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Structure and Electronic Properties of Saturated and Unsaturated Gallium Nitride Nanotubes Zhiguo Wang,*,†,‡ Shengjie Wang,† Jingbo Li,*,‡ Fei Gao,*,§ and William J. Weber§ Department of Applied Physics, UniVersity of Electronic Science and Technology of China, Chengdu, 610054, People’s Republic of China, State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, People’s Republic of China, and Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352 ReceiVed: August 8, 2009; ReVised Manuscript ReceiVed: September 21, 2009
The atomic and electronic structures of saturated and unsaturated GaN nanotubes along the [001] direction with (100) lateral facets are studied using first-principles calculations. Atomic relaxation of nanotubes shows that appreciable distortion occurs in the unsaturated nanotubes. All the nanotubes considered, including saturated and unsaturated ones, exhibit semiconducting, with a direct band gap. Surface states arisen from the 3-foldcoordinated N and Ga atoms at the lateral facets exist inside the bulklike band gap. When the nanotubes are saturated with hydrogen, these dangling bond bands are removed from the band gap, but the band gap decreases with increasing the wall thickness of the nanotubes. 1. Introduction One-dimensional semiconductor nanostructures are receiving ever-increasing attention because of their potential applications in single-electron memories,1 nanowire laser,2 and singlemolecule sensors.3 As an important III-V semiconductor, gallium nitride (GaN) is a wide-band-gap semiconductor of interest for high brightness, blue light-emitting diodes, laser, and flat panel displays.4 Rapid synthesis of GaN nanostructures is now being explored due to their importance in basic scientific research and potential technology applications.5–7 Indeed, onedimensional GaN nanowires and nanotubes have been achieved using various chemical/physical methods.8–14 Some of these nanostructures have demonstrated interesting electronic properties that have demonstrated important applications in optoelectronic nanodevices.15–18 For these nanowires, most atoms are positioned in the cores of crystalline wurtzite wires. Compared with bulklike nanowires and nanorods, a tubular structure may offer physical properties different from the bulklike structure because they may possess higher exterior surface reactivity, which facilitates both sidewall decorations. Lee et al.19 have investigated the stabilities and electronic structures of GaN nanotubes using a self-consistent charge density, functionalbased, tight-binding method and showed that zigzag GaN nanotubes are semiconductors with a direct band gap, whereas armchair nanotubes have an indirect band gap. Furthermore, the energy gap of a zigzag GaN nanotube decreases with decreasing tube diameter. The disintegration temperature of GaN nanotubes has been investigated by Kang et al.20 using molecular dynamics simulations with Tersoff potential. The results revealed that the disintegration temperature decreases with decreasing diameter of the GaN nanotubes. In addition, the mechanical properties of single-walled GaN nanotubes investigated by Kang et al.21 and Jeng et al.22 using molecular dynamics simulations with Tersoff potentials showed strong dependence on the * Corresponding author: E-mail:
[email protected] (Z.W.), jbli@ semi.ac.cn (J.L.),
[email protected] (F.G.). † University of Electronic Science and Technology of China. ‡ Institute of Semiconductors, Chinese Academy of Sciences. § Pacific Northwest National Laboratory.
