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Band Gap Characters and Ferromagnetic/Antiferromagnetic Coupling in Group-IV Monolayers Tuned by Chemical Species and Hydrogen Adsorption Configurations
© Yu et al. 2015
- Received: 26 June 2015
- Accepted: 6 August 2015
- Published: 4 September 2015
One-side semihydrogenated monolayers of carbon, silicon, germanium, and their binary compounds with different configurations of hydrogen atoms are investigated by density functional theory. Among three considered configurations, zigzag, other than the most studied chair configuration, is energetically the most favorable structure of one-side semihydrogenation. Upon semihydrogenation, the semimetallic silicene, germanene, and SiGe become semiconductors, while the band gap in semiconducting SiC and GeC is reduced. Semihydrogenated silicene, germanene, SiGe, and GeC with chair configuration are found to be ferromagnetic semiconductors. For semihydrogenated SiC, it is ferromagnetic when all hydrogen atoms bond with silicon atoms, while an antiferromagnetic coupling is predicted when all hydrogen atoms bond with carbon atoms. The effect of interatomic distance between two neighboring magnetic atoms to the ferromagnetic or antiferromagnetic coupling is studied. For comparison, properties of one-side and both-side fully hydrogenated group-IV monolayers are also calculated. All fully hydrogenated group-IV monolayers are nonmagnetic semiconductors with band gaps larger than those of their semihydrogenated counterparts.
- Group-IV monolayers
- Band gap
- FM/AFM coupling
Currently, tremendous attention has been focused on two-dimensional (2D) monolayers composed of group-IV elements, such as carbon, silicon, and germanium. Theoretical and experimental studies show that silicon [1–16] and germanium [4, 17–21] can form graphene-like structures, namely silicene and germanene. The first hypothesis of silicene and germanene can be traced back to 1994 , but the experimental synthesis becomes possible only in recent years. Fabrications of silicene on various substrates such as silver [6–13], iridium , and zirconium diboride  and germanene on gold , platinum , and gallium arsenide  have been reported. Different from graphene that prefers a perfectly planar structure, silicene and germanene are stabilized by a low-buckled structure. They both, however, resemble the electronic characteristic of graphene, i.e., an energy band crossing at the Dirac cone and linear dispersion around the crossing [4, 5, 13, 23–26]. By applying an external electric field perpendicular to the silicene or germanene lattices [27–32], the band gap of silicene and germanene can be opened. The opening of the band gap as well as introducing the quantum anomalous Hall effect in silicene or germanene can also be obtained by decorating 3d or 5d transition metal atoms [33–36] or small organic molecule adsorption . In addition to silicene and germanene which consist only one type of element, monolayer compounds consisting two types of elements are also of great interest, including planar silicon carbide (SiC) [26, 38–43] and germanium carbide (GeC) [26, 43] which open a band gap to become semiconducting, and low-buckled silicon germanide (SiGe) [26, 44, 45] with a band structure similar to those of graphene and silicene.
With good feasibility, reversibility, and controllability [46, 47], hydrogenation is a promising method to further tune the properties of 2D monolayers and to expand the scope of their application. Previous work found that different ratio of hydrogenation significantly changes the electronic and magnetic properties of group-IV monolayers [44, 45, 48–62]. Full hydrogenation opens a band gap for silicene and germanene [53–59] and enlarges the band gap of monolayer SiC [44, 59–61]. Among boat, chair, and zigzag configurations of fully hydrogenated silicene [53, 56, 58], germanene , and monolayer SiC [60, 61], chair configuration has the lowest energy. After full hydrogenation, hydrogen atoms on one side can be removed to achieve one-side semihydrogenation on the other side. Based on phonon calculation, Wang et al. confirmed the dynamical stability of semihydrogenated silicene and germanene with chair configuration and they reported that both silicene and germanene become ferromagnetic semiconductors upon semihydrogenation with chair configuration . Ferromagnetism in semihydrogenated silicene with chair configuration was predicted using first principles by other groups as well [50, 56, 57]. In monolayer SiC, ferromagnetism or antiferromagnetism can be induced by semihydrogenation with chair configuration when hydrogen atoms bond with silicon atoms or carbon atoms, respectively, and this kind of hydrogenation slightly reduces the band gap of monolayer SiC [44, 48]. Zhou et al. stated that semihydrogenated monolayer SiGe with chair configuration is a ferromagnetic semiconductor, no matter hydrogen atoms bond with silicon or germanium atoms . Ma et al. found ferromagnetism in semihydrogenated monolayer GeC with chair configuration .
