(acetylene) is a metallic conductor

108

I2 excess I2

q = 0s = q = +es = 0 q = +nes = 0+ +

I3

I3


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Reductive (N-Type) Doping of Poly(acetylene)

negative solitons have charge, no spin; in organic chemistry view delocalized carbanions at high doping levels, negative solitons start to interact, form narrow bands charge carriers in delocalized states; strongly doped poly(acetylene) is a metallic conductor

109

Na excess Na

q = 0s = q = es = 0 q = nes = 0

Na

Na


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A Charged Soliton as a Defect Structure in a Poly(acetylene)

110


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Ground and Excited States In Other Conjugated Polymers

poly(acetylene) has two degenerate (energetically and geometrically equivalent) ground states domains of the two ground states along polymer chains in crytalline poly(acetylene)

111

ground state

excited state

E


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Hypothetical Solitons in Other Conjugated Polymers

neutral, positive, or negative solitons can not exist in other conjugated polymers two solitons would spontaneously recombine

112

ground state ground state

soliton

excited state

negativesoliton

positivesoliton

soliton

ground state ground stateexcited state


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Oxidative (P-Type) Doping of Conjugated Polymers

positive polarons have charge, spin; in organic chemistry view delocalized radical cations

positive bipolarons have double charge, no spin; in organic chemistry view delocalized dications polarons/bipolarons are one single species, correlation length = effective conjugation length at high doping levels, formation of narrow bands; charge carriers in delocalized states

114

I2 excess I2q = +e

s =

q = +2e

s = 0

q = +2ne

s = 0

I2

positive polaron positive bipolaron high doping levels

I3 I3I3

+ + + + +


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Reductive (N-Type) Doping of Conjugated Polymers

negative polarons have charge, spin; in organic chemistry view delocalized radical anions

negative bipolarons have double charge, no spin; in organic chemistry view delocalized dianions polarons/bipolarons are one single species, correlation length = effective conjugation length at high doping levels, formation of narrow bands; charge carriers in delocalized states

115

Na excess Naq = e

s =

q = 2e

s = 0

q = 2ne

s = 0

Na

negative polaron negative bipolaron high doping levels

Na Na Na


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Example: Band Structure of Doped Poly(pyrrole)

high doping levels required (typically 150% w/w) for organic semiconductors conduction bands are narrow, limited conductivity (in three dimensions)

116

FeCl3 FeCl3Eg 3.2 eV

FeCl3

33% w/w

+ +

xNH

Eg 3.6 eV

Eg 0.5 eV

Eg 1.3 eV

Eg 1.0 eV

++ +

0.4 eV


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Electrochemical Polymerization of Anilin

electrochemical polymerization for poly(thiophene), poly(pyrrole), poly(anilin)

polymers deposited on electrodes additional electrolyte needed to provide counterions yields in situ doped conjugated polymers, with mixed valence states

117

NH2

electrochemicalpolymerization H

N

NH

HN

NH

3

+1

+23

xe.g., in DMF

NaBF4

BF4

BF4


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Charge Transfer Complexes between Electron Donor and Acceptor Materials (1)

118

Electron donor materials high-lying HOMO

high electron density

low ionization energy

S

S

S

S

S

S

S

S

SS

xS xS

OO

FF

F

F F F F F

F

FFFFF

O

RN

O

O

NR

O

NC

NC

CN

CN

xS

R

S

S

S

S

S

SR R

tetrathiofulvalene (TTF) and derivatives

polyl(thiophene), poly(3-alkylthiophene) (P3AT),poly(3,4-ethylenedioxythiophene) (PEDOT)

oligothiophene derivatives

tetracyanoquinodimethyne (TCNQ)

perfluoropentacene

perylene bisimide derivatives

Electron acceptor materials low-lying LUMO

low electron density

high electron affinity


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Phys. Rev. Lett. 1988, 60, 1418.

Charge Transfer Complex of TTF and TCNQ

120

Tetrathiafulvalene (TTF) Tetracyanoquinodimethane (TCNQ)

NC

NC

CN

CNS

S

S

S

105 S cm1

= 2 cm2/Vs 105 S cm1

TTF TCNQ Single Crystal

= 500 S cm1, metallic at T < 54 K


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Band Conductivity

within doped conjugated polymers or within single-crystalline stacks of conjugated molecules bands and charge carriers, macroscopically delocalized (although limited delocalization) charge transport within molecules/domains by diffusion in electric field

121

+

+

E

E

E

E

+

+


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Quantum-Mechanical Resonant Tunneling

finite potential well results in finite probability of electron inside the well identical energy levels required for resonance; electronic frequency unchanged amplitude decreases with distance; close contact required

123

vacuum level

molecule A molecule Bpotential well

tunneling probability t ~ eBd

d < 5 nm

E


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Variable Range Hopping

in a disordered material, the energy levels will not be aligned; excitation needed hopping is thermally assisted tunneling; range varies with temperature amplitude decreases with distance; close contact required

124

vacuum level

molecule A molecule Bpotential well

hopping probability

d < 5 nm

E

h=0 e

T0

T

1n+1


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Summary

125

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Class Organic Electronic Materials 23