Triplet state diffusion in organometallic and organic semiconductors - - PowerPoint PPT Presentation

Triplet state diffusion in

• rganometallic and organic semiconductors

From materials properties To device applications

• Prof. Anna Köhler

Experimental Physik II University of Bayreuth Germany

Organic semiconductors allow for attractive displays ... OLED display by Sony

... and lighting producs and solar cells Lighting windows by Osram Flexible solar cells

• n fabric

...and electronic reader devices ... The E‐ink reader by Plastic Logic, fabricated in Dresden

What makes organic semiconductors so attractive ?

Mechanical properties

• f plastic

Opto‐electronic properties

• f semiconductors

flexible robust → novel products light‐weight soluble → new fabrication technologies conduction → transistors, absorption solar cells, emission light emitting diodes +

The different physics of organic semiconductors I ‐ Energetics

R R R R R R

strong coupling : bands weak coupling : localised states … … amorphous organic film large e‐h distance weak binding weak exchange energy high dielectric constant: low dielectric constant : small e‐h distance (≈0.3 nm) strong binding (≈0.4 eV) high exchange energy (≈0.7 eV) Inorganic crystal ‐ + + ‐

Density of states

Energetic disorder

+ ‐ + ‐

initial

Electron phonon coupling

E final

The different physics of organic semiconductors II ‐ Dynamics

glass V 100 nm ITO Ca

Operate LED Place spin 1/2 electrons and spin 1/2 holes in π and π* orbitals π π∗

Energy

What happens in an organic LED ?

HOMO LUMO Conduction‐states Valence‐states … …

glass V 100 nm ITO Ca

Operate LED Place spin 1/2 electrons and spin 1/2 holes in π and π* orbitals π π∗

Energy

π π∗

Energy

S1 T1 S0

Energy

X

1 spin = 0 : Singlet state emission allowed (fluorescence) 3 spin = 1 : Triplet state emission forbidden (phosphorescence) Singlet S1 Triplet T1 They form two types of states OR

What happens in an organic LED ?

ΔE ISC

Triplet state photophysics

We need to know: Energetics: How big is the exchange energy, and how can we modify it? Dynamics: How is triplet state energy transferred and what controls it? For OLEDs with phosphorescent host‐guest‐systems For solar cells using triplet excitons (W.Y. Wong, Macromol. Chem. Phys. 2008)

Y.Sun + S. Forrest, Nature 2006 QEext=19 % , 30 lm/W for white OLED

It depends on the electron‐hole wavefunction overlap In π‐conjugated polymers with π‐π* transition, it is 0.7 eV In associated shorter oligomers, it raises up to 1.3 eV To reduce the exchange energy, spatially separate electron and hole use n‐π* transitions and non‐conjugated linkages use charge‐transfer states

Zhang, Köhler JCP 2006 p. 244701 06

• A. Köhler, AFM 2004

What do we know about the exchange energy

Brunner, Van Dijken, JACS 2004

Depends on wavefunction overlap Depends on electron‐phonon coupling Depends on Donor‐Acceptor energies Along a chain or between chains? Chain length dependence? Triplet diffuses via exchange interaction Simultaneous transfer of two electrons Dependence on energetic disorder?

Triplet state energy transfer

2,0 2,5 3,0 3,5 4,0 4,5

Photoluminescence (a.u.) Energy (eV) Absorption (a.u.)

monomer polymer

Strong Spin‐orbit coupling strong phosphorescence Some conjugation is preserved along the chain

T1 S1 Monomer Polymer

S0 T1 S1

Energy

Our workhorse: Pt‐containing model systems

Temperature dependence of phosphorescence intensity

50 100 150 200 250 300

Phosphorescence intensity Temperature (K)

Polymer Monomer

Different temperature dependence for polymer and monomer not due to internal conversion (Wilson, Köhler et al. JACS (2001)) Triplet exciton mobility is increased in polymer

