Band gap estimation from temperature dependent Seebeck measurement—Deviations from the 2e|S|maxTmax relation

Abstract

In characterizing thermoelectric materials, electrical and thermal transport measurements are often used to estimate electronic band structure properties such as the effective mass and band gap. The Goldsmid-Sharp band gap, Eg = 2e|S|maxTmax, is a tool widely employed to estimate the band gap from temperature dependent Seebeck coefficient measurements. However, significant deviations of more than a factor of two are now known to occur. We find that this is when either the majority-to-minority weighted mobility ratio (A) becomes very different from 1.0 or as the band gap (Eg) becomes significantly smaller than 10 kBT. For narrow gaps (Eg ≲ 6 kBT), the Maxwell-Boltzmann statistics applied by Goldsmid-Sharp break down and Fermi-Dirac statistics are required. We generate a chart that can be used to quickly estimate the expected correction to the Goldsmid-Sharp band gap depending on A and Smax; however, additional errors can occur for S < 150 μV/K due to degenerate behavior.