Line Shape
The shape of the zero-phonon line is Lorentzian with a width determined by the excited state lifetime T10 according to the Heisenberg uncertainty principle. Without the influence of the lattice, the natural line width (full width at half maximum) of the chromophore is γ0 = 1/T10 . The lattice reduces the lifetime of the excited state by introducing radiationless decay mechanisms. At absolute zero the lifetime of the excited state influenced by the lattice is T1. Above absolute zero, thermal motions will introduce random perturbations to the chromophores local environment. These perturbations shift the energy of the electronic transition, introducing a temperature dependent broadening of the line width. The measured width of a single chromophore’s zero phonon line, the homogeneous line width, is then γh(T) ≥ 1/T1 .
The line shape of the phonon side band is that of a Poisson distribution as it expresses a discrete number of events, electronic transitions with phonons, during a period of time. At higher temperatures, or when the chromophore interacts strongly with the matrix, the probability of multiphonon is high and the phonon side band approximates a Gaussian distribution.
The distribution of intensity between the zero-phonon line and the phonon sideband is characterized by the Debye-Waller factor α.
Read more about this topic: Zero-phonon Line And Phonon Sideband
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