10-2 10-1 100 Polymer Ea = 60 meV Monomer Ea = 100 meV 20 40 60 80 100 120 log (1/τ) (μs-1) 80 K 250 K 1000/T (K-1)

c

Temperature dependence of phosphorescence lifetime

There is a temperature activated high‐energy branch, and a transition temperature below which the thermal activation changes (consistent with the Holstein Small Polaron model)

⎟ ⎠ ⎞ ⎜ ⎝ ⎛− kT EA exp ~

Consider exchange transfer as a double electron transfer Markus theory describes electron transfer (at high temp)

D+ A‐ Ea ΔG0 λ DA D+A‐

2

1 4 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ + = λ λ G Ea

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ∝ kT E J W

a if if

exp

2

Activation energy Configuration Coordinate Energy λ = the reorganisation energy (electron‐phonon coupling) The transfer rate is given by:

Where does this temperature dependence come from

Triplets and Marcus theory

λ ΔG*

4 λ =

a

E

For a self‐reaction, ΔG0=0 (neglecting energetic disorder)

Qj Epot

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ∝ kT J W

if if

4 exp

2

λ

ΔG0=0 The rate of electron transfer kif depends on the coupling between two sites Vif the reorganisation energy λ.

2

1 4 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ + = λ λ G Ea

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ∝ kT E J W

a if if

exp

2

Triplets and Marcus theory

λ ΔG*

4 λ =

a

E

For a self‐reaction, ΔG0=0 (neglecting energetic disorder)

Qj Epot

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ∝ kT J W

if if

4 exp

2

λ

ΔG0=0 The rate of electron transfer kif depends on the coupling between two sites Vif the reorganisation energy λ.

2

1 4 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ + = λ λ G Ea

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ∝ kT E J W

a if if

exp

2

Wavefunction overlap, good along chain

The reorganization energy

Erel

f

Qj Epot Brédas et al, Chem. Rev. 2004, 104, 4971; Markvart & Greef, JCP, 2004, 121, 6401

Can we experimentally determine the reorganisation energy?

+ ‐ + ‐

i f

rel f rel i rel

E E E 2 = + = λ

Erel

i

Erel

f

Erel

i

The reorganisation energy λ for the triplet transfer relates to the geometric relaxation energy associated with optical transitions We can derive the activation energy for energy transfer just by analysing the absorpton and emission spectra !

The reorganization energy

Erel

f

Qj Epot Brédas et al, Chem. Rev. 2004, 104, 4971; Markvart & Greef, JCP, 2004, 121, 6401

∑ ∑

= =

j j j j j rel rel

S E E ω h ,

Can we experimentally determine the reorganisation energy?

+ ‐ + ‐

i f

S= Huang‐Rhys parameter For optical transitions

! n e S I

S n n − − =

rel f rel i rel

E E E 2 = + = λ

Erel

i

Erel

f

Erel

i

0.0 0.2 0.4 0.6 0.8 1.0 1.2 Phosphorescence (a.u.) Polymer

0-0 0-1 0-2

1 3 6 7 5 4 +

1.8 2.0 2.2 2.4 2.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Monomer

1 3 6 7 5

0-0 0-1 0-2

4 +

Energy (eV) Phosphorescence (a.u.)

mode 1 61 0.03 2 2 104 0.12 13 3 136 0.03 4 4 145 0.06 9 5 152 0.06 9 6 198 0.18 36 7 261 0.11 29

j

ω h

j

rel

E

j

S

100 = = ∑

j j j rel

S E ω h

meV

180 = = ∑

j j j rel

S E ω h

meV Polymer Monomer:

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ∝ kT E J W

a if if

exp

2

2

rel a

E E =

Ea=50 meV Ea=90 meV

The activation energy for triplet diffusion

50 meV Polymer 90 meV Monomer 60 meV Polymer ~100 meV Monomer

10-2 10-1 100 Polymer Ea = 60 meV Monomer Ea = 100 meV 20 40 60 80 100 120 log (1/τ) (μs-1) 80 K 250 K 1000/T (K-1)

c

From Analysis

• f optical spectra

from temp. dep.

