Electronic and transport properties of phosphorene nanoribbons

By combining density functional theory and nonequilibrium Green's function, we study the electronic and transport properties of monolayer black phosphorus nanoribbons (PNRs). First, we investigate the band gap of PNRs and its modulation by the ribbon width and an external transverse electric field. Our calculations indicate a giant Stark effect in PNRs, which can switch on transport channels of semiconducting PNRs under low bias, inducing an insulator-metal transition. Next, we study the transport channels in PNRs via the calculations of the current density and local electron transmission pathway. In contrast to graphene and ${\mathrm{MoS}}_2$ nanoribbons, the carrier transport channels under low bias are mainly located in the interior of both armchair and zigzag PNRs, and immune to a small amount of edge defects. Last, a device of the PNR-based dual-gate field-effect transistor, with high on/off ratio of ${10}^3$, is proposed based on the giant electric-field tuning effect.

Figure 1

Top view and side view of the optimized geometry structure of hydrogen saturated phosphorene nanoribbons (PNRs): (a) zigzag phosphorene nanoribbons (ZPNRs) and (b) armchair phosphorene nanoribbons (APNRs).

Figure 2

Band structures and partial charge densities of the CBM and VBM of the (a) 8-ZPNR and (b) 10-APNR. The distribution of charge densities shows both electrons and holes are distributed in the center of ribbons. (c) Variation of band gaps of APNRs (up to 5.8 nm) and ZPNRs (up to 8.1 nm) as a function of ribbon width $N$. The scale law of band gap is $\sim 1/w$ for ZPNRs and $\sim 1/w^2$ for APNRs, where $w$ is width of ribbon (in units of Å). The blue dashed line indicates the band gap of monolayer phosphorene.

Figure 3

The current density of APNR (a) and ZPNR (b) at the energy level sampling on the VBM, which shows the transport channels are at the center of ribbons.

Figure 4

The local electron transmission pathway of armchair PNRs (a) and zigzag PNRs (b) with the energy-level sampling on the valance-band maximum.

Figure 5

The current density of ZPNR with a P vacancy defect (a) and H2 defect (b) at the energy-level sampling on the VBM.

Figure 6

(a) Band structure of the armchair PNR. The red solid circles indicate the weight of states of outermost edge P atoms. (b)–(d) The current density at different energy levels (Ef, VBM and Ef-1.02 eV). (e) A schematic diagram of the APNR $I-V$ curve.

Figure 7

Band structures of the 10-APNR (a) and 8-ZPNR (b) under electric fields. The figures show VBM and CBM energy levels shift and split both in APNRs and ZPNRs, leading to a reduction in the band gap and closure at the Fermi level.

Figure 8

(a), (b) The total charge density of 10-APNRs under a 0-V/nm and 5-V/nm electric field. (c) The charge-density difference of (a) and (b). (d) Electric-field induced charge-density difference $\mathrm{\Delta }\rho ={\rho }_{E_{\mathrm{ext}}}-{\rho }_0$ as a function of the position across the nanoribbon of the 10-APNR. $\mathrm{\Delta }\rho$ is averaged over the plane perpendicular to the electric-field direction ($yz$ plane). (e) The accumulated charge $\mathrm{\Delta }{\rho }_{\mathrm{acc}}$ as a function of the external electric field, which shows a parallel-plate-capacitor-like behavior.

Figure 9

Variation of band gaps of ZPNRs (a) and APNRs (b) as a function of external electric field. Three different widths of ribbons were considered for each case. (c) Calculated giant Stark effect coefficient ${\mathrm{S}}_L$ as a function of the ribbon width $W$.

Figure 10

(a) Top view of a dual-gate field effect transistor based on ZPNR. Semi-infinite metallic bare ZPNRs serve as two leads while hydrogen saturated ZPNR is used as semiconducting channel (scattering area). (b) Transmission spectrum under $E=0$ V/nm (black line) and $E=7$ V/nm (red line). Inset: the DOS of the hydrogen saturated ZPNR (the scattering region) under an external electric field of 7 V/nm. (c) Transmission eigenstates at $E_f$ and at the (0,0) point of the $k$ space under $E=0$ V/nm and $E=7$ V/nm.