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

We investigate the energetic stability and the structural and electronic properties of semiconductor/semiconductor and semiconductor/metal 2D van der Waals heterostructures composed by combinations of single layer InSe, bilayer phosphorene (BP), and graphene. For the semiconductor/semiconductor BP/InSe heterostructure, we found that the lowest (highest) unoccupied (occupied) states lie on the InSe (BP) layers, giving rise to a type-II band alignment, with electrons (holes) localized in the InSe (BP) layers. The semiconductor/metal interface composed by a single layer of InSe stacked on graphene (InSe/G) presents a $n$-type Schottky barrier, which can be tuned by applying an external electric field perpendicular to the InSe/G interface (${E}_{\ensuremath{\perp}}^{\mathrm{ext}}$). Upon further increase of ${E}_{\ensuremath{\perp}}^{\mathrm{ext}}$, the InSe/G contact becomes Ohmic, promoting a net charge transfer from the graphene sheet to the InSe layer, $n$-type doping. This is in contrast with the other semiconductor/metal van der Waals heterojunction, BP/G, where the BP sheet becomes $p$-type doped as a function of ${E}_{\ensuremath{\perp}}^{\mathrm{ext}}$. Exploiting the electron-hole separation in BP/InSe, and the formation of Ohmic contacts at the InSe/G and BP/G interfaces, we propose a $p\ensuremath{-}n$ 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 InSe/BP.