We investigate the possibility of band structure engineering in the recently predicted 2D layered form of blue phosphorus via an electric field (E$_z$) applied perpendicular to the layer(s). Using density functional theory, we study the effect of a transverse electric field in monolayer, as well as three differently stacked bilayer structures of blue phosphorus. We find that, for E$_z > 0.2$ V/AA the direct energy gap at the $Gamma$ point, which is much larger than the default indirect band gap of mono- and bilayer blue phosphorus, decreases linearly with the increasing electric field; becomes comparable to the default indirect band gap at E$_z approx 0.45 (0.35)$ V/AA for monolayer (bilayers) and decreases further until the semiconductor to metal transition of 2D blue phosphorus takes place at E$_zapprox 0.7 (0.5)$ V/AA for monolayer (bilayers). Calculated values of the electron and hole effective masses along various high symmetry directions in the reciprocal lattice suggests that the mobility of charge carriers is also influenced by the applied electric field.
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