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

Abstract

Charge carriers that execute multi-phonon hopping generally interact strongly enough with phonons to form polarons. A polaron's sluggish motion is linked to slowly shifting atomic displacements that severely reduce the intrinsic width of its transport band. Here a means to estimate hopping polarons' bandwidths from Seebeck-coefficient measurements is described. The magnitudes of semiconductors' Seebeck coefficients are usually quite large (>k/|q| = 86 μV/K) near room temperature. However, in accord with the third law of thermodynamics, Seebeck coefficients must vanish at absolute zero. Here, the transition of the Seebeck coefficient of hopping polarons to its low-temperature regime is investigated. The temperature and sharpness of this transition depend on the concentration of carriers and on the width of their transport band. This feature provides a means of estimating the width of a polaron's transport band. Since the intrinsic broadening of polaron bands is very small, less than the characteristic phonon energy, the net widths of polaron transport bands in disordered semiconductors approach the energetic disorder experienced by their hopping carriers, their disorder energy.