Unusual structural and electronic properties of porous silicene and germanene: insights from first-principles calculations
- Yi Ding^{1}Email author and
- Yanli Wang^{2}
https://doi.org/10.1186/s11671-014-0704-3
© Ding and Wang; licensee Springer. 2015
Received: 4 December 2014
Accepted: 23 December 2014
Published: 27 January 2015
Abstract
Using first-principles calculations, we investigate the geometric structures and electronic properties of porous silicene and germanene nanosheets, which are the Si and Ge analogues of α−graphyne (referred to as silicyne and germanyne). It is found that the elemental silicyne and germanyne sheets are energetically unfavourable. However, after the C-substitution, the hybrid graphyne-like sheets (c-silicyne/c-germanyne) possess robust energetic and dynamical stabilities. Different from silicene and germanene, c-silicyne is a flat sheet, and c-germanyne is buckled with a distinct half-hilled conformation. Such asymmetric buckling structure causes the semiconducting behaviour into c-germanyne. While in c-silicyne, the semimetallic Dirac-like property is kept at the nonmagnetic state, but a spontaneous antiferromagnetism produces the massive Dirac fermions and opens a sizeable gap between Dirac cones. A tensile strain can further enhance the antiferromagnetism, which also linearly modulates the gap value without altering the direct-bandgap feature. Through strain engineering, c-silicyne can form a type-II band alignment with the MoS _{2} sheet. The combined c-silicyne/MoS _{2} nanostructure has a high power conversion efficiency beyond 20% for photovoltaic solar cells, enabling a fascinating utilization in the fields of solar energy and nano-devices.
Keywords
Si/Ge nanosheet Tunable bandgap Solar energy applicationBackground
Since the discovery of graphene, two-dimensional (2D) carbon nanostructures, due to their superior physical properties, have attracted substantial concerns from the fields of nano-sciences and nano-materials [1-3]. As a 2D carbon nanosheet, graphene is made of s p ^{2}-hybridized C atoms that are regularly arranged in a honeycomb lattice. The p _{ z } orbitals of C atoms are half-filled in graphene, which results in the Dirac-like electronic structure with a semimetallic feature [2,4]. Derived from graphene, several 2D carbon allotropes have been proposed [5]. Among them, a porous carbon sheet called graphyne, which is made of both s p ^{2}- and sp-hybridized C atoms, becomes a rising star on the horizon of graphene-related studies [6,7]. In the graphyne sheet, sp-hybridized C atoms form acetylene bonds to link the s p ^{2}-hybridized ones. Depending on the ratio of sp constitute, graphyne can be generally classified into the α, β and γ types [8]. In the α type, each acetylene bond links one s p ^{2}-hybridized C atom, while in the β and γ types, it links a pair and a hexagon of s p ^{2}-hybridized C atoms, respectively [8-11]. The α type (α-graphyne) is a representative system for graphyne, which keeps the same hexagonal symmetry as graphene [12-16]. Alpha-graphyne can be regarded as an amplified graphene by inserting additional acetylene bonds into the place of C-C bonds. The semimetallic behaviour is still presented in the sheet [12-15], and the corresponding one-dimensional graphyne nanoribbons also possess similar electronic properties to the graphene ones [15,16]. Besides these common types of graphyne, theoretical studies also predict the existence of other possible structures, such as graphdiyne [17,18], 6,6,12-graphyne [10,19], δ-graphyne [20] and so on. In the experiments, graphdiyne and γ−graphyne have been synthesized through the metal-catalyzed cross-coupling reaction [21,22]. The graphdiyne-based nanotubes and nanowires have also been fabricated by the special templated synthesis method [23,24]. Experimenters further find the doping of graphdiyne benefits the photoconversion processes, which raises the power conversion efficiency of solar cells [25,26].
