From a fullerene-like cage (SiC)12 to novel silicon carbide nanowires: An ab initio study

Chemical Physics Letters 442 (2007) 384–389 www.elsevier.com/locate/cplett

From a fullerene-like cage (SiC)12 to novel silicon carbide nanowires: An ab initio study Jiling Li

a,*

, Yueyuan Xia a, Mingwen Zhao a, Xiangdong Liu a, Chen Song a, Lijuan Li a, Feng Li b, Boda Huang c a

School of Physics and Microelectronics, Shandong University, Jinan, Shandong 250100, China b Department of Physics, Taishan University, Taian, Shandong 271021, China c School of Information Science and Engineering, Shandong University, Jinan 250100, China Received 10 January 2007; in final form 1 June 2007 Available online 8 June 2007

Abstract We have performed ab initio calculations on the stability and structural and electronic properties of the fullerene-like cage (SiC)12 and its derivative products, the (SiC)12–(SiC)12 dimers and (SiC)12-based nanowires. The (SiC)12–(SiC)12 dimers and (SiC)12-based nanowires are found more stable than the (SiC)12. The optimized configurations of the (SiC)12-based nanowires are especially regular and exhibit stable dumbbell-shaped chain structures. The electronic structure calculations indicate that the two novel (SiC)12-based nanowires have band gaps of 1.586 eV and 2.055 eV, respectively, which may be promising for application in nanotechnology. Ó 2007 Elsevier B.V. All rights reserved.

1. Introduction Recently, the exploration of possible fullerene-like structures or nanotubes composed of noncarbon elements has attracted more and more attention [1–6]. For instance, fullerene-like cages and tubular structures of III–V compounds have been theoretically predicted [7,8] and experimentally synthesized [9–12]. BN and AlN fullerenelike cages [1,4,13] and nanotubes [14–16] have been reported. Very recently, theoretical investigations addressing the stability of SiC nanostructures based on ab initio calculations using density functional theory (DFT) were reported [2]. The structures and stability of fullerene-like cages of (SiC)n (n = 6–36) were studied and it was suggested that the fullerene-like cage (SiC)12 was energetically the most stable cluster among those cage structures and would be possibly synthesized under certain condition [2]. In the previous theoretical studies on the (BN)n [1] and

*

Corresponding author. E-mail address: [email protected] (J. Li).

0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.06.008

(AlN)n [13] clusters, the fullerene-like cages (BN)12 and (AlN)12 were also predicted to be the most stable ones. Therefore, the fullerene-like cage structure (XY)n may be a magic cluster when n is equal to 12. On the other hand, SiC nanomaterials may be promising semiconductors for preparation of nanoelectronic devices for high-temperature, high-power, and high-frequency applications [17]. So it is interesting to study the fullerene-like cage (SiC)12 and, especially, the novel nanomaterials derived from it, and to predict the electronic and optoelectronic properties of these potential materials. In this work, we performed ab initio studies on the stabilities and structural, as well as, electronic properties of the (SiC)12 fullerene-like cage, (SiC)12–(SiC)12 dimers and (SiC)12-based SiC nanowires obtained from the (SiC)12 clusters. 2. Theoretical approaches and computations We performed ab initio calculations by using SIESTA computation code [18,19], which is based on the standard Kohn–Sham self-consistent DFT. A flexible linear combination of numerical atomic-orbital basis sets was used for

J. Li et al. / Chemical Physics Letters 442 (2007) 384–389

the description of valence electrons and norm-conserving nonlocal pseudopotentials were adopted for the atomic cores. The pseudopotentials were constructed using Trouiller–Martins scheme [20] to describe the interaction of valence electrons with the atomic cores. The nonlocal components of pseudopotential were expressed in the fully separable form of Kleiman and Bylander [21,22]. The Perdew–Burkle–Ernzerhof (PBE) form generalized gradient approximation (GGA) corrections were adopted for the exchange-correction potential [23]. The atomic orbital set employed throughout was a double-f plus polarization (DZP) function. The numerical integrals were performed and projected on a real space grid with an equivalent cutoff of 120Ry for calculating the self-consistent Hamiltonian matrix elements. For the two (SiC)12-based SiC nanowires under study, periodic boundary condition along the wire axis was employed with a lateral vacuum region larger than ˚ to avoid the image interactions. The supercell of the 25 A (SiC)12-based SiC nanowires contains one (SiC)12–(SiC)12 dimer component as translational unit. To determine the equilibrium configurations of these (SiC)12-based nanomaterials, we relaxed all the atomic coordinates involved by using a conjugate gradient (CG) algorithm, until the max˚ . In the calculations imum atomic forces less than 0.02 eV/A of the total energies and the energy band structures, we used four k sampling points along the tube axis according to the Monkhorst–Pack approximation [24]. Binding energies were calculated according to the expression: Eb ¼ ðE  mESi  nEC Þ=ðm þ nÞ;

