Band engineering of phosphorene/graphene van der Waals nanoribbons toward high-efficiency thermoelectric devices

Vertical integration of dissimilar layered materials in a so-called van der Waals (vdW) heterostructure (HS) has emerged as a useful tool to engineer band alignments and interfaces. In this paper, we investigate thermoelectric currents in a phosphorene/graphene vdW nanoribbon consisting of an armchair graphene nanoribbon (AGNR) stacked on an armchair phosphorene nanoribbon (APNR). We focus on the currents driven by a temperature difference between the leads in a two-probe junction. In contrast to pristine AGNRs and APNRs, such an armchair-edged HS can provide several nanoamperes of the current at room temperature, without any external field. External electric fields modify the electronic band structure and can induce a type I-to-II band alignment transition and a direct-to-indirect band gap transition. Biasing the APNR/AGNR by an external electric field is found to strongly increase the thermally induced current and control the direction of current flow at moderate temperatures. These results are important for potential applications of the APNR/AGNR vdW HS in flexible electronics and thermoelectric devices.

Figure 1

(a) Different views of the supercell of phosphorene/graphene van der Waals (vdW) heterostructure (HS) consisting of a 1×4 monolayer graphene supercell stacked on top of a 1×3 monolayer phosphorene supercell. (b) Schematic of two-dimensional (2D) HS. Black lattice is graphene and the orange one is phosphorene. The atomic sites are labeled per supercell, and the different hopping parameters are indicated.

Figure 2

(a) The band dispersion of the two-dimensional (2D) heterostructure (HS), graphene, and phosphorene. The enlarged views of the regions indicated by the black circles are shown in (b)–(e), representing (b) the Dirac cone, and (c)–(e) band anticrossings.

Figure 3

(a) The band dispersion of 19APNR/25AGNR, together with the band edges of 19APNR and 25AGNR, depicted by the dashed lines. Local density of states (LDOS) of 19APNR/25AGNR at (b) conduction band minimum (CBM) and (c) valence band maximum (VBM), projected at the layers.

Figure 4

The electron transmission of (a) 18APNR/24AGNR, (b) 19APNR/25AGNR, and (c) 20APNR/26AGNR, as a function of energy.

Figure 5

The thermally induced current against the width of the heterostructure (HS) at $T_{\mathrm{L}}=300\mathrm{K}$.

Figure 6

The band dispersion of 19APNR/25AGNR in the (a) absence and (b) presence of the perpendicular electric field of $|E_{\mathrm{z}}|=0.1\mathrm{V}/\AA$. Local density of states (LDOS) of 19APNR/25AGNR at (c) conduction band minimum (CBM), and (d) valence band maximum (VBM) projected at the layers. The direction of the applied perpendicular electric field is depicted in (d).

Figure 7

The thermally induced current of (a) 19APNR/25AGNR and (c) 20APNR/26AGNR vs $T_{\mathrm{L}}$ for different perpendicular electric fields. The threshold temperature for the current of 19APNR/25AGNR as a function of $E_{\mathrm{z}}$ is shown in the inset of (a). The critical point of the current-$T_{\mathrm{L}}$ curve as a function of $E_{\mathrm{z}}$ is shown in the inset of (c). The electron and (the absolute value of) the hole currents of (b) 19APNR/25AGNR and (d) 20APNR/26AGNR vs $E_{\mathrm{z}}$ at room temperature for $\mathrm{\Delta }T=10\mathrm{K}$.

Figure 8

The evolution of the band edges of 19APNR/25AGNR under a transverse electric field.

Figure 9

(a) The thermally induced current of 19APNR/25AGNR as a function of $T_{\mathrm{L}}$ for different transverse electric fields. (b) The electron and (the absolute value of) the hole currents of 19APNR/25AGNR as functions of $E_{\mathrm{y}}$ at room temperature and $\mathrm{\Delta }T=10\mathrm{K}$.