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Bulk and Edge States in an Atomic Layer Semiconductor, Phosphorene

Osada Group

Phosphorene is a single atomic layer of the layered crystal of black phosphorus. Its realization using the standard mechanical exfoliation technique was reported by Liu et al. in 2014. Since then, a great amount of researches have been performed on phosphorene. There exist many first-principle calculations on the electronic structure of phosphorene, but the tight-binding approach is an easier way to extract the physical picture. We have qualitatively investigated the bulk and edge electronic structure of monolayer and bilayer phosphorene under vertical electric fields by employing the Slater-Koster-Harrison tight-binding model, which assumes transfer integrals depending only on the inter-atomic distance.

Fig. 1. Band structure of (a) monolayer phosporene, (b) monolayer phosphorene under the vertical electric field, and (c) bilayer phosphorene. The blue and red surfaces indicate the conduction band and the valence band, respectively.

Fig. 2. Energy spectra in phosphorene nanoribbon with the zigzag edge. (a) monolayer nanoribbon. (b) bilayer nanoribbon. (c) bilayer nanoribbon under vertical electric field. Insets show the crystal structure of phosphorene and detail of edge states in bilayer nanoribbon.

The crystal structure of monolayer phosphorene is a puckered honeycomb lattice where phosphorus atoms exist on two parallel planes. So, the external vertical electric field can modify the electronic structure by introducing the potential difference between the two planes. The calculated global band structures under the zero and finite fields are shown in Fig. 1(a) and Fig. 1(b), respectively. The electric field decreases the energy gap as seen in the Fig. 1. The band structure of bilayer phosphorene is shown in Fig. 1(c). The energy gap becomes smaller than monolayer, resulting from lifting of valence band top. This unsymmetrical behavior originates from the fact that the valence band top, mainly consisting of 3pz orbitals, is largely raised up by interlayer coupling comparing to the conduction band bottom.

The edge state existing in the gap is a remarkable feature of phosphorene. Figure 2(a) shows the energy spectrum of monolayer phosphorene nanoribbon with the zigzag edge. We can see that a flat edge subband appears in the middle of the main gap. It has two-fold degeneracy and isolated from the conduction and valence bands. Under the electric field, it splits into two subbands corresponding to the two phosphorus planes.

In the bilayer phosphorene, two edge subbands, which correspond to bonding and anti-bonding of monolayer edge states, appear around the main gap at the zigzag edge under zero electric field (Fig. 2(b)). Each one is doubly degenerated corresponding to two sides of the nanoribbon. Reflecting the valence band lifting, the upper subband is almost tangent to the valence band top, whereas the lower one penetrates the valence band. So, the most part of both edge states overlap with the valence band in energy. The overlap between the edge state and the valence band causes the hole transfer from the upper edge subband into the valence band. In other words, the upper edge state works as acceptor. This intrinsic hole doping mechanism around the edge might be responsible for the natural p-type doping in the bulk black phosphorus. In fact, the estimated averaged hole density is in good agreement with the reported effective acceptor concentration in black phosphorus.

Under the vertical electric field, the bulk gap is slightly reduced, and the edge states doubly split since edge states at both sides of the nanoribbon lie on different atomic planes (Fig. 2(c)). As the electric field is increased, the upper two split edge states move into the gap separating from the valence band top. This causes the reduction of the intrinsic hole doping from the upper edge state.

In monolayer phosphorene, the existence of the midgap edge state might be crucial for device application, since it causes current leakage at room temperature. In contrast, the bilayer phosphorene has fewer midgap state. Therefore, we can expect better device characteristics in bilayer phosphorene. The level of intrinsic hole doping can be controlled by the vertical electric field. These features of bilayer phosphorene might be better suited for device application.


References
  • [1] T. Osada, J. Phys. Soc. Jpn. 84, 013703 (2015).
Authors
  • T. Osada, T. Taen, and S. Fukuoka