Non-universal scaling of thermoelectric efficiency in 3D and 2D thermoelectric semiconductors

Kevin Octavian and Eddwi H Hasdeo

Abstract

We performed the first-principles calculation on common thermoelectric semiconductors Bi₂Te₃, Bi₂Se₃, SiGe, and PbTe in bulk three-dimension (3D) and two-dimension (2D). We found that miniaturisation 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 PbTe (0.32) and 2D SiGe (0.04) are smaller than their 3D counterparts (0.49 and 0.09, respectively). Meanwhile, the ZT values of 2D Bi₂Te₃ (0.57) and 2D Bi₂Se₃ (0.43) are larger than the bulks (0.54 and 0.18, respectively), which agrees 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 (σ) and electronic thermal conductivity (κ_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 Bi₂Te₃ and Bi₂Se₃ 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.