temperature and strain rate. The Young’s modulus of a (5, 5) GaN nanotube is about 796 GPa. Recently, the electronic properties of native defects and substitutional impurities in single-walled GaN nanotubes have been theoretically studied on the basis of spin-polarized density functional theory.23 However, all the above calculations are based on hypothetical single-walled GaN nanotubes, but there is no experimental evidence showing that the stable form of single-walled GaN nanotubes is successfully synthesized. The model systems of single-walled GaN nanotubes do not represent realistic singlecrystalline nanotubes, which have been prepared experimentally.12–14 The synthesized nanotubes show hexagonal cross sections, with their axial direction along the [001] direction. The side surfaces of GaN nanotubes may consist of {100} or {110} planes, but it has been shown that the nanotubes with {100} side surfaces are more stable.14 It has also been theoretically predicted that a faceted tubular structure is energetically more favorable than a standard cylindrical tube.24 The electrical properties of nanowires depend on their size, geometry, and relaxation and also on whether the dangling bonds of surface atoms are passivated with hydrogen.25,26 Subsequently, it is important to theoretically study GaN tubular nanotubes, which would provide a better understanding of their electronic and structural properties. It has been noticed that there are no comprehensive theoretical studies of atomic and electronic structures of these single-crystalline GaN nanotubes. Malkova et al.27 calculated the band structure of GaN nanotubes using a tight-binding approach, but the surfaces of nanotubes were not relaxed and reconstructed. Xu et al.28 studied the electronic and optical properties of unsaturated GaN nanotubes with a thin wall thickness 0.6 nm. The present work carries out an extensive study of saturated and unsaturated GaN nanotubes using firstprinciples density functional theory (DFT) to provide a detailed analysis, which is important not only for their applications in optoelectronic nanodevices, but also for the fundamental interest in understanding of their size effects on their atomic and electronic structures.
10.1021/jp907657z CCC: $40.75 2009 American Chemical Society Published on Web 10/09/2009
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Figure 1. Cross-section of (a) unsaturated and (b) saturated GaN nanotubes with different wall thicknesses along the [001] direction.
2. Computational Details GaN nanotubes with growth direction along the [001] direction and side surfaces of {100} planes were previously investigated, and the result revealed that the surface energy is ∼5 meV/Å2 lower than that of the (110) surface.29 The initial structures of the nanotubes are obtained by cutting the outside and inside parts of a large hexagonal GaN, as described previously.30 The inner diameter of the nanotubes is ∼1.84 nm, and the wall thicknesses of these nanotubes are 0.36, 0.64, 0.92, and 1.2 nm, which consist of 192, 324, 480, and 660 atoms, respectively. The atoms on free surfaces of these nanotubes have three coordination numbers and one dangling bond. The atomic structure and electronic properties of both unsaturated and saturated (with hydrogen) nanotubes are investigated. The top views of all the nanotubes considered are shown in Figure 1. DFT calculations were performed using the SIESTA code.31 Geometry optimization and energy calculations were carried out within the framework of local density approximation using the parametrized functional of Perdew and Zunger32 for electron exchange and correlation functional. The electron-ion interactions were described by normconserving Troullier-Martins33 pseudopotentials factorized in the Kleinman-Bylander form.34 In the pseudopotential generation, nonlinear core corrections35 were included for the Ga atom, and relativistic effects were taken into account. The reference electronic configurations for the pseudopotentials are 4s24p14d0 for the Ga atom, 2s22p3 for the N atom, and 1s1 for the H atom. The pseudopotential core radii for Ga and N were taken from the calculations performed by Al-Brithen et al.36 The valence electron wave functions were expanded using a double-ζ basis set plus polarization function. The charge density was projected onto a real space grid with a cutoff of 90 Ry to calculate the self-consistent Hamiltonian matrix elements. Periodic boundary conditions were applied along the tube axis (taken as the z axis), and sufficient vacuum space (up to 1.0 nm) was retained along the x and y directions to make sure that there was no interaction between the GaN nanotube and its image. The supercells of the GaN nanotubes contain four layers of atoms along the tube axis. The Brillouin zone was sampled by (1 × 1 × 6) mesh points in the k space within the Monkhorst-Pack scheme.37 The test calculations with the Brillouin zone sampled by (1 × 1 × 10) mesh points gave the same results. The criterion of convergence for energy was chosen to be 10-5 eV between two ionic steps, and the maximum force allowed on each atom was 0.05 eV/Å. The optimized lattice parameters for wurtzite bulk GaNsa ) 3.24 Å, axial ratio c/a ) 1.623, and internal parameter u ) 0.377sare in very agreement with the experimental values: a ) 3.19 Å, c/a ) 1.627, u ) 0.377.38
Figure 2. (a) Atomic arrangements of a section in a hexagonal GaN nanotube, illustrating the Ga-N bond along the axial direction L//, tilted Ga-N bond with a N atom at the outmost layer LX_N and tilted Ga-N bond with a Ga atom at the outmost layer LX_Ga, and (b) a cross section of the GaN nanotube wall showing the surface rippling and Ga and N layers, which is part of the unsaturated GaN nanotube with thickness of 0.92 nm in Figure 1 enclosed by the dotted line.
