Layer-dependent band alignment of few layers of blue phosphorus and their van der Waals heterostructures with graphene

Renato B. Pontes, Roberto H. Miwa, Antônio J. R. da Silva, Adalberto Fazzio, and José E. Padilha

Phys. Rev. B 97, 235419 – Published 12 June 2018

Abstract

The structural and electronic properties of few layers of blue phosphorus and their van der Waals heterostructures with graphene were investigated by means of first-principles electronic structure calculations. We study the four energetically most stable stacking configurations for multilayers of blue phosphorus. For all of them, the indirect band-gap semiconductor character, are preserved. We show that the properties of monolayer graphene and single-layer (bilayer) blue phosphorus are preserved in the van der Waals heterostructures. Further, our results reveal that under a perpendicular applied electric field, the position of the band structure of blue phosphorus with respect to that of graphene is tunable, enabling the effective control of the Schottky barrier height. Indeed, for the bilayer blue phosphorene on top of graphene, it is possible to even move the system into an Ohmic contact and induce a doping level of the blue phosphorene. All of these features are fundamental for the design of new nanodevices based on van der Waals heterostructures.

Received 10 April 2018
Revised 31 May 2018

DOI:https://doi.org/10.1103/PhysRevB.97.235419

Physics Subject Headings (PhySH)

Graphene Heterostructures Phosphorene Two-dimensional electron system

Ab initio calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Renato B. Pontes^1,*, Roberto H. Miwa^2,†, Antônio J. R. da Silva^3,4,‡, Adalberto Fazzio^5,6,§, and José E. Padilha^7,∥

¹Instituto de Física, Universidade Federal de Goiás, Campus Samambaia, 74690-900 Goiânia, GO, Brazil
²Instituto de Física, Universidade Federal de Uberlândia, Caixa Postale 593, 38400-902 Uberlândia, MG, Brazil
³Instituto de Física, Universidade de São Paulo, Caixa Postale 66318, 05315-970 São Paulo, SP, Brazil
⁴Laboratório Nacional de Luz Síncrotron, Caixa Postale 6192, 13083-970 Campinas, SP, Brazil
⁵Brazilian Nanotechnology National Laboratory (LNNano)/CNPEM, P.O. Box 6192, 13083-970 Campinas, SP, Brazil
⁶Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 49960-001, Brazil
⁷Campus Avançado Jandaia do Sul, Universidade Federal do Paraná, 86900-000 Jandaia do Sul, PR, Brazil

^*pontes@ufg.br
^†hiroki@ufu.br
^‡jose.roque@lnls.br
^§fazzio@if.usp.br
^∥jose.padilha@ufpr.br

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 97, Iss. 23 — 15 June 2018

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Top panel: A ball-and-stick representation of the structure of a single layer of blue phosphorus. The lattice vectors ( $a_{1}$ and $a_{2}$ ) that define the unit cell (gray region) are also indicated. Bottom panel: A side view of the blue phosphorus monolayer. Dashed black lines indicate the buckling height, $h$ . (b) Schematic representation of the first Brillouin zone of a hexagonal lattice. The reciprocal lattice vectors ( $b_{1}$ and $b_{2}$ ) and the high-symmetry points are highlighted. (c)–(f) Top and side views of the four stacking configurations considered in our calculations. The different colors in the P atoms are used to distinguish the upper from lower layers. The distance, $d$ , between the layers is also shown. The solid (dashed) red lines in (c)–(f) represent the atoms that are located on the top of other P atoms (center of an hexagon).
Reuse & Permissions
Figure 2
Electronic band structures for one, two, three, and four layers of blue phosphorus in the stacking modes: (a) ${AA}_{1}$ , (b) ${AA}_{2}$ , (c) ${AB}_{1}$ , and (d) ${AB}_{2}$ . The valence and conduction bands are highlighted. All band structures were aligned with respect to the vacuum level. The arrows in (a) indicate the important band gaps ( $Λ$ and $Γ$ ). The single-layer band structure is repeated in (a), (b), (c), and (d) just for comparison.
Reuse & Permissions
Figure 3
Band gaps $Δ_{g}^{Γ}$ and $Δ_{g}^{Λ}$ as a function of the number of layers for (a) ${AA}_{1}$ , (b) ${AA}_{2}$ , (c) ${AB}_{1}$ , and (d) ${AB}_{2}$ . The HSE06-DFT calculated band gaps are indicated by the solid squares and circles. The fitting curves are presented by the solid lines. The horizontal dashed lines indicate the bulk ( $n \to \infty$ ) band gaps. (e)–(h) Evolution of the band edges as a function of the number of layers for the stacks ${AA}_{1}, {AA}_{2}, {AB}_{1}$ , and ${AB}_{2}$ , respectively.
Reuse & Permissions
Figure 4
(a) Schematic representations of single-layer graphene and blue phosphorus. The lattice vectors, $a_{1} ({\vec{b}}_{1})$ and $a_{2} ({\vec{b}}_{2})$ , for graphene (blue phosphorus) are indicated. The buckling height, $h_{b}$ , is also shown. (b) Top and side views of a monolayer blue phosphorus on top of graphene. The lattice vectors $c_{1}$ and $a_{2}$ that define the unit cell (light gray region) and the distance between monolayer graphene and blue phosphorus ( $d_{blue-P@G}$ ) are shown. (c) Variation of the total $energy (Δ E$ ), in eV, as a function of displacements $δ_{x, y}$ of the monolayer blue phosphorus relative to graphene. The zero was set as the total energy of the lowest energy configuration. (d) Binding energy as a function of the distance, $δ_{z}$ , between blue-P and graphene. The zero was set as the equilibrium ( $d_{blue-P@G}^{eq}$ ) distance.
Reuse & Permissions
Figure 5
Left panels: DFT-calculated project electronic band structures of single-layer blue-P (a) and bilayer blue-P (b) on graphene. Right panels: Schematic comparison between the band structures of the single-layer blue-P (bilayer blue-P) with graphene with pristine single-layer (bilayer) blue phosphorus in the vicinity of the Fermi level. The red crossed lines represent the Dirac cone of graphene. The scales indicate the magnitude of the projections. All band structures were aligned with respect to the vacuum level.
Reuse & Permissions
Figure 6
(a)–(c) Evolution of the band structure as a function of the external electric field for single-layer blue phosphorus on monolayer graphene and (e)–(g) bilayer blue phosphorus. (d), (h) Evolution of the band edges as a function of the field relative to the graphene Dirac point for single-layer blue phosphorus and bilayer blue phosphorus, respectively. The electric field is applied along the $\hat{z}$ direction as defined in Fig. 1. The Fermi level of the heterostructures was set to zero and VB (CB) represents the top (bottom) of the valence (conduction) band. All band structures were aligned with respect to the vacuum level.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics