Electro-optical properties of phosphorene quantum dots

We study the electronic and optical properties of single-layer phosphorene quantum dots with various shapes, sizes, and edge types (including disordered edges) subjected to an external electric field normal to the structure plane. Compared to graphene quantum dots, in phosphorene clusters of similar shape and size there is a set of edge states with energies dispersed at around the Fermi level. These states make the majority of phosphorene quantum dots metallic and enrich the phosphorene absorption gap with low-energy absorption peaks tunable by the electric field. The presence of the edge states dispersed around the Fermi level is a characteristic feature that is independent of the edge morphology and roughness.

Figure 1

Classification of phosphorene quantum dots. Shaded and numbered irregular hexagons are used for cluster-size identification. The phosphorus atoms without “a pair” in the opposite layer are highlighted in light gray.

Figure 2

The bounding polygon randomization. (a) The triangular notch used in the ideal Koch curve generation together with the main geometrical parameters. (b) and (c) The outward and the inward notches with $a$ and $b$ parameters randomized. (d) The replacement of a polygon edge with the ideal and randomized Koch curve for the regular triangle and hexagon.

Figure 3

The tight-binding and structural parameters of the phosphorene lattice.

Figure 4

Energy levels of phosphorene QDs vs graphene QDs for triangular and hexagonal shapes with both zigzag and armchair termination.

Figure 5

The energy levels as a continuous function of the electric field strength for (a) ZTRI, (b) ZHEX, (c) ATRI, and (d) AHEX phosphorene quantum dots.

Figure 6

Optical-absorption cross sections of different graphene QDs vs the corresponding phosphorene QDs.

Figure 7

The effect of a perpendicular electric field on the optical-absorption cross section (a,c,e) and the corresponding energy levels (b,d,f) of zigzag triangular phosphorene QDs.

Figure 8

The optical absorption cross section (a,c,e) and energy levels (b,d,f) of zigzag hexagonal phosphorene QDs at different values of electric field.

Figure 9

The optical-absorption cross section (a,c,e) and the corresponding energy levels (b,d,f) of triangular armchair phosphorene QDs under the effect of an electric field.

Figure 10

The effect of a perpendicular electric field on the optical-absorption cross section (a,c,e) and corresponding energy levels (b,d,f) of hexagonal armchair phosphorene QDs.

Figure 11

The effect of the electric field on the energy levels and optical absorption of disordered PQDs based on those with armchair edges. (a,c) The energy levels and (b,d) normalized absorption cross sections of hexagonal and triangular clusters, respectively.

Figure 12

The same as Fig. 11 but for disordered PQDs based on those with zigzag edges. (a,c) Energy levels and (b,d) absorption cross section of hexagonal and triangular clusters, respectively.

Figure 13

The energy levels (a) and optical-absorption cross section (b) for a dielectric phosphorene quantum dot. The inset in (a) shows how the coordinate system is oriented with respect to the cluster.