3. Results and Discussion The relaxed configurations of the unsaturated nanotubes show that the atoms of the outer surface layer undergo a bond-length contraction, where the N surface atoms relax only parallel to the surface, but the Ga surface atoms relax both parallel and perpendicular to the surface, moving radically inward by 0.025-0.028 nm (depending on the thickness of the nanotube) and leading to the buckling of the Ga-N dimers. In fact, this phenomenon has also been found in recent first principles calculations for AlN nanowires.39 The Ga-N bond lengths along the axial direction are obviously different from those on the surface and in the middle region. Surface Ga-N bond lengths along the [001] direction remarkably contracted, ranging from 1.843 to 1.852 Å (see L// in Figure 2), which were somewhat smaller than those of bulk GaN and contracted 6.0-7.3%, as compared to the corresponding bulk value. These values are close to the contractions of GaN nanowires.25,40 The length of the surface tilted Ga-N bond with a N atom at the outmost layer (see LX_N in Figure 2) ranges from 1.915 to 1.931 Å, whereas the length of the tilted Ga-N bond with a Ga atom at the outmost layer (see LX_Ga in Figure 2) ranges from 1.931 to 1.948 Å. These lengths are close to those in the bulk GaN, whereas the LX_Ga is longer than the LX_Ga at the surface of the nanotubes, which is induced by the different relaxations of the Ga and N atoms on the surfaces. Upon relaxation, the inner surface Ga and N atoms all move outward, but not by the same amount; the relaxation of the N
Saturated and Unsaturated GaN Nanotubes
Figure 3. The rippling as a function of atom layers, where the positive value indicates the N atom layer located outside the Ga atom layer, and negative value via versus.
atom is very small, only about 0.1-0.2 Å, while Ga relaxes about 0.3-0.4 Å from its bulk position. The bond lengths of L//, LX_N, and LX_Ga (Figure 2) are in the range of 1.845-1.856, 1.921-1.952, and 1.937-1.952 Å, respectively. In the middle region, the bond length remains very close to the bulk value, and the relaxations of atoms are very small. The averaged Ga-N bond lengths at the surfaces of GaN nanotubes is smaller than that in the bulk, which is due to reduced coordination numbers. Similar distortion has also been observed in other wurtzite nanowires with hexagonal cross sections, such as ZnS,41 CdS, CdSe,42 and AlN.39 The obvious difference between the optimized and initial structures is that the in-plane Ga-N bonds on the surface are no longer within the same plan after relaxation due to the buckling of the Ga-N atoms. We define rippling to represent the distance between the Ga atom layer and the N atom layer in the directions parallel to the surface (as shown in Figure 2b). The rippling as a function of atom layers is shown in Figure 3. The positive value indicates that the N atom layer is outside the Ga atom layer, and the negative value, vice versa. From the figure, we can see that the rippling is very small in the middle of the nanotubes with large thicknesses. It can also be found that the rippling increases with decreasing thickness of the nanotubes. For example, the rippling is 0.28 and 0.25 Å for the outermost layer in the nanotubes with thicknesses of 0.36 and 1.2 nm, respectively.