385

Fig. 1. The optimized configurations of the fullerene-like cage (SiC)12 and (SiC)12-based SiC nanomaterials: (a) fullerene-like cage (SiC)12, (b) (SiC)12–(SiC)12 dimer (I), (c) (SiC)12–(SiC)12 dimer(II), (d) (SiC)12-based nanowire(I), and (e) (SiC)12-based nanowire(II) obtained from coalescing of (SiC)12–(SiC)12 units, the translational periodicity of the two kinds of ˚ and p = 6.48 A ˚ , respectively nanowires shown in (d) and (e) is L = 7.35 A (the blue color for Si atoms and the gray color for C atoms). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

ð1Þ

where E is the total energy of the (SiC)12-based SiC nanomaterial, m and n (here m = n) are the numbers of the Si and C atoms involved, respectively, ESi and EC are the energies of an isolated Si and C atom, respectively. 3. Results and discussions The fully optimization configurations of the (SiC)12based nanomaterials are shown in Fig. 1. Our calculations indicate that the (SiC)12-based nanomaterials under study show structural stability, since they keep the basic structural feature of the intact (SiC)12 cage. First, we analyzed the possible structure of the fullerene-like cage (SiC)12. Previous theoretical study for SiC nanotube indicates that a SiC nanotube having Si atoms and C atoms allocated alternatively on the wall is more stable. We designed the (SiC)12 cage based on the rule of alternative distribution of Si and C atoms, and on the way used for constructing (AlN)n clusters [16], following the conclusions that the polyhedrons of fullerene-like clusters having four-numbered rings(4MRs) and six-numbered rings(6MRs) on the cage faces show higher stability [25]. As deduced from the Euler polytope [26], for the (XY)n fullerene-like cage consisting of 4MRs and 6MRs, the number of 4MRs is always equal to 6, while the number of 6MRs is n  4. Besides, the stability of the constructed cages depends on the separation of the 4MRs faces, the larger the separation, the more stable the system.

The cage molecule with the maximal separation of 4MRs faces should be the most stable one, in line with the pentagon rule in fullerene chemistry [27]. Following the rules mentioned above, we designed the fullerene-like cage (SiC)12 and the optimized structure is shown in Fig. 1a, which has six 4MRs and eight 6MRs and is found to have Th symmetry. The calculated bond lengths and bond angles are listed in Table 1. It is found that in the 4MRs, the C–Si bonds have the ˚ , which is longer than the C–Si bond same length of 1.86 A ˚ in the 6MRs and very close to the bond length of 1.78 A ˚ in the bulk 3C–SiC structure [28]. The length of 1.89 A bond angels of C–Si–C and Si–C–Si are 95.5° and 82.5°, respectively, in the 4MRs, and 127.7° and 109.2° in the 6MRs, respectively. To compare the structural parameters from the Siesta code with those from other theoretical method, we optimized the (SiC)12 cage using GAUSSIAN 03 [29] at the theoretical level of PW91PW91/6–31G(d). The calculated bond lengths and bond angels are also given in Table 1. Both the results from Siesta and GAUSSIAN 03 are in good agreement with the results of Ref. [2], where they drew the conclusion that (SiC)12 is the most stable one of all the fullerene-like clusters (SiC)n (n = 6–36) and has inherent special stability. To further evaluate the stability of this fullerene-like cage (SiC)12, we computed its ringlike, graphite-like and fullerene-like isomers consisting of pentagons and hexagons. The optimized configurations of

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Table 1 Siesta results of C–Si bond lengths, and C–Si–C and Si–C–Si bond angels in the fullerene-like cage (SiC)12 and (SiC)12-based nanomaterials shown in Fig. 1 ˚) Material C–Si (A C–Si–C (°) Si–C–Si (°) (SiC)12

4MRs 6MRs

1.86 (1.834a) 1.85b 1.78 (1.777a) 1.79b

95.5 (95.4a) 95.8b 127.7 (125.8a) 126.7b

82.5 (83.5a) 82.7b 109.2 (112.2a) 110.5b

(SiC)12–(SiC)12 dimer(I)

