- Email: [email protected]
Thickness-dependent electronic and optical properties of faceted hexagonal aluminum nitride nanotubes
ARTICLE IN PRESS Physica E 41 (2008) 254–257
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Thickness-dependent electronic and optical properties of faceted hexagonal aluminum nitride nanotubes Karim Rezouali a,, Mohamed Akli Belkhir a, JinBo Bai b a b
Groupe de Physique du Solide, Laboratoire de Physique The´orique, De´partement de Physique, Universite´ de Bejaia, Bejaia 06000, Algeria ˆtenay Malabry Cedex, France Laboratoire MSSMAT, CNRS UMR 8579, Ecole Centrale Paris, 92295 Cha
a r t i c l e in f o
a b s t r a c t
Article history: Received 24 March 2008 Received in revised form 13 July 2008 Accepted 14 July 2008 Available online 7 September 2008
Electronic and optical properties of aluminum nitride nanotubes are studied in the framework of density-functional theory. It is found that the surface atoms attribute their electronic states near the upper valence band edge as well as the lower conduction band edge as defect states. Moreover, the absorption spectrum of a AlN nanotube is shown to be correlated with the ratios of the surface atoms to the bulk atoms. As tube thickness increases, a AlN tube is observed to have an increased tendency to show an optical absorption of bulk wurtzite AlN. Therefore, we predict that for realistic AlN nanotubes with large thicknesses (30–80 nm), the absorption spectra are most probably originating from the electronic states arising from the bulk portion. & 2008 Elsevier B.V. All rights reserved.
PACS: 72.80.Ey 73.22.–f 74.25.Gz 74.25.Jb Keywords: AlN nanotubes Hexagonal cross-sections Electronic properties Optical properties Thickness-dependence
1. Introduction One-dimensional and quasi-one-dimensional nanometer scale structures are nowadays of enormous fundamental interest, because of their broad spectrum of unique and fascinating properties [1,2], which are relevant for technological applications [3,4]. These are the reasons why significant research efforts are devoted to synthesize and to examine tubular forms of various systems ever since the discovery of carbon nanotubes [1]. Examples are the nanotubes of layered materials such as metal dichalcogenides [5,6]. There are reports of tubular structures made from materials that do not have a layered or anisotropic structure such as the III nitrides [7–9]. Unlike the case of other nonlayered materials, where template confinement is needed to obtain the corresponding nanotubes [7,9], the AlN nanotubes were synthesized without template [8]. These nanotubes are strikingly different from the nanotubes of layered materials and are faceted with hexagonal cross-sections. They are typically a few micrometers in length with the diameters from 30 to 80 nm. Most tubes
Corresponding author.
E-mail address: [email protected] (K. Rezouali). 1386-9477/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2008.07.008
have both ends open. The tetrahedral particles of AlN nanotubes may permit the realization of nanoscale optoelectronic devices with advanced features such as high thermal conductivity and superior stability using this system. Despite of the scientific and technological importance, the knowledge of structural, electronic and optical properties of AlN nanotubes is still lacking. Moreover, on the theoretical side, reports on these nanotubes are restricted to few studies of the physical properties of hypothetical nanotubes [10,11]. In this letter we address, for the first time, the problem of the electronic properties of faceted hexagonal AlN nanotubes in the framework of density-functional theory (DFT) [12]. It is found that the surface atoms attribute their electronic states near the upper valence band edge as well as the lower conduction band edge as defect states. Furthermore, the calculated imaginary part of dielectric functions (e2) curves showed that the optical properties of AlN nanotubes are strongly sizedependent.
