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Excitons Excitons –– Types, Energy TransferTypes, Energy Transfer

@ MITFebruary 27, 2003 – Organic Optoelectronics - Lecture 7

•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)

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Caption from IUPAC Compendium of Chemical Terminologycompiled by Alan D. McNaught and Andrew Wilkinson (Royal Society of Chemistry, Cambridge, UK).

ExcitonIn 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.

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MOLECULAR PICTURE

GROUND STATE FRENKEL EXCITON

SEMICONDUCTOR PICTURE

GROUND STATE WANNIER EXCITON

CONDUCTIONBAND

VALENCEBAND

S1

S0

Wannier exciton(typical of inorganic

semiconductors)

Frenkel exciton(typical of organic

materials)

binding energy ~10meVradius ~100Å

binding energy ~1eVradius ~10Å

treat excitons as chargeless

particlescapable of diffusion,

also view them as

excited states of the

molecule

Charge Transfer (CT) Exciton

(typical of organicmaterials)

Excitons (bound

electron-hole pairs)

Electronic Processes in Organic Crystals and Polymers by M. Pope and C.E. Swenberg

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Wannier-Mott Excitons

Columbic interaction between the hole and the electron is given by

EEX = -e2/∈r

The exciton energy is then

E = EION – EEX/n2 , n = 1,2, …

EION – energy required to ionize the moleculen – 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

n = ∞ ----------

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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

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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.

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Crystalline Organic Films

PTCDAPTCDA

x

y

z

11.96 Å

17.34 Å

3.21Å

substrate

GOOD CARRIER MOBILITYIN THE STACKING DIRECTION

µ = 0.1 cm2/Vs – stacking directionµ = 10-5 cm2/Vs – in-plane direction

CHARGED CARRIER MOBILITY INCREASES WITH INCREASED

π−π ORBITAL OVERLAP

Highest mobilities obtained onsingle crystal

pentacene µ = 10 5 cm2/Vs at 10Ktetracene µ = 10 4 cm2/Vs at 10K

(Schön, et al., Science 2000).

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PTCDA monolayer on HOPG(STM scan)

Organic Semiconducting MaterialsVan der Waals-BONDED

ORGANIC CRYSTALS (and amorphous films)

HOMO of3,4,9,10- perylene tetracarboxylic dianhydride

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PTCDA Solution (~ 2µM in DMSO)

1.5 2.0 2.5 3.0 3.5

Energy [eV]

AbsorptionFluorescence

S1

[0-3

]

S1

[0-2

]

S1

[0-1

]

S1

[0-0

]

CT

[0-S

T]C

T [0

-F]

S1

[0-1

]

S1

[0-0

]

10

PTCDA Thin Film

1.5 2.0 2.5 3.0 3.5

Fluorescence

Absorption

CT

[ST-

1]

CT

[ST-

2]

CT

[ST-

3]

S1

[0-3

]S1

[0-2

]

S1

[0-1

]

CT

[0-S

T]

S1

[0-0

]

CT

[0-F

]

Energy [eV]

11

PTCDA Solution(~ 2µM in DMSO)

1.5 2.0 2.5 3.0 3.5

Energy [eV]

AbsorptionFluorescence

PTCDA Thin Film

0.6 eV

12

Solution Absorption

1.8 2.0 2.2 2.4 2.6 2.8 3.00

2

4

6

...

2 µM

Abs

orpt

ion

[a.u

.]

Energy [eV]

PTCDA in DMSO

AGGREGATEAGGREGATEStateState AGGREGATE

STATE ABSORPTION

increases with PTCDA solution concentration

1.6 µM

0.25 µM

13

1

0.01

0.1

1

0.5 42

r = 0.53 ± 0.02

r = 1.75 ± 0.02

r = 1.00 ± 0.02

r = 0.73 ± 0.02S1 [0-0]: 2.39 eV

S1 [0-2]: 2.74 eV

CT [0-ST]: 2.23 eV

S1 [0-1]: 2.55 eV

Rel

ativ

e O

scill

ator

Stre

ngth

PTCDA Concentration in DMSO [ µM]

2.0 2.4 2.8

0

2

4

6Measurement

Fit

[k] = 0.8 µM

Abs

orpt

ion

[a.u

.]

Energy [eV]

Absorption of Vibronic Transitions – Change with Solution Concentration

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1.8 2.0 2.2 2.4

0

2

4

6

.

.

.

0.25 µM

2 µM

Fluo

resc

ence

[a.u

.]

Energy [eV]

0 1 20

1

2

3

4

I ∝ [k]0.65

Inte

grat

ed F

luor

esce

nce

Inte

nsity

[a.u

.]

