The gap modulation by effectively external control is an intriguing feature of the black phosphorene which may enable a flexible design and optimization of electronics. In this paper, combined electric field and external strain effects are systematically investigated to tailor the electrical properties of bilayer black phosphorene (BP) in four stacking order by using density functional theory (DFT). The electronic structures and density of states of bilayer black phosphorene can be modulated by the two external controls, the direct semiconductor-indirect semiconductor-metal transitions emerge under uniaxial in-plain strains and vertical electric field. The band gap is more likely to be modulated by the electric field under compressive strain along armchair direction for the AB stacking structures. The greater the compressive strain, the gap closed at a lower electric field. The partial density of states (PDOS) shows the energy band was mainly contributed by p orbital, and the partial charge density of the VBM and CBM further indicates the shifting trend of electrons and holes between the double layers. Our results provide potential reference information for nano-electronic and optoelectronic applications.

通过有效的外部控制进行间隙调制是黑磷烯的一个有趣特征，它可以实现电子设备的灵活设计和优化。在本文中，系统地研究了电场和外部应变效应的组合，以通过使用密度泛函理论 (DFT) 以四种堆叠顺序定制双层黑磷烯 (BP) 的电性能。双层黑磷烯的电子结构和态密度可以通过两个外部控制进行调制，在单轴平面应变和垂直电场下出现直接半导体-间接半导体-金属跃迁。对于 AB 堆叠结构，带隙更可能在沿扶手椅方向的压缩应变下受电场调制。压缩应变越大，间隙在较低的电场下闭合。部分态密度（PDOS）表明能带主要由 p 轨道贡献，VBM 和 CBM 的部分电荷密度进一步表明双电层之间电子和空穴的移动趋势。我们的结果为纳米电子和光电应用提供了潜在的参考信息。