4MRs 6MRs 4MRs 6MRs 4MRs 6MRs 4MRs 6MRs

1.84, 1.86 1.81 1.83–1.88, 1.91 1.80, 1.85, 1.89 1.84, 1.92 1.81 1.83–1.87, 1.91 1.79–1.89

96.3, 95.0 118.7, 127.3, 128 83.5–98.1 117.2–129.9 97.1, 91.8 118.5, 127.6, 126.9 90.6, 97.3 122.5, 116.5, 131.2, 122.4

82.5, 83.0 117.3, 109.4, 114.0 82.8, 87.7 109.1–118.6 81.4, 88.2 118.0, 109.0, 113.7 88.1, 83.3 117.3, 119.7, 114.5, 109.3

(SiC)12–(SiC)12 dimer(II) (SiC)12-based nanowire(I) (SiC)12-based nanowire(II) a b

Ref. [2]. Obtained from GAUSSIAN 03.

Fig. 2. Different (SiC)12 isomer structures and (SiC)24 fullerene-like isomer strucures: (a) (SiC)12 ring-like isomer, (b) (SiC)12 graphite-like isomer, (c) (SiC)12 5MR–6MR fullerene-like isomer, (d) (SiC)24 4MR– 6MR isomer, and (e) (SiC)24 5MR–6MR isomer (the blue color for Si atoms and the gray color for C atoms). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

them are shown in Fig. 2. As shown in Fig. 2a, the ring-like (SiC)12 isomer has a ‘zigzag’ structure caused by the electron transfer from Si atoms to C atoms and the different hybridization trends of Si and C atoms. As listed in Table 2, the total energies of the ring-like (Fig. 2a) and graphitelike (Fig. 2b) isomers are about 21.18 and 10.99 eV, respectively, higher than that of the (SiC)12 (Fig. 1a). The total energy of the pentagon–hexagon fullerene-like isomer (5MR–6MR fullerene-like), shown in Fig. 2c, is 0.08 eV lower than that of the (SiC)12. Clearly, the fullerene-like cage (SiC)12 is much more stable than the ring-like and graphite-like isomers and almost Table 2 The total energy differences (DE) of the (SiC)12 isomers relative to the 4MR–6MR (SiC)12 cage shown in Fig. 1a Model

4MR–6MR cage

Ring-like

Graphite-like

5MR–6MR cage

DE (eV)

0

21.18

10.99

0.08

has the same stability with the 5MR–6MR fullerene-like isomer (Fig. 2c) since the difference of their total energies is only 0.08 eV for 24 atoms. Further more, the 5MR– 6MR (SiC)12 isomer must have several Si–Si bonds and C–C bonds on the cage. It is essential not a SiC material, but a C–Si heteromaterial structure, which has totally different electronic properties from that of the (SiC)12 cage under study, as will be shown later. In the following calculations, we focus our attention on the construction of (SiC)12-based nanostructures, as shown in Fig. 1b–e. The two (SiC)12–(SiC)12 dimers, shown in Fig. 1b and c, were just obtained from the (SiC)12 by coalescing two 4MRs of two (SiC)12 and two 6MRs of two (SiC)12 clusters, respectively, followed by global structure optimization processes. Both of the optimized (SiC)12– (SiC)12 dimer structures have very good axial symmetry feature. Therefore, the (SiC)12-based SiC nanowires can be formed by translational symmetry. The segments of the structurally optimized (SiC)12-based SiC nanowires obtained are shown in Fig. 1d and e, respectively. To study the stability of the (SiC)12-based SiC nanomaterials, we calculated the binding energies of them and the bulk 3C–SiC (zinc-blende). The cohesive energies of bulk SiC and the (SiC)12 are 8.28 and 6.99 eV/atom, respectively. The binding energies (the absolute value of the cohesive energies) of the (SiC)12–(SiC)12 dimer(I) and dimer(II), shown in Fig. 1b and c, are about 140 and 196 meV/atom, respectively, higher than that of the (SiC)12 cage shown in Fig. 1a. Therefore, these (SiC)12–(SiC)12 dimers are more stable than the (SiC)12 cage. The (SiC)12–(SiC)12 dimer(II) is more stable than the (SiC)12–(SiC)12 dimer(I). The cohesive energies of the two (SiC)12-based SiC nanowires, shown in Fig. 1d and e, are 7.27 and 7.38 eV/atom, respectively. The binding energies of these nanowires are lower than that of the bulk 3C–SiC, but about 272 and 389 meV/atom higher than that of the (SiC)12 cage. In terms of energy favorable order, among all these structures under study, bulk 3C–SiC is the most stable one, then followed by the (SiC)12-based SiC nanowire(II), the (SiC)12-based SiC nanowire(I), the (SiC)12–(SiC)12 Dimer(II), (SiC)12– (SiC)12 Dimer(I), and finally the (SiC)12 cage. Therefore,

