NANO LETTERS
Substitutional Si Doping in Deformed Carbon Nanotubes
2004 Vol. 4, No. 5 975-977
S. B. Fagan,† R. Mota,*,‡ Antoˆnio J. R. da Silva,§ and A. Fazzio§ Departamento de Fı´sica, UniVersidade Federal do Ceara´ , Caixa Postal 6030, Campus do Picı´, 60455-900, Fortaleza, CE, Brazil, Departamento de Fı´sica, UniVersidade Federal de Santa Maria, CEP 97105-900, Santa Maria, RS, Brazil, and Instituto de Fı´sica, UniVersidade de Sa˜ o Paulo, Caixa Postal 66318, CEP 05315-970, Sa˜ o Paulo, SP, Brazil Received February 4, 2004
ABSTRACT A suggestion for substitutional Si doping in single-wall carbon nanotubes (SWNTs) through radial tube deformation is presented. Although the doping of buckyballs with substitutional Si atoms has been experimentally achieved, so far the synthesis of silicon-doped SWNT has not been reported. Using theoretical methods based on first-principles, the formation energies for Si doping on deformed (10,0) SWNTs are calculated, and their electronic and structural properties are investigated. It is established that, upon tube compression, the formation energy for Si doping in the large curvature region of the SWNT is reduced to values similar to the ones obtained for Si in buckyballs, indicating that this procedure may help to surmount the experimental difficulties associated with Si doping of SWNTs.
The peculiar electronic and structural properties of carbon nanotubes, since their discovery in the early 1990s,1,2 have triggered many alternatives to build materials with novel properties that may be synthesized using single-wall carbon nanotubes (SWNTs) as the starting point. Many devices associated with different applications, having chemical compositions beyond that of pure SWNT have been proposed and experimentally realized.2 It has been shown that doping induces fundamental modifications when compared to the undoped material.3 In particular, the isovalent substitutional Si doping of SWNTs has been recently investigated,4 and it has been recently shown that it may be of special interest, with predictions of unique electronic and structural properties and good potential as a binding center to attach different atoms or molecules for nanotube functionalization.5 In contrast to C, which has sp2-configuration structures as the most stable ones, Si is known to strongly prefer sp3like bonding. As a consequence, fullerene-like structures fully based on Si are difficult, if not impossible, to obtain.6 Recently, doping buckyballs with substitutional Si atoms has been reported through the synthesis of C59Si heterofullerenes,7 a system that has also been studied theoretically.8 Despite this fact, as far as we know, there are no reported experimental results for silicon-doped SWNTs. * Corresponding author. E-mail:
[email protected]. † Universidade Federal do Ceara ´. ‡ Universidade Federal de Santa Maria. § Universidade de Sa ˜ o Paulo. 10.1021/nl049805l CCC: $27.50 Published on Web 03/30/2004
© 2004 American Chemical Society
In this work we propose a new route to make it easier to dope SWNTs with substitutional Si atom through the deformation of the tube. This is possible since the relatively high formation energy (around 3.1 eV) for Si on nondeformed SWNTs4 decreases as the tube is deformed, if the Si is at the large curvature region of the nanotube. This procedure leads to values for the formation energy that are similar to the ones obtained for Si in buckyballs,9 which is encouraging since C59Si has already been experimentally synthesized,7 as previously mentioned. The calculations are based on first-principles densityfunctional theory using numerical atomic orbitals as basis sets. We have used the SIESTA code,10 which solves the standard Kohn-Sham (KS) equations. The calculations are done using the local density approximation for the exchangecorrelation term, as proposed by Perdew-Zunger.11 The standard norm-conserving Troullier-Martins pseudopotentials are used.12 The KS orbitals are expanded using a linear combination of numerical pseudoatomic orbitals, similar to the ones proposed by Sankey and Niklewski.13 In all procedures we have used a split-valence double-ζ basis set with polarization function.14 A cutoff of 150 Ry for the grid integration was utilized to represent the charge density. Our study was performed using a (10,0) semiconductor SWNT. Periodic-boundary conditions and a supercell approximation with a lateral separation of 20 Å between tube centers are used to make sure that the nanotubes do not interact with their periodic images. The supercell had 80 C atoms, with a total length of 8.52 Å. Along the tube axis, 3
Table 1. Structural and Electronic Properties of a Deformed SWNT Substitutionally Doped with Sia Se SWNT+structure SWNT+Si nondeformed deformed-yy)0.1 Si low Si high deformed-yy)0.2 Si-high Si-low deformed-yy)0.3 Si-low Si-high deformed-yy)0.4 Si-low Si-high
dSi-C(Å)
E[form-Si](eV)
gap (eV)
1.77/1.72
3.12
0.65
1.77/1.72 1.79/1.73
3.68 3.01
0.68 0.47
1.77/1.72 1.81/1.73
3.82 2.84
0.60 0.31
1.71/1.74 1.83/1.73
3.94 2.63
0.28 0.13
1.71/1.74 1.84/1.73
4.00 2.21
a
dSi-C are the distances between the Si atom and its three nearestneighbor C atoms (in Å), E[form-Si] and gap are the corresponding formation energies and the resulting gaps (in eV), respectively. The Si-low and Si-high correspond to substitutional Si in the region near the end of the minor (low curvature) and major (high curvature) axis of the ellipse, respectively.
