23633
2006, 110, 23633-23636 Published on Web 10/27/2006
Density Functional Theory Study of Geometrical Structures and Electronic Properties of Silica Nanowires Dongju Zhang,*,† Guanlun Guo,† Chengbu Liu,† and R. Q. Zhang‡ Institute of Theoretical Chemistry & School of Chemistry and Chemical Engineering, Shandong UniVersity, Jinan, 250100, P. R. China, and Center of Super-Diamond and AdVanced Films (COSDAF) & Department of Physics and Materials Science, City UniVersity of Hong Kong, Hong Kong SAR, China ReceiVed: August 11, 2006; In Final Form: October 9, 2006
Silica nanowires are expected to possess structural diversity like bulk silica. We modeled three silica nanowires based on the side-shared two-membered rings, spiro-united two-membered rings, and three-membered rings, respectively. By performing density functional theory calculations, we studied their geometrical structures and electronic properties with and without the presence of external electric field. It is found that the stability of silica nanowires increases with length and diameter. As indicated by calculated large HOMO-LUMO gaps, silica nanowires are expected to be good insulating materials. The energy gaps, however, gradually decrease with applied electronic field and finally close, resulting in the breakdown of the insulating nanowires. Moreover, it is shown that the breakdown threshold remarkably increases with the nanowire diameter. These significant findings from the present calculations for the simplest silica nanowires will provide relevant insight into the structures and properties of much more complicated real silica nanowires.
In recent years, great progress in the synthesis of onedimensional (1D) nanomaterials has been driven due to their potential applications in fabricating nanoscale electronic and optoelectronic devices.1 As an important photoluminescence and waveguide material, silica (SiO2) nanowires are of special interest among inorganic nanowires. Several advanced methods have been used to synthesize silica nanowires, such as excimer laser ablation,2 carbothermal reduction,3 catalyzed thermal decomposition,4 electrochemically induced sol-gel,5 chemicalvapor deposition,6 and complex template assisted polymerizations/condensations.7 With the great success in fabricating silica nanowires, it becomes increasingly interesting to develop their potential applications in nanotechnology. For example, silica nanowires have been found to be able to emit intense blue light and thus are expected to have potential applications in highresolution optical heads of scanning near-field optical microscope or nanointerconnections in future integrated optical devices.2 Several recent theoretical studies have shown that silica nanowires possess large energy gaps between the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) and thus were proposed to be good insulating materials.8-10 It should be noted that in many practical applications, insulating materials are in an applied external electric field. So apart from size, the external electric field can be regarded as another important parameter to modulate the structures and properties of nanoscale materials and devices. Insulating materials, however, will be subject to damage (breakdown) in a strong electric field; i.e., their HOMO/LUMO energy levels will cross and the HOMO-LUMO gaps will close. * Corresponding author. E-mail address:
[email protected]. † Shandong University. ‡ City University of Hong Kong.
10.1021/jp0652143 CCC: $33.50
In this sense, it is interesting to study the transitions of the structures and properties of silica nanowires induced by the applied electric field, which is of crucial importance in fabricating novel nanodevices. Recently, Sun et al.10 reported the breakdown behavior of silica nanowires in an applied electric field by performing density functional theory (DFT) calculations. They modeled a silica nanowire using the thinnest silica molecular chain consisting of the side-shared two-membered rings (ES-2MRs), as shown by panel a in Figure 1 (referred to as the silica nanochain hereafter), and predicted that the silica nanochain would be broken when the applied field is 22 MV cm-1 (8.1 V). It should be borne in mind that silica nanowires were synthesized via various methods,2-7 and thus they are expected to possess characteristic microstructures and unique properties. In other words, the structures of silica nanowires depend on the given synthesis conditions. Very recently, to understand the nucleation and growth mechanism of silica nanowires, several appropriate structural models of silica nanowires have been proposed.8-10 Because bulk silica is a good insulating material with a HOMO-LUMO gap of around 9.2 eV,11,12 it is interesting to study how the HOMO-LUMO gap changes with dimension and applied electric field. In the present work, aiming at providing useful information for developing the potential applications of silica nanowires, we focus our attention on the structures and properties of silica nanowires and study their behaviors in an applied electric field. It is well-known that the structures of nanomaterials are generally very different from their bulks. In the immense variety of bulk silica, six- and eight-membered rings are most common, which form three-dimensional networks via the silicon-centered, corner-sharing SiO4 tetrahedra. Fewer-membered rings, how© 2006 American Chemical Society
23634 J. Phys. Chem. B, Vol. 110, No. 47, 2006
Letters
Figure 1. Structural models of silica nanowires: (a) a ES-2MR nanochain of (SiO2)12 assembled from the ES-2MRs; (b) a SU-2MR nanorod of (SiO2)12 assembled from the SU-2MRs; (c) a 3MR-based nanostrip of (SiO2)16 assembled from the 3MRs.
