Enhanced thermoelectric performance of phosphorene by strain-induced band convergence

The newly emerging monolayer phosphorene was recently predicted to be a promising thermoelectric material. In this work, we propose to further enhance the thermoelectric performance of phosphorene using the strain-induced band convergence. The effect of the uniaxial strain on the thermoelectric properties of phosphorene was investigated by using the first-principles calculations combined with the semiclassical Boltzmann theory. When the zigzag-direction strain is applied, the Seebeck coefficient and electrical conductivity in the zigzag direction can simultaneously be greatly enhanced at the critical strain of 5%, at which the band convergence is achieved. The largest $ZT$ value of 1.65 at 300 K is then conservatively estimated by using the bulk lattice thermal conductivity. When the armchair-direction strain of 8% is applied, the room-temperature $ZT$ value can reach 2.12 in the armchair direction of phosphorene. Our results indicate that strain-induced band convergence could be an effective method to enhance the thermoelectric performance of phosphorene.

Figure 1

(a) The top and (b) side views of phosphorene. The dashed rectangle denotes the primitive cell, with the corresponding first Brillouin zone shown in the insert.

Figure 2

Band structures of phosphorene under the uniaxial strain applied along the zigzag direction. The Fermi level is set to be 0 eV.

Figure 3

Effective mass $m^{*}$ and carrier mobility $\mu$ of phosphorene at 300 K along (a) the zigzag and (b) the armchair directions as a function of the applied strain along the zigzag direction. At the critical strain of 5%, the carrier mobilities of band extrema I, II, and IV are denoted by the red stars.

Figure 4

Carrier concentration dependence of the electronic transport coefficients at 300 K when the uniaxial strain is applied along the zigzag direction: (a) electrical conductivity along the zigzag direction, (b) electrical conductivity along the armchair direction, (c) Seebeck coefficient along the zigzag direction, (d) Seebeck coefficient along the armchair direction, (e) power factor (PF) along the zigzag direction, and (f) PF along the armchair direction.

Figure 5

Dimensionless figure of merit $ZT$ as a function of carrier concentration at 300 K in the (a) zigzag and (b) armchair directions under different uniaxial strains applied along the zigzag direction.

Figure 6

Dimensionless figure of merit $ZT$ as a function of carrier concentration at 300 K in the (a) zigzag and (b) armchair directions under uniaxial strain applied along the armchair direction.