Very recently, silicene and germanene nanosheets, which are the Si and Ge counterparts of graphene, have been produced in the experiments [27,28]. Different from graphene, the basal planes of silicene and germanene are buckled with a chair-like buckled conformation [29]. The Dirac-like electronic structures are still present in these buckled sheets [30]. A lots of investigations have been performed on silicene and germanene [31-45], which are found to possess several peculiar characteristics, such as electric-field/substrate-induced gaps [31-35], strain-induced self-dopings [36-39], high-efficient thermoelectric performances [40-42], and promising applications for Li batteries [43-45]. However, so far, the information about the porous silicene and germanene, especially the graphyne-like Si and Ge ones (which we refer to as silicyne and germanyne thereafter), is still unknown. What are favourable structures for these porous sheets? How about their stability comparing to other 2D Si/Ge nanosheets? Do they possess particular electronic properties? To address these issues, we perform a comprehensive first-principles investigation on silicyne and germanyne, for which the unusual atomic structures and electronic properties are revealed in detail.
Methods
The first-principles calculations are performed by the VASP code with projector augmented wave pseudopotentials and plane-wave basis sets [46,47]. The cutoff energy of plane-wave basis is set to 500 eV, and a vacuum layer up to 15 Å is utilized to simulate the isolated 2D sheet. The Monkhorst-Pack scheme is adopted to sample the Brillouin zone, which uses a 9×9×1 and 15×15×1k-mesh in the relaxed and static calculations, respectively. During the structural relaxation, the Perdew-BurkeErnzerhof (PBE) exchange and correlation (XC) functional are used. All the lattice constants as well as atomic coordinates are fully optimized until the convergence of force on each atom is less than 0.01 eV/Å. The hybrid XC functional of Heyd-Scuseria-Ernzerhof (HSE) is also used in the band structure calculations, which adopts the HSE06 form with a screening parameter of 0.11 bohr ^{−1} [48]. In view of the large computing resources required for the hybrid functional, HSE calculations are performed by the FHI-aims code with a numeric local orbital basis set [49]. We find that the two codes give consistent results despite of the basis set difference. The dynamical stabilities of nanosheets are studied by the Phonopy code [50], which is performed on a supercell with 4×4 units.
Results and discussion
Structural stability
The cohesive energies of different nanosheets in the unit of eV per atom
Nanosheets | Energies |
---|---|
Graphene | −7.95 |
Graphyne | −7.03 |
Silicene | −3.95 |
Silicyne | −3.11 |
Germanene | −2.60 |
SiC nanosheet | −5.97 |
c-Silicyne | −6.09 |
GeC | −4.91 |
c-Germanyne | −5.52^{ a }/ −5.55^{ b } |
The C-substituted silicyne (c-silicyne) can be formed by inserting −C≡C− (acetylene part) into the place of Si-Si bonds of silicene sheet, as shown in Figure 1c. In the calculations, a buckled sheet is initially set for c-silicyne, but the optimized structure becomes a flat plane akin to graphyne. The C-C distance in c-silicyne is 1.24 Å, which is a typical value for the C-C triple bond. The Si-C distance is 1.76 Å, also close to the Si-C bond length in a hexagonal SiC sheet. As shown in Table 1, the cohesive energy of c-silicyne is −6.09 eV, which is about 3 eV smaller than that of elemental silicyne and even lower than that of the SiC sheet (−5.97 eV). Comparing to graphyne (−7.03 eV), the discrepancy in the cohesive energy stems from the bond difference between c-silicyne and graphyne. In the primitive cell of c-silicyne, it contains six Si-C bonds and three C ≡C bonds, while in graphyne the C-C bonds replace the Si-C ones. The energy difference between C-C and Si-C bonds (Δ E _{CC−SiC}) can be evaluated from the cohesive energy difference between graphene and SiC sheets, which is 3/2Δ E _{CC−SiC}=E _{coh}(graphene)−E _{coh}(SiC)=−1.98 eV. Based on this bond difference, the discrepancy of cohesive energy between graphyne and c-silicyne would be E _{coh}(graphyne)−E _{coh}(c−silicyne)=3/4Δ E _{CC−SiC}=−0.99 eV, which agrees well with the first-principles result of −0.94 eV. Thus, owing to the C-substitution, the weaker Si-Si and Si ≡Si bonds are replaced by the Si-C and C ≡C ones, which greatly enhances the energetic stability of silicyne. Moreover, the phonon calculations in Figure 1d show that the c-silicyne sheet has no soft modes as a dynamically stable system. The good energetic and dynamical stabilities imply that the c-silicyne could be possibly synthesized experimentally. It is found that the acetylene part in c-silicyne induces high frequencies around the 2,000 cm ^{−1}. These modes are from the stretching vibration of C ≡C bonds, which would be a Raman signature for the finding of c-silicyne [51,52].
