Exciton Bandwidth and Coupling to Intramolecular Phonons in PTCDA
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(I)
EM is the gas-phase excitation energy, I is the gas-to-solid shift of a localized excitation, k is the wavevector in the first Brillouin zone, -it < kc 0 and k = 0 at the top of the band. PTCDA is an ideal system for other reasons than its uniform isolated stacks. EM is strongly coupled to single vibration and is sufficiently below other excited states for a vibronic progression. The simulated absorption and fluorescence in Fig. I closely follow PTCDA spectra in methylene chloride solution [3]. The spacing hwo = 0.18 eV is typical of polyenes and polyacetylene and represents out-of-phase C-C and C=C stretches [4]. The same ag mode is the effective conjugation coordinate discussed by Zerbi and coworkers in conjugated polymers [5]. The relative intensities of the 0-n vibronics go as g2 n/n!, where g = 0.82 is the dimensionless electron-phonon (e-ph) coupling constant used in Fig 1.The emission has characteristically smaller quanta -0.16 eV and a Stokes shift of -0.07 eV. Perylene has almost unit quantum yield for fluorescence and PTCDA's yield is over 50 %. At this resolution PTCDA mimics a diatomic and has negligible e-ph coupling to any other vibration. The Holstein model [6] for polarons is a chain with linear e-ph coupling to a molecular harmonic oscillator. We take EM + I as the reference energy and model each PTCDA stack as 171
Mat. Res. Soc. Symp. Proc. Vol. 488 © 1998 Materials Research Society
N
N
Ha
+
)
+
++
h(bb+-l/ 2)
(2)
where the bosons bn+ create a vibrational quantum in the nth molecule and the fermions an+ create a molecular excitation. As in the polaron problem, we seek solutions of (2) with a single electronic excitation. In contrast to previous applications, the parameters ho) = 0.18 eV and g = 0.82 are accurately known from solution data and only the hopping V is adjustable in crystals. The structural, electronic, and vibrational simplicity of PTCDA make it arguably the best realization of Holstein's one-dimension chain of H 2 molecules. In this paper, we analyze PTCDA spectra in terms of (2) to obtain the exciton bandwidth and to identify phonon-assisted processes. An exciton band and V > 0 rationalize a red-shifted emission and low (-1%) quantum yield in films, since the lowest state at k = it has vanishing transition dipole with the ground state. Crystal selection rules are regained in phonon-assisted processed. Finite V accounts naturally for features that were previously treated phenomenologically and relates PTCDA to polaron theory. The idealized model (2) omits important PTCDA features, notably charge transfer (CT) states, and complete solution for arbitrary V, g, and o is still pending [7]. Since polaron discussions have focused on transport [6-8], PTCDA spectra are interesting new applications of a familiar solid-state model.
EXCITON-PHONON COUPLING IN PTCDA STACKS The time scales of nuclear and electronic motions must be considered for transport and are comparable when V - hco. In the Condon approximation, absorption or emission is vertical and the nuclei are fixed. Ex
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