Up to now, most studies of semihydrogenated group-IV monolayers are limited to the chair configuration [44, 45, 48–50, 56, 57]. One-side semihydrogenation with boat and zigzag configurations is only examined in silicene . The energetic, electronic, and magnetic properties of semihydrogenated germanene, SiC, GeC, and SiGe with boat and zigzag configurations still remain unclear. There is, however, neither theoretical nor experimental evidence can prove the preference of chair configuration to boat, zigzag, and other configurations. In this work, based on our first-principle calculations on the total energies of one-side semihydrogenated silicene, germanene, SiC, GeC, and SiGe monolayers with boat, chair, and zigzag configurations, zigzag configuration is shown to have the lowest energy for all considered group-IV monolayers. The effect of semihydrogenation to the electronic properties of semihydrogenated group-IV monolayers are revealed by band structure calculations. For silicene, germanene, and monolayer SiGe, semihydrogenation opens a band gap, while for monolayer SiC and GeC, the semiconducting band gap is reduced by semihydrogenation. Ferromagnetism or antiferromagnetism exists in semihydrogenated group-IV monolayers only with chair configuration. The distance between two neighboring magnetic atoms is a factor that influences whether ferromagnetic or antiferromagnetic coupling forms. If further hydrogenated to full hydrogenation, all semihydrogenated group-IV monolayers become nonmagnetic semiconductors with larger band gaps.
All calculations are performed using the pseudopotential plane-wave method as implemented in the CASTEP code . The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE)  parametrization and norm-conserving pseudopotential are used for most calculations unless mentioned otherwise. The cut-off energy for the plane-wave basis set is 1000 eV. To carry out the Brillouin-zone integration, 12 × 12 × 1 Monkhorst-Pack k-point grid  is used for one-side semihydrogenated silicene, germanene, SiGe, SiC, and GeC monolayers with chair configuration and 6 × 12 × 1 k-point grid for boat and zigzag configurations. The unit cell of semihydrogenated group-IV monolayers with boat or zigzag configuration is twice as large as the unit cell of chair configuration. To avoid spurious interactions between adjacent layers, a vacuum space of 20 Å is introduced along the direction perpendicular to the 2D plane. Semi-empirical dispersion interaction correction  with TS method  is adopted to treat the van der Waals interaction of the layered system. The lattice parameters and atomic positions are fully relaxed under Broyden-Fletceher-Goldfarb-Shanno (BFGS)  scheme until the energy difference between two steps is smaller than 5 × 10−6 eV/atom, and the maximum force is smaller than 0.01 eV/Å. All the computational parameters mentioned above are carefully tested to achieve convergence of the total energy. There is no spin-orbit coupling implemented in the CASTEP code.
