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ZOO OF EXCITONS

Serguei Brazovskii and Natasha Kirova Natal 2012 Physics of synthetic conductors as low dimensional correlated electronic systems. Lecture 2, part 2. ZOO OF EXCITONS. Optically active polymers. Anode (Al). V. Conjugated Material. Cathode (ITO) . Glass.

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ZOO OF EXCITONS

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  1. SergueiBrazovskii and Natasha Kirova Natal 2012 Physics of synthetic conductors as low dimensional correlated electronic systems. Lecture 2, part 2 ZOO OF EXCITONS

  2. Optically active polymers

  3. Anode (Al) V ConjugatedMaterial Cathode (ITO) Glass Organic displays: basic element – organic light emitting diode (OLED), emissive layer is an organic compound. Injection 1 Migration 2 Recombination 3 Excitons L L H H Singlet Triplet - Spin statistics : 25 %

  4. Metal electrode Donor + Acceptor ITO hν Organicsolar cell e- hν e- e- EF h+ Metal electrode (Al, Ca/Al etc.) ITO/PEDOT h+ h+ h+

  5. E Created electrons and holes are either free, or bound EXCITON : electron-hole pair, bound by long range Coulomb forces Compare – the atom of positronium Important question – what kind of particles are created: band electrons and holes, or excitons? Optical pumping: creation of electron-hole pairs under illumination Band electrons and holes give the photoconductivity Excitons give the photolumunescence Ee+Eh=Eg Eex = Ee+Eh-e2/Rex<Eg

  6. Singlet and triplet excitons: creation and annihilation Optical pumping Charge injection Singlet E E Triplet ps ms µs Luminescence, primary singlet Phosphorescence Fluorescence, singlets trapped by the impurities Lattice vibrations (phonons) nonradiative channel

  7. 1D CRYSTALS Main ingredients Periodic lattice. In 1D: x→x+a Periodic reciprocal space k. In 1D k →k+G G=2π/a - π/a<k< π/a Quasi-momentap=ћk Energy spectra: for electrons E(k) for molecular vibrations (phonons) ћω(k)

  8. Ring of n atoms: = 0 Born- Karman cyclic conditions

  9. Cyclobutadiene, N = 4 C C 2T 0 C C -2T E E=-2T l = 1/2 E=0 gl= cos(πl/2)/2 ul = sin(πl/2)/ 2 E=2T l = (-1)l /2 k

  10. H H C C H C C H C C H H y + + - - + + + + 0 0 - - + - 0 0 - + + - + - + - g g* u* u x E Benzene ring k 2T T 0 -T -2T Two types of wave functions with respect to x axis: even odd

  11. Benzene ring Polymer Even wave functions – overlaptoa traditional dispersive band D g  D g*  D* Odd wave functions – no overlap, nondispersiveflat band L u  L u*  L*

  12. immobile electron + immobile hole LL* exciton – the ghost of benzene ring mobile electron + immobile hole and vice versa: DL*±LD* exciton mobile electron + mobile hole: DD* exciton Band structure and possible excitons:

  13. Excitons • Exciton 1: weakly-bound delocalized e-h Localization radius: Binding energy: R1~ 15 Å; Eb~ 0.1-0.2 eV • Exciton 2: intermediate-bound delocalized e - localized h R~ 10 Å; Eb~ 0.8 eV • Exciton 3: Strongly-bound intra- or inter-ring exciton

  14. Visualization of exciton by electricfield (fieldinduced exciton dissociation) High electric field F – exciton is destroyed and particles participate in photoconductivity small electric field F – exiton is preseved eFRex>Eb -e2/x-F

  15. Field induced exciton dissociation ξ=x/a*, β=(E-Eg)/Eb*, f= F/F0 Γ=|ψ(-k2/f )|2v

  16. Mystery of triplet excitons and some unresolved questions • The reduction of benzene ring scales 5-6 eV of transition energies to the level of 2-3 eV in the polymer is the effect of electronic delocalization. • The common attempts to build a strongly localized exciton to gain the Coulomb attraction oppositely face the losses of the kinetic energy and push the exciton energy upwards the high intra-molecular values, 4.8eV for S and 3.6eV for T exciton. • But: • Too small energy of the exciton • A drastic discrepancy between the low binding energy of S exciton in compare to the strong S - T splitting. Within the usual theory of shallow excitons they are of the same order. • The origin of the 1/N dependence of Eex in oligomers (n is the number of monomer units) • The origin of Ag–Bu exciton level crossing in nonluminescent polymers

  17. Singlet -Triplet One electron in magnetic field: Zeeman splitting in two levels s=±1/2 Two electrons in magnetic field: S=0 S=1 Singlet state – no splitting S=|↓↓> Coordinate part of wave function Triplet state S=0 Gain of the exchange energy S=|↑↑> Gain of the kinetic energy S=1

  18. Compatibility of spins and coordinates for fermions: S=0 – only symmetric ψ(x1,x2) – kinetic energy gain S=1 – only antisymmetricψ(x1,x2) – repulsiveenergy energy gain S-T splitting (exchange energy) Es Eg ET But: from the experiment on PPV Es~0.1-0.2 eV, ET~0.9eV

  19. gg*-uu* gu*+ug* T 0 -T 4.8 eV 6.76 eV gg*+uu* 5.96 eV T 0 -T gu*-ug* 4.71 eV Benzene ring, optical transitions In reality Without Coulomb correlations Exciton energy is higher then the energy of free e+h on the molecule, e-h binding energy is positive effective on-site e-h repulsion! Onsite e-e and e-h repulsion (e,h from different bands !)

  20. Polymer 1E1u gu*+ug* gg*-uu* Isolated benzene ring 6.76 eV LL* 6eV 1B1u gg*+uu* 5.96eV DD* DL*±LD* 4.71eV 1B2u gu*-ug* 2.4 –3eV Delocalization breaks the intra ring scheme !

  21. Intra-monomer Coulomb correlations • Semiconducting picture of shallow excitons: • Quantum oscillations of e and h in the mutual attractive potential –e2/|x|. • Effects of multi-particle electronic correlations are incorporated to band width, effective mass m*, dielectric susceptibility , as given material parameters. • For polymers : • The energy density of electronic correlations is distributed in space like~1/x3 , which average converges to smallest distances of the order of the monomer unit a and only there it is sufficient to take them into account. • Even at |x|~a, the impact kinetic energy m*Vmax2/2=e2/a, is still small (with respectto molecular level splitting) and the quantum wave length l is large, l=/m*Vmax>>a. • The only quantity we need to know is the penetration/reflection probability for the colliding e-h pair. • The impact interaction is equivalent to adding the central repulsion peak potential U0, the particles must tunnel through.

  22. Bu -singlet Triplet x a Interaction potential Electronic correlations : the impact interaction U0 N.B. The life time of exciton increases U0 depends on overlap between quantum states of free band particles (e,h) and exact correlated intra-molecular states. It differs for various excitons. US-UT- effective exchange interaction

  23. Electronic correlations Dynamics, kinetics, spin relaxation etc. of excitons U0depends on overlap between quantum states of free band particles (e,h) and exact correlated intra-molecular states. It differs for various excitons. US-UT- effective exchange interaction Excitonenergy Exciton radius INTYRA-MONOMER COULOMB REPULSION The exciton binding energy goes down!!! Correlations result in lightly bound excitons!

  24. E Bu Ag Ag Bu x a Interaction potential Ag Bu Luminescent qnd nonluminescent polymers.Ag - Bu level crossing,

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