Vibrational Modes Near Impurities

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Abstract
In many cases, the interaction between the electronic state of an impurity in a solid and the motion of the atoms in the lattice is controlled by the relative motion of the impurity with respect to its nearest neighbors. We therefore examine the nature of the vibrations of the lattice near an impurity. In particular, two problems are considered: First, the direct absorption of light by the "localized" mode introduced by the presence of the impurity, and the relation of its frequency to that of the "reststrahlen" absorption; second, the relative importance of the "localized" modes and of the "lattice" modes in producing the observed broadening of the spectra due to electronic transitions of the impurity center. It is found that the large number of lattice modes together produce a mean displacement of the same order of magnitude as do the very few local ones. The implications for the "configuration coordinate" model for phosphors are examined; both theory and experiment suggest that if only one mode, or group of modes, are effective in producing broadening, their frequency is substantially lower than that of the localized modes which are optically active.

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