Content

• Motivation
  
• The structure of PTCDA
  
• Optical properties of a single molecule
  
• Absorption of crystalline PTCDA
  
  • part1
    
  • part2
    
  • part3
    
• Exciton dispersion and EELS
  
• Photoluminescence
  
• Ultrathin films
  
• Electroabsorption
  
• Conclusion
  

Motivation

• PTCDA - prototypic organic material short stacking distance large PI-overlap between stack neighbours grows on most substrates in rather well-ordered films absorbs in the visible
  
• Even though PTCDA films have been investigated for more than 10 years, the knowledge about absorption, relaxation and recombination processes in PTCDA crystals and films is still rather limited
  

The structure of perylene (C24H12)

The structure of PTCDA: 3,4,9,10,-Perylene TetraCarboxylic DiAnhydride (C24H8O6)

The structure of PTCDA crystals

• Monoclinic structure
  
• C2h symmetry space group
  
• 2 molecules per unit cell
  
• alpha- and beta- phases
  

Optical properties of a single molecule

• Optical HOMO-LUMO gap: E00 ~ 2.5 eV
  
• Distribution of the overlap charges
  
• delocalized transition dipole moment
  

Optical cycle of a single molecule

• Deformation of the molecule during excitation
  
• Pronounced vibrational structure
  
• Displaced harmonic oscillator
  
• Absorption: Poisson-distribution over vibronic sublevels
  

Absorption and recombination on a single PTCDA molecule

• Small Stokes shift:
  E(stokes) = E(abs) - E(PL)
  E(average,abs) - E(average,PL) = 2 lambda
  
• Reduction of exciton-phonon coupling constant
  alpha^2 = 1.18 - calculated
  alpha^2 = 0.77 - influence of solvent
  

PTCDA Absorption and PL: Single molecule vs. Crystalline film

• Deformation of the absorption lineshape ; Large Stokes shift
  
• No symmetry absorption - photoluminescence
  

Frenkel exciton: related models

• dimer model, Frenkel and CT excitons:
  Z. G. Soos, M. H. Hennessy, and G. Wen, Chem. Phys. 227, 19 (1998)
  
• single 1-dim stack, Frenkel and CT excitons:
  M. Hoffmann, K. Schmidt, T. Fritz, T. Hasche, V.M. Agranovich, and K. Leo, Chem. Phys. 258, 73 (2000)
  
• two molecules per unit cell, only Frenkel exciton:
  absorption: I. Vragovic, R. Scholz, M. Schreiber, Europhys. Lett. 57, 288 (2002)
  photoluminescence: R. Scholz, I. Vragovic, A. Yu. Kobitski, M. Schreiber, H.-P. Wagner, and D.R.T. Zahn, phys. stat. sol. (b) 234, 402 (2002)
  
• Frenkel and CT excitons, spreading of vibronic cloud:
  M. Hoffmann and Z.G. Soos, Phys. Rev. B 66, 024305 (2002)
  
• Frenkel and CT excitons, applied to electro-absorption:
  G. Mazur, P. Petelenz, and M. Slawik, J. Chem. Phys. 118, 1423 (2003)
  

International School of Physics "Enrico Fermi" CXLIX
Organic Nanostructures: Science and Application

Crystal states and Model Hamiltonian

• The electronic ground state:
  
  
• The vibronicaly and electronicaly excited state:
  
  
• The Frenkel exciton model Hamiltonian:
  
  
• Decomposition of the transfer matrix element into an electronic and vibronic part:
  
  
• The Fourier transformation into wavevector representation:
  
  
  

Block Structure of the Hamiltonian

• diagonal blocks - deformed lineshape:
  
  
• off-diagonal blocks - Davydov splitting:
  
  
• rotation into basis of Davydov components:
  
  

Exciton Transfer Energies

• point-dipole approximation:
  
  
• delocalized nature of transition dipole:
  
  
• Interaction between atomic distributions of overlap charges in an anisotropic dielectric medium:
  
  

Calculation

Dielectric properties

• The frequency-dependent dielectric tensor:
  
  
• Kramers-Kronig consistent lineshape based on Gaussian broadenings
  
  
• Shift of spectral weight to higher energies for increased transfer between equivalent molecules (X):
  
  
• Splitting into two Davydov components for non-zero transfer between non-equivalent molecules (V):
  
  

Refractive Index

• Real and imaginary part of the refractive index:
  
  
• Anisotropy of dielectric tensor:
  
  
  
  
• Model parameters:
  
  transition dipole moment, d = 6.45 Debye
  exciton-phonon coupling constant, alpha^2 = 1.0
  maximum number of vibrational sublevels, n(max) = 5
  effective vibrational mode: 0.17 eV
  
  exciton on-site energy, E(00) + D = 2.180 eV
  transfer energy between equivalent molecules, X(0) = 150 meV
  transfer energy between non-equivalent molecules, V(0) = 47 meV
  
  background strenght = 2.38
  background energy = 7.5 eV
  static dielectric constant, e(in-plane) = 4.07
  
  

Multi-Mode Model

• several nondegenerate vibrational modes:
  
  
• a single effective mode is a valid approximation if the dominant contribution to the deformation of the relaxed excited molecule arises from two nearly degenerate modes.
  
