Variations of thermoelectric performance by electric fields in bilayer MX₂ (M = W, Mo; X = S, Se)

A gate electrode is usually used to controllably tune the carrier concentrations, further modulating the electrical conductivity and the Seebeck coefficient to obtain the optimum thermoelectric figure of merit (ZT) in two-dimensional materials. On the other hand, it is necessary to investigate how an electric field induced by a gate voltage affects the electronic structures, further determining the thermoelectric properties. Therefore, by using density functional calculations in combination with Boltzmann theory, the thermoelectric properties of bilayer MX₂ (M = W, Mo; X = S, Se) with or without a 1 V nm^-1 perpendicular electric field are comparatively investigated. First of all, the variations of the electrical conductivity (σ), electron thermal conductivity and Seebeck coefficient (S) with the carrier concentration are studied. Due to the trade-off relationship between S and σ, there is an optimum concentration to obtain the maximum ZT, which increases with the temperature due to the enhancement of the Seebeck coefficient. Moreover, N-type bilayers have larger optimum ZTs than P-type bilayers. In addition, the electric field results in the increase of the Seebeck coefficient in low hole-doped MS₂ bilayers and high hole-doped MSe₂ bilayers, thus leading to similar variations in ZT. The optimum ZTs are reduced from 2.11 × 10^-2, 3.19 × 10^-2, 2.47 × 10^-2, and 2.58 × 10^-2 to 1.57 × 10^-2, 1.51 × 10^-2, 2.08 × 10^-2, and 1.43 × 10^-2 for the hole-doped MoS₂, MoSe₂, and WSe₂ bilayers, respectively. For N-type bilayers, the electric field shows a destructive effect, resulting in the obvious reduction of the Seebeck coefficient in the MSe₂ layers and the low electron-doped MS₂ bilayers. In electron-doped bilayers, the optimum ZTs will decrease from 3.03 × 10^-2, 6.64 × 10^-2, and 6.69 × 10^-2 to 2.81 × 10^-2, 3.59 × 10^-2, and 4.39 × 10^-2 for the MoS₂, MoSe₂, and WSe₂ bilayers, respectively.