NANO LETTERS
Cluster Assembled Metal Encapsulated Thin Nanotubes of Silicon
2002 Vol. 2, No. 11 1243-1248
Abhishek Kumar Singh,*,† Vijay Kumar,†,‡,§ Tina M. Briere,† and Yoshiyuki Kawazoe† Institute for Materials Research, Tohoku UniVersity, Sendai 980-8577, Japan, Center for Interdisciplinary Research, Tohoku UniVersity, Sendai 980-8578, Japan, and Dr. Vijay Kumar Foundation, 45 Bazaar Street, K.K. Nagar (West), Chennai 600078, India Received September 11, 2002; Revised Manuscript Received September 30, 2002
ABSTRACT Using ab initio total energy calculations we demonstrate that the recently found metal encapsulated silicon clusters Si12Be can be assembled to form hexagonal nanotubes of silicon. This is in contrast to undoped silicon structures that are distorted and have a tendency to agglomerate. The finite nanotubes have varying HOMO−LUMO gaps depending upon the length and amount of doping. However, infinite nanotubes are metallic, symmetric, and stable, making metal encapsulation a useful route to generate metallic silicon nanowires for miniature devices.
Current interest in finding suitable components for miniature electronic devices has led to a focus on the bottom-up approach1-6 in which nanoparticles and nanowires could be the building blocks. Intense research is being carried out to understand the properties of nanostructures of Si because of its use in present day technologies and its potential as an optical material for future devices integrating photonics with electronics.7 Nanowires could be used as interconnects between device elements or it may be possible to incorporate device elements within nanowires.4,5 For this to be realized, successful fabrication of Si nanowires with control of size8,9 is very important. While experimental progress in the development of silicon nanowires is remarkable, the thickness of the nanowires is still in the range of several nm and precise control of the nanowire thickness as well as the composition is still problematic. Furthermore, in most cases these nanowires are oxidized and the interface between silicon and silicon oxide is ill-defined. An attractive alternative possibility of using carbon nanotubes as device components is currently being explored intensely. This is due to the nanotubes’ inherent stability as well as the possibilities of modifying their properties by changing the type of nanotube or by doping. This may, however, require a completely new approach to the development of devices. Silicon is still an attractive proposition as much is known about it and the technology is well established. Therefore, it is interesting to question the * Corresponding author. E-mail:
[email protected] † Institute for Materials Research, Tohoku University. ‡ Center for Interdisciplinary Research, Tohoku University. § Dr. Vijay Kumar Foundation. 10.1021/nl025789l CCC: $22.00 Published on Web 10/18/2002
© 2002 American Chemical Society
possibility of developing small nanotubes of silicon and their potential properties. Recently a new development has taken place in which novel metal encapsulated clusters have been obtained from silicon10,11 and germanium.12 These clusters have higher stabilities compared to pure Si or Ge clusters as well as higher symmetries. Such clusters are likely to be produced in large and size-selected quantities, which makes these new species attractive. Here we show that the clusters can be assembled to grow nanotubes of silicon stabilized by metal (M) atoms. As the structure and properties of such silicon nanotubes can be controlled by a suitable choice of M atom, this could offer a new way of developing components for nanodevices. There have been a few efforts to understand the properties of silicon in the form of a nanowire. Read et al.13 have studied the photoluminescent properties of Si nanowires by considering a rectangular cross section of silicon and showed that such structures have a direct band gap as compared to bulk Si, which is an indirect band gap semiconductor. Grossman and Mitas14 studied silicon nanowires of finite sizes by stacking triangular units of Si capped with a Si atom. These structures are not symmetrically stacked but rather have tendencies for distortion. The stability of these finite wires was found to increase by changing the capping atom to a divalent M atom. Hypothetical zigzag and armchair Si nanotubes having structures similar to carbon nanotubes have been shown to be metallic or semiconducting15 from firstprinciples calculations. However, it is unlikely that such nanotubes can be realized, as high-temperature calculations show agglomeration of Si.16 Menon et al.17 have shown that
Figure 1. Finite undoped Si nanostructures: (a) Si24, (b) Si36, and (c) Si48.
