Blue and black phosphorene on metal substrates: a density functional theory study

We have performed density functional theory calculations to study blue phosphorene and black phosphorene on metal substrates. The substrates considered are the (111) and (110) surfaces of Al, Cu, Ag, Ir, Pd, Pt and Au and the (0001) and (10$\bar{1}$0) surfaces of Zr and Sc. The formation energy $E_{\rm F}$ is negative (energetically favorable) for all 36 combinations of overlayer and substrate. By comparing values of $\Delta{\Omega}$, the change in free energy per unit area, as well as the overlayer-substrate binding energy $E_{\rm b}$, we identify that Ag(111), Al(110), Cu(111), Cu(110) and possibly Au(110) may be especially suitable substrates for the synthesis and subsequent exfoliation of blue phosphorene, and the Ag(110) and Al(111) substrates for the synthesis of black phosphorene. However, these conclusions are drawn assuming the source of P atoms is bulk phosphorus, and can alter upon changing synthesis conditions (chemical potential of phosphorus). Thus, when the source of phosphorus atoms is P$_4$, blue phosphorene is favored only over Pt(111). We find that for all combinations of overlayer and substrate, the charge transfer per bond can be captured by the universal descriptor $\mathcal{D} = \Delta \chi/\Delta \mathcal{R}$, where $\Delta \chi$ and $\Delta \mathcal{R}$ are, respectively, the differences in electronegativity and atomic size between phosphorus and the substrate metal.