  

Vibronic Cloud Model

• delocalization of vibronic excitation around electronically excited molecule:
  
  
• interpretation of the increased broadening of the absorption lineshape at higher energies requires extended clouds with radius beyond the nearest stack neighbour.
  
  

Exciton Dispersion

• Dispersion for three characteristic directions in k-space
  
• „negative“ dispersion has origin in the dominating positive exciton transfer energy between the nearest stack neighbours (W)
• minimum at (0,0,p) - a possible origin of the red-shifted photoluminescence
  
  

Electron Energy Loss Spectroscopy

• Inelastic scattering of electrons and creation of an optical excitation.
  
• Shift of the loss function towards lower energies for momentum orthogonal to the plane of molecules.
  
  

PL components at low temperature

• Time-resolved PL measurements on single crystals of alpha-PTCDA at low temperatue T = 11 K
  
• a component with Tm is interpreted as Frenkel excitons a component with Ts is a composition of charge-transfer exciton bands at around 1.79 eV and 1.66 eV.
  
  

Frenkel excitons: optical cycle

• Optical absorption,
  
• Relaxation towards the edge of the Brillouin zone,
  
• PL recombination.
  
• total Stokes shift: 0.43 eV (exp: 0.41 eV).
  
  

PL model Hamiltonian:

Coupling Strengths:

• Reduction of the available coupling strengths
  
• Slowing down of the PL decay rate with respect to the monomer
  
  

Radiative Decay Rates and PL Lineshape

• Asymmetric lineshape is modelled by a Poisson distribution of an effective mode of 30 meV with g^2=2.
  
• Reduction of the energetic difference between vibrational subbands ~ 0.16 eV
  
• Resulting radiative decay times (12.6 ns and 13 ns) coincide with the measured value within the experimental uncertainty
  (12.7 pm 0.4 ns).
  
  

Frenkel excitons: lineshapes

Ultrathin Films

Quantum confinement:

• finite film thicknesses: 1 – 10 ML
  
• partial spatial Fourier transformation
  
• energy spectra is strictly discrete
  
• finite number of allowed kz values
  
• the importance of the surface conditions
  
• non-perturbed (ideal) films: E(bulk) = 2.18 eV
  
• perturbed films: E(1ML) = 2.30 eV; E(surf) = 2.24 eV and E(bulk) = 2.18 eV
  
• appearance of localized surface states
  
  

• Bulk-like states have envelopes resembling states in a quantum well
  
• Appearance of localized surface states outside the range of bulk energies
  
  

• Bulk-like states delocalized over the entire film
  
• Appearance of localized states at symmetrically perturbed surfaces
  
  

• Non-perturbed film: energy shift to the red
  
• Perturbed film: energy shift to the blue
  
  

Electro-absorption

Conclusion

Optical Absorption:

• Influence of the exciton transfer between different molecules onto the deformation of an effective vibrational mode
  
• Quantitative interpretation of the frequency-dependent dielectric tensor and the complex index of refraction
  
• Anisotropy of optical properties – Davydov splitting
  
  

Exciton Dispersion:

• Computed for three characteristic directions in k-space
  
• Strong “negative” dispersion for direction orthogonal to the plane of molecules – minimum at the boundary of Brillouin zone
  
• Interpretation of the red-shift of the EEL function
  
  

Photoluminescence:

• Origin: the low-lying excited states around the minimum of the lowest branch of the Frenkel exciton dispersion
  
• Interpretation of the large Stokes shift of crystalline samples
  
• PL lineshape, energetic positions and radiative decay times are in good agreement with the experiment
  
  

Ultrathin Films:

• Quantum confinement: discretization of the exciton energy spectra
  
• Appearance of localized surface states
  
• Interpretation of the observed blue-shift of the optical absorption
  
  

Electro-absorption:

• Follows the first derivative of the absorption curve
  
• Limitation of the pure Frenkel exciton model: possible contribution of Charge-Transfer excitons