Enhanced Thermoelectric Properties of Phosphorene via Quantum Size Effects and Relaxation Time Tuning

Black phosphorus is a promising thermoelectric (TE) material because of its high Seebeck coefficient and high electrical conductivity. In this work, the TE performance of bulk black phosphorus and single-layer phosphorene under uniaxial strain is studied using first-principles calculations and Boltzmann transport theory. The results show relatively excellent TE performance along the armchair direction for both black phosphorus and phosphorene in our study. However, high lattice thermal conductivity is the key adverse factor for further enhancing the TE performance of phosphorus. The <i>ZT</i> value can only reach up to 0.97 and 0.73 for <i>n</i>- and <i>p</i>-type black phosphorus at 700 K, respectively. Owing to quantum size effects, black phosphorene has lower lattice thermal conductivity than black phosphorus. At the same time, two-dimensional (2D) phosphorene exhibits increased electronic energy compared with bulk black phosphorus, resulting in a larger bandgap and reduced electrical conductivity due to the quantum confinement effect. Thus, the TE performance of <i>n</i>-type phosphorene can be partially improved, and the <i>ZT</i> value reaches up to 1.41 at 700 K. However, the <i>ZT</i> value decreases from 0.73 to 0.70 for <i>p</i>-type phosphorene compared with bulk phosphorus at 700 K. To further improve the TE performance of phosphorene, a tensile strain is applied along the armchair direction. Subsequent work indicates that uniaxial strain can further optimize phosphorene's TE properties by tuning hole relaxation time to improve electrical conductivity. Strikingly, the <i>ZT</i> values exceed 1.7 for both <i>n</i>- and <i>p</i>-type phosphorene under 4.5% tensile strain along the armchair direction at 700 K because of increased electrical conductivity and decreased lattice thermal conductivity.