Excitons – Types, Energy Transfer
•Wannier exciton
•Charge-transfer exciton
•Frenkel exciton
•Exciton Diffusion
•Exciton Energy Transfer (Förster, Dexter)
Handout (for Recitation Discusssion):
J.-S. Yang and T.M. Swager, J. Am. Chem. Soc. 120, 5321 (1998)
Q. Zhou and T.M. Swager, J. Am. Chem. Soc. 117, 12593 (1995)
@ MIT
February 27, 2003 – Organic Optoelectronics - Lecture 7
1
Exciton
In some applications it is useful to consider electronic excitation as if a
quasi-principle, capable of migrating, were involved. This is termed as
exciton. In organic materials two models are used: the band or wave model
(low temperature, high crystalline order) and the hopping model (higher
temperature, low crystalline order or amorphous state). Energy transfer in
the hopping limit is identical with energy migration.
Caption from IUPAC Compendium of Chemical Terminology
compiled by Alan D. McNaught and Andrew Wilkinson
(Royal Society of Chemistry, Cambridge, UK).
2
Wannier exciton
(typical of inorganic
semiconductors)
Excitons
Frenkel exciton
(bound
electron-hole
pairs)
(typical of organic
materials)
treat excitons
as chargeless
particles
capable of
diffusion,
SEMICONDUCTOR PICTURE
CONDUCTION
BAND
also view
them as
excited states
of the
molecule
MOLECULAR PICTURE
S1
S0
VALENCE
BAND
GROUND STATE
WANNIER EXCITON
binding energy ~10meV
radius ~100Å
Charge Transfer (CT)
Exciton
(typical of organic
materials)
GROUND STATE
FRENKEL EXCITON
binding energy ~1eV
radius ~10Å
Electronic Processes in Organic Crystals and Polymers by M. Pope and C.E. Swenberg
3
Wannier-Mott Excitons
Columbic interaction between
the hole and the electron is given by
EEX = -e2/∈r
n = ∞ ----------
The exciton energy is then
E = EION – EEX/n2 , n = 1,2, …
EION – energy required to ionize the molecule
n – exciton energy level
EEX = 13.6 eV µ/m∈
µ– reduced mass = memh / (me+mh)
Adapted from Electronic Processes in Organic Crystals and Polymers by M. Pope and C.E. Swenberg
4
An Example of Wannier-Mott Excitons
exciton progression
fits the expression
ν[cm-1] = 17,508 – 800/n2
corresponding to
µ = 0.7 and ∈ = 10
The absorption spectrum of Cu2O
at 77 K, showing the exciton lines
corresponding to several values
of the quantum number n. (From
Baumeister 1961).
Quoted from Figure I.D.28.
Electronic Processes in Organic
Crystals and Polymers by M. Pope
and C.E. Swenberg
5
Charge Transfer Excitons
The lowest CT exciton state
in the ab plane of an
anthracene crystal with two
inequivalent molecules per
unit cell; the plus and minus
signs refer to the center of
gravity of charge distribution.
The Frenkel exciton obtains
when both (+) and (–) occupy
essentially the same
molecular site.
6
Crystalline Organic Films
PTCDA
PTCDA
CHARGED CARRIER MOBILITY
INCREASES WITH INCREASED
π−π ORBITAL OVERLAP
11.96 Å
GOOD CARRIER MOBILITY
IN THE STACKING DIRECTION
17.34 Å
µ = 0.1 cm2/Vs – stacking direction
µ = 10-5 cm2/Vs – in-plane direction
z
3.21Å
Highest mobilities obtained on
single crystal
pentacene µ = 10 5 cm2/Vs at 10K
tetracene µ = 10 4 cm2/Vs at 10K
(Schön, et al., Science 2000).
y
x
substrate
7
Organic Semiconducting Materials
Van der Waals-BONDED
ORGANIC CRYSTALS
(and amorphous films)
PTCDA monolayer on HOPG
(STM scan)
HOMO of
3,4,9,10- perylene tetracarboxylic dianhydride
8
S1 [0-3]
S1 [0-2]
S1 [0-1]
CT [0-F]
CT [0-ST]
S1 [0-0]
S1 [0-0]
PTCDA Solution (~ 2µM in DMSO)
S1 [0-1]
Fluorescence
1.5
2.0
2.5
3.0
Absorption
3.5
Energy [eV]
9
1.5
CT [0-ST]
2.0
2.5
S1 [0-3]
S1 [0-2]
S1 [0-0]
S1 [0-1]
CT [0-F]
CT [ST-2]
Fluorescence
CT [ST-1]
CT [ST-3]
PTCDA Thin Film
Absorption
3.0
3.5
Energy [eV]
10
PTCDA Solution
PTCDA Thin Film
(~ 2µM in DMSO)
0.6 eV
Fluorescence
1.5
2.0
Absorption
2.5
3.0
3.5
Energy [eV]
11
Solution Absorption
PTCDA in DMSO
6
2 µM
Absorption [a.u.]
AGGREGATE
State
1.6 µM
.
.
.
4
0.25 µM
AGGREGATE
STATE
ABSORPTION
increases with
PTCDA solution
concentration
2
0
1.8
2.0
2.2
2.4
2.6
2.8
3.0
Energy [eV]
12
Absorption of Vibronic Transitions
– Change with Solution Concentration
S 1 [0-1]: 2.55 eV
1
S 1 [0-0]: 2.39 eV
r = 0.73 ± 0.02
S 1 [0-2]: 2.74 eV
CT [0-ST]: 2.23 eV
6
0.1
r = 1.00 ± 0.02
4
Absorption [a.u.]
