Triplet state diffusion in organometallic and organic semiconductors Prof. Anna Köhler Experimental Physik II University of Bayreuth Germany From materials properties To device applications
Organic semiconductors allow for attractive displays ... OLED display by Sony
... and lighting producs and solar cells Flexible solar cells Lighting windows on fabric by Osram
...and electronic reader devices ... The E ‐ ink reader by Plastic Logic, fabricated in Dresden
What makes organic semiconductors so attractive ? + Mechanical properties Opto ‐ electronic properties of plastic of semiconductors conduction → transistors, flexible absorption solar cells, robust → novel products emission light emitting diodes light ‐ weight soluble → new fabrication technologies
The different physics of organic semiconductors I ‐ Energetics R R R R … … R R + ‐ ‐ + amorphous organic film Inorganic crystal strong coupling : weak coupling : bands localised states high dielectric constant: low dielectric constant : small e ‐ h distance ( ≈ 0.3 nm) large e ‐ h distance strong binding ( ≈ 0.4 eV) weak binding high exchange energy ( ≈ 0.7 eV) weak exchange energy
The different physics of organic semiconductors II ‐ Dynamics Electron phonon coupling Energetic disorder + ‐ initial E + ‐ final Density of states
What happens in an organic LED ? V Ca 100 nm ITO glass Operate LED … Conduction ‐ states π∗ Energy LUMO π HOMO Valence ‐ states … Place spin 1/2 electrons and spin 1/2 holes in π and π * orbitals
What happens in an organic LED ? They form two types of states V Ca S 1 1 spin = 0 : 100 nm Δ E ISC Singlet state ITO glass T 1 emission allowed Energy X (fluorescence) Operate LED S 0 3 spin = 1 : Triplet state emission forbidden (phosphorescence) π∗ π∗ Energy Energy OR π π Triplet T 1 Singlet S 1 Place spin 1/2 electrons and spin 1/2 holes in π and π * orbitals
Triplet state photophysics Y.Sun + S. Forrest, Nature 2006 QE ext =19 % , 30 lm/W For OLEDs with phosphorescent host ‐ guest ‐ systems for white OLED For solar cells using triplet excitons (W.Y. Wong, Macromol. Chem. Phys. 2008) 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?
What do we know about the exchange energy 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 A. Köhler, AFM 2004 To reduce the exchange energy, spatially separate electron and hole use n ‐ π * transitions and non ‐ conjugated linkages use charge ‐ transfer states Brunner, Van Dijken, JACS 2004 Zhang, Köhler JCP 2006 p. 244701 06
Triplet state energy transfer Triplet diffuses via exchange interaction Simultaneous transfer of two electrons Depends on wavefunction overlap Along a chain or between chains? Depends on electron ‐ phonon coupling Chain length dependence? Depends on Donor ‐ Acceptor energies Dependence on energetic disorder?
Our workhorse: Pt ‐ containing model systems Monomer Polymer Photoluminescence (a.u.) monomer S 1 polymer T 1 S 1 T 1 Absorption (a.u.) Energy S 0 Strong Spin ‐ orbit coupling strong phosphorescence Some conjugation is preserved 2,0 2,5 3,0 3,5 4,0 4,5 along the chain Energy (eV)
Temperature dependence of phosphorescence intensity Phosphorescence intensity Different temperature dependence for polymer and monomer Monomer not due to internal conversion (Wilson, Köhler et al. JACS (2001)) Polymer 0 50 100 150 200 250 300 Temperature (K) Triplet exciton mobility is increased in polymer
Temperature dependence of phosphorescence lifetime c 10 0 Polymer E a = 60 meV Monomer E a = 100 meV ⎛− kT ⎞ log (1/ τ ) ( μ s -1 ) E A ⎜ ⎟ ~ exp ⎝ ⎠ 10 -1 80 K 250 K 10 -2 0 20 40 60 80 100 120 1000/T (K -1 ) 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)
Where does this temperature dependence come from A ‐ D + Consider exchange transfer as a double electron transfer Markus theory describes electron transfer (at high temp) The transfer rate is given by: DA 2 ⎡ ⎤ λ Δ ⎛ − ⎞ 0 G E = + 2 ∝ a ⎜ ⎟ E a ⎢ ⎥ 1 W J exp λ D + A ‐ ⎣ ⎦ 4 if if ⎝ ⎠ kT λ Activation energy Energy E a λ = the reorganisation energy (electron ‐ phonon coupling) Δ G 0 Configuration Coordinate
Triplets and Marcus theory For a self ‐ reaction, Δ G 0 =0 (neglecting energetic disorder) E pot 2 ⎡ ⎤ λ Δ ⎛ − ⎞ 0 G E 2 = + a ∝ ⎜ ⎟ ⎢ ⎥ E a 1 W J exp λ ⎣ ⎦ 4 if if ⎝ ⎠ kT λ Δ G 0 =0 Δ G* λ Q j ⎛ − λ ⎞ = 2 E ∝ ⎜ ⎟ a W J exp 4 if if ⎝ ⎠ kT 4 The rate of electron transfer k if depends on the coupling between two sites V if the reorganisation energy λ .
