Use of similatity criteria for evaluating the thermoelectric figure of merit of superlattices

TL;DR

This paper derives relationships to evaluate the thermoelectric figure of merit for superlattices and crystals, showing superlattices generally have lower merit unless certain parameters are significantly higher.

Contribution

It introduces general formulas for assessing the thermoelectric figure of merit in superlattices and crystals with quadratic isotropic energy spectra.

Findings

Superlattices have lower figure of merit than 3D crystals at the same parameters.

Higher dimensionless temperature or scattering coefficient can make superlattices outperform crystals.

The relationships help compare thermoelectric efficiency across different material structures.

Abstract

In this paper, general relationships that allow evaluating the figure of merit of both two-dimensional superlattices and three-dimensional crystals with a quadratic and isotropic energy spectrum of free charge carriers are derived. It is shown that with the same values of the so-called dimensionless temperature and scattering coefficient, the figure of merit of superlattices is always lower than that of three-dimensional crystals. The figure of merit of superlattices can become higher that that of three-dimensional crystals if the dimensionless temperature of free charge carrier gas and (or) scattering coefficient in them is considerably higher than in three-dimensional crystals.