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
Background
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
References
- Geim AK, Novoselov KS. The rise of graphene. Nat Mater. 2007; 6(3):183–91.View ArticleGoogle Scholar
- Avouris P, Dimitrakopoulos C. Graphene: synthesis and applications. Mater Today. 2012; 15(3):86–97.View ArticleGoogle Scholar
- Tang Q, Zhou Z. Graphene-analogous low-dimensional materials. Prog Mater Sci. 2013; 58(8):1244–315.View ArticleGoogle Scholar
- Allen MJ, Tung VC, Kaner RB. Honeycomb carbon: a review of graphene. Chem Rev. 2009; 110(1):132–45.View ArticleGoogle Scholar
- Peng Q, Dearden AK, Crean J, Han L, Liu S, Wen X, et al.New materials graphyne, graphdiyne, graphone, and graphane: review of properties, synthesis, and application in nanotechnology. Nanotechnol Sci Appl. 2014; 7:1–29.View ArticleGoogle Scholar
- Ivanovskii AL. Graphynes and graphdyines. Prog Solid State Chem. 2013; 41:1–19.View ArticleGoogle Scholar
- Li Y, Xu L, Liu H, Li Y. Graphdiyne and draphyne: from theoretical predictions to practical construction. Chem Soc Rev. 2014; 43:2572–86.View ArticleGoogle Scholar
- Kim BG, Choi HJ. Graphyne: Hexagonal network of carbon with versatile dirac cones. Phys Rev B. 2012; 86:115435.View ArticleGoogle Scholar
- Zhang Y, Pei Q, Wang C. Mechanical properties of graphynes under tension: a molecular dynamics study. Appl Phys Lett. 2012; 101(8):081909.View ArticleGoogle Scholar
- Chen J, Xi J, Wang D, Shuai Z. Carrier mobility in graphyne should be even larger than that in graphene: a theoretical prediction. J Phys Chem Lett. 2013; 4(9):1443–48.View ArticleGoogle Scholar
- Padilha JE, Fazzio A, da Silva AJR. Directional control of the electronic and transport properties of graphynes. J Phys Chem C. 2014; 118(32):18793–8.View ArticleGoogle Scholar
- Leenaerts O, Partoens B, Peeters F. Tunable double dirac cone spectrum in bilayer α-graphyne. Appl Phys Lett. 2013; 103(1):013105.View ArticleGoogle Scholar
- Ozcelik VO, Ciraci S. Size dependence in the stabilities and electronic properties of α-graphyne and its boron nitride analogue. J Phys Chem C. 2013; 117(5):2175–82.View ArticleGoogle Scholar
- Ducere J-M, Lepetit C, Chauvin R. Carbo-graphite: structural, mechanical, and electronic properties. J Phys Chem C. 2013; 117(42):21671–81.View ArticleGoogle Scholar
- Yue Q, Chang S, Kang J, Tan J, Qin S, Li J. Magnetic and electronic properties of α-graphyne nanoribbons. J Chem Phys. 2012; 136(24):244702.View ArticleGoogle Scholar
- Yue Q, Chang S, Tan J, Qin S, Kang J, Li J. Symmetry-dependent transport properties and bipolar spin filtering in zigzag α-graphyne nanoribbons. Phys Rev B. 2012; 86:235448.View ArticleGoogle Scholar
- Long M, Tang L, Wang D, Li Y, Shuai Z. Electronic structure and carrier mobility in graphdiyne sheet and nanoribbons: theoretical predictions. ACS Nano. 2011; 5(4):2593–600.View ArticleGoogle Scholar
- Niu X, Mao X, Yang D, Zhang Z, Si M, Xue D. Dirac cone in α-graphdiyne: a first-principles study. Nano Res Lett. 2013; 8(1):469.View ArticleGoogle Scholar
- Malko D, Neiss C, Viñes F, Görling A. Competition for graphene: graphynes with direction-dependent dirac cones. Phys Rev Lett. 2012; 108:086804.View ArticleGoogle Scholar
- Zhao M, Dong W, Wang A. Two-dimensional carbon topological insulators superior to graphene. Sci Rep. 2013; 3:3532.Google Scholar
