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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
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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
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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
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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
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T or h
HOMO
LUMO
conduction band
valence band
hole, q = +e, s =
electron, 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
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Si Si Si
Si P Si
SiSiSi
T or h
HOMO
LUMO
conduction band
valence band
hole, q = +e, s = 0q = 0, s =
+
electron, q = e, 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)
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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
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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
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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
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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
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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)
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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
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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)
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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
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