Non-universal Scaling of Thermoelectric Efficiency in 3D and 2D Thermoelectric Semiconductors

TL;DR

This study uses first-principles calculations to analyze thermoelectric efficiency in 3D and 2D semiconductors, revealing that miniaturization does not universally enhance the figure of merit ($ZT$) and that the Hicks-Dresselhaus theory breaks down due to changes in band structure.

Contribution

The paper provides the first comprehensive first-principles comparison of thermoelectric properties in 3D and 2D semiconductors, highlighting the non-universality of $ZT$ scaling and the limitations of Hicks-Dresselhaus theory.

Findings

2D $Bi_2Te_3$ and $Bi_2Se_3$ have higher $ZT$ than bulk counterparts.

Miniaturization does not always increase $ZT$, contradicting HD theory.

Band structure changes upon dimensional reduction affect thermoelectric performance.

Abstract

We performed the first-principles calculation on common thermoelectric semiconductors $\rm Bi_2Te_3$, $\rm Bi_2Se_3$, $\rm SiGe$, and $\rm PbTe$ in bulk three-dimension (3D) and two-dimension (2D). We found that miniaturization of materials does not generally increase the thermoelectric figure of merit ($ZT$) according to the Hicks and Dresselhaus (HD) theory. For example, $ZT$ values of 2D $ \rm PbTe$ (0.32) and 2D $ \rm SiGe$ (0.04) are smaller than their 3D counterparts (0.49 and 0.09, respectively). Meanwhile, the $ZT$ values of 2D $\rm Bi_2Te_3$ (0.57) and 2D $\rm Bi_2Se_3$ (0.43) are larger than the bulks (0.54 and 0.18, respectively), which agree with HD theory. The HD theory breakdown occurs because the band gap and band flatness of the materials change upon dimensional reduction. We found that flat bands give a larger electrical conductivity ($\sigma$) and electronic thermal conductivity ($\kappa_{el}$) in 3D materials, and smaller values in 2D materials. In all cases, maximum $ZT$ values increase proportionally with the band gap and saturate for the band gap above $10\ k_BT$. The 2D $Bi_2Te_3$ and $Bi_2Se_3$ obtain a higher $ZT$ due to the flat corrugated bands and narrow peaks in their DOS. Meanwhile, the 2D PbTe violates HD theory due to the flatter bands it exhibits, while 2D SiGe possesses a small gap Dirac-cone band.