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 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 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 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 (σ) and electronic thermal conductivity (κel) 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 10kBT. 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.Comment: 18 pages, 12 figure