the icosahedral structure of Si could be stabilized by Ni doping. They have considered the possibility of making a nanotube of staggered pentagons of silicon with Ni atoms placed between. However, formation of a nanotube from icosahedral clusters would first require dissociation of the capping Si atoms. On the other hand, W doping has been shown to lead to Si12W clusters with hexagonal prism structure.18 Unfortunately though, due to the large size of W, it is not possible to stabilize a hexagonal nanotube or nanowire with W doping, as the structures become distorted. Recently a chair-shaped Si12Be structure has been shown to be stable and have the lowest energy.19 Here we show that these units can serve as the building blocks for the development of symmetric hexagonal nanotubes. As M encapsulation leads to several new forms of silicon with differing properties, the cluster assembly approach could play an important role in developing novel nanostructures. Our effort has been to explore the possibility of stable thin nanowires or nanotube forms of Si. Hexagonal units are an interesting possibility as a building block since their sp2 bonding may be stabilized with M encapsulation in Si nanostructures. To achieve this, we performed ab initio calculations of the total energies to obtain the optimized atomic structures and electronic properties of finite and infinite Si nanotubes with and without doping of Be atoms. We used a planewave method20 incorporating density functional theory within the generalized gradient approximation for the exchange-correlation energy21 with ultrasoft pseudopotentials22 for Be and Si. The cutoff energy for the plane wave expansion was taken to be 300 eV. Γ-point sampling was used for the Brillouin zone integrations in the case of finite nanotubes, and 15 k-point sampling along the nanotube axis was used for the optimization of the infinite nanotubes. Optimizations were performed without symmetry constraint until the forces were converged to 0.001 eV/Å. The band structures of the infinite nanotubes were calculated by considering 256 k-points in the half Brillouin zone along the nanotube axis. We first studied the stability of finite undoped silicon nanotubes, considering stacking of six-membered units of chair shape. The optimized structures of these short nanotubes show a tendency for agglomeration to 3-D structures as shown in Figure 1, where several of the atoms can be seen to become somewhat tetrahedrally coordinated, demonstrating Si’s clear preference for sp3 bonding. Therefore it is unlikely that long symmetric Si wires of small dimension can be assembled directly from such units. This result is not unexpected, as clusters of pure Si with up to about 10 atoms 1244
have close-packed structures. Larger clusters have prolate structures, and above 27 atoms there is a transition23 from prolate to 3-D structures. To stabilize these finite nanotubes we tried doping with Be atoms. We placed two or three Be atoms in a Si12 cluster as shown in Figure 2a in order to examine the structural stability as a function of the number of Be atoms. We find that in all cases the Si12 cluster has a chair structure of sixmembered units. Packing of two Si12Be clusters as shown in Figure 2b results in a transformation from chair-shaped units to those of hexagonal shape. Thus M doping provides not only stability but also long-range ordering in the nanotube. The amount of doping and the position of the Be atoms control the symmetry, HOMO-LUMO gap, and stability of the nanotube. The binding energies (BEs) and gaps are listed in Table 1. It can be seen that a different distribution of Be atoms or an increase in the number of Be atoms placed between the Si12M units can lead to distortions in the structure. The optimized structures show that the Be atoms are not at the center of the Si12 units but displaced toward one of the hexagons in order to provide optimal bonding with the Si atoms. Considering three units of Si12Be, we find that the rings are again stable and hexagonal in shape but the Be atoms are not symmetrically arranged due to their odd number (Figure 2c (I)). There is a double well potential for the central Be atom between the two central rings. Another arrangement of Be atoms (Figure 2c (II)) shows the doped portion of the nanotube to be symmetric, while the undoped portion is distorted, giving a clear indication of stabilization due to M doping. Further doping of Be atoms between the Si12Be units slightly distorts the nanotube structure. We find the BEs and HOMO-LUMO gaps for the three cases to be quite close (Table 1). Further continuation of the packing leads to a symmetric (Si12Be)4 nanotube (Figure 2d (I)). This structure has a reflection plane passing through its center, normal to the tube axis. Interestingly, this nanotube is composed of two units of the Si24Be2 structure shown in Figure 2b (I). Thus, Si24Be2 represents a stable unit that can be repeated to obtain a nanotube of desired length. Another distribution of dopants in which the two central Be atoms are located further from the central Si rings was found to be higher in energy. Again if a different distribution is taken in which four Be atoms are placed between successive hexagons (Figure 2d (II)), then the doped portion is quite symmetric but the remaining nanotube becomes distorted, as was found in the case of (Si12Be)3. Further doping with Be such that there is one Be atom Nano Lett., Vol. 2, No. 11, 2002
