Excitons

Mott-Wannier Excitons in Inorganic Semiconductors Molecular Excitations

Frenkel-Excitons in Molecular Aggregates Exciton-Polaritons, 1D Excitons and others

Dieter Neher, Mai 2015

Wannier Excitons

Kittel: Festkörperphysik

One-Electron versus Two-Electron Representation

Yu+Cardona: Fundamentals of Semiconductors

One-Electron versus Two-Electron Representation

Yu+Cardona: Fundamentals of Semiconductors Kittel: Festkörperphysik

wrong: correct:

Excitonic Absorption Properties

Yu+Cardona: Fundamentals of Semiconductors

π-Conjugated Carbon Hydrates

Molecular Orbitals of Hexatriene

http://wps.prenhall.com/wps/media/objects/724/741576/chapter_01.html

CH2

CH

CH

CH

CH

CH2

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

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

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!!

The Jablonski Diagram for Molecular Excitations

singlet ground state

excited singlet states excited

triplet states

Light Absorption

Fluorescence

Phosphorescence

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

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

Physical Dimers

Pope & Svenberg: Electronic Processes in Organic Crystals and Polymers

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 ±=

Physical Dimers

Distorted crystal of 1,4 dibromonaphthalene

Pope & Svenberg: Electronic Processes in Organic Crystals and Polymers

β = 6.7 cm-1 = 1 meV

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

Chiral J-Aggregates

R. Marty et al., ACS Nano 2013, 7, 8498 helical nanowires of pi-pi stacked perylene diimides

Chiral J-Aggregates

R. Marty et al., J. Chem. Phys. B 2014,118, 11152 nanowires exhibit circular dichroism

J-Aggregates

S.Kirstein and S. Dähne, Int. J. Photoenergy 2006, 20363-1-21

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

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

1D Exitons in Single Polydiacetylene

F. Dubin et al., Nature Physics 2006, 2, 32

Microphotoluminescence of singly PDA chains in a diacetylene crystal