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.