Triplets and Marcus theory For a self ‐ reaction, Δ G 0 =0 (neglecting energetic disorder) E pot 2 ⎡ ⎤ λ Δ ⎛ − ⎞ 0 G E 2 = + a ∝ ⎜ ⎟ ⎢ ⎥ E a 1 W J exp λ ⎣ ⎦ 4 if if ⎝ ⎠ kT λ Δ G 0 =0 Δ G* λ Q j ⎛ − λ ⎞ = 2 E ∝ ⎜ ⎟ a W J exp 4 if if ⎝ ⎠ kT 4 The rate of electron transfer k if depends on Wavefunction overlap, the coupling between two sites V if good along chain the reorganisation energy λ .
The reorganization energy Can we experimentally determine the reorganisation energy? E pot i f + ‐ i E rel f E rel + ‐ f E rel λ = + = i f E E 2 E rel rel rel i E rel The reorganisation energy λ for the triplet Q j 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 ! Brédas et al, Chem. Rev. 2004, 104, 4971; Markvart & Greef, JCP, 2004, 121, 6401
The reorganization energy Can we experimentally determine the reorganisation energy? E pot i f + ‐ i E rel f E rel + ‐ f E rel λ = + = i f E E 2 E rel rel rel For optical transitions i E rel ∑ ∑ = = ω h E E , S Q j rel rel j j j j j − n S S e − = S= Huang ‐ Rhys parameter I 0 n n ! Brédas et al, Chem. Rev. 2004, 104, 4971; Markvart & Greef, JCP, 2004, 121, 6401
1.2 Polymer Polymer 0-0 1.0 = ∑ ω = Phosphorescence (a.u.) h E S 100 meV rel j j 0.8 j 0.6 ω 0-1 h E E a =50 meV S mode rel j j j 0.4 4 1 61 0.03 2 + 5 0.2 3 6 2 104 0.12 13 1 7 0-2 3 136 0.03 4 0.0 4 145 0.06 9 1.2 5 152 0.06 9 Monomer 0-0 1.0 6 198 0.18 36 0-1 Phosphorescence (a.u.) 7 261 0.11 29 0.8 4 0.6 + 0-2 5 6 3 1 ⎛ − Monomer: ⎞ 7 0.4 E 2 = ∑ a ∝ ⎜ ⎟ W J exp ω = h meV E S 180 if if ⎝ ⎠ 0.2 kT rel j j j E E = rel 0.0 E a =90 meV a 2 1.8 2.0 2.2 2.4 2.6 Energy (eV)
The activation energy for triplet diffusion c 10 0 Polymer E a = 60 meV Monomer E a = 100 meV 50 meV Polymer From Analysis log (1/ τ ) ( μ s -1 ) of optical spectra 90 meV Monomer 10 -1 60 meV Polymer from temp. dep. 80 K of phosporescence ~100 meV Monomer 250 K 10 -2 E E = rel 0 20 40 60 80 100 120 a 2 1000/T (K -1 ) ⎛ − ⎞ E 2 a ∝ ⎜ ⎟ W J exp if if ⎝ ⎠ kT
The different physics of organic semiconductors II ‐ Dynamics Electron phonon coupling Energetic disorder + ‐ initial E σ + ‐ final σ Density of states
How to consider the effect of disorder on the transport Holstein small polaron theory, modified by Emin, D. Emin, Adv. Phys. 24, 305, (1975) + effective medium approximation I. I. Fishchuk et al., PRB 67, 224303 (2003) I. I. Fishchuk et al., PRB (2008) High Temperature ( ) ⎡ ⎤ 2 ⎛ ⎞ ⎡ ⎤ σ ε − ε ε − ε 2 E 1 E ⎜ ⎟ ⎢ − − ⎥ a − − − ⎢ j i j i ⎥ W ~ exp ⎜ ⎟ a W ~ exp e ⎢ ⎥ ⎝ ⎠ ij k T 8 k T ⎢ ⎥ ⎣ ⎦ k T 2 k T 16 E k T ⎣ ⎦ B B B B a B Multiphonon hopping Low Temperature ⎡ ⎤ ( ) 2 ⎛ ⎞ σ ⎛ ⎞ 1 ε − ε + ε − ε ⎢ ⎜ ⎟ ⎥ − ⎜ ⎟ W ~ exp ⎜ ⎟ − j i j i W ~ exp e ⎢ ⎥ ⎝ ⎠ ⎜ ⎟ 2 k T ij ⎣ ⎦ 2 k T B ⎝ ⎠ B Phonon ‐ assisted tunneling
And what happens if we increase the energetic disorder? ⎡ ⎤ 2 ⎛ ⎞ σ E 1 ⎜ ⎟ ⎢ − − ⎥ a W ~ exp ⎜ ⎟ e ⎢ ⎥ ⎝ ⎠ k T 8 k T ⎣ ⎦ B B The two regimes, 0 multiphonon hopping and -1 σ /E a phonon ‐ assisted tunneling, -1 ) -2 0.05 log(W e ), (W e in μ s are no longer distinct! 0.10 -3 0.15 0.20 -4 The exp ( ‐ 1/T 2 ) dependence a/L=10 0.25 12 sec -1 ν 0 =3x10 -5 0.50 dominates the energy transfer J 0 =250 meV 0.30 -6 E a =50 meV 0.70 -7 0 5 10 15 20 25 -1 ) 1000/T (K ⎡ ⎤ 2 ⎛ ⎞ σ 1 ⎢ − ⎜ ⎟ ⎥ W ~ exp ⎜ ⎟ e ⎢ ⎥ ⎝ ⎠ 2 k T ⎣ ⎦ B I. I. Fishchuk et al., PRB 2008
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