ever, such as four- (4MR), three- (3MR), and extreme twomembered (2MR) rings, have been experimentally confirmed to be more frequent in nanometer-sized silica particles than in the bulk.13-15 We here model silica nanowires using the 2MR and 3MR as the building blocks. The rationality of assembling these fewer-membered rings into tailored silica nanostructures has been confirmed in recent publications.8-10,16-18 Figure 1 shows three structural models of silica nanowires: (a) the thinnest silica nanochain based on the side-shared 2MRs (ES2MRs),10,11 (b) the compact silica nanorod based on spiro united 2MRs (SU-2MRs),8 and (c) the extended silica nanostrip based on the magic 3MR molecular rings.9 We have performed density functional theory (DFT) calculations for a series of clusters of each silica nanowire, (SiO2)n, with sizes varying from n ) 2 to 26 using Gaussian 03 code.19 Full geometry optimizations without constraining the cluster symmetry were undertaken at the B3LYP/6-31G(d) level of theory. This combination of the hybrid functional and the standard polarization basis set has been shown in numerous previous studies to be suitable for modeling silica systems.8,9,20,21 Our calculated results show that all three silica nanowires gracefully extend along the axes, as shown in Figure 1. To examine whether the optimized structures are real minima, the harmonic vibrational frequencies were computed at the same level for all clusters considered. There is no any imaginary frequency for every silica cluster, indicating these nanowires are dynamically stable. To assess the relative stabilities of these silica nanowires, we calculated their binding energies (Eb) per SiO2 unit, which is defined as the energy difference between the total energy of a cluster and the corresponding isolated monomers, as given by
Eb ){E[(SiO2)n] - nE(SiO2)}/n
(1)
where E(SiO2) and E[(SiO2)n] are the energies of monomer SiO2 and its cluster (SiO2)n, respectively. The negative value of Eb denotes an exothermic process. The smaller the value of Eb is,
the larger the stability of the silica cluster is. We find that the stabilities of three silica nanowires monotonously increase with the cluster size but at different speeds, as shown by curves a-c in Figure 2. Clearly, the ES-2MR chains are energetically favorable structures for the small clusters due to their small numbers of the dangling bonds. The intrinsic strain in the ES2MR chains, however, plays an inverse role for stabilizing silica clusters. Thus the silica nanochain becomes energetically less favorable with size as compared with the nanorod and nanostrip. Of course, we must stress that ground state motifs are not always necessary during 1D nanomaterial growth,22 as confirmed by the recent experiments.23 Considering the structural diversity of silica nanowires, we believe that all three structures shown in Figure 1 can be regarded as appropriate models of silica nanowires. Our calculations demonstrate that these three silica nanowires possess identical frontier orbital characteristics: both the HOMOs and LUMOs highly localized on the ends of the nanowires, indicating that these ends are highly reactive and favorable to the continuous growth of the nanowires. Further, it is noted that the HOMOs mainly consist of the lone-pair orbitals on O atoms, whereas the LUMOs are characterized by large contributions from partly occupied p orbitals on Si atoms with some admixture of O-based orbitals. The varieties of the HOMO-LUMO energy gaps for the three silica nanowires with cluster sizes are shown by curves d-f in Figure 2. Clearly, the gap for each nanowire increases with the cluster size and rapidly tends to a constant, which is 6.45 eV for the ES-2MR nanochain, 5.91 eV for the SU-2MR nanorod, and 6.15 eV for the nanonstrip. These large HOMO-LUMO gaps indicate that silica nanowires possess high chemical stability and good insulating capability like bulk silica. However, as mentioned above, in many practical applications insulating materials are in an applied external electric field. So it is interesting to study the transitions of structures and properties of silica nanowires induced by an external electric field. To study the behaviors of the HOMOs and LUMOs of the silica nanowires in an applied electric field, we choose three
Letters
J. Phys. Chem. B, Vol. 110, No. 47, 2006 23635
Figure 2. Binding energies (Eb) and HOMO-LUMO gaps (Eg) as a function of the cluster size. (a), (b) and (c) denote Eb’s of the ES-2MR chain, SU-2MR rod, and 3MR-based strip, respectively, and (d), (e) and (f) are the corresponding Eg’s.
