measuring energetic disorder and its effect on organic solar cells · 2020. 7. 9. · pope &...
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Excitons
Mott-Wannier Excitons in Inorganic Semiconductors Molecular Excitations
Frenkel-Excitons in Molecular Aggregates Exciton-Polaritons, 1D Excitons and others
Dieter Neher, Mai 2015
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Wannier Excitons
Kittel: Festkörperphysik
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One-Electron versus Two-Electron Representation
Yu+Cardona: Fundamentals of Semiconductors
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One-Electron versus Two-Electron Representation
Yu+Cardona: Fundamentals of Semiconductors Kittel: Festkörperphysik
wrong: correct:
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Excitonic Absorption Properties
Yu+Cardona: Fundamentals of Semiconductors
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π-Conjugated Carbon Hydrates
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Molecular Orbitals of Hexatriene
http://wps.prenhall.com/wps/media/objects/724/741576/chapter_01.html
CH2
CH
CH
CH
CH
CH2
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Ionization Energy
ELUMO
EHOMO
+ + e-
Generate positive charge on molecule by removing electron from the molecule
IE Requires Ionization Energy
Evac E
Koopmans’ Theorem: IE = - EHOMO
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Electron Affinity
- + e-
Generate negative charge on molecule by placing electron onto the molecule Approximated by donating one electron to the LUMO
EA = -ELUMO Releases electron affinity
ELUMO
EHOMO
Evac E
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Molecular Frenkel Excitons
Occupation of LUMO with one electron
HOMO becomes partially emptied
http://wps.prenhall.com/wps/media/objects/724/741576/chapter_01.html
but this is not a state!! It is a configuration!!
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The Jablonski Diagram for Molecular Excitations
singlet ground state
excited singlet states excited
triplet states
Light Absorption
Fluorescence
Phosphorescence
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Exciton Binding Energy
C. Deibel et al., PRB 81, 085202 (2010)
eVEG 6.2= eVES 9.11 =
eVEb 7.0≅Exciton Binding Energy Band absorption hidden below exciton
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Effective Conjugation Length Nakanishi et al., J. Org. Chem 1998, 63, 8632 Izumi et al., JACS 2003, 125, 5286
relaxed exciton localized over ca. 5 nm along a well defined chain
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Physical Dimers
Pope & Svenberg: Electronic Processes in Organic Crystals and Polymers
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Physical Dimers
General case:
1α 2α
Molekül “1” Molekül “2”
d
30
212112 2
)(3)(3d
nnVrεπε
µµµµ −=
Point dipole interaction:
Transition dipole moment:
21 mmM ±=
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Physical Dimers
Distorted crystal of 1,4 dibromonaphthalene
Pope & Svenberg: Electronic Processes in Organic Crystals and Polymers
β = 6.7 cm-1 = 1 meV
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Dispersion of Frenkel Excitons
E. Zojer et al., J. Phys. Cond. Matter. 2000, 12, 1753
e++W’+2β
e++W’-2β
e++W’
+π/d -π/d
electron energy loss (EEL) spectrum of a 6P crystal perp. molecular axis
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Chiral J-Aggregates
R. Marty et al., ACS Nano 2013, 7, 8498 helical nanowires of pi-pi stacked perylene diimides
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Chiral J-Aggregates
R. Marty et al., J. Chem. Phys. B 2014,118, 11152 nanowires exhibit circular dichroism
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J-Aggregates
S.Kirstein and S. Dähne, Int. J. Photoenergy 2006, 20363-1-21
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Exciton Diffusion in J-Aggregates
K. Clark et al., J. Phys. Chem. Lett. 2014, 5, 2274
2 µm 2 µm
excitons diffuse more than 500 nm
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1D Exitons in Polydiacetylene
Y. Lifshitz et al., Phys. Chem.Chem. Phys. 2010, 12, 713 J. Lee et al., Nature Comm. 2014, 5, 3736 http://www.chem.sunysb.edu:81/faculty/jlauher.htm
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1D Exitons in Single Polydiacetylene
F. Dubin et al., Nature Physics 2006, 2, 32
Microphotoluminescence of singly PDA chains in a diacetylene crystal