Role of Interlayer Coupling on the Evolution of Band Edges in Few-Layer Phosphorene

Using first-principles calculations, we have investigated the evolution of band-edges in few-layer phosphorene as a function of the number of P layers. Our results predict that monolayer phosphorene is an indirect band gap semiconductor and its valence band edge is extremely sensitive to strain. Its band gap could undergo an indirect-to-direct transition under a lattice expansion as small as 1% along zigzag direction. A semi-empirical interlayer coupling model is proposed, which can well reproduce the evolution of valence band-edges obtained by first-principles calculations. We conclude that the interlayer coupling plays a dominated role in the evolution of the band-edges via decreasing both band gap and carrier effective masses with the increase of phosphorene thickness. A scrutiny of the orbital-decomposed band structure provides a better understanding of the upward shift of valence band maximum surpassing that of conduction band minimum.Comment: 25 pages, 9 figure

Native point defects in few-layer phosphorene

Using hybrid density functional theory combined with a semiempirical van der Waals dispersion correction, we have investigated the structural and electronic properties of vacancies and self-interstitials in defective few-layer phosphorene. We find that both a vacancy and a self-interstitial defect are more stable in the outer layer than in the inner layer. The formation energy and transition energy of both a vacancy and a self-interstitial P defect decrease with increasing film thickness, mainly due to the upward shift of the host valence band maximum in reference to the vacuum level. Consequently, both vacancies and self-interstitials could act as shallow acceptors, and this well explains the experimentally observed p-type conductivity in few-layer phosphorene. On the other hand, since these native point defects have moderate formation energies and are stable in negatively charged states, they could also serve as electron compensating centers in n-type few-layer phosphorene.Comment: 10 pages, 12 figure