Two-dimensional van der Waals p-n junction of InSe/Phosphorene

We investigate the energetic stability, the structural and electronic properties of van der Waals heterostructures composed by a combination of single layer InSe, bilayer phosphorene (BP), and graphene. We found that a single layer of InSe stacked on graphene (InSe@G) present a n-type Schottky barrier, which can be tuned by applying an external electric field perpendicularly to the InSe/G interface ($E^{\rm ext}_{\perp}$). Upon further increase of $E^{\rm ext}_{\perp}$ we may promote a n-type doping of the InSe layer. This is in contrast with the other semiconductor/metal vdW heterojunction, BP@G, where the BP sheet becomes p-type doped as a function of $E^{\rm ext}_{\perp}$. By considering a semiconductor/semiconductor vdW system, namely BP@InSe, we found that lowest (highest) unoccupied (occupied) states lie on the InSe (BP) layers. The BP/InSe interface presents a type-II band alignment. Exploiting the electron-hole separation in BP@InSe, and the formation of ohmic contacts in InSe@G and BP@G, tuned by $E^{\rm ext}_{\perp}$, we propose a p-n junction composed by p-type BP and n-type InSe, with the graphene acting as electrodes and also as a source of electrons/holes in the n-type/p-type InSe/BP heterostructure.