- Li G, Li Y, Liu H, Guo Y, Li Y, Zhu D.Architecture of graphdiyne nanoscale films. Chem Commun. 2010; 46(19):3256–8.View ArticleGoogle Scholar
- Tahara K, Yamamoto Y, Gross DE, Kozuma H, Arikuma Y, Ohta K, et al. Syntheses and properties of graphyne fragments: trigonally expanded dehydrobenzo[12]annulenes. Chem Eur J. 2013; 19(34):11251–60.View ArticleGoogle Scholar
- Li G, Li Y, Qian X, Liu H, Lin H, Chen N, et al.Construction of tubular molecule aggregations of graphdiyne for highly efficient field emission. J Phys Chem C. 2011; 115(6):2611–5.View ArticleGoogle Scholar
- Qian X, Ning Z, Li Y, Liu H, Ouyang C, Chen Q, et al. Construction of graphdiyne nanowires with high-conductivity and mobility. Dalton Trans. 2012; 41(3):730–33.View ArticleGoogle Scholar
- Du H, Deng Z, Lv Z, Yin Y, Yu L, Wu H, et al. The effect of graphdiyne doping on the performance of polymer solar cells. Synth Met. 2011; 161(19):2055–7.View ArticleGoogle Scholar
- Tang H, Hessel CM, Wang J, Yang N, Yu R, Zhao H, et al. Two-dimensional carbon leading to new photoconversion processes. Chem Soc Rev. 2014; 43(13):4281–99.View ArticleGoogle Scholar
- Vogt P, De Padova P, Quaresima C, Avila J, Frantzeskakis E, Asensio MC, et al. Silicene: compelling experimental evidence for graphenelike two-dimensional silicon. Phys Rev Lett. 2012; 108(15):155501.View ArticleGoogle Scholar
- Daila ME, Xian L, Cahangirov S, Rubio A, Lay GL. Germanene: a novel two-dimensional germanium allotrope akin to graphene and silicene. New J Phys. 2014; 16(9):095002.View ArticleGoogle Scholar
- Jose D, Datta A. Structures and chemical properties of silicene: unlike graphene. Acc Chem Res. 2014; 47(2):593–602.View ArticleGoogle Scholar
- Roome NJ, Carey JD. Beyond graphene: Stable elemental monolayers of silicene and germanene. ACS Appl Mater Interfaces. 2014; 6(10):7743–50.View ArticleGoogle Scholar
- Drummond N, Zolyomi V, Fal’Ko V. Electrically tunable band gap in silicene. Phys Rev B. 2012; 85(7):075423.View ArticleGoogle Scholar
- Houssa M, van den Broek B, Scalise E, Pourtois G, Afanas’ ev V, Stesmans A. An electric field tunable energy band gap at silicene/(0001) ZnS interfaces. Phys Chem Chem Phys. 2013; 15(11):3702–5.View ArticleGoogle Scholar
- An X-T, Zhang Y-Y, Liu J-J, Li S-S. Quantum spin hall effect induced by electric field in silicene. Appl Phys Lett. 2013; 102(4):043113.View ArticleGoogle Scholar
- Zhu J, Schwingenschlogl U. Structural and electronic properties of silicene on MgX2 (X = CI, Br, and I). ACS Appl Mater Interfaces. 2014; 6(14):11675–81.Google Scholar
- Li X, Wu S, Zhou S, Zhu Z. Structural and electronic properties of germanene MoS2 monolayer and silicene/MoS2 monolayer superlattices. Nano Res Lett. 2014; 9(1):110.Google Scholar
- Kaloni T, Schwingenschlögl U. Stability of germanene under tensile strain. Chem Phys Lett. 2013; 583:137–40.View ArticleGoogle Scholar
- Wang Y, Ding Y. Strain-induced self-doping in silicene and germanene from first-principles. Solid State Commun. 2013; 155:6–11.View ArticleGoogle Scholar
- Kaloni T, Cheng Y, Schwingenschlögl U. Hole doped dirac states in silicene by biaxial tensile strain. J Appl Phys. 2013; 113(10):104305.View ArticleGoogle Scholar
- Qin R, Zhu W, Zhang Y, Deng X. Uniaxial strain-induced mechanical and electronic property modulation of silicene. Nano Res Lett. 2014; 9(1):521.View ArticleGoogle Scholar
