Deformed octagon-hexagon-square structure of group-IV and group-V elements and III-V compounds

We report the prediction of a two-dimensional (2D) allotrope common to group-IV and group-V elements and III-V compounds, which consist of two nonplanar atomic layers connected by vertical bonds and form deformed octagon, hexagon, and squares (dohs) with threefold and fourfold coordinated atoms. Specifically for silicon, it is a semiconductor with cohesion stronger than silicene and can be chemically doped to have localized donor and acceptor states in the band gap. This allotrope can be functionalized to construct quasi-2D clathrates with transition metal atoms and attain spin polarized metallic, half-metallic, or semiconducting states. It is demonstrated that these properties can be maintained, when it is grown on a specific substrate. Stringent tests show that the atomic structure is dynamically stable and can sustain thermal excitation at high temperatures. Additionally, stable bilayer, as well as 3D layeredlike structures, can be constructed by the vertical stacking of single-layer dohs. Surprisingly, C, Ge, AlP, and GaAs can form also similar 2D semiconducting structures. In contrast to semiconducting black and blue phosphorene, P-dohs is a semimetal with band inversion. While the premise of using well-developed silicon technology in 2D electronics has been hampered by the semimetallic silicene, the realization of this 2D, semiconducting allotrope of silicon and compounds can constitute a productive direction in 2D nanoelectronics/spintronics.

Figure 1

(a) Top $\left[\right(xy)$ plane] and side views of the metallic $\mathrm{P}6/\mathrm{m}-{\mathrm{Si}}_6$ clathrate structure with the calculated cohesive energy of $E_c=4.50$ eV/atom. (b) Top view of Si-dohs with the 2D oblique unit cell delineated. 2D lattice constants a and b are indicated. Its perspective side view below consists of deformed hexagons and squares. (c) Two nonplanar atomic layers of Si-dohs are made of deformed octagons, which are connected by two vertical bonds per unit cell and constitute deformed squares and hexagons in the side view. (d) Calculated charge density contour plots on a plane passing through specific Si-Si bonds described on the left. (e) Calculated charge density of semimetallic silicene monolayer is shown for comparison.

Figure 1

(a) Top $\left[\right(xy)$ plane] and side views of the metallic $\mathrm{P}6/\mathrm{m}-{\mathrm{Si}}_6$ clathrate structure with the calculated cohesive energy of $E_c=4.50$ eV/atom. (b) Top view of Si-dohs with the 2D oblique unit cell delineated. 2D lattice constants a and b are indicated. Its perspective side view below consists of deformed hexagons and squares. (c) Two nonplanar atomic layers of Si-dohs are made of deformed octagons, which are connected by two vertical bonds per unit cell and constitute deformed squares and hexagons in the side view. (d) Calculated charge density contour plots on a plane passing through specific Si-Si bonds described on the left. (e) Calculated charge density of semimetallic silicene monolayer is shown for comparison.

Figure 2

(a) Variation of frequency $\mathrm{\Omega }\left(\mathbf{k}\right)$ of the vibration modes of Si-dohs structure along high-symmetry directions of Brillouin zone shown by inset. (b) Top and side views of atomic configurations of Si atoms obtained AIMD calculations at high temperature. The temperature has been raised from 0 to 900 K in three steps with 2-ps simulation time at each step. (c) AIMD calculations for the annealing; 900 K $\to$ 300 K in 0.3 ps $\to$ 0 K in 0.3 ps.

Figure 2

(a) Variation of frequency $\mathrm{\Omega }\left(\mathbf{k}\right)$ of the vibration modes of Si-dohs structure along high-symmetry directions of Brillouin zone shown by inset. (b) Top and side views of atomic configurations of Si atoms obtained AIMD calculations at high temperature. The temperature has been raised from 0 to 900 K in three steps with 2-ps simulation time at each step. (c) AIMD calculations for the annealing; 900 K $\to$ 300 K in 0.3 ps $\to$ 0 K in 0.3 ps.

Figure 3

Electronic energy-band structure of the optimized 2D Si-dohs and corresponding total density of states (DOS) calculated using PBE (solid lines) and the HSE functional including SOC (dotted lines). The band gap between the conduction and valence bands is shaded, and the indirect band gap $E_{g,i}$ is indicated by an arrow. The inset shows the variation of the fundamental band gap with uniaxial strain ($0<\epsilon <8$)%.

Figure 3

Electronic energy-band structure of the optimized 2D Si-dohs and corresponding total density of states (DOS) calculated using PBE (solid lines) and the HSE functional including SOC (dotted lines). The band gap between the conduction and valence bands is shaded, and the indirect band gap $E_{g,i}$ is indicated by an arrow. The inset shows the variation of the fundamental band gap with uniaxial strain ($0<\epsilon <8$)%.

