Intrinsic Charge Carrier Mobility in Single-Layer Black Phosphorus

TL;DR

This paper develops a theory for charge carrier mobility in single-layer black phosphorus, highlighting the effects of phonon scattering and anisotropy, and providing estimates of mobility limits at room temperature.

Contribution

It introduces a detailed phonon scattering model specific to black phosphorus, contrasting it with graphene, and quantifies the anisotropic electron and hole mobilities.

Findings

Hole mobility is weakly anisotropic with a ratio of about 1.4.

Electron mobility is strongly anisotropic with a ratio of about 6.2.

Room temperature mobilities are estimated to be up to 250 cm²V⁻¹s⁻¹ for holes and 700 cm²V⁻¹s⁻¹ for electrons.

Abstract

We present a theory for single- and two-phonon charge carrier scattering in anisotropic two-dimensional semiconductors applied to single-layer black phosphorus (BP). We show that in contrast to graphene, where two-phonon processes due to the scattering by flexural phonons dominate at any practically relevant temperatures and are independent of the carrier concentration $n$, two-phonon scattering in BP is less important and can be considered negligible at $n\gtrsim10^{13}$ cm$^{-2}$. At smaller $n$, however, phonons enter in the essentially anharmonic regime. Compared to the hole mobility, which does not exhibit strong anisotropy between the principal directions of BP ($\mu_{xx}/\mu_{yy}\sim1.4$ at $n=10^{13}$ cm$^{-2}$ and $T=300$ K), the electron mobility is found to be significantly more anisotropic ($\mu_{xx}/\mu_{yy}\sim6.2$). Absolute values of $\mu_{xx}$ do not exceed 250 (700) cm$^2$V$^{-1}$s$^{-1}$ for holes (electrons), which can be considered as an upper limit for the mobility in BP at room temperature.