- Zberecki K, Wierzbicki M, Barnaś J, Swirkowicz R. Thermoelectric effects in silicene nanoribbons. Phys Rev B. 2013; 88(11):115404.View ArticleGoogle Scholar
- Zberecki K, Swirkowicz R, Wierzbicki M, Barnaś J. Enhanced thermoelectric efficiency in ferromagnetic silicene nanoribbons terminated with hydrogen atoms. Phys Chem Chem Phys. 2014; 16:12900–08.View ArticleGoogle Scholar
- Yang K, Cahangirov S, Cantarero A, Rubio A, D’Agosta R. Thermoelectric properties of atomically thin silicene and germanene nanostructures. Phys Rev B. 2014; 89(12):125403.View ArticleGoogle Scholar
- Tritsaris GA, Kaxiras E, Meng S, Wang E. Adsorption and diffusion of lithium on layered silicon for Li-ion storage. Nano Lett. 2013; 13(5):2258–63.View ArticleGoogle Scholar
- Setiadi J, Arnold MD, Ford MJ. Li-ion adsorption and diffusion on two-dimensional silicon with defects: a first principles study. ACS Appl Mater Interfaces. 2013; 5(21):10690–95.View ArticleGoogle Scholar
- Tan X, Cabrera CR, Chen Z. Metallic BSi3 silicene: a promising high capacity anode material for lithium-ion batteries. J Phys Chem C. 2014; ASAP:10–1021503597.Google Scholar
- Kresse G, Furthmuller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci. 1996; 6(1):15–50.View ArticleGoogle Scholar
- Kresse G, Furthmuller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B. 1996; 54(16):11169–86.View ArticleGoogle Scholar
- Brothers EN, Izmaylov AF, Normand JO, Barone V, Scuseria GE. Accurate solid-state band gaps via screened hybrid electronic structure calculations. J Chem Phys. 2008; 129(1):011102.View ArticleGoogle Scholar
- Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren X, et al. Ab initio molecular simulations with numeric atom-centered orbitals. Comput Phys Commun. 2009; 180(11):2175–96.View ArticleGoogle Scholar
- Togo A, Oba F, Tanaka I. First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures. Phys Rev B. 2008; 78:134106.Google Scholar
- Popov VN, Lambin P. Theoretical raman fingerprints of α-, β-, and γ-graphyne. Phys Rev B. 2013; 88:075427.View ArticleGoogle Scholar
- Perkgoz NK, Sevik C. Vibrational and thermodynamic properties of α-, β-, γ- and 6, 6, 12-graphyne structures. Nanotechnology. 2014; 25(18):185701.View ArticleGoogle Scholar
- Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, et al. Quantum espresso: a modular and open-source software project for quantum simulations of materials. J Phys: Condens Matter. 2009; 21(39):395502–119.Google Scholar
- Janesko BG, Henderson TM, Scuseria GE. Screened hybrid density functionals for solid-state chemistry and physics. Phys Chem Chem Phys. 2009; 11(3):443–54.View ArticleGoogle Scholar
- Barone V, Hod O, Peralta JE, Scuseria GE. Accurate prediction of the electronic properties of low-dimensional graphene derivatives using a screened hybrid density functional. Acc Chem Res. 2011; 44(4):269–79.View ArticleGoogle Scholar
- Lee S-H, Kim S, Kim K. Semimetal-antiferromagnetic insulator transition in graphene induced by biaxial strain. Phys Rev B. 2012; 86(15):155436.View ArticleGoogle Scholar
- Longuinhos R, Moujaes EA, Alexandre SS, Nunes RW. Theoretical chemistry of α-graphyne: functionalization, symmetry breaking, and generation of dirac-fermion mass. Chem Mater. 2014; 26(12):3701–08.View ArticleGoogle Scholar
- Li J, Shan Z, Ma E. Elastic strain engineering for unprecedented materials properties. MRS Bull. 2014; 39(02):108–14.View ArticleGoogle Scholar
