J. Semicond. > 2015, Volume 36 > Issue 7 > 072002
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SEMICONDUCTOR PHYSICS

Optimized geometry and electronic structure of three-dimensional β-graphyne

Yang Pei1, Haibin Wu1 and Jingmin Liu2

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DOI: 10.1088/1674-4926/36/7/072002

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Abstract: β-graphyne, a carbon allotrope, is a gapless semiconductor with hexagonal lattice symmetry, just like graphene. We calculated the optimized structure and electronic structures of some possible three-dimensional β-graphyne stacking arrangements by means of the first-principles frozen-core projector augmented-wave method implemented in the Vienna ab initio simulation package. The optimized lattice constant a of the three-dimensional β-graphyne turns out to be 9.46 Å, which is slightly smaller than its two-dimensional counterpart. The binding energy is about 90% of that of graphite, which suggests that three-dimensional β-graphyne will be stable when it is synthesized. The band structure is calculated via the hybrid functional. We found that the most stable three-dimensional stacking arrangement is an indirect band gap semiconductor with an energy gap of 0.1 eV.

Key words: β-graphyne, optimized geometry, electronic structure, first principles calculations



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Fig. 1.  (a) The structure of 2D $\beta $-graphyne. The dashed parallelogram represents a unit cell with the lattice constant $a$. The planar projection of the AAA stacking arrangement structure $\beta_{0}$ is the same. (b) Brillouin zone of all crystal structures.

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Fig. 2.  Three different ABA stacking arrangement structures (a) $\beta_{1}$, (b) $\beta_{2}$, and (c) $\beta_{3}$. Black: $A$ layer; gray: $B$ layer.

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Fig. 3.  (a) The electronic structure on the $LAHL$ plane. (b) The electronic structure along the $\Gamma A$, $KH$, $ML$ line. (c) The electronic structure on the $M \Gamma KM$ plane. (d) Densities of states for 3D layer stacking arrangement structure $\beta_0$. Structure $\beta_0$ exhibits metallic and the density of states at $E_{\rm F}$ are not zero.

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Fig. 4.  (a) The electronic structure on the $LAHL$ plane. (b) The electronic structure along the $\Gamma A$, $KH$, $ML$ line. (c) The electronic structure on the $M \Gamma KM$ plane. (d) Densities of states for 3D layer stacking arrangement structure $\beta_1$. The top of the valence band is $-0.1$ eV and the bottom of the conduction band is $-0.2$ eV, they are indicated by arrows. Structure $\beta_1$ exhibits metallic and the density of states at $E_{\rm F}$ are not zero.

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Fig. 5.  (a) The electronic structure on the $LAHL$ plane. (b) The electronic structure along the $\Gamma A$, $KH$, $ML$ line. (c) The electronic structure on the $M \Gamma KM$ plane. (d) Densities of states for 3D layer stacking arrangement structure $\beta_2$. Structure $\beta_2$ exhibits indirect band gap semiconductor. The energy gap of structure $\beta_2$ is 0.1 eV by HSE06.

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Fig. 6.  (a) The electronic structure on the $LAHL$ plane. (b) The electronic structure along the $\Gamma A$, $KH$, $ML$ line. (c) The electronic structure on the $M \Gamma KM$ plane. (d) Densities of states for 3D layer stacking arrangement structure $\beta_3$.

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Table 1.   Optimized lattice constant $a$, interlayer distance $d$, bond lengths $b$ and binding energies $E_{\rm b}$ of 3D $\beta $-graphyne. The values for 2D $\beta $-graphyne and 3D graphite are also given. $b_{\rm s1}$, $b_{\rm s2}$ denote two different single bond lengths and $b_{\rm t}$ denotes the triple bond length. Experimental values for graphite are given in parenthesis.

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Table 2.   Band gap and effective masses for valence band $m_{\rm v}^{\ast}$ and conduction band $m_{\rm c}^{\ast}$ of 3D arrangement structure $\beta_{2}$.

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    Received: 29 October 2014 Revised: Online: Published: 01 July 2015

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      Article Navigation >  Journal of Semiconductors  > 2015  >  36(7): 072002
      Yang Pei, Haibin Wu, Jingmin Liu. Optimized geometry and electronic structure of three-dimensional β-graphyne[J]. Journal of Semiconductors, 2015, 36(7): 072002. doi: 10.1088/1674-4926/36/7/072002 ****Y Pei, H B Wu, J M Liu. Optimized geometry and electronic structure of three-dimensional β-graphyne[J]. J. Semicond., 2015, 36(7): 072002. doi: 10.1088/1674-4926/36/7/072002.
      Citation:
      Yang Pei, Haibin Wu, Jingmin Liu. Optimized geometry and electronic structure of three-dimensional β-graphyne[J]. Journal of Semiconductors, 2015, 36(7): 072002. doi: 10.1088/1674-4926/36/7/072002 ****
      Y Pei, H B Wu, J M Liu. Optimized geometry and electronic structure of three-dimensional β-graphyne[J]. J. Semicond., 2015, 36(7): 072002. doi: 10.1088/1674-4926/36/7/072002.
      shu

      Optimized geometry and electronic structure of three-dimensional β-graphyne

      DOI: 10.1088/1674-4926/36/7/072002
      • 1.

        State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

      • 2.

        Beijing Orient Institute of Measurement & Test, Beijing 100094, China

      • Received Date: 2014-10-29
      • Accepted Date: 2015-02-05
      • Published Date: 2015-01-25

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