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
C H2 CH
CH CH
CH CH2
Ionization Energy
E
LUMOE
HOMO+ + e -
Generate positive charge on molecule by removing electron from the molecule IE
Requires Ionization Energy
E
vacE
Koopmans’ Theorem: IE = - E
HOMOElectron Affinity
-
+ e -
Generate negative charge on molecule by placing electron onto the molecule Approximated by donating one electron to the LUMO
EA = -E
LUMOReleases electron affinity
E
LUMOE
HOMOE
vacE
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
Lig ht Ab sor pti on Fl uo re sce nce Pho spho re sce nce
Exciton Binding Energy
C. Deibel et al., PRB 81, 085202 (2010)
eV
E
G= 2 . 6 E
S1= 1 . 9 eV
eV E
b≅ 0 . 7
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:
α1 α2
Molekül “1” Molekül “2”
d
3 0
2 1
2 1
12
2
) (
3 ) (
3
d n V n
ε
rπε
µ µ
µ
µ −
=
Point dipole interaction:
Transition dipole moment:
2
1
m
m
M = ±
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