Zero-phonon Line and Phonon Sideband - Line Shape

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 γ_h(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.