Electronic structures
For c-germanyne, its flat conformation has a similar electronic property to c-silicyne as shown in the inset of Figure 4c. However, the half-hilled conformation discards the semimetallic feature in c-germanyne, transforming it into a semiconductor as shown in Figure 4c. The valence band maximum (VBM) and conduction band minimum (CBM) are both at the K point, which causes a direct bandgap with the PBE value of 0.86 eV. Such gap opening is due to the breaking of sublattice symmetry by the half-hilled buckling in c-germanyne, whose VBM and CBM are located at different Ge atoms as shown in Figure 4e,f. The PDOSs analysis shows that the p _{ z } orbitals of Ge _{ u } atoms compose the top valence band and the Ge _{ f } p _{ z } ones contribute to the bottom conduction band. As indicated in Figure 2f, the Ge _{ u } atoms are buckled out of plane, while the Ge _{ f } ones stay in the same plane with neighbouring C atoms. The corresponding angle of ∠ _{ C−G e−C } is 104° and 120° for the Ge _{ u } and Ge _{ f } atoms, respectively. Thus, the hybridization of Ge _{ u } atom possesses evident s p ^{3} composition, while the Ge _{ f } one has a pure s p ^{2} hybridization. Since the s p ^{3} hybridization is more favourable than the s p ^{2} one for Ge element, the p _{ z } orbital of Ge _{ u } atom is occupied while the Ge _{ f } one is empty. Therefore, the asymmetric buckling results in two inequivalent Ge atoms, which causes a semiconducting behaviour into c-germanyne.
Strain engineering
Under the strains, an arc-shaped variation of bandgap is found in c-germanyne. As shown in Figure 6d, the tensile strain firstly decreases the gap value, which reaches the minimum of 0.79 eV at the 0.03 strain. Then, the bandgap rises with the increasing strain. It gets to the maximum of 1.52 eV at the critical 0.08 strain. Such non-monotonic variation is attributed to two competitive factors of bandgap in c-germanyne. One is the buckling effect in the structure, which helps the opening of bandgap. While the other is the localization effect induced by strains, which lowers the orbital overlapping. Consequently, the band widths are narrowed and the corresponding bandgap is broadened by the localization effect. Under the strains, the buckles of Ge atoms are weakened, which causes the decrease of bandgap under a small tension. When the strain is increasing, the localization effect becomes more pronounced under the large tension, which increases the bandgap. Thus, the strain-modulated c-germanyne possesses an arc-shaped variation for the bandgap.
For c-silicyne, its NM state is always a semimetal under the strains, similar to the graphene case [61]. While for AFM state, the stability of antiferromagnetism is enhanced under the tensions. The strain-induced localization effect reduces the electronic hopping integral t, which leads to a larger value U/t and avails to a stronger antiferromagnetism. As shown in the inset of Figure 6c, at the 0.02 strain, the magnetic energy (E _{ M }=E _{AFM}−E _{NM}) of c-silicyne is increased to 0.026 eV/unit, which is approximately the energy of thermal fluctuation at room temperature (E _{ T }∼k _{ B } T=0.0258 eV). When the strain grows up to 0.08 to 0.09, the E _{ M } is even larger than 0.1 eV. It indicates that the AFM state has a robust stability in these strained sheets. Accompanied with the strengthening of AFM state, the bandgap of c-silicyne is also raised. Since the opening gap is dependent on the antiferromagnetism, a monotonic increasing of bandgap is obtained as shown in Figure 6c. The linear relationship exists between the bandgap and tensile strain, and the slope corresponds to a bandgap-deformation potential of 4.39 eV/Å for c-silicyne. At the 0.09 strain, the gap value of c-silicyne can get to 1.46 eV without altering the direct-bandgap feature, suggesting the promising applications for solar energy.
