Optical Spectra Line-Shape Representations and Broad Bands in Solids

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Abstract
Three methods of analyzing the temperature-dependent optical spectra line shape of a defect center are presented: a representation consisting of a convergent series of n-phonon distributions, a Fourier transform representation, and the moments of line shape. For each of these the calculations proceed from a one-phonon distribution, ρ1(E), which is proportional to the probability of a phonon of energy E being excited. The deriving model is that used for a configurational coordinate model with a removal of the limitation to a single one-phonon energy. Detailed comparisons are made between phonon-broadened line shapes for a defect center coupling to a distribution of phonon energies and CC model parameterizations of the line shapes. Results are that the CC model parameterizes very well the entire line shape for centers with a large Huang–Rhys S factor and the high-energy tail of narrow bands. Parameterization of the smooth tails of bands aids in the separation of overlapping bands. However, the CC parameters (S and effective phonon energy) are not precisely the quantities implied by the CC model.