Figure 4

(a) Top and side views of optimized atomic structure of bilayers (BLs) constructed from three different vertical stacking sequences of Si-dohs and their cohesive energies $E_c$. These are AA, ${\mathrm{AA}}^{\prime }$, and AB. BL-AA and BL-${\mathrm{AA}}^{\prime }$ transform to BL-AB at $T\sim 300$ K. (b) Top and side views of the optimized, 3D periodic structures constructed from AA, ${\mathrm{AA}}^{\prime }$, and AB vertical stacking of Si-dohs.

Figure 4

(a) Top and side views of optimized atomic structure of bilayers (BLs) constructed from three different vertical stacking sequences of Si-dohs and their cohesive energies $E_c$. These are AA, ${\mathrm{AA}}^{\prime }$, and AB. BL-AA and BL-${\mathrm{AA}}^{\prime }$ transform to BL-AB at $T\sim 300$ K. (b) Top and side views of the optimized, 3D periodic structures constructed from AA, ${\mathrm{AA}}^{\prime }$, and AB vertical stacking of Si-dohs.

Figure 5

Substrate effects on Si-dohs. (a) Top and side views of optimized atomic structure of Si-dohs overlayer on Ag(111) substrate. The total density of states (DOS) and those projected (PDOS) to Si and Ag atoms display a metallic character. Strong overlayer-substrate interaction is clarified by the charge density contour plots shown by inset. (b) Same for Si-dohs on graphene with a large spacing between them. DOS and PDOS indicate that the semimetallic state of the substrate and semiconductor state of the Si-dohs overlayer are preserved.

Figure 5

Substrate effects on Si-dohs. (a) Top and side views of optimized atomic structure of Si-dohs overlayer on Ag(111) substrate. The total density of states (DOS) and those projected (PDOS) to Si and Ag atoms display a metallic character. Strong overlayer-substrate interaction is clarified by the charge density contour plots shown by inset. (b) Same for Si-dohs on graphene with a large spacing between them. DOS and PDOS indicate that the semimetallic state of the substrate and semiconductor state of the Si-dohs overlayer are preserved.

Figure 6

(a) Top and side views of equilibrium atomic structure of the Si-dohs phase after the adsorption of Al atom and calculated the total and adatom projected densities of states for a single Al adatom adsorbed to $6\times 4$ supercell of Si-dohs phase. (b) Top and side views of the atomic configuration of $6\times 4$ supercell of Si-dohs used to tread the adsorbed P adatom and the total and adatom projected densities of states calculated for a single P adatom adsorbed to $6\times 4$ supercell of Si-dohs phase at equilibrium sites.

Figure 6

(a) Top and side views of equilibrium atomic structure of the Si-dohs phase after the adsorption of Al atom and calculated the total and adatom projected densities of states for a single Al adatom adsorbed to $6\times 4$ supercell of Si-dohs phase. (b) Top and side views of the atomic configuration of $6\times 4$ supercell of Si-dohs used to tread the adsorbed P adatom and the total and adatom projected densities of states calculated for a single P adatom adsorbed to $6\times 4$ supercell of Si-dohs phase at equilibrium sites.

Figure 7

Si-dohs decorated by transition metal atoms forming a quasi-2D clathrate structure, where Cr or V atoms are kept in the hexagonal rings. (a) Quasi-2D ${\mathrm{CrSi}}_6$ or ${\mathrm{VSi}}_6$ clathrate structures: Top and side views of optimized atomic structure. (b) Spin-split energy bands calculated by HSE. (c) Same as (b) for quasi-2D ${\mathrm{VSi}}_6$ clathrate. The zero energy is set to the Fermi level. Spin-up and spin-down bands are highlighted by different colors.

Figure 7

Si-dohs decorated by transition metal atoms forming a quasi-2D clathrate structure, where Cr or V atoms are kept in the hexagonal rings. (a) Quasi-2D ${\mathrm{CrSi}}_6$ or ${\mathrm{VSi}}_6$ clathrate structures: Top and side views of optimized atomic structure. (b) Spin-split energy bands calculated by HSE. (c) Same as (b) for quasi-2D ${\mathrm{VSi}}_6$ clathrate. The zero energy is set to the Fermi level. Spin-up and spin-down bands are highlighted by different colors.

Figure 8

Top and side views of optimized atomic structure of some other group-IV elements C, Ge, and group-III-V compounds GaAs, AlP constructing stable 2D structures like Si-dohs. The PBE calculated (average) cohesive energy $E_c$ per atom and fundamental band gap is presented. For comparison, values calculated for counterparts in 2D hexagonal structure are also given.

Figure 8

Top and side views of optimized atomic structure of some other group-IV elements C, Ge, and group-III-V compounds GaAs, AlP constructing stable 2D structures like Si-dohs. The PBE calculated (average) cohesive energy $E_c$ per atom and fundamental band gap is presented. For comparison, values calculated for counterparts in 2D hexagonal structure are also given.

Figure 9

(a) Top and side views of optimized atomic structure of P-dohs. (b) Energy bands structure calculated using PBE (solid lines) and HSE (dotted lines) functional.