Physics of conducting polymers

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Physics of conducting polymers Powered By Docstoc
					          Serguei Brazovskii and Natasha Kirova
                         Natal 2012

Physics of synthetic conductors as low dimensional correlated
                      electronic systems.
                      Lecture 2, part 2




          ZOO OF EXCITONS


                                                          1
Optically active polymers




                            2
    Organic displays: basic element – organic light emitting diode (OLED),
                    emissive layer is an organic compound.

                                                   1        Injection

                                                   2        Migration

                                                   3        Recombination



                                                               Excitons

                 Anode (Al)                            L                       L

V
            Conjugated Material
               Cathode (ITO)                           H                   H
                                                           Singlet   Triplet
                   Glass
                                                                               3
                                                    - Spin statistics : 25 %
     Organic solar cell




                                                e-


                               hν
                                                     e-

                                                          e-

                                           EF
                           ITO/PEDOT h
                                       +
                                                               Metal electrode
                                           h+   h+
                                                     h+        (Al, Ca/Al etc.)
        Metal electrode
        Donor + Acceptor
        ITO


hν



                                                                        4
Optical pumping: creation of electron-hole pairs under illumination
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?
Band electrons and holes give                  Excitons give the
the photoconductivity                          photolumunescence

   E




       Ee+Eh=Eg                             Eex = Ee+Eh -e2/Rex <Eg
                                                                          5
6
 Singlet and triplet excitons: creation and annihilation

          E                          E




     Optical pumping                     Charge injection



                           Singlet                           Triplet
                  ps
                                                       ms
Luminescence,               µs
primary singlet                               Phosphorescence

Fluorescence,                             Lattice vibrations (phonons)
singlets trapped by the impurities        nonradiative channel
                                                                         7
 1D CRYSTALS

                 Main ingredients

ØPeriodic lattice.           In 1D:     x→x+a
ØPeriodic reciprocal space k. In 1D     k →k+G
      G=2π/a
                                 - π/a<k< π/a
ØQuasi-momenta                   p=ћk
ØEnergy spectra: for electrons   E(k)
Ø molecular vibrations (phonons) ћω(k)
 for



                                                 8
Ring of n atoms:




                                      =0




     Born- Karman cyclic conditions
Cyclobutadiene, N = 4

   C      C
                               2T
                               0
  C       C                    -2T


E=-2T ￿ 1/2                E
      l=
E=0   gl= cos(πl/2)/2
      ul = sin(πl/2)/ 2             k
E=2T ￿= (-1)l /2
       l
            Benzene ring                                           E

  H                   H
   C                 C                                                              k
H C                    C H
     C               C
    H                 H
                              2T
                              T
                            0
                           -T
                          -2T
                       Two types of wave functions with respect to x axis:
    +       -           +     +            +    +              +     -          y
+       g        -    -       g*       -   0       u       0   0       u*   0
                                                                                        x
    +       -             +        +           -       -           -    +
                                                                                11
                even                                           odd
Benzene ring   Polymer




                Even wave functions –
                overlap to a traditional
                dispersive band D

                g D
                g*  D*


                 Odd wave functions –
                 no overlap,
                 nondispersive flat band L

                u L
                u*  L*
                                           12
                                        immobile electron + immobile hole
Band structure and possible excitons:
                                        LL* exciton –
                                        the ghost of benzene ring



                                        mobile electron + immobile hole
                                        and vice versa:
                                        DL*±LD* exciton




                                         mobile electron + mobile hole:
                                         DD* exciton




                                                                     13
                          Excitons
Ø Exciton 1: weakly-bound delocalized e-h

     Localization
     radius:
      Binding
      energy:

                     R1~ 15 Å; Eb~ 0.1-0.2 eV

Ø Exciton 2: intermediate-bound delocalized e - localized h
                       R~ 10 Å; Eb~ 0.8 eV

 Ø Exciton 3: Strongly-bound intra- or inter-ring exciton



                                                              14
Visualization of exciton by electric field (field induced exciton dissociation)




                                                  High electric field F – exciton is destroyed
    small electric field F – exiton is preseved
                                                  and particles participate in photoconductivity
                                                            eFRex>Eb




                                                  -e2/x-F
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   Singlet state – no splitting

                                                           S=|↓↓>
S=1         Triplet state
                                                          S=|↑↑>

Coordinate part of wave function

S=0                                   Gain of the kinetic energy

S=1                                      Gain of the exchange energy   18
   Compatibility of spins and coordinates for fermions:

   S=0 – only symmetric ψ(x1,x2) – kinetic energy gain

   S=1 – only antisymmetric ψ(x1,x2) – repulsive energy 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
   Benzene ring,
                                                     In reality
 optical transitions
                                    gg*-uu*
                                                                   6.76 eV
                                    gu*+ug*
Without Coulomb correlations
                 T 4.8 eV           gg*+uu*                        5.96 eV
                 0
                -T                  gu*-ug*                        4.71 eV



                  T
                  0
                 -T    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
     Isolated benzene ring
 1E        gu*+ug*
      1u               6.76 eV                                       LL*
           gg*-uu*                            6eV

1B
     1u   gg*+uu*     5.96eV                            DD*      DL*±LD*


1B
      2u   gu*-ug*   4.71eV




                                           2.4 –3eV



                                                                     21
                     Delocalization breaks the intra ring scheme !
                     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 respect to 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
              Electronic correlations : the impact interaction U   0




                                       Bu -singlet
Triplet

                                                    x

 Interaction potential   a


                                                          N.B. The life time
U0 depends on overlap between quantum states              of exciton increases
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


Exciton energy                      U0 depends on overlap between
                                    quantum states of free band particles
                                    (e,h) and exact correlated intra-
                                    molecular states. It differs for various
                                    excitons.
Exciton radius
                                    US-UT - effective exchange
                                    interaction




      INTYRA-MONOMER COULOMB REPULSION
      The exciton binding energy goes down!!!
      Correlations result in lightly bound excitons!                 24
              Luminescent qnd nonluminescent polymers.
                       Ag - Bu level crossing,

     E

Ag
                                                         Bu
         Bu               Ag

                                                               x

                         Interaction potential   a




Ag       Bu




                                                              25

				
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posted:8/6/2014
language:English
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