2. Theoretical details We adopt an efficient ab-initio-DFT method called SIESTA [13] for the total energy calculations. The exchange-correlation
ARTICLE IN PRESS K. Rezouali et al. / Physica E 41 (2008) 254–257
potential has been approximated by the generalized gradient approximation (GGA) as parameterized by Perdew–Burke– Ernzerhof (PBE) [14]. The GGA has been successfully used in studying of ionic compounds [15,16]. The mesh cutoff, an energy which corresponds to the grid spacing, was chosen to be 80 Ry. The pseudopotentials were constructed according to the Troullier– Martins scheme [17] in order to take into account the effect of core electrons. The basis set was double zeta plus polarization orbitals. To compress the basis set, an energy cutoff of 0.02 Ry was used. Brillouin-zone integrations are done using special k-points sampling, as suggested by Monkhorst and Pack [18]. The energy is minimized using the Broyden method. We first chose a supercell of 48 atoms for ideal wurtzite AlN (Al24N24) in order to be used as a reference. Periodical boundary condition along the three directions was employed. Brillouin-zone integrations along the three axes are done using twelve special k-points sampling. The average nearest neighbour’s distance is about 1.89 A˚. The calculated band gap is found to be 4.64 eV, being smaller than that the experimental value of 6.2 eV [19]. This result is expected since DFT calculations are known to underestimate the semiconductor band gaps. The error can be corrected by using more elaborate approaches with GW approximations. These features are in good agreement with results from band structure calculations for bulk wurtzite AlN [20].
3. Results and discussions When we start to construct AlN nanotubes, it is natural for us to pay a special attention to the experimental evidence [8]. With this reference, we propose an approach to create AlN nanotubes from wurtzite AlN. That consists to isolate a hexagonal cylinder with the [0 0 1] direction in a wurtzite AlN and to remove the atoms from a coaxial cylinder with smaller diameter. The residual is a AlN nanotube with hexagonal-shaped cross-section. Following this scheme, we construct two AlN nanotubes with lateral facets in the [1 0 0] direction and composed of a double layer and a triple layer of atoms (Fig. 1). The AlN nanotubes generated this way have atomic structures match well with the structural aspects from experiment. The number of atoms in each supercell for the double and triple atomic layers nanotubes contains 96 and 180 atoms, respectively. Periodical boundary condition along each tube axis and large vacuum regions between nanotubes were employed.
255
Brillouin-zone integrations are done using eleven special k-points sampling, respectively. The convergence in force was set to 0.001 eV/A˚. We find that the optimal structures are almost identical to the initial ones. The optimized Al–N bond length is about 1.87 and 1.88 A˚ for the double and triple atomic layers tubes, respectively. These bond lengths are smaller than that of wurtzite AlN (1.89 A˚). It is noted that the bond length increases as the thickness of the nanotube increases showing a thickness effect clearly. Such a size dependence of structural properties of AlN nanotubes has not been reported elsewhere. Therefore, we predict that for a realistic AlN nanotube with large thickness, the Al–N bond length will approach that of the wurtzite AlN. In these nanotubes there are both threefold- and fourfold-coordinated atoms. The fourfold-coordinated atoms have the same bonding character as that of the wurtzite AlN. In addition, it is noted that there is dangling bond on each surface atoms for all of the nanotubes. These dangling bonds should have a major effect on the electronic structures of the tubes. Mulliken population analysis show that the charge transfer difference from aluminum to nitrogen between the tubes and wurtzite AlN is minor. The main features of the calculated electronic densities of states (DOS) curves (Fig. 2) are quite distinct for all tubes and also different to that of the wurtzite AlN. The DOS (Fig. 2(a)) of the double-layer tube is characterized, at the valence band edge, by a sharp peak (T1) mainly formed by the p states of threefold-coordinated N atoms. So the peak is surface states. This is following, at the lower energy, by others formed by hybridized of the electronic states of fourfold- and threefoldcoordinated atoms. In the conduction band edge, there is a peak (T2) at about 7 eV above the Fermi level which arises from atomic orbitals of threefold-coordinated Al atoms at lateral facets. This peak is also surface states and is essentially formed by hybridized of Al s and Al p states. Apart from these states; the others in the conduction band are formed by hybridized of electronic states arising from the surface atoms and bulk atoms. One can conclude that the threefold-coordinated atoms give rise to surface states near the band edges in the energy gap. In the case of a triplelayer nanotube, the surfaces states arising from the threefoldcoordinated atoms arranging at the inner and outer shells form subbands within the energy gap. The band structures curves (not shown here) around the Fermi energy show the nanotubes as semiconductors with direct band gaps at the G point. The calculated band structures have not been reported elsewhere.
Fig. 1. The fully relaxed geometries of (a) double-layer, and (b) triple-layer faceted hexagonal nanotubes of aluminum nitride. The smaller ball and the larger ball represent Al and N, respectively.