Figure 3. Variation of the HOMO/LUMO levels with the applied field for three silica nanowires, as shown by the insets. Filled circles, triangles, and asterisks indicate the calculated HOMO levels, empty circles, triangles, and asterisks mean the corresponding LUMO levels. The solids and dotted lines indicate the linearly fitted results, respectively. The arrows near the insets indicate the directions of applied electric fields.
representative structures, (SiO2)12 for the 2MR nanochain, (SiO2)16 for the SU-2MR nanorod, and (SiO2)24 for the 3MR nanostrip, as shown in Figure 1. We apply uniform electric fields along the nanowire axis for all three nanowires and fully optimize their geometries at the B3LYP/6-31G(d) level. The magnitude of the field varies from 5.14 to 56.56 MV cm-1. Figure 3 shows the calculated results for three silica nanowires. We find that both the HOMO and LUMO levels for each nanowire vary linearly but with different trends: the former monotonously increases, whereas the latter decreases over the range. Thus the HOMO-LUMO gap reduces with the applied field, and finally a cross between the HOMO and LUMO levels will occur as the field is strong enough. The magnitude of the field corresponding to the intersection is referred to as the “breakdown threshold” of the nanowire, which is an important index for assessing the insulating property of materials. This breakdown behavior can be correlated with the polarizing effect of the applied electric field on the nanowire. The applied electric
field induces the nanowire to produce a dipole, which causes the shift of the electron density from the induced positive end to the induced negative end and results in the redistributions of the energy levels and the compositions of the molecular orbitals. As a result, the electron-donating HOMO is destabilized due to the increase of the Coulomb repulsion and the electronaccepting LUMO is stabilized due to the increase of the Coulomb attraction. Thus the HOMO/LUMO gap is reduced and finally closed. The calculated data are fitted to extrapolate the breakdown threshold. As shown in Figure 3, the breakdown thresholds are about 29 MV cm-1 for the ES-2MR nanochain, 57 MV cm-1 for the nanorod, and 104 MV cm-1 for the nanostrip, respectively. These large values of breakdown thresholds indicate that the silica nanowires are highly resistive to the external electric field. From the present calculations it appears that the breakdown threshold is sensitive to the diameter of silica nanowires; i.e., the breakdown threshold remarkably increases with the diameter. The conclusion, however, would not simply extend to bulk silica; i.e., we cannot expect that the breakdown threshold would become much bigger for silica film and bulk. This is because that the structure of bulk silica is very different from those of nanometer-sized silica wires. The SiO4 tetrahedra containing six- and eight-membered rings dominate the immense variety of bulk silica, whereas fewermembered rings such as 2MR, 3MR, and 4MR are frequent in silica nanostructures, as demonstrated by the recent experimental and theoretical studies on nanometer-sized silica particles.8,9, 17,18, 20-22, 24-27 Thus the breakdown behavior of bulk silica in an applied electric field is expected to be quite different from silica nanowires. In this sense, it is easy to understand that the reported breakdown thresholds for the high-quality SiO2 (13.5 MV cm-1)28,29 and SiO2 film (18-27 MV cm-1)30 are smaller than those of the silica nanowires. It should be noted that the variation of the HOMO-LUMO gap for the 2MR nanochain with an applied electric field, calculated at the B3LYP/6-31G(d) level, is different from those in the previous study,10 where the calculations were performed using the same hybrid functional with a composite basis set, 6-31G(d) for O and 3-21G for Si. Obviously, this discrepancy arises from the basis set effect. It is well-known that the splitvalence basis sets extended with polarization functions is more