- Cadelano E, Palla PL, Giordano S, Colombo L. Elastic properties of hydrogenated graphene. Phys Rev B. 2010; 82(23):235414.View ArticleGoogle Scholar
- Wang Y, Ding Y. Mechanical and electronic properties of stoichiometric silicene and germanene oxides from first-principles. Phys Status Solidi-RRL. 2013; 7(6):410–3.View ArticleGoogle Scholar
- Choi S-M, Jhi S-H, Son Y-W. Effects of strain on electronic properties of graphene. Phys Rev B. 2010; 81:081407.View ArticleGoogle Scholar
- Guo H, Lu N, Dai J, Wu X, Zeng XC. Phosphorene nanoribbons, phosphorus nanotubes and van der Waals multilayers. J Phys Chem C. 2014; 118(51):14051–9.View ArticleGoogle Scholar
- Dai J, Zeng XC. Bilayer phosphorene: effect of stacking order on bandgap and its potential applications in thin-film solar cells. J Phys Chem Lett. 2014; 5(7):1289–93.View ArticleGoogle Scholar
- Dai J, Wu X, Yang J, Zeng XC. AlxC monolayer sheets: two-dimensional networks with planar tetracoordinate carbon and potential applications as donor materials in solar cell. J Phys Chem Lett. 2014; 5:2058–65.View ArticleGoogle Scholar
- Zhou L-J, Zhang Y-F, Wu L-M. SiC2 siligraphene and nanotubes: novel donor materials in excitonic solar cells. Nano Lett. 2013; 13(11):5431–6.Google Scholar
- Bernardi M, Palummo M, Grossman JC. Semiconducting monolayer materials as a tunable platform for excitonic solar cells. ACS Nano. 2012; 6(11):10082–9.View ArticleGoogle Scholar
- Scharber MC, Mühlbacher D, Koppe M, Denk P, Waldauf C, Heeger AJ, et al. Design rules for donors in bulk-heterojunction solar cells: towards 10% energy-conversion efficiency. Adv Mater. 2006; 18(6):789–94.View ArticleGoogle Scholar
- Dennler G, Scharber MC, Ameri T, Denk P, Forberich K, Waldauf C, et al. Design rules for donors in bulk-heterojunction tandem solar cells towards 15% energy-conversion efficiency. Adv Mater. 2008; 20(3):579–83.View ArticleGoogle Scholar
- Bieri M, Treier M, Cai J, Ait-Mansour K, Ruffieux P, Groning O, et al. Porous graphenes: two-dimensional polymer synthesis with atomic precision. Chem Commun. 2009; 45:6919–21.View ArticleGoogle Scholar
- Bieri M, Nguyen M-T, Groning O, Cai J, Treier M, Ait-Mansour K, et al. Two-dimensional polymer formation on surfaces: insight into the roles of precursor mobility and reactivity. J Am Chem Soc. 2010; 132(46):16669–76.View ArticleGoogle Scholar
- Cardenas L, Gutzler R, Lipton-Duffin J, Fu C, Brusso JL, Dinca LE, et al. Synthesis and electronic structure of a two dimensional [small pi]-conjugated polythiophene. Chem Sci. 2013; 4(8):3263–8.View ArticleGoogle Scholar
- Eichhorn J, Nieckarz D, Ochs O, Samanta D, Schmittel M, Szabelski PJ, et al. On-surface ullmann coupling: the influence of kinetic reaction parameters on the morphology and quality of covalent networks. ACS Nano. 2014; 8(8):7880–9.View ArticleGoogle Scholar
- Landers J, Cherioux F, Santis MD, Bendiab N, Lamare S, Magaud L, et al. Convergent fabrication of a nanoporous two-dimensional carbon network from an aldol condensation on metal surfaces. 2D Mater. 2014; 1(3):034005.View ArticleGoogle Scholar
- Sumpter BG, Liang L, Nicolai A, Meunier V. Interfacial properties and design of functional energy materials. Acc Chem Res. 2014; 47(11):3395–405.View ArticleGoogle Scholar
- CSID:9019624. http://www.chemspider.com/Chemical-Structure.9019624.html. Accessed 16 Jan 2015.
Copyright
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.