J. Phys. Chem. C, Vol. 113, No. 44, 2009 19283 The facets of hexagonal nanotubes contain an equal number of cations and anions, and thus, surfaces are nonpolar. There is one dangling bond per surface atom, and therefore, only one H-atom is required to passivate each surface atom of the GaN nanotubes. Upon the passivation of the surface atoms by H-atoms, the bond length of the Ga-N bond does not change, and the contraction is less than 1%. However, the Ga-H and N-H bond lengths are different because of the different ionicities of Ga and N ions, and their values are approximately 1.559 and 1.038 Å, respectively. The band structures of unsaturated and saturated GaN nanotubes along the Γ-X direction (parallel to the growth direction of the nanotube) are shown in the top and bottom of Figure 4, respectively. All the wires exhibit a semiconducting character, with a direct band gap at the Γ point, which suggests that these nanotubes may preserve strong electroluminescence, and thus, have high potential for full-color display applications.43,44 In the unsaturated nanotubes, surface states appear in the fundamental electron energy gap. Because the actual band gap without surface states is unknown, we define here an apparent energy gap as the energy difference between the topmost filled valence state and the lowest state in the conduction band. It can be clearly seen that the “band gaps” for the unsaturated nanonanotubes are smaller than those for the saturated ones. This may be due to the existing dangling bonds of edge atoms on the unsaturated surface. These dangling bonds produce edgeinduced states (bands) in the band gaps located above the valence band maximum (VBM) and below the conduction band minimum (CBM). It is of interest to note that this phenomenon is quite different from ZnO nanowires, in which surface states lie just below the VBM or above the CBM.45 Furthermore, the band gap of unsaturated nanotubes (i.e., the gap between the surface atom-induced states) does not change significantly with the nanotube thickness, since surface states are quite localized. When the nanotubes are saturated with hydrogen, these danglingbond bands are removed from the band gap, and the band gap generally decreases with increasing nanotube wall thickness. The band gap is 1.78, 1.57, 1.60, and 1.58 eV for the unsaturated nanotubes with a thickness of 0.36, 0.64, 0.92, and 1.20 nm,
Figure 4. The band structures of the unsaturated (top) and the saturated (bottom) GaN nanotubes with an inner diameter of 1.84 nm, but with different wall thickness. The Fermi energy is denoted by the dashed lines.
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Figure 5. Projected density of states for the unsaturated (left) and the saturated (right) GaN nanotubes.
respectively, whereas the band gap is 4.04, 3.29, 2.97, and 2.75 eV for the saturated nanotubes, respectively. To gain more insights into the detailed characteristics for the top of the valence bands and the bottom of the conduction band, the projected density of states (PDOS) of surface and core atoms onto the Ga and N atoms of unsaturated and saturated GaN nanotubes are shown in the left and right of Figure 5, respectively. All the nanotubes show semiconducting behavior. In general, the shapes of the PDOS are similar for the unsaturated and saturated GaN nanotubes, but the band gap of the saturated nanotubes increases in energy with decreasing nanowire thickness, which is associated with quantum confinement effects. For the unsaturated nanowires, there appears a peak at -2.2 eV, and this is due to the fact that the 3-fold-coordinated Ga atoms attribute their atomic orbital to this state more than the 4-foldcoordinated Ga atoms. In the valence band, there is also a peak at -5.7 eV, which arises mainly from the 3-fold-coordinated N atoms. For a nitrogen or a gallium atom at the edge of the saturated nanotube, there is little difference between surface atoms compared with that of a similar atom in the middle of a nanotube. Passivation of the dangling bonds of semiconducting nanowires by hydrogen atoms results in significant changes in their electronic structures. The hydrogen atoms have effects on stabilizing the bonding molecular orbital and pushing the antibonding molecular orbital up, which moves the edge states away from the band gap. The PDOSs of the surface atoms are different from that of the core atoms in unsaturated nanotubes, since the core atoms have one more neighbor than surface atoms, but the difference can be removed by hydrogen saturation, and the surface states within the band gap can be removed. As a result, the band gap of nanowires with a diameter of 0.64 nm
Figure 6. Band gap as a function of the nanotube wall thickness.
