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

TL;DR

This paper presents a method to estimate the bandwidth of hopping polarons in disordered semiconductors using Seebeck coefficient measurements, linking thermoelectric behavior to microscopic transport properties.

Contribution

It introduces a novel approach to determine polaron bandwidths from Seebeck coefficient data, connecting thermodynamic and transport characteristics in non-crystalline semiconductors.

Findings

Seebeck coefficients are large near room temperature and vanish at absolute zero.

The transition temperature and sharpness depend on carrier concentration and transport band width.

Polaron transport band widths approximate the energetic disorder in disordered semiconductors.

Abstract

Charge carriers that execute multi-phonon hopping generally interact strongly enough with phonons to form polarons. A polarons 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 (greater than 86 microvolts/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 depends on the concentration of carriers and on the width of their transport band. This feature provides a means of estimating the width of a polarons 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.