Highly anisotropic and tunable charge carrier of monolayer phosphorus allotropes by bi-axial strain

•The electron mobilities of γ-P produce obvious strain reversal under bi-axial strain.•γ-P is transformed into a direct bandgap semiconductor under bi-axial strain.•The bandgaps of γ- and δ-P are completely closed at critical levels bi-axial strain.•The electron mobility of γ-P is 60-70 times greater than the pristine under bi-axial strain.•The hole mobility of α-P in the x direction is 73 times greater than the pristine under bi-axial strain. The complex variation of electronic properties and carrier mobility of four typical allotropes of phosphorus are investigated using first-principles calculations of bi-axial strain. Our study shows that the electronic properties and carrier mobility of single-layer α-, β-, γ- and δ-P are sensitive to bi-axial strain, and that the carrier mobility can even be increased by several orders of magnitude under specific tensile or compressive strain. Moreover, the anisotropy of their mobility in the two-dimensional plane shows different changes according to the variation of the bi-axial strain. In particular, the electron mobility of α-P (γ-P) along the two main axis directions is reversed when the bi-axial strain increased by 5% (−4%). This transformation is mainly caused by changes in the effective mass anisotropy due to alterations in band dispersion under external strain, as illustrated by the distribution of effective mass anisotropy and the corresponding changes of electronic properties under strain.