Solution Concentration[k] [µ M]

Solution Luminescence

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10.01

0.1

1

20.5Nominal Solution Concentration [k]

Monomer and Aggregate Concentration in Solution

AGGREGATE

[ka] ∝ [k] 1.75

MONOMER

[km] ∝ [k] 0.65

[µM]

MonomerConcentration

[km]

AggregateConcentration

[ka]

[µM]

rate of riser = 1.75

Monomer and Aggregate

concentrationsare derived from

integrated solutionfluorescence efficiency by

assuming thatthe 2.3 eV solution

fluorescence is dueto monomers and

that the most dilutesolution primarily

contains monomers.

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21

0

3S0

S1

21

0

2.12

eV

CT F

CT ST2.

20 e

V2.

39 e

V2.

55 e

V2.

74 e

V

MONOMERTRANSITIONS

THIN FILMTRANSITIONS

21

0

3

S1

21

0

2.17

eV 1.

55 e

V1.

70 e

V1.

85 e

V

CT F

CT ST

2.32

eV

S0

MONOMERTRANSITIONS

THIN FILMTRANSITIONS

PTCDA Electron Energy Structure

Absorption Luminescence

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PTCDA Solution(~ 2µM in DMSO)

1.5 2.0 2.5 3.0 3.5

Energy [eV]

AbsorptionFluorescence

PTCDA Thin Film

0.6 eV

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Solution and Thin Film Fluorescence

1.8 2.0 2.2 2.4

0.0

0.2

0.4

0.6

0.8

1.0

2.0 µM Solution

0.25 µMThin Film

(E + 0.60 eV)Fluo

resc

ence

[a.u

.]

Energy [eV]

0 20 40 60

101

102

103

Solutionτ = 4.0 ± 0.5 ns

Thin Filmτ = 10.8 ± 0.5 ns

Nor

mal

ized

Cou

ntsTime [ns]

FLUORESCENCE LIFETIME* Thin film fluorescence is red-shifted by 0.60 eV from solution fluorescence

* Minimal fluorescence broadening due to aggregation

* Fluorescence lifetime is longer in thin films

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Thin Film Excitation Fluorescence

2.0 2.4 2.8 3.2 3.6

0

10

20

30

650 nm PTCDAThin Film

Inte

grat

ed F

luor

esce

nce

[a.u

.]

Excitation Energy [eV]

CT

[0-S

T]

CT

[0-F

]

S 1[0

-0]

S 1[0

-1]

S 1[0

-2]

S 1[0

-3]

* Fluorescence energy and shape is not affected by the change in excitation energy

* Fluorescence efficiency increases when exciting directly into CT state

S1

S0

CTT1

S1

S0

CTT1

20

10 100 1000

0

10

20

30

mh, ⊥ = 0.14 mo

mh, ⊥ = 0.16 mo

mh, ⊥ = 0.18 mo

∆E

1s[m

eV]

d [Å]

∆E LUMO

∆E HOMO

d

PTC

DA

NTC

DA

PTC

DA

PTC

DA

NTC

DA

Exciton Quantum Confinement in Multi Quantum Wells

So and Forrest, Phys. Rev. Lett. 66, 2649 (1991).Shen and Forrest, Phys. Rev. B 55, 10578 (1997).

Exciton radius = 13 Å

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-3

-2

-1

0

1

Bandwidth >> VPSEUDO

Delocalized CT ExcitonV

[eV

]

ϕ∗ϕ

r

Bandwidth << VPSEUDO

Localized CT Exciton

ϕ∗ϕ

r

-3

-2

-1

0

1

V [e

V]

(a) (b)

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T1S1

S0FL

UO

RE

SC

EN

CE

PH

OS

PH

OR

ES

CE

NC

E

ENERGY TRANSFER

FÖRSTER, DEXTERor RADIATIVE

INTE

RN

AL

CO

NV

ER

SIO

N

AB

SO

RP

TIO

N

10 ps

1-10 ns

>100 ns

Ener

gy

density of availableS and T states on

surrounding molecules

Electronic Processes in Molecules

JABLONSKI DIAGRAM

INTERSYSTEMCROSSING

S: spin=0 (singlet) statesT: spin=1 (triplet) states

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400 500 600 700 800

0.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

EL

Inte

nsity

Wavelength [nm]

Alq3

PtOEP:Alq3

DCM2:Alq3

PtN N

NN

AlN

O 3

O

CNNC

N

Effect of Dopants on the Luminescence Spectrum

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Nonradiative Energy Transfer

How does an exciton in the host transfer to the dopant?

Energy transfer processes:

1. Radiative transfer

2. Förster transfer

3. Dexter transfer

host molecules

dopant molecules(generate luminescence)