• f phosporescence

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ∝ kT E J W

a if if

exp

2

2

rel a

E E =

Density of states

Energetic disorder

+ ‐ + ‐

initial

Electron phonon coupling

E final

The different physics of organic semiconductors II ‐ Dynamics σ σ

How to consider the effect of disorder on the transport

Holstein small polaron theory, modified by Emin, + effective medium approximation

• D. Emin, Adv. Phys. 24, 305, (1975)
• I. I. Fishchuk et al., PRB 67, 224303 (2003)

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − −

2

8 1 exp ~ T k T k E W

B B a e

σ

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −

2

2 1 exp ~ T k W

B e

σ High Temperature Low Temperature

( )

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + − − T k W

B i j i j ij

2 exp ~ ε ε ε ε

( )

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − − − − − T k E T k T k E W

B a i j B i j B a ij

16 2 exp ~

2

ε ε ε ε

Multiphonon hopping Phonon‐assisted tunneling

• I. I. Fishchuk et al., PRB (2008)

5 10 15 20 25

• 7
• 6
• 5
• 4
• 3
• 2
• 1

log(We), (We in μs

• 1)

1000/T (K

• 1)

a/L=10

ν0=3x10

12 sec

• 1

J0=250 meV Ea=50 meV 0.05 0.20 0.25 0.30 0.10 0.15 0.50 0.70

σ/Ea

And what happens if we increase the energetic disorder?

The two regimes, multiphonon hopping and phonon‐assisted tunneling, are no longer distinct! The exp (‐1/T2) dependence dominates the energy transfer ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −

2

2 1 exp ~ T k W

B e

σ

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − −

2

8 1 exp ~ T k T k E W

B B a e

σ

• I. I. Fishchuk et al., PRB 2008

10 20 30 40 50

• 2,5
• 2,0
• 1,5
• 1,0
• 0,5

0,0 input parameters from experiment E a=60 meV, J=0.0174 meV, ν0=3x10

12 s

• 1

fitting parameters

σ=3 meV, a/L=9.6

Miller-Abrahams model (eq. 13) Marcus model (eq. 12) log10(We) , (We in μs

• 1)

1000/T (K

• 1)

transition temperature 80 K a

500 1000 1500 2000 2500

• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0 Marcus model (eq. 12) Miller-Abrahams model (eq. 13) log10(We) , (We in μs

• 1)

(1000/T(K))

2

transition temperature 80 K b

Test against experimental data

High Temp.: Multiphonon hopping

Adiabatic, multiphonon hopping

Low Temp.: Phonon‐assisted tunneling

2,0 2,5 3,0 3,5 4,0 4,5 0,0 0,5 1,0 1,5 2,0 2,5 3,0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 700600 500 400 300 PF PF PF Ph Ph DF DF DF Ph

absorption (arb. units) luminescence intensity (arb. units) Energy [eV] wavelength (nm) a)

Does our model for triplet diffusion also apply to

• rganic polymers?

Organic model compound: Polyfluorene polymer, trimer and dimer

0.00 0.02 0.04 0.06 0.08 0.10 1E-3 0.01 0.1 1 10 141meV

polymer trimer dimer 1/τ [ms

• 1]

1/T [K

• 1]

109 meV 215 meV 50 100 150 200 250 300 0,0 0,2 0,4 0,6 0,8 1,0

polymer trimer dimer normalized integrated phosphorescence intensity T [K]

Yes, it does apply!

Ea

It is transferred via a multiphonon hopping process above TT and a single‐phonon tunneling process below TT

Summary and Conclusion

Triplets diffuse faster along polymer chains than between them Triplets diffuse much faster in polymers than in oligomers How is triplet state energy transferred and what controls it? It is controlled by wavefunction overlap, the amount of geometric reorganization energy and energetic disorder

Acknowledgements

Experimental Physics: Lekshmi Sudha Devi Sebastian Hoffmann Jo Wilson Ning Zhang Synthetic chemistry: Muhammad Khan, Oman + students Ullrich Scherf, Wuppertal + students Peter Strohriegel, Bayreuth+ students Theoretical calculations: Ivan Fishchuk, Kiev Andrey Kadashuck, Kiev Discussions: Richard Friend, UK Heinz Bässler, Marburg