van der Waals Heterostructure of Phosphorene and Graphene: Tuning the Schottky Barrier and Doping by Electrostatic Gating

In this Letter, we study the structural and electronic properties of single-layer and bilayer phosphorene with graphene. We show that both the properties of graphene and phosphorene are preserved in the composed heterostructure. We also show that via the application of a perpendicular electric field, it is possible to tune the position of the band structure of phosphorene with respect to that of graphene. This leads to control of the Schottky barrier height and doping of phosphorene, which are important features in the design of new devices based on van der Waals heterostructures.

Figure 1

(a) Side and top view of a single layer of phosphorene on top of graphene. (b) Side and top view of a bilayer of phosphorene on top of graphene. (c) Evolution of the total energy as a function of displacements ${\delta }_{x/y}$ of the phosphorene layer relative to graphene, taking the origin at the lowest energy configuration. (d) Binding energy as a function of the distance $d_{P/G}$, for the single-layer and bilayer system.

Figure 2

Band structure of single-layer phosphorene on top of graphene projected at the (a) phosphorene layer and (b) graphene layer. Band structure of bilayer phosphorene on top of graphene projected at the (c) bilayer phosphorene and (d) graphene layer. The scale indicates the magnitude of the projection.

Figure 3

(a) Band structure of single-layer phosphorene with graphene (1P@Gr), (b) band structure of single-layer phosphorene (1P) without graphene, and (c) band edges of the (left panel) composed system and (right panel) pristine single-layer phosphorene. (d) Band structure of bilayer phosphorene with graphene (2P@Gr), (e) band structure of bilayer phosphorene (2P) without graphene, and (f) band edges of the (left panel) composed system and (right panel) pristine bilayer phosphorene. The horizontal blue lines in (c) and (f) represent the valence band (VB) and conduction band (CB) of phosphorene. The red crossed lines represent the Dirac cone of graphene and $W$ is the work function. All values presented in this figure were aligned with respect to the vacuum level.

Figure 4

Evolution of the band structure as a function of the external electric field for (a)–(c) single-layer phosphorene and (e)–(g) bilayer phosphorene. Evolution of the band edges, as a function of the field relative to the graphene Dirac point, for (d) single-layer phosphorene and (h) bilayer phosphorene. The field is applied along the $z$ direction defined in Fig. 1 (perpendicular to the layers). The Fermi level of the systems were set to zero and VB (CB) represents top (bottom) of the valence (conduction) band.