NANO LETTERS
From Pure Carbon to Silicon−Carbon Nanotubes: An Ab-initio Study
2003 Vol. 3, No. 11 1481-1484
A. Mavrandonakis and George E. Froudakis* Physical and Theoretical Chemistry, UniVersity of Crete, P.O. Box 1470, Heraklio, Crete, Greece 71409
M. Schnell and Max Mu1 hlha1 user† Physical and Theoretical Chemistry, UniVersity of Bonn, D-53115 Bonn, Germany Received May 20, 2003; Revised Manuscript Received August 28, 2003
ABSTRACT Ab initio methods are used for investigating structural and electronic properties of silicon−carbon nanotubes (SiCNTs). Tubes with different Si to C ratios were tested and the trend from C-rich to Si-rich SiCNTs is examined. Our results show that SiCNTs lose stability when the ratio of Si over C increases. Nevertheless they remain stable until the ratio reaches 50:50, and after that the Si-rich tubes collapse to nanowires or clusters with solid interiors. The electronic density of states of different SiCNTs is also presented and analyzed.
In the past 10 years, one-dimensional nanomaterials have attracted considerable attention for their potentional use in nanoelectronics. After the discovery of carbon nanotubes (CNTs) by Iijima in 1991,1 much scientific interest was focused on the physical and electronic properties of these new materials. Generally speaking there are two research directions: studying the properties of existing nanomaterials and designing new materials that present specific properties. Following the second direction, many research groups tried either to synthesize new nanotubes (NTs) based on elements other than carbon2-4 or to theoretically model hypothetic tubes.5 In both cases the first candidate to substitute carbon was silicon. Today, it is well known that C and Si present completely different bonding characteristics, despite the fact that they both are in the fourth row of the periodic table and both have the same number of valence electrons. This happens because in carbon sp2 hybridization is more stable while in silicon the preferable hybridization is sp3. Starting from elementary clusters, carbon makes linear chains and planar structures, while silicon prefers 3-dimensional (3-D) formations. The first attempt to replace C atoms with Si in cage formations took place in fullerenes with no success. Si likes real 3-D, compact structures and is completely unstable in empty shells. Nevertheless, large spherical Si clusters exist, and some of them (Si33, Si45) present remarkable stability (magic numbers) but they are solid, containing atoms in the * Corresponding author. E-mail:
[email protected]. † Present address: FH-Studiengang Verfahrens-und Umwelttechnik, MCIManagement Center Innsbruck GmbH, Egger-Lienz-Strasse 120, A-6020 Innsbruck, Austria. 10.1021/nl0343250 CCC: $25.00 Published on Web 09/30/2003
© 2003 American Chemical Society
interior.6 Following the bonding character that Si presents in small and large clusters, it is not surprising why Si nanotubes (SiNTs) are still hypothetical materials,5 whereas the synthesis of Si (and Ge) nanowires took place already in 1992.7 Even though the complete replacement of C with Si atoms in cage materials was due to fail from the beginning, the partial substitution, which results in coexistence of C and Si atoms, is in principle possible. In 1999, the production of heterofullerenes containing Si up to 50% was achieved,8 and in 2001 there was the first synthesis of silicon carbon nanotubes (SiCNTs).2 In this new category of nanomaterials there are many important open questions. How does the relative stability change from the pure CNTs to SiCNTs? What is the maximum percentage of Si with which the SiCNTs remain stable - since pure SiNTs are unstable? What are the structural and electronic properties of the SiCNTs and how do these properties vary as the percentage of Si atoms increases? The few experimental studies that have been performed in the past two years on SiCNTs are not able to answer these questions,2,3,9-11 and the need of a theoretical investigation of these novel materials is obvious. Only by the use of quantum chemistry techniques can we understand the real nature of SiCNTs and specify their properties. In this letter we attempt to combine our previous experience in Si-C mixed clusters12-15 with recently developed techniques for modeling of C nanotubes16-20 to investigate structural and electronic properties of SiCNTs. We use the DFT method in the cluster approximation. A large enough part of an armchair (4,4) SWNT containing