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if the fullerene-like cage (SiC)12 had inherent special stability and could be synthesized experimentally, it would be easier to synthesize the (SiC)12-based SiC nanowires. This gives a guide for the experimental scientists to search for the novel (SiC)12-based nanowires as a new kind of SiC nanomaterial. These nanowires are expected to find novel applications for nanotechnology. From the optimized configurations of both the (SiC)12based SiC nanowires, shown in Fig. 1d and e, it is clear that the tubular structure shows a unique dumbbell-shaped chain structure. The translational periodicity of the ˚, (SiC)12-based SiC nanowire(I) and (II) is 7.35 and 6.48 A respectively, along the longitudinal axis. The C–Si bonds forming the ‘neck’ joining the unit cells (Fig. 1d and e) have ˚ , respectively, which is a bit the length of 1.92 and 1.91 A ˚ in the bulk 3C–SiC longer than the bond length of 1.89 A structure [30]. The bond lengths of C–Si bonds both in the 4MRs and in the 6MRs, shown in Table 1, are slightly ˚ in the bulk 3C–SiC. shorter than the bond length of 1.89 A The special shape with certain effects of quantum confinement, the local strain and the mixed material feature make this nanostructure particular attractive for finding novel applications. To perform further understanding of the possibility of the (SiC)12 cages coalescing into the (SiC)12-based nanostructures, we constructed and optimized the (SiC)24 spheroids containing 24 Si atoms and 24 C atoms, as shown in Fig. 2d and e, respectively. Fig. 2d is a 4MR–6MR fullerene-like spheroid isomer (4–6 spheroid) and Fig. 2e is a pentagon–hexagon fullerene-like spheroid isomer (5–6 spheroid). The calculated binding energy of the 4–6 spheroid is about 105.2 and 160.7 meV/atom lower than those of the (SiC)12–(SiC)12 dimer(I) and dimer(II), respectively. It indicates that both of the (SiC)12–(SiC)12 dimers are more stable than the 4–6 spheroid. However, the 5–6 (SiC)24 spheroid (Fig. 2e) has almost the same binding energy as that of the (SiC)12–(SiC)12 dimer(II). Therefore, the (SiC)12–(SiC)12 dimer(II) and the 5–6 (SiC)24 spheroid should coexist, in terms of the view point of the energies. However, considering the two possible growth paths, i.e., growth to a tubular nanowire and growth to a bigger and bigger spheroid, the nanowire can continue to increase the length, while the spheroid fullerene can not continue to grow over a certain size since too large cavity is not favorable. In fact, single-walled carbon nanotubes can growth to many micrometers long, even to millimeters long, whereas single shell fullerene molecule larger than C960 has not been reported. For the (SiC)12-based SiC nanowire(II), there is one thing should be mentioned, that is, whether the 6MRs of a (SiC)12 tend to coalesce with the 6MRs in the side wall of the (SiC)12–(SiC)12 dimer(II) during the growth to form bent-chain or branched-chain structure instead of forming the longitudinal (SiC)12-based SiC nanowire(II). We constructed two (SiC)12-based trimers and the fully optimized configurations are shown in Fig. 3a and b, respectively. For the trimer(I), one 6MR of the (SiC)12 is coalesced with the 6MR on the side-wall