Monkhorst-Pack k-points for the Brillouin zone integration were used.4,5 The relaxed atomic structures of the tubes are obtained by a minimization of the total energy using Hellmann-Feynman forces including Pullay-like corrections. Structural optimizations were performed until the residual forces were smaller than 0.05 eV/Å. The radial deformation is generated by applying a uniaxial stress along the opposite surfaces of a SWNT. Such deformation simulates the tube being pressed between two rigid, flat, and parallel surfaces. Thus, the SWNT radius is squeezed in one direction, resulting in an elliptical cross section.15,16 We adopt the constraint that two diametrically opposite carbon lines (associated with the minor axis) are kept fixed, whereas all the remaining atoms are relaxed. The major and minor axes, labeled a and b from now on, are assumed to be along the x and y directions, respectively. The magnitude of the radial deformation along the minor axis can be expressed as yy ) (R0 - b)/R0
(1)
where R0 is the original, undistorted SWNT radius. The formation energy is defined as E[form-Si] ) ET[SWNT+Si] - ET[SWNT] - µSi+µC
(2)
in terms of the total energy of undoped SWNT, ET[SWNT], and the total energy of a SWNT with a substitutional Si atom, ET[SWNT+Si]. The chemical potentials for Si and C, µSi and µC, are calculated as the total energy per atom for bulk Si and the total energy per atom in the undoped SWNT, respectively. In Table 1, we present the corresponding structural and electronic properties of substitutional Si doped in deformed and nondeformed SWNT. We focus on three quantities: (i) 976
Figure 1. Variation of the formation energy for a substitutional Si-atom in a zigzag (10,0) SWNT as a function of the elliptic radial deformation yy. The upper curve corresponds to the substitutional Si doping in the small curvature region near the minor axis of the ellipse. The lower curve is for the substitutional Si doping in the large curvature region at the end of the major axis of the ellipse.
the Si-C nearest neighbor distances, dSi-C, (as pointed out previously,4 there is an outward local distortion of the Si and its three nearest neighbor C atoms, resulting in two equivalent and one nonequivalent bond length, which is consistent with the symmetry of the system); (ii) the formation energy E[form-Si], as defined above; and (iii) the local band gap at the deformed region. Positive formation energy values indicate that the substitutional doping requires such energy to occur, considering that the process happens under thermodynamical equilibrium with the atomic reservoirs. However, even if such conditions are not applicable to the particular experimental situation required to dope the nanotubes, the changes in the formation energies as calculated here serve as hints of how hard or how easy it will be to substitute a C by a Si atom. The variations of E[form-Si] with radial deformation are presented in Table 1 and in Figure 1. As can be seen from Figure 1, for substitutional Si doping in the small curvature region (upper curve), the formation energy increases with deformation and eventually saturates at a value corresponding to that of a graphene plane. A rather distinct behavior is observed for the Si doping occurring in the large curvature region. Figure 1 shows that the formation energy decreases with the deformation in such a way that the larger the curvature the lower is its value. This behavior suggests that squeezing a SWNT should make it much more feasible to substitutionally dope it with Si, even more so if we consider that the values are close to the ones obtained for buckyballs.7,9 In Figure 2, the electronic charge densities of the lowest unoccupied band states, around the Γ point, help to understand the effect of tube deformation on the charge densities. As can be seen in case (a), before applying the deformation, these states are strongly localized at the Si atom, as pointed out previously.4 As the deformation is increased from (b) to (d), a stronger mixing with the nanotube states is observed, which results in a more delocalized charge density. It is also interesting to observe that for higher deformations the charge Nano Lett., Vol. 4, No. 5, 2004
since at the high curvature region it would be easier to overcome the experimental problem of inserting a substitutional Si atom in a SWNT. Acknowledgment. We thank the CENAPAD-SP for the computer time. This research was supported by CNPq, CAPES, and FAPERGS. References
Figure 2. Electronic charge densities for the lowest unoccupied band states around the Γ point for (I) Si-doped SWNT at the small curvature region and (II) Si-doped SWNT at the large curvature region, for different applied deformations. (a), (b), (c) and (d) correspond to yy ) 0.1, 0.2, 0.3, and 0.4, respectively. The values for the plotted electronic charge densities are the same for all systems (2.4 × 10-4 e/Å3).
concentration over the Si atom is less noticeable for the high than for the low curvature regions. This is also a consequence of the fact that the charge moves from the low to the high curvature regions as the deformation is increased. In summary, we suggest that the Si doping of SWNTs may be facilitated through the radial deformation of the tube,
Nano Lett., Vol. 4, No. 5, 2004
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