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

## TL;DR

This paper explores how quantum effects and strain can improve the thermoelectric performance of phosphorene, a form of black phosphorus.

## Contribution

The study introduces strain tuning and quantum size effects to enhance the thermoelectric properties of phosphorene.

## Key findings

- Phosphorene shows lower lattice thermal conductivity than bulk black phosphorus due to quantum size effects.
- Applying 4.5% tensile strain along the armchair direction increases ZT values above 1.7 for both n- and p-type phosphorene.
- Uniaxial strain improves TE performance by tuning hole relaxation time and electrical conductivity.

## Abstract

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 ZT value can only reach up to 0.97 and 0.73 for n- and p-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 n-type phosphorene can be partially improved, and the ZT value reaches up to 1.41 at 700 K. However, the ZT value decreases from 0.73 to 0.70 for p-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 ZT values exceed 1.7 for both n- and p-type phosphorene under 4.5% tensile strain along the armchair direction at 700 K because of increased electrical conductivity and decreased lattice thermal conductivity.