Optical absorption small polaron

The small polaron concept offers a possibility to formirlate a quantitative theory for the optical absorption Small polarons are created when electrons polarize their sitrroundings so that localization of the wavefimction takes place essentially to one lattice site. A small overlap between wavefunctions corresponding to adjacent sites, as well as strong disorder, are conducive to polaron formation. Theoretically, the small polaron absorption ap, can be expressed... 

It is normally unnecessary for the electrochemist to be concerned with the mobility of carriers in most of the semiconductors whose properties have been studied, since the very low conductivity of "small polaron samples would normally preclude their measurement. However, a proviso must be entered here in the case of binary and, more especially, ternary samples. It may well be the case that the majority carriers in a particular material are indeed itinerant (i.e. have mobilities in excess of ca. 1 cm2 V 1s 1), but there is no guarantee that this will be true of the minority carriers generated by optical absorption. Thus, the oxide MnTi03 shows a marked optical charge transfer absorption from Mn(II) to Ti(IV), the latter being the CB. The resultant holes reside on localised sites in the Mn levels, presumably as local Mn(III) centres, and are comparatively immobile. The result is that there is... 

Since the small polaron is a localized electron state it should absorb light, too. Theory predicts a Gaussian-shaped absorption at hv = 2Wp = 4Ea (Bogomolov and Mirlin, 1968). For liquid propane, the activation energy of the mobility was determined to be Eg = 0.15 eV (Bakale et al., 1975) which would correspond to an optical transition at hv = 0.6 eV. The absorption of localized electrons in liquid propane (see Chapter 3, Figure 32) exhibits a maximum at about 0.5 eV close to the expected value. The foregoing discussion of the small polaron does also apply to tt e case of a localized positive hole (see Section 7.3). 

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