387

Fig. 3. The optimized configurations of (a) (SiC)12-based trimer(I), (b) (SiC)12-based trimer(II), (c) (SiC)12-based tetramer(I), and (d) (SiC)12based tetramer(II) (the blue color for Si atoms and the gray color for C atoms). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

of the (SiC)12–(SiC)12 dimer(II). The binding energy of the tubular structure of trimer(II) is only about 3.74 meV/atom higher than that of the (SiC)12-based trimer(I). Although the tubular structure is more stable than the bent-chain structure, such a small energy difference can not prevent the bent-chain isomers from coexistence with the tubular products. Further more, we constructed and optimized two (SiC)12-based tetramers, which are respectively shown in Fig. 3c and d. For the tetramer(I), one (SiC)12 cage was coalesced with the middle cage of the (SiC)12-based trimer(II) by coalescing the 6MRs of them to form a branched-chain configuration. The binding energy of the constructed branched-chain structure, tetramer(I) is about 15.6 mev/atom lower than that of the tubular structure tetramer(II). It indicates that the tubular structure is energetically somewhat favorable than the branched-chain structure, although the energy difference is small. To lend further understanding of the properties of the fullerene-like cage (SiC)12 and the (SiC)12-based nanomaterials considered above, we have calculated the electronic structures of all the configurations shown in Fig. 1. The energy gaps, DE, between the HOMO and LUMO for all the configurations (Fig. 1) and the bulk 3C–SiC are listed in Table 3. The HOMO–LUMO gaps of the (SiC)12–(SiC)12 dimer(I) and the (SiC)12-based nanowire(I) are both smaller than that of the isolated (SiC)12 cluster, while the HOMO–LUMO gaps of the (SiC)12-(SiC)12 dimer(II) and the (SiC)12-based nanowire(II) have larger energy gaps Table 3 The energy gaps (DE) between the HUMO and LUMO of the fullerenelike (SiC)12-based materials shown in Fig. 1 and bulk 3C–SiC Material

DE = EHOMO  ELUMO (eV)

(SiC)12 (SiC)12–(SiC)12 dimer(I) (SiC)12–(SiC)12 dimer(II) (SiC)12-based nanowire(I) (SiC)12-based nanowire(II) 3C–SiC(zinc-blende)

2.000 1.700 2.018 1.586 2.055 1.651

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optimized structures of the two (SiC)12-based nanowires are regular and exhibit interesting dumbbell-shaped chain structures. The calculated HOMO–LUMO gaps of all these configurations of (SiC)12-based materials are not recognized to have a remarkable difference from that of the (SiC)12 cluster. The (SiC)12-based nanowire(I) has an indirect band gap of 1.586 eV, while the (SiC)12-based nanowire(II) has a direct band gap of 2.055 eV. They have the similar semiconducting electrical properties as SiC nanotubes [30]. We hope this finding could motivate further studies on the (SiC)12-based materials, for instance, on the synthesis methods, the applications and functionalizations of this novel material family.

Fig. 4. The energy band structures of (a) (SiC)12-based SiC nanowire(I), and (b) (SiC)12-based SiC nanowire(II).

than that of the (SiC)12 cage. All the energy gaps of the (SiC)12-based nanomaterials are different from that of the bulk 3C–SiC. As mentioned above, the 5–6 (SiC)12 (Fig. 2c) and the 5–6 (SiC)24 (Fig. 2e) isomers, which have Si–Si bonds and C–C bonds, are Si–C heterofullerene, rather than SiC fullerene-like isomers. The energy gaps of the 5–6 (SiC)12 and 5–6 (SiC)24 are 0.78 and 0.024 eV, respectively. They have totally different electronic properties from those structures shown in Fig. 1. We also calculated the electronic energy band structures of the (SiC)12-based SiC nanowires. The energy bands near the Fermi surface are shown in Fig. 4. The Fermi levels are denoted by the dashed line in this figure. The two band structures clearly show finite gaps, the widths of which are 1.586 eV for the (SiC)12-based SiC nanowire(I) and 2.055 eV for the (SiC)12-based SiC nanowire(II). Comparing the band-gap widths of the structures listed in Table 3, it is clear that although the formation of the tubular linkage structures does not cause essential changes in band-gap width, it provides a way of adjusting the gap width by forming different nanostructures. The (SiC)12-based nanowire(I) is an indirect gap semiconductor, while the (SiC)12-based nanowire(II) is a direct gap semiconductor. The energy band structures of the (SiC)12-based SiC nanowires are similar with the SiC nanotube(SiCNTs) as they are always semiconductors with wide gaps [30]. So it is worth further studying to find the path of synthesis of these novel and promising materials as a new kind of SiC nanomaterials. If the new SiC materials could be successfully synthesized, it is expected to find novel applications in nanotechnology. 4. Conclusions Our calculations show that the stable fullerene-like cage (SiC)12 can form a new family of SiC nanomaterials, including (SiC)12-based dimers and nanowires, which are energetically more stable than the (SiC)12 cluster. The fully

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