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Phonon broadening of spectral lines in impurity doped solids Rystephanick, Raymond Gary

Abstract

The theory of the phonon broadening of optical absorption lines in impurity doped semiconductors is discussed starting with Kubo's formulation of the adiabatic dielectric susceptibility. The absorption constant is related to a two particle temperature Green's function using Matsubara's method. The interaction of the electrons (or holes) with the lattice vibrations is assumed to be small so that it can be treated as a perturbation to the independent electron and lattice vibration systems. Using this approximation, Dyson equations are obtained, using the technique of Feynman diagrams, for the one particle electron and phonon Green's functions and for the two particle Green's function and these are solved within the framework of the approximation. The line shape function is calculated explicitly and it is found that the line consists of a sharp peak whose width depends on temperature and is due to the finite lifetime of the bound carrier states, and of a continuous background due to multi-phonon processes which accompany the optical absorption. The technique used here is compared with previous work on this problem employing temperature dependent double-time advanced and retarded Green's functions. The results obtained are compared with those obtained by previous authors.

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