Solar cell applications
Here, the band-fill factor (β _{FF}) is adopted to 0.65, the open-circuit voltage (V _{oc}) is set to \({E_{g}^{d}}-\Delta E_{c}-0.3\), where \({E_{g}^{d}}\) is the bandgap of donor, Δ E _{ c } is the conduction band offset between the acceptor and donor, and 0.3 is an empirical factor for energy conversion kinetics [66,67]. The integral in the numerator is the short circuit current J _{sc} calculated in a limit external quantum efficiency of 100% [67,68], and the denominator is the integrated AM 1.5 solar energy flux, which amounts to 1,000 W/m ^{2} [62-66]. We find that under the strains of 0.06 to 0.09, the η of c-silicyne/MoS _{2} heterostructure can exceed 20% as shown in Figure 7d. When a 0.06 strain is applied to c-silicyne, the power conversion efficiency η reaches the maximum value of 23.1%. Under larger strains of 0.7 to 0.9, η becomes 22.5%, 22.4% and 21.4%, respectively. These high power conversion efficiencies are comparable to those of recent proposed phosphorene and graphene-like Si-C nanostructures [62-65]. Therefore, the c-silicyne sheet would be a fascinating nanomaterial for solar energy applications, especially in thin-film photovoltaic systems.
Finally, we briefly discuss the possible synthesis approach for c-silicyne. Benefited from the recent development of metal-assisted coupling methods, several porous nanostructures have been successfully fabricated by self-assembling the molecular building blocks [21,22,69]. Through changing different molecular precursors and metal substrates, the experimenters can design the morphology of novel porous nanosheets and manufacture the well-defined nanostructures [70-74]. It seems the ethynyl(methylene)silyl [75], which contains both Si-C and Si-C ≡C parts in its molecular structure, will be a possible molecular building block for silicyne. After choosing a suitable metal surface as substrates, the metal-catalyzed cross-coupling reaction, which has been used in the synthesis of graphyne [21,22], would be also valid to fabricate the silicyne sheet.
Conclusions
In summary, we have systematically investigated the structures and properties of porous silicene and germanene nanosheets, i.e. silicyne and germanyne ones. We find that the C-substitution could significantly enhance the energetic and dynamical stabilities of these systems. Different from silicene, the c-silicyne sheet prefers a flat plane, while the c-germanyne favors a unique half-hilled buckled conformation. Such half-hilled conformation brings a semiconducting behaviour into c-germanyne, which is distinct from the graphyne and germanene nanosheets. For c-silicyne, it exhibits a zero-bandgap semimetallic behaviour at the nonmagentic state but becomes a direct-bandgap semiconductor at the antiferromagnetic state. Under tensile strains, the antiferromagnetism in c-silicyne could be strengthened and the bandgap is also linearly raised. More interestingly, when the strained c-silicyne sheet is superimposed onto a MoS _{2} monolayer, the heterostructure can be a promising solar-cell material with high power conversion efficiencies exceeding 20%. Our studies demonstrate that the silicyne and germanyne nanosheets possess peculiar electronic and magnetic properties, which have potential applications in the fields of solar energy and nano-devices.
Declarations
Acknowledgements
Some of the calculations were performed in the Shanghai Supercomputer Center of China. Authors acknowledge the support from the National Natural Science Foundation of China under Grant No. 11474081, 11104052, and 11104249.
Authors’ Affiliations
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