Structure and Stability
Lattice constants, buckling constants, formation energies (E f ), band gap energies (E g ), and magnetism of one-side semihydrogenated silicene, germanene, SiGe, SiC, and GeC monolayers with boat, chair, and zigzag configurations. The NM, FM, and AFM represent nonmagnetism, ferromagnetism, and antiferromagnetism, respectively
Lattice constant (Å)
Buckling constant (Å)
E f (eV)
E g (eV)
FM(e, g, h, i)
Depending on which type of elements hydrogen atoms bond with, there are two possible structures for semihydrogenated monolayer SiGe with chair configuration. The structure in which all hydrogen atoms bond with silicon atoms is denoted by H-SiGe, and the structure in which all hydrogen atoms bond with germanium atoms is denoted by SiGe-H. For semihydrogenated monolayer SiC and GeC with chair configuration, the same denotation is used. In each case of semihydrogenated monolayer SiGe, SiC, and GeC with chair configuration, formation energies are different when hydrogen atoms are bonded with different group-IV atoms, indicating a bonding preference of hydrogen to different group-IV elements. Formation energies of H-SiGe, SiC-H, and GeC-H are lower than those of SiGe-H, H-SiC, and H-GeC, respectively. Thus, hydrogen atoms have higher bonding preference to silicon atoms than to germanium atoms in monolayer SiGe and have higher preference to carbon atoms than to silicon (germanium) atoms in monolayer SiC (GeC), i.e., hydrogen atoms prefer to bond with the lighter element in the monolayer group-IV binary compound. For monolayer SiGe, Zhou et al. found the same bonding preference as us, and they believed this bonding preference facilitates the synthesis of one-side semihydrogenated SiGe with chair configuration . Indeed, due to the different types of elements in the unit cells of monolayer SiGe, SiC, and GeC, it seems that when hydrogenation process occurs, hydrogen atoms will tend to bond with one particular type of atoms to form chair configuration. Our calculation, however, gives an energetic order of zigzag < boat < chair, in semihydrogenated silicene, germanene, as well as binary SiGe, SiC, and GeC monolayers. Formation energy of boat configuration is slightly higher than that of zigzag configuration, while formation energy of chair configuration is much higher than those of boat and zigzag configurations (see Table 1). Exchange-correlation functional of local density approximation (LDA) and ultrasoft pseudopotential are employed to recalculate the energies of semihydrogenated silicene and monolayer SiC for comparison. A same order of energies is confirmed. In fact, this order has also been found for semihydrogenated graphene and semifluorinated graphene in our previous DFT calculation . Therefore, zigzag configuration, other than the most studied chair configuration, has the lowest formation energy among different configurations of one-side semihydrogenated group-IV monolayers. If directly hydrogenating one side of group-IV monolayers, zigzag configuration is more likely to appear than chair and boat configurations.
Formation energies (E f ) and band gap energies (E g ) of one-side and both-side fully hydrogenated silicene, germanene, SiGe, SiC, and GeC monolayers with chair, boat, and zigzag configurations
E f (eV)
E g (eV)
Band structure calculation is carried out for semihydrogenated group-IV monolayers with boat, chair, and zigzag configurations. According to our analysis of the energetic stability, chair configuration is not energetically the most favorable among the three considered configurations of one-side semihydrogenation. We present, for the first time, the band structures of one-side semihydrogenated germanene, SiGe, SiC, and GeC monolayers with boat and zigzag configurations.
Semihydrogenated silicene and germanene with boat and zigzag configurations are semiconducting. Indirect band gaps of 1.105 and 0.262 eV are predicted for semihydrogenated silicene and germanene with boat configuration, respectively (Fig. 3c, g), while direct band gaps of 0.161 and 0.347 eV are predicted for semihydrogenated silicene and germanene with zigzag configuration, respectively (Fig. 3d, h). A metallic nature was reported by Zhang et al. for semihydrogenated silicene with zigzag configuration , inconsistent with what we found. To confirm our result, LDA and ultrasoft pseudopotential are used to recalculate the electronic structure of semihydrogenated silicene with zigzag configuration and a band dispersion similar to that calculated using GGA and norm-conserving pseudopotential is obtained, with a slightly smaller band gap of 0.132 eV.
Our calculated band gap energies of semihydrogenated silicene and germanene are close to other reported DFT-GGA results [49, 50, 56]. It is well known that DFT calculation at LDA or GGA level underestimates band gap energy. Using HSE06 functional and taking spin-orbit coupling into consideration, Wang et al. calculated band gaps of semihydrogenated silicene and germanene with chair configuration and reported values of 1.74 and 1.32 eV, respectively . Also using HSE06 functional, Zhang et al. stated that band gap energies for semihydrogenated silicene with chair and boat configurations are both 1.79 eV . These reported HSE06 band gap energies are larger than our DFT-GGA results. In addition to hydrogenation, decorating silicene and germanene with transition metal atoms or small organic molecules also opens a band gap and simultaneously induces a quantum anomalous Hall state [33–37]. By applying an external electric field perpendicular to the 2D plane, a band gap increasing with the electric field strength is obtained in silicene and germanene [27, 28, 30, 31].