Table 1. Energetic, Structural, and Electronic Characteristics of All Studied Structuresa energy
tube diameter
case
stoichiometry
total (Hartree)
B. E./atom (eV)
C
Si
HOMO-LUMO gap (eV)
I II III IV V VI VII VIII IX
C56 C55Si C54Si2
-2142.066127 -2393.355348 -2644.667359 -2644.660102 -2644.679661 -5158.006401 -8174.380359 -8173.839303 -9179.983654
8.229 8.126 8.035 8.031 8.040 7.226 6.466 6.171 6.241
5.52 5.45 5.50 5.60 5.66 5.87 6.27 6.86 7.05
6.30 6.35/7.05 6.21 6.19 6.88 6.50 7.10 6.77
1.026 0.832 0.691 0.816 0.804 0.784 1.573 0.426 2.013
C44Si12 C32Si24 C28Si28
atomic charges C
Si
0 -0.1 -0.1 -0.1 -0.1 -0.1 +0.2/-0.4 -0.1 -0.6
+0.2 +0.3 +0.3 +0.3 +0.3 +0.5 +0.3 +0.6
a Tube diameters are presented in middle values and atomic charges are in |e|. When two values are listed, two different characters of the same kind of atom exist in the structure. The binding energy per atom is calculated with respect to dissociation into elements:
BE/atom ) -
[Enanotube - xEC - yESi - 16EH] x+y
where x, y is the number of the carbon and silicon atoms, respectively, in the nanotube (x + y ) 56 in all cases studied) and EC, ESi, and EH are the atomic energies of the elements.
Figure 1. DFT optimized geometries of finite-sized, single-walled silicon-carbon nanotubes (SiCNT) with various Si/C ratios.
56 carbon or silicon atoms was separated and treated as an individual system. The dangling bonds at the ends of the tubes were saturated by hydrogen atoms (Figure 1). Similar methodology was used successfully before studying the atomic19 and the molecular20 hydrogen adsorption to SWNTs. The resolution of identity DFT (RI-DFT) as implemented in the TURBOMOLE program package21 in combination with the SPV auxiliary basis set was employed for the geometry optimizations. We examine finite-sized, single-walled silicon-carbon nanotubes with various Si/C ratios. All the structures discussed are fully optimized without any symmetry constraints. The most interesting of these tubes are presented in Figure 1. The equilibrium geometry of structure I (the pure carbon tube) is given for comparison reasons. Energetic, structural, and electronic characteristics of all studied structures are listed in Table 1. 1482
Isomer II is derived from the pure carbon tube by the substitution of one carbon with a silicon center. The equilibrium distance of the Si-C bond is calculated with a value of 1.80 Å in accordance with Si-C bond lengths in various silicon-carbon clusters. The C-C bond lengths next to the silicon center in II remain almost unchanged (1.43 Å) compared to the pure carbon tube. In addition, the silicon center is laying 3.5 Å from the tube axis leading to an elbowing of the tube surface. Consequently, the HOMOLUMO gap is lowered by approximately 0.19 eV when one carbon is replaced by a silicon center. The substitutions of two carbon centers in the same hexagonal ring with silicon gives rise to the three possible isomers III, IV, and V, also given in Figure 1. In structure III, the silicon centers are next to each other with an optimized Si-Si bond length of 2.22 Å, while in the equilibrium geometry of structures IV and V the silicon centers are separated by one (IV) or two (V) carbon atoms, respectively. The Si-C bonds are calculated with values of 1.82 Å in all cases. The optimized distance of the silicon atoms from the tube axis is 3.46 and 4.17 Å (III), 3.44 Å (IV), and 3.42 Å (V), while the linked carbon centers are placed at 2.96 Å to 3.03 Å (III), 2.91 Å to 3.28 Å (IV), and 2.92 Å to 3.05 Å (V). The calculated binding energy per atom of III, IV and V is very similar, slightly favoring V over IV and III. Since Si atoms are positively charged (+0.3 |e|, Table 1) the antidiametric position of the Si atoms in structure V reduces the repulsive electrostatic forces between the two silicon atoms, resulting in the lowering of the energy. This is in line with what we have obtained for six-member ring Si2C4 clusters in earlier calculations, according to which the ring structure with two strong C-C linkages corresponding to structure V is favored over the competing isomers.13 The HOMO of structure V is presented in Figure 2. We can see the perturbation to the π-system that the Si atoms introduce. When the Si atoms are placed in different hexagonal rings the structure is energetically less favored (E ) -2644.6423 Hy) since the perturbation of hexagonal π-systems doubles. Nano Lett., Vol. 3, No. 11, 2003
Figure 2. Highest occupied molecular orbital (HOMO) of structure V.
