Abstract
The small polaron model describes the motion of an electron in a semiconducting crystal in which there is a strong electron-phonon interaction. In this paper, Holstein's model of the small polaron is generalized by the inclusion of electron-phonon interaction terms which are not only linear in the phonon displacements but also quadratic. The high temperature mobility of the electron is calculated. The electronic motion occurs in a diffusive manner, by hopping between adjacent lattice sites. The mobility of an electron which is subjected to purely quadratic electron-phonon interactions, has a markedly different temperature variation than the temperature variation associated with the usual small polaron. The temperature variation of the drift mobility may be found from photoexcitation experiments.
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