One-side and both-side fully hydrogenated group-IV monolayers with boat, chair, and zigzag configurations are all semiconductors with band gaps considerably larger than those of their semihydrogenated counterparts. Their band gap energies are listed in Table 2. All both-side fully hydrogenated group-IV monolayers except for fully hydrogenated silicene with chair configuration and fully hydrogenated germanene with zigzag configuration have direct band gaps, while all one-side fully hydrogenated group-IV monolayers as well as fully hydrogenated silicene with chair configuration and fully hydrogenated germanene with zigzag configuration have indirect band gaps. Detailed band structures of fully hydrogenated group-IV monolayers are provided in Additional file 1.
Our spin-polarized calculation shows that one-side semihydrogenated group-IV monolayers with boat and zigzag configurations are non-spin polarized, while semihydrogenated group-IV monolayers with chair configuration are spin polarized. As discussed in “Structure and Stability” section, since zigzag configuration of semihydrogenation is energetically more preferable than boat and chair configurations, it is more probable to obtain nonmagnetic semiconductor with zigzag configuration by direct one-side semihydrogenation to group-IV monolayers. However, when it comes to full hydrogenation, chair configuration has the lowest total energy [53, 56, 58, 60, 61]. Therefore, magnetism in group-IV monolayers must be achieved through the two-step strategy: first fully hydrogenating to get chair configuration on both side, then removing hydrogen atoms from one side to get semihydrogenation with chair configuration on the other side.
Relative total energies (per unit containing one hydrogen atom) of different magnetic states to the energetically most stable states of one-side semihydrogenated group-IV monolayers with chair configuration and Curie temperatures (T C ) of ferromagnetic states. For each material (in each row), the lowest value among total energies of NM, FM, and AFM states is set to 0 meV
T C (K)
Using first-principle calculations, structural, electronic, and magnetic properties of semihydrogenated and fully hydrogenated group-IV monolayers, including silicene, germanene, SiGe, SiC, and GeC, with boat, chair, and zigzag configurations are systematically studied. For semihydrogenated group-IV monolayers, zigzag configuration is found to have the lowest formation energy, while chair configuration is found to have the highest formation energy. For fully hydrogenated group-IV monolayers, energy of one-side hydrogenation is higher than that of both-side hydrogenation. Among boat, chair, and zigzag configurations of both-side full hydrogenation, chair configuration has the lowest energy.
Band structures of semihydrogenated germanene, SiGe, SiC, and GeC monolayers with boat and zigzag configurations are presented for the first time. Band gap opening due to semihydrogenation is predicted in silicene, germanene, and monolayer SiGe, regardless of the arrangement of hydrogen atoms, in contrast to reduced band gaps in semihydrogenated monolayer SiC and GeC. Semihydrogenated group-IV monolayers with boat and zigzag configurations are nonmagnetic, while semihydrogenated group-IV monolayers with chair configuration are magnetic. A two-step strategy is proposed to obtain magnetism in group-IV monolayers: first, fully hydrogenate the group-IV monolayers to get chair configuration on both side; second, remove hydrogen atoms from one side to get chair configuration of semihydrogenation on the other side. The spin moments are mainly carried by the group-IV atoms that are not bonded with hydrogen atoms. Semihydrogenated monolayer SiC with chair SiC-H configuration is an antiferromagnetic semiconductor, while other semihydrogenated group-IV monolayers with chair configuration are all ferromagnetic semiconductors. Our calculations indicate that the interatomic distance between two neighboring magnetic atoms can influence whether ferromagnetism or antiferromagnetism forms. If fully hydrogenated, semihydrogenated group-IV monolayers will become nonmagnetic semiconductors with larger band gaps. Our results will provide guidance for future researches of group-IV monolayer materials suitable for electronic and spintronic applications.
This work is supported by the State Key Development Program of Basic Research of China (Grant No. 2011CB606406), the Science and Technology Commission of Shanghai Municipality, China (Grant No. 14521100606) and the Innovation Program of Shanghai Municipal Education Commission (Grant No. 15ZZ001).
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