Relative Oscillator Strength
r = 0.53 ± 0.02
Measurement
Fit
[k] = 0.8 µ M
2
0
r = 1.75 ± 0.02
2.0
0.01
0.5
1
2.4
Energy [eV]
2
2.8
4
PTCDA Concentration in DMSO [ µ M]
13
Fluorescence [a.u.]
6
4
Integrated Fluorescence
Intensity [a.u.]
Solution Luminescence
2 µM
4
3
.
2
.
I ∝ [k] 0.65
1
.
0
0
0.25 µ M
1
2
Solution Concentration
[k] [µ M]
2
0
1.8
2.0
2.2
2.4
Energy [eV]
14
Monomer and Aggregate Concentration in Solution
[µM]
1
MONOMER
[km] ∝ [k] 0.65
Monomer
Concentration
[km]
0.1
Aggregate
Concentration
[ka]
AGGREGATE
[ka] ∝ [k] 1.75
rate of rise
r = 1.75
Monomer and
Aggregate
concentrations
are derived from
integrated solution
fluorescence
efficiency by
assuming that
the 2.3 eV solution
fluorescence is due
to monomers and
that the most dilute
solution primarily
contains monomers.
0.01
1
0.5
Nominal Solution Concentration [k]
2 [µM]
15
PTCDA Electron Energy Structure
S1
S1
2
2
1
1
0
0
CT F
3
2
S0
1
2.32 eV
2.17 eV
1.85 eV
1.70 eV
1.55 eV
2.74 eV
2.55 eV
2.39 eV
2.20 eV
2.12 eV
CT ST
CT F
CT ST
3
2
S0
1
0
MONOMER THIN FILM
TRANSITIONS TRANSITIONS
Absorption
0
MONOMER THIN FILM
TRANSITIONS TRANSITIONS
Luminescence
16
PTCDA Solution
PTCDA Thin Film
(~ 2µM in DMSO)
0.6 eV
Fluorescence
1.5
2.0
Absorption
2.5
3.0
3.5
Energy [eV]
17
Solution and Thin Film Fluorescence
* Minimal
fluorescence
broadening due
to aggregation
* Fluorescence
lifetime is longer
in thin films
1.0
Fluorescence [a.u.]
* Thin film
fluorescence is
red-shifted by
0.60 eV from
solution
fluorescence
0.8
0.6
Normalized Counts
FLUORESCENCE LIFETIME
10
3
10
2
10
1
Thin Film
τ = 10.8 ± 0.5 ns
Solution
τ = 4.0± 0.5 ns
0
20
40
60
Time [ns]
0.4
0.2
Thin Film
(E + 0.60 eV)
0.25 µM
2.0 µM Solution
0.0
1.8
2.0
2.2
2.4
Energy [eV]
18
S0
* Fluorescence energy
and shape is not
affected by the change
in excitation energy
* Fluorescence
efficiency increases
when exciting directly
into CT state
S1 [0-3]
S1 [0-2]
S1 [0-1]
S1 [0-0]
T1
Integrated Fluorescence [a.u.]
CT
CT [0-ST]
S1
CT [0-F]
Thin Film Excitation Fluorescence
30
650 nm PTCDA
Thin Film
20
10
0
2.0
2.4
2.8
3.2
3.6
Excitation Energy [eV]
19
Exciton Quantum Confinement in Multi Quantum Wells
Exciton radius = 13 Å
So and Forrest, Phys. Rev. Lett. 66, 2649 (1991).
Shen and Forrest, Phys. Rev. B 55, 10578 (1997).
mh, ⊥ = 0.18 mo
∆E LUMO
∆E HOMO
mh, ⊥ = 0.16 mo
20
d
mh, ⊥ = 0.14 mo
PTCDA
NTCDA
PTCDA
NTCDA
10
PTCDA
∆ E 1s [meV]
30
0
10
100
1000
d [Å]
20
(a)
Delocalized CT Exciton
(b)
Bandwidth >> VPSEUDO
Bandwidth << VPSEUDO
ϕ∗ϕ
ϕ∗ϕ
1
1
0
0
r
V [eV]
V [eV]
r
-1
Localized CT Exciton
-1
-2
-2
-3
-3
21
Electronic Processes in Molecules
JABLONSKI DIAGRAM
INTERNAL
CONVERSION
10 ps
FÖRSTER, DEXTER
or RADIATIVE
ENERGY TRANSFER
INTERSYSTEM
CROSSING
1-10 ns
PHOSPHORESCENCE
S: spin=0 (singlet) states
T: spin=1 (triplet) states
FLUORESCENCE
S1
ABSORPTION
Energy
density of available
S and T states on
surrounding molecules
T1
>100 ns
S0
22
Effect of Dopants on the Luminescence Spectrum
1.0
N
Normalized EL Intensity
O
Alq3
0.8
0.6
Al
NC
N
O
CN
DCM2:Alq3
PtOEP:Alq3
3
0.4
N
N
Pt
N
N
0.2
0.0
400
500
600
700
800
Wavelength [nm]
23
Nonradiative Energy Transfer
dopant molecules
(generate luminescence)
host molecules
How does an exciton in the host transfer to the dopant?
Energy transfer processes:
1. Radiative transfer
2. Förster transfer
3. Dexter transfer
24