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Charge carriers that execute multi-phonon hopping generally interact stronglyenough with phonons to form polarons. A polarons sluggish motion is linked toslowly shifting atomic displacements that severely reduce the intrinsic widthof its transport band. Here a means to estimate hopping polarons bandwidthsfrom Seebeck-coefficient measurements is described. The magnitudes ofsemiconductors Seebeck coefficients are usually quite large (greater than 86microvolts/K) near room temperature. However, in accord with the third law ofthermodynamics, Seebeck coefficients must vanish at absolute zero. Here thetransition of the Seebeck coefficient of hopping polarons to itslow-temperature regime is investigated. The temperature and sharpness of thistransition depends on the concentration of carriers and on the width of theirtransport band. This feature provides a means of estimating the width of apolarons transport band. Since the intrinsic broadening of polaron bands isvery small, less than the characteristic phonon energy, the net widths ofpolaron transport bands in disordered semiconductors approach the energeticdisorder experienced by their hopping carriers, their disorder energy.

Determining a hopping polarons bandwidth from its Seebeck coefficient: Measuring the disorder energy of a non-crystalline semiconductor