Charge-transport anisotropy in black phosphorus: critical dependence on the number of layers

Abstract

Phosphorene is a promising candidate for modern electronics because of the anisotropy associated with high electron–hole mobility. Additionally, superior mechanical flexibility allows the strain-engineering of various properties including the transport of charge carriers in phosphorene. In this work, we have shown the criticality of the number of layers to dictate the transport properties of black phosphorus. Trilayer black phosphorus (TBP) has been proposed as an excellent anisotropic material, based on the transport parameters using Boltzmann transport formalisms coupled with density functional theory. The mobilities of both the electron and the hole are found to be higher along the zigzag direction (∼10⁴ cm² V⁻¹ s⁻¹ at 300 K) compared to the armchair direction (∼10² cm² V⁻¹ s⁻¹), resulting in the intrinsic directional anisotropy. Application of strain leads to additional electron–hole anisotropy with 10³ fold higher mobility for the electron compared to the hole. Critical strain for maximum anisotropic response has also been determined. Whether the transport anisotropy is due to the spatial or charge-carrier has been determined through analyses of the scattering process of electrons and holes, and their recombination as well as relaxation dynamics. In this context, we have derived two descriptors (S and F(k)), which are general enough for any 2D or quasi-2D systems. Information on the scattering involving purely the carrier states also helps to understand the layer-dependent photoluminescence and electron (hole) relaxation in black phosphorus. Finally, we justify trilayer black phosphorus (TBP) as the material of interest with excellent transport properties.