Simulated scanning tunneling microscopy images of few-layer phosphorus capped by graphene and hexagonal boron nitride monolayers

Elemental phosphorous is believed to have several stable allotropes that are energetically nearly degenerate, but chemically reactive. These structures may be capped by monolayers of hexagonal boron nitride $(h-\mathrm{BN})$ or graphene to prevent chemical degradation under ambient conditions. We perform ab initio density functional calculations to simulate scanning tunneling microscopy (STM) images of different layered allotropes of phosphorus and study the effect of the capping layers on these images. At scanning energies within its intrinsic conduction gap, protective monolayers of insulating $h-\mathrm{BN}$ allow to distinguish between the different structural phases of phosphorus underneath due to the electronic hybridization with orbitals from the upmost phosphorus atoms: $h-\mathrm{BN}$ capping monolayers thus provide a promising route to tell few-layer phosphorus allotropes from one another with local probes.

Figure 1

Atomistic structure of five-layer phosphorene slabs capped with hexagonal boron nitride ($h$-BN) or graphene (Gr) monolayers (only the two uppermost phosphorene layers and one capping monolayers are shown). As it will turn out, we will be unable to register significant phosphorene features through graphene at an equilibrium relative separation in our STM simulations. In addition, the structures capped by h-BN or graphene are quite similar [c.f. structures (a) and (b)]; only their relative separation $d$ changes (c.f. Table 2). For these two reasons, only one structure capped by graphene is shown on this figure [structure (b)].

Figure 2

Electronic structure properties of five-layer phosphorene slabs capped with hexagonal boron nitride ($h$-BN, subplots a,c,e, and f) and graphene (subplots b and d) monolayers. Electronic bands are in the left subpanels, and Brillouin zones are seen as insets of these plots. The arrows in subplot a for $\Delta z=-0.4$ Å indicate a clear hybridization within the nominal gap of h-BN. This hybridization produces a height-dependent shift of the band edges that is clearly seen in subplot (a) by comparing the bold red and the thin horizontal dashed lines. Although less visible, such hybridization occurs for all h-BN capped slabs. The projected $h$-BN and total density of states are shown in the right subpanels. The density of states for isolated graphene and for $h$-BN, and their projections into $p_z$ orbitals are displayed in the (g) and (h) subplots.

Figure 3

Band structures and projected density of states onto B, N, C, and P atoms within $\pm 1$ eV for phosphorene slabs capped by $h$-BN and graphene monolayers. Note that $h$-BN hybridizes with phosphorus states within its nominal band gap (c.f. Table 3). Graphene states in capped structures exhibit an intrinsic charge that is one order of magnitude larger than the charge induced on $h$-BN by hybridization, and only shallow additional hybridization by phosphorene is visible in subplots (b) and (d), as highlighted by horizontal dashed lines. The hybridized states shown here are those observed on STM images in Figs. 4 to 7.

Figure 4

Simulated STM images of a $10\times 10$ Å area of bare (a) black phosphorene, (b) blue phosphorene, (c) $\delta$-P, and (d) $\gamma$-P slabs. Presented is ${\rho }_{\mathrm{STM}}$ at constant height, corresponding to the current imaging mode, at different values of the bias voltage $V_{\mathrm{bias}}$. For the sake of simple comparison, the geometry of the topmost two layers of the slabs is reproduced to scale in the left panels, with topmost atoms shown in white. Streaks seen on black phosphorene, $\delta$-P and $\gamma$-P reflect their “ridged” atomistic structure, also highlighted in the structural models. The different threefold symmetry of blue phosphorene with a triangular sublattice, associated with the white-colored P atoms in the topmost layer, is clearly reflected in the STM images in (b).

Figure 5

Simulated STM images of a $10\times 10$ Å area of a black phosphorene slab capped by a monolayer of (a) graphene, (b) $h$-BN and (c) a horizontally displaced $h$-BN monolayer. Presented is ${\rho }_{\mathrm{STM}}$ at constant height, corresponding to the current imaging mode, at different values of the bias voltage $V_{\mathrm{bias}}$. The lower subpanels represent ${\rho }_{\mathrm{STM}}$ in a plane normal to the surface. For the sake of simple comparison, the geometry of the topmost layers of the slabs is reproduced to scale in the left panels, with topmost P atoms shown in white. The ridged structure of black P, which is clearly visible in Fig. 2 at $V_{\mathrm{bias}}=-1.0$ V, is completely obscured by a graphene layer in (a), but is visible underneath an $h$-BN layer in (b) and (c).

Figure 6

Simulated STM images of a $10\times 10$ Å area of a blue phosphorene slab capped by a graphene monolayer.

Figure 7

Simulated STM images of a $10\times 10$ Å area of a (a) blue phosphorene, (b) $\delta$-P, and (c) $\gamma$-P slab capped with an $h$-BN monolayer. Presented is ${\rho }_{\mathrm{STM}}$ at constant height, corresponding to the current imaging mode, at different values of the bias voltage $V_{\mathrm{bias}}$. The lower subpanels represent ${\rho }_{\mathrm{STM}}$ in a plane normal to the surface. For the sake of simple comparison, the geometry of the topmost layers of the slabs is reproduced to scale in the left panels, with topmost P atoms shown in white.