Figure 2. Finite doped Si nanostructures: (a) Si12Bex (x ) 2 and 3), (b) Si24Bex (x ) 2 and 3), (c) Si36Bex (x ) 3 and 5), and (d) Si48Bex (x ) 4 and 7). Groups I and II represent structures with the same number of Si and Be atoms but different distributions of Be atoms, while the structures in group III have higher concentrations of Be atoms. Table 1: Binding Energies (BEs) and HOMO-LUMO Gaps for the Doped Si Nanostructures, Where (I) and (II) Refer to Two Different Distributions of Be Atoms (Figure 2) system
BE (eV/atom)
gap (eV)
Si12Be2 (I) Si12Be2 (II) Si12Be3 Si24Be2 (I) Si24Be2 (II) Si24Be3 Si36Be3 (I) Si36Be3 (II) Si36Be5 Si48Be4 (I) Si48Be4 (II) Si48Be7
3.74 3.65 3.62 3.81 3.81 3.82 3.83 3.84 3.83 3.86 3.86 3.84
1.71 1.01 1.04 1.00 1.28 0.91 0.62 0.59 0.51 0.42 0.62 0.42
between hexagons leads to slight distortions in the nanotube. This is due to the variations in the Si-Be bond lengths as the Be atoms are not symmetrically distributed. The BEs for the different distributions again remain nearly the same. However, the HOMO-LUMO gap shows significant variation. These results demonstrate that nanotubes with stoichiometry (Si12Be)n are quite symmetric and stable. However, an increase in doping tends to lead to a disordered distribution of Be atoms that gives rise to distortions in the nanotube. Table 1 shows the BE per atom and the HOMO-LUMO gaps for the doped nanostructures. For the short finite nanotubes, the gap depends not only on the number of dopants but also on the position of the dopant in the nanotube. In the case of Si12Be2 the two different configurations have different binding energies and gaps. The cluster with the higher binding energy has the higher gap. However, we found a mixed trend for variation in the gap with respect to binding energy in the other cases. Increasing the number of dopant atoms from two to three in Si12 causes only a small Nano Lett., Vol. 2, No. 11, 2002
change in the binding energy and gap. For the unit cells containing 24-48 Si atoms, the binding energy decreases very slightly (∼0.01 eV) with increasing number of Be atoms. Our results show that Be doping can result in clusters that are quite stable, straight, and symmetric, and thus this method could be used to develop nanotubes as nanowires for device applications. We now examine the stability of doped infinite nanotubes using a unit of 12 Si atoms and one Be atom at the center, and another unit of 24 Si atoms and two, three, and four Be atoms as shown in Figure 3. The structures were optimized with respect to the cell size along the nanotube axis, allowing the atoms to freely relax. The BEs in these cases are higher than in the finite systems. Like the finite nanotubes we find that the Be atoms in the lowest energy structures of Si24Be2, Si24Be3, and Si24Be4 do not lie exactly between the hexagonal rings but slightly toward one ring. Interestingly, though, for Si12Be the Be atoms are centered. One Si24Be2 nanotube (Figure 3b (I)) is nearly degenerate with the ground state (Figure 3b (II)) and has the same structure and BE as Si12Be. The placement of Be in the lowest energy Si24Be2 nanotube (Figure 3b (II)) is the same as for the symmetric finite structures seen in Si24Be2 and Si48Be4 (Figures 2b (I) and 2d (I)). Thus we might consider these as building blocks for the infinite nanotubes. As shown in Table 2, the BEs are nearly the same for all of the structures. This is indicative of the weak interaction between Be atoms. A plot of the band structure for Si24Be4 is shown in Figure 4a. The band crossing near the Fermi energy shows the metallic character of this infinite nanotube. This behavior occurs in all the nanotubes studied here. Be is not directly responsible for the metallic behavior of this system, as even a hypothetical Si nanotube with the same structure is metallic (Figure 4b). It can be seen that some of 1245
Figure 3. Infinite Si nanotubes with different doping concentrations: (a) Si12Be, (b) Si24Be2, (c) Si24Be3, and (d) Si24Be4. For Si24Be2, structure I is the same as that of Si12Be, while structure II is very slightly lower in energy.
