Modulation of the electronic property of phosphorene by wrinkle and vertical electric field

The electronic properties of wrinkled phosphorene and its response to charge injection and external vertical electric field have been studied using first-principles calculations. It is found that small-size wrinkle systems have lower energy than wrinkle-free monolayer, suggesting that free-standing phosphorene spontaneously forms small protrusion on its nanosheet. The ratio of wrinkle height to curvature radius increases with enlarging height, indicating a promotion of field enhancement factor. Furthermore, the injected charges mostly distribute at peak and valley. Direct-to-indirect band-gap transition has been found for zigzag wrinkle with height of 14.81-Å. The band gaps of wrinkled nanosheets decrease almost linearly with increasing field, which is caused by charge separation of valence band maximum and conduction band minimum.