Figure 3. Binding energy per atom in eV versus the silicon/carbon ratio. 0,0 means pure C-tube while 1,0 means 50% Si (Si:C ) 1:1).
A further increase of the silicon-to-carbon ratio derives the structures VI to IX. VI originated from structure V, the most stable dimmer case, by substituting 12 of the 56 carbon centers. Despite the small enlargement of the tube diameter, the electronic properties of VI remain similar to V (Table 1). Replacement of 24 of the 56 carbon centers by silicon leads to the two structural possibilities VII and VIII. The basic structural difference between VII and VIII isomers is that in structure VII silicon and carbon centers are alternating, while in VIII pure carbon-carbon and silicon-silicon linkages are present. As expected and confirmed from our calculations, the structure VII shows stronger C-Si bonds, which can be justified by the fact that there is a larger contribution from ionic forces between the positively charged Si atoms (+0.5 |e|) and the negatively charged C atoms (-0.4 |e|) (Table 1). In contrast to VII, structure VIII shows a much smaller charge separation, +0.3 |e| for the Si atoms and -0.1 |e| for C. The innermost bonds of VIII were obtained with values 2.27 Å (Si-Si), 1.84 Å (Si-C), and 1.43 Å (C-C), while the corresponding structure VII shows somewhat shortened Si-C bonds (1.80 Å). The stronger ionic bonding of VII over VIII is stabilizing the first by 0.3 eV/atom. This energy difference is also reflected in the HOMO-LUMO gap, which is 1.57 eV for VII and 0.43 eV for VIII. Nano Lett., Vol. 3, No. 11, 2003
Figure 4. Qualitative picture of the electron density of states (DOS) and the eigenvalue spectra of several SiCNTs. The DOS is built by fitting a Gaussian function in each eigenvalue and then summing them. The zero of energy axis is the Fermi level.
Finally, replacing half of the carbon centers by silicon led to structure IX, in which silicon and carbon atoms are alternating. This results in a stable nanotube showing a great ionic character, where each silicon atom is strongly positively charged (+0.6 |e|) and each carbon atom negatively charged (-0.6 |e|). The HOMO-LUMO gap is increased to 2.01 eV. As the number of silicon atoms inserted in the tube increases, the diameter of the tube also increases. While in 1483
pure carbon nanotube the diameter is 5.52 Å, the replacement of half of carbon atoms by silicon ends up in a tube (IX) with 7.05 Å diameter. In Figure 3 the binding energy per atom is plotted versus the silicon-carbon ratio. All structures examined in this study are stabilized by 6.2 eV/atom to 8.2 eV/atom with respect to dissociation into the elements. Furthermore, we observed a clear trend that the binding energy decreases when the Si ratio increases. This is in line with qualitative MO considerations: while “carbon-rich” SiCNTs are stabilized by the typical delocalization energy in a “planar” molecular surrounding with sp2 hybridization of the carbon centers, inclusion of silicon (sp3) centers leads to a three-dimensional perturbation and thus destabilizes the tube. Consequently, corresponding silicon-rich structures can be expected to be even more destabilized, which is supported from our computational study, that did not result in any stable “siliconrich” tube although numerous attempts were carried out. All different “silicon-rich” structures that we test, during the geometry optimization, collapse to corresponding amorphous nanowires or clusters with solid interiors. In Figure 4 we present qualitatively the electron density of states (DOS) and the eigenvalue spectra of several SiCNT. Comparing the