23636 J. Phys. Chem. B, Vol. 110, No. 47, 2006 reliable for describing the valence shell orbital of the atoms for polar compound systems, such as SiO2 considered here. In the previous study,31 it has been demonstrated that the basis sets smaller than 6-31G(d) are not suitable for calculating the structures and properties of silica nanoclusters. Thus, the present results obtained from the B3LYP/6-31G(d) calculations are expected to be reliable. In addition, it is noted that the geometry changes of the silica nanowires resulting from the applied electric field are negligible, indicating that nuclear rearrangement appears to play a less important role in the HOMO-LUMO shift. In conclusion, we have performed DFT calculations for the structures and properties of three silica nanowires with and without an applied external electric field. These three silica nanowires are found to be structurally and dynamically stable and possess large HOMO-LUMO energy gaps and good insulating capabilities. The calculated results show that the stability of silica nanowires increases with the wire length and diameter, the HOMO-LUMO energy gap is more sensitive to the wire diameter than to the wire length, and the nanowires will be subject to breakdown in the strong electric field and the breakdown threshold increases remarkably with the wire diameter. These findings from the present calculations for the simplest silica nanowires will provide valuable guidance for the potential application of silica nanowires in nanoscience and nanotechnology. Acknowledgment. The work described in this paper was supported by the National Natural Science Foundation of China (No. 20473047) and the Major State Basic Research Development Program of China (No. 2004CB719902). We thank the High Performance Computational Center of Shandong University for computer resources. References and Notes (1) Huang, M.; Mao, S.; Feick, H.; Yan, H.; Wu, Y.; Kind, H.; Weber, E.; Russo, R.; Yang, P. Science 2001, 292, 1897-1899. (2) Yu, D. P.; Hang, Q. L.; Ding, Y.; Zhang, H. Z.; Bai, Z. G.; Wang, J. J.; Zou, Y. H. Appl. Phys. Lett. 1998, 73, 3076-3078. (3) Wu, X. C.; Song, W. H.; Wang, K. Y.; Hu, T.; Zhao, B.; Sun, Y. P.; Du, J. J. Chem. Phys. Lett. 2001, 336, 53-56. (4) Liu, Z. Q.; Xie, S. S.; Sun, L. F.; Tang, D. S.; Zhou, W. Y.; Wang, C. Y.; Liu, W.; Li, Y. B.; Zou, X. P.; Wang, G. J. Mater. Res. 2001, 16, 683-686. (5) Xu, D. S.; Yu, Y. X.; Zheng, M.; Guo, G. L.; Tang, Y. Q. Electrochem. Commun. 2003, 5, 673-676. (6) Zheng, B.; Wu, Y. Y.; Wang, P. D.; Liu, J. AdV. Mater. 2002, 14, 122-124. (7) Yang, S. M.; Yang, H.; Coombes, N.; Sokolov, I.; Kresge, C. T.; Ozin, G. A. AdV. Mater. 1999, 11, 52-55.
Letters (8) Zhang, D. J.; Zhang, R. Q. Chem. Phys. Lett. 2004, 394, 437440. (9) Zhang, D. J.; Zhang, R. Q. J. Phys. Chem. B 2006, 110, 13381343. (10) Sun, Q.; Wang, Q.; Kawazoe, Y.; Jena, P. Nanotechnology 2004, 15, 260-263. (11) Xu, Y. N.; Ching, W. Y. Phys. ReV. B 1991, 44, 11048-11059. (12) Fisher, B.; Pollak, R. A.; Distefano, T. H.; Grobman, W. D. Phys. ReV. B 1977, 15, 3193-3199. (13) Galeener, F. L. Solid State Commun. 1982, 44, 1037-1040. (14) Pasquarello, A.; Car, R. Phys. ReV. Lett. 1998, 80, 5145-5147. (15) Umari, P.; Gonze, X.; Pasquarello, A. Phys. ReV. Lett. 2003, 90, 027401. (16) Bromley, S. T. Nano Lett. 2004, 4, 1427-1432. (17) Zhao, M. W.; Zhang, R. Q.; Lee, S. T. Phys. ReV. B 2004, 69, 153403. (18) Lu, W. C.; Wang, C. Z.; Ho, K. M. Chem. Phys. Lett. 2003, 378, 225-231. (19) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision D.01; Gaussian, Inc.: Wallingford, CT, 2004. (20) Bromley, S. T. Nano Lett. 2004, 8, 1427-1432. (21) Flikkema, E.; Bromley, S. T. J. Phys. Chem. B 2004, 108, 96389645. (22) Bromley, S. T.; Zwijnenburg, M. A.; Flikkema, E.; Maschmeyer, T. Phys. ReV. Lett. 2004, 92, 039602. (23) Kronik, L.; Fromherz, R.; Ko, E.; Gantefor, G.; Chelikowsky, J. R. Nature Mater. 2002, 1, 49-53. (24) Uchino, T.; Aboshi, A.; Kohara, S.; Ohishi, Y.; Sakashita, M.; Aoki, K. Phys. ReV. B 2004, 69, 155409. (25) Zhang, D. J.; Zhang, R. Q.; Han, Z.; Liu, C. B. J. Phys. Chem. B 2006, 110, 8992-8997. (26) Zhang, D. J.; Zhang, R. Q. J. Phys. Chem. B 2006, 110, 1526915274. (27) Zhang, D. J.; Wu, J.; Zhang, R. Q.; Liu, C. B. J. Phys. Chem. B 2006, 110, 17757-17762. (28) Murrell, M. P.; Welland, M. E.; O’Shea, S. J.; Wong, T. M. H.; Barnes, J. R.; McKinnon, A. W.; Heyns, M.; Verhaverbeke, S. Appl. Phys. Lett. 1993, 62, 786-788. (29) Sofield, C. J.; Stoneham, A. M. Semicond. Sci. Technol. 1995, 10, 215-244. (30) Pompl, T.; Engel, C.; Wurzer, H.; Kerber, M. Microelectron. Reliab. 2001, 41, 543-551. (31) Nedelec, J. M.; Hench, L. L. J. Non-Cryst. Solids 2000, 277, 106113.