Figure 4. Band structure of the infinite (a) Si24Be4 nanotube and (b) hypothetical Si24 nanotube with the same structure as in (a). The Fermi energies are represented by the dashed lines. Table 2: Binding Energies (BEs) for the Doped Infinite Nanotubes system
BE (eV/atom)
Si12Be Si24Be2 (I) Si24Be2 (II) Si24Be3 Si24Be4
3.92 3.92 3.92 3.93 3.90
the bands are nearly unchanged by Be doping. However, a rigid band model is not applicable. To further understand the role of the Be atoms, we determined the local charges by integrating the electron density over Voronoi cells. The results show a small charge transfer to Be due to its deeper potential, which leads to the occupation of the p states. The bonding can be considered predominantly sp2 like within the hexagonal rings and p-p like between the rings. There is a small depletion of charge from the lobes protruding from the rings to the space between 1246
the Si and Be atoms. Thus, the major role of Be is to stabilize the packing of the hexagonal rings. The partial density of states (Figure 5) shows that there are only two nonequivalent atoms, as can be expected from the symmetry of the structure. Figures 5b and c show that the states near the Fermi energy arise mostly from the Be and Si p levels, showing hybridization of the p states. It may be possible to change this character by changing the dopant. We also performed a charge density analysis by subtracting the charge densities of Si24 and Be4 at their respective positions from that of Si24Be4. Examination of the charge accumulation and depletion (Figure 6) shows that a strong depletion of charge takes place between the Be atoms, implying that there is no dimerization of the Be atoms. Observing the accumulation, we find that maximum charge is accumulated between the Be atom and the nearest Si ring, while a very slight charge transfer takes place between the Be atom and the other Si ring. This provides further evidence Nano Lett., Vol. 2, No. 11, 2002
Figure 6. (a) Charge accumulation and (b) charge depletion calculated by subtracting the charge densities of isolated Si24 and Be4 at their respective positions from the charge density of the infinite Si24Be4 nanotube.
Figure 5. (a) Total density of states (DOS) as a function of energy for the infinite Si24Be4 nanotube. (b) and (c) represent the Si and Be partial DOS, respectively. The s, p, and d partial DOS are represented by the red, green, and blue lines, respectively. The Fermi energy is represented by the vertical dotted line.
that the Be atoms provide stability to the Si hexagonal rings. These results should be contrasted with the possibilities of metal-encapsulated carbon nanotubes as the bonding in the carbon nanotube is much stronger than in Si. Thus, doping of the carbon nanotube generally does not change its structure. However, for Si, metal doping has a very important role in controlling the structure as shown here as well as for metal-encapsulated clusters.10-12 In summary, we have examined the stability of finite and infinite Si nanotubes doped with Be. We find that pure Si cannot be expected to form thin nanowires/nanotubes, but doping with Be provides stability to the nanotube structures. The HOMO-LUMO gaps of the finite tubes can be changed Nano Lett., Vol. 2, No. 11, 2002
by a suitable amount of doping. The best structures are obtained from assemblies of Si12Be units. Doped infinite Si nanotubes are most stable, symmetric, and metallic. The transport behavior of such wires could be modified by suitable doping that would affect the distribution of states around the Fermi energy. This could lead to interesting transport properties in that the transport in such nanotubes could be along the center or the surface of the tube. Moreover, metal chains have been a subject of much current interest. Metal encapsulation of silicon could offer a novel way of combining the properties of metal atomic wires as well as a tubular structure of silicon including tubular superlattices to realize promising new nanostructures for future nanodevice technology. Acknowledgment. The authors are grateful to Professor Marcel Sluiter for helpful scientific discussions. We thankfully acknowledge the support of the staff of the Center for Computational Material Science, IMR, Tohoku University for the use of the SR8000/H64 supercomputer facilities. A.K.S. is also thankful for the support of Monbusho. V.K. gratefully acknowledges the hospitality at IMR and CIR of Tohoku University. References (1) Huang, Y.; Duan, X.; Cui, Y.; Lauhon, K. K.; Lieber, C. M. Science 2001, 294, 1313. (2) Huang, Y.; Duan, X.; Wei, Q.; Lieber, C. M. Science 2001, 291, 630. (3) Cui, Y.; Lieber, C. M. Science 2001, 291, 851. (4) Tsutsumi, T.; Tomizawa, K. J. Vac. Sci. Technol. B 2000, 18, 2640. (5) Chung, S.; Yu, J.; Heath, J. R. Appl. Phys. Lett. 2000, 76, 2068. (6) Brus, L. J. Phys. Chem. 1994, 98, 3575. (7) Polmen, A. Nature Mater. 2002, 1, 10. 1247
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NL025789L
Nano Lett., Vol. 2, No. 11, 2002