first three plots (structures I, II, V), we can point out that the substitution of C atoms by Si in a C-rich tube inserts energy levels in the HOMO-LUMO gap. Nevertheless, when the Si ratio increases to 50% the HOMO-LUMO gap increases because the structure is becoming symmetric again. Our theoretical results are in significant agreement with the experiment. Pham-Huu et al.2 reported that the SiCNTs they produced are similar in shape with the starting CNTs. As we can see in Figure 1 and Table 1, this is verified from our theoretical calculations, too. In addition Sun et al.3 propose a 50% SiCNT with strong Si-C bonds exactly as the structure IX that came from our theoretical calculations. Summarizing, our ab initio results clearly show that SiCNTs are stable. Nevertheless, we predict that SiCNTs lose stability when the ratio of Si over C increases. The cross point, for replacing C with Si atoms without making the tube to collapse to a cluster or a nanowire, is the 50% substitution, which results in a stable nanotube with ionic character. The electronic DOS of different SiCNTs shows that the substitu-
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tion of few C atoms by Si inserts levels in the gap, while in the 50% SiCNTs the gap increases again due to symmetry reasons. Acknowledgment. Financial support from the Ministry of Education and European Union through the postgraduate program EPEAEK, Applied Molecular Spectroscopy, and the Greek-German collaborative program IKYDA 2000 is gratefully acknowledged. References (1) Iijima, S. Nature 1991, 354, 56. (2) Pham-Huu, C.; Keller, N.; Ehret, G.; Ledouxi, M. J. J. Catal. 2001, 200, 400-410. (3) Sun, X. H; Li, C. P.; Wong, W. K.; Wong, N. B.; Lee, C. S.; Lee, S. T.; Teo, B. K. J. Am. Chem. Soc. 2002, 124, 14464-14471. (4) Dai, H. J.; Wong, E. W.; Lu, Y. Z.; Fan, S. S.; Lieber, C. M. Nature 1999, 375, 769-772. (5) Fagan, S. B.; Baierle, R. J.; Mota, R.; Silva, A. J. R.; Fazzio, A. Phys. ReV. B 2000, 61, 9994-9996. (6) Mistriotis, A.; Zdetsis, A.; Froudakis, G.; Madhu, M. J. Phys. C 1993, 5, 6183. (7) Saunders, G.; Chang, Y. Phys. ReV. B 1992, 45, 9202. (8) Pellarin, M.; Ray, C.; Lerme, J.; Vialle, J. L.; Broyer, M.; Blase´, M.; Keghelian, P.; Melinon, P.; Perez, A. Eur. Phys. J. D 1999, 9, 49-54. (9) Liu, J. W.; Zhoang, D. Y.; Xie, F. Q.; Sun, M.; Wang, E. G.; Liu, W. X. Chem. Phys. Lett. 2001, 348, 357-360. (10) Weiqiang, H.; Shoushan, F.; Qunqing, L.; Wenjie, L.; Binli, G.; Dapeng, Y. Chem. Phys. Lett. 1997, 265, 374-378. (11) Munoz, E.; Dalton, A. B.; Collins, S.; Zakhidov, A. A.; Baughman, R. H.; Zhou, W. L.; He, J.; O’Connor, C. J.; McCarthy, B.; Blau, W. J. Chem. Phys. Lett. 2002, 359, 397-402. (12) Muhlhauser, M.; Froudakis, G.; Zdetsis, A.; Peyerimhoff, S. Chem. Phys. Lett. 1993, 204, 617. (13) Froudakis, G.; Zdetsis, A.; Muhlhauser, M.; Engels, B.; Peyerimhoff, S. J. Chem. Phys. 1994, 101, 6790. (14) Froudakis, G.; Muhlhauser, M.; Zdetsis, A. Chem. Phys. Lett. 1995, 233, 619. (15) Zdetsis, A.; Froudakis, G.; Muhlhauser, M.; Thumnel, H. J. Chem. Phys. 1996, 104, 2566. (16) Menon, M.; Andriotis, A.; Froudakis, G. Chem. Phys. Lett. 2000, 320, 425-434. (17) Andriotis, A.; Menon, M.; Froudakis, G. Appl. Phys. Lett. 2000, 76, 3890-3892. (18) Andriotis, A.; Menon, M.; Froudakis, G. Phys. ReV. Lett. 2000, 85, 3193-3196. (19) Froudakis, G. E. Nano Lett. 2001, 1, 179-182. (20) Froudakis, G. E. Nano Lett. 2001, 1, 531-533. (21) Ahlrichs, R.; von Arnim, M. Methods and Techniques in Computational Chemistry METECC-95; Clementi, E., Corongiu, G., Eds.; STEF: Cagliari, 1995.
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