changed from 1.57 to 3.29 eV. In view of the importance of surface states to the properties of nanotubes, we suggest that the electronic and optical properties can be modulated by controlling the surface states of nanotubes by hydrogen saturation. The wall-thickness dependence of the band gap for the unsaturated and saturated GaN nanotubes is shown in Figure 6. The band gap of the unsaturated nanotubes does not change significantly with nanotube thickness, whereas the band gap of the saturated ones decreases with increasing wall thickness and can be described by Eg ) (2.88637 ( 0.055)t-0.34558(0.031. 4. Conclusion In summary, we have performed first-principles calculations on [001]-oriented GaN nanotubes with (100) lateral facets and different wall thicknesses. After atomic relaxation, the atoms in the outer and inner surface layers undergo a bond-length contraction for the unsaturated nanotubes. All the nanotubes, either saturated or unsaturated, are semiconducting, with a direct
Saturated and Unsaturated GaN Nanotubes band gap at the Γ point. It is of interest to find that the surface atoms attribute their electronic states at the near edge of the upper valence bands and the edge of the lower conduction band, described as defect states. The band gap of the unsaturated nanotube does not change significantly with the nanotube thickness. The 3-fold-coordinated Ga and N atoms at lateral facets in the GaN nanotube give rise to these defect states. When the nanotubes saturated with hydrogen, these dangling bond bands are removed from the band gap, and the band gap decreases with increasing nanotube wall thickness. Acknowledgment. Z. Wang was financially supported by the National Natural Science Foundation of China (10704014) and the Young Scientists Foundation of Sichuan (09ZQ026-029) and UESTC (JX0731). J. Li gratefully acknowledges financial support from the “One-Hundred Talents Plan” of the Chinese Academy of Sciences. F. Gao and W. J. Weber were supported by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract DE-AC05-76RL01830. References and Notes (1) Nilsson, H. A.; Thelander, C.; Fro¨berg, L. E.; Wagner, J. B.; Samuelson, L. Appl. Phys. Lett. 2006, 89, 163101. (2) Duan, X.; Huang, Y.; Agarval, R.; Lieber, C. M. Nature 2003, 421, 241. (3) Wang, W. U.; Chen, C.; Lin, K. H.; Fang, Y.; Lieber, C. M. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 3208. (4) Nakamura, S.; Senoh, M.; Mukai, T. Appl. Phys. Lett. 1993, 62, 2390. (5) Greytak, A. B.; Barrelet, C. J.; Li, Y.; Lieber, C. M. Appl. Phys. Lett. 2005, 87, 151103. (6) Zhong, Z. H.; Qian, F.; Wang, D. L.; Lieber, C. M. Nano Lett. 2003, 3, 343. (7) Sirbuly, D. J.; Law, M.; Yan, H. Q.; Yang, P. D. J. Phys. Chem. B 2005, 109, 15190. (8) Duan, X. F.; Lieber, C. M. J. Am. Chem. Soc. 2000, 122, 188. (9) Seryogin, G.; Shalish, I.; Moberlychan, W.; Narayanamurti, V. Nanotechnology 2005, 16, 2342. (10) Wang, T.; Ranalli, F.; Parbrook, P. H.; Airey, R.; Bai, J.; Rattlidge, R.; Hill, G. Appl. Phys. Lett. 2005, 86, 103103. (11) Kipshidze, G.; Yavich, B.; Chandolu, A.; Yun, J.; Kuryatkov, V.; Ahmad, I.; Aurongzeb, D.; Holtz, M.; Temkin, H. Appl. Phys. Lett. 2005, 86, 033104. (12) Goldberger, J.; He, R. R.; Zhang, Y. F.; Lee, S.; Yan, H. Q.; Choi, H. J.; Yang, P. D. Nature (London) 2003, 422, 599. (13) Hung, S. C.; Su, Y. K.; Chen, S. J.; Ji, L. W.; Fang, T. H.; Tu, L. W.; Chen, M. Appl. Phys. A: Mater. Sci. Process. 2005, 80, 1607.
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