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B1
Total B2
T2
DOS (arb. units)
T1
Surface atoms
Bulk atoms
Total
B1 T1
B2
DOS (arb. units)
T2
Surface atoms
Bulk atoms
-20
-15
-10
-5
0
5
10 15 Energy (eV)
20
25
30
35
40
Fig. 2. The calculated DOS for (a) double-layer, and triple-layer AlN nanotubes. Solid lines stand for the Al s states, the dashed lines for the Al p states, the dash–dot lines for N s, and the short-dashed lines for the N p states. The Fermi level is shifted to zero.
The band gaps are evaluated to be about 5.17 and 4.99 eV, respectively. It is noted that the gap size decreases with increasing tube thickness, but still being larger than the gap of wurtzite AlN (4.46 eV), showing a size-dependence clearly. Similar behavior has been reported for GaN nanotubes with different thicknesses [21]. Furthermore, that the gap size vanishes results from the downward shift of conduction band minimum, while the top of the valence band seems to be insensitive to a change of tube thickness. The imaginary parts of e2 are calculated so as to determine the optical absorption of AlN nanotubes. We also calculate e2 for the wurtzite AlN for comparison. Fig. 3 shows the dispersion of e2 as a function of photon energy (hn) of all tubes, as well as the wurtzite AlN. The main features of the calculated e2 curves are quite distinct for all tubes and also different to that of the wurtzite AlN. Such a difference in the absorption spectra is expected since the AlN nanotubes concerned have different electronic DOS. The e2 curves (Fig. 3) also show that the longitudinal components eL2 (solid lines) are different from the transversal components eT2(dashed lines) indicating that the calculated e2 is anisotropic for each tube. Here the focus is on the calculated eL2 curves. From Fig. 3(a), we find that the eL2 curve of the double-layer nanotube is characterized by several peaks which stem from the transition of electrons between related peaks in the DOS (Fig. 2(a)). The major peaks labelled with S and B are evaluated at about 7.98 and
11.26 eV, respectively. The former corresponds to the transition of electrons between T1 and T2 originating from the surface atoms, whereas the latter is associated with the transition of electrons from B1 to B2 arising from the bulk atoms (Fig. 2(a)). For the case of triple-layer tube, these two main peaks are at 7.8 and 10.79 eV (Fig. 3(b)). From eL2 curves (Fig. 3), it is observed that the relative intensities of these peaks decrease with increasing tube thickness. Furthermore, the peak S and B show an infrared shift as the tube thickness increases. One can conclude that the positions as well as the relative intensities of these peaks are dependent on the thickness of the AlN nanotubes, showing a thickness effect clearly. Therefore, we predict that when the thickness of a AlN nanotube is very large (realistic nanotubes), the intensity of the peak S vanishes nearly and the position of the peak B will approach that of the wurtzite AlN. In other words, the optical absorption of a realistic AlN nanotube stems from the bulk atoms. In summary, we have studied the electronic and optical properties of AlN nanotubes by means of ab-initio supercell calculations. It is found that the surface atoms attribute their electronic states near the upper valence band edge as well as the lower conduction band edge as defect states. Moreover, the imaginary part of e2 curves; exhibit two main peaks originating from the surface atoms and bulk atoms, respectively. The former as well as the latter peak show an infrared shift as the tube thickness increases. Furthermore, their relative intensities are
ARTICLE IN PRESS K. Rezouali et al. / Physica E 41 (2008) 254–257
257
0.9 B
S 0.6
Imaginary part of dielectric function
0.3
0.0 1.5 B 1.0
S
0.5
0.0 12 B
9 6 3 0
4
6
8
10
12 14 16 Photon energy (eV)
18
20
22
24
Fig. 3. The calculated imaginary part of dielectric functions for (a) double-layer, (b) triple-layer AlN nanotubes, and (c) bulk wurtzite AlN. The solid lines and the dashed lines show the longitudinal components (along the z direction) and the transverse components (in the xy plane), respectively.
strongly dependent upon tube thickness showing a thickness effect clearly.
Acknowledgment We thank Anne-Sophie Mouronval for her computational assistance. References [1] [2] [3] [4] [5] [6] [7]
S. Iijima, Nature (London) 56 (1991) 354. C. Lieber, P. Yang, Nature 319 (2002) 553. P. Kim, C.M. Lieber, Science 286 (1999) 2148. A. Bachtold, P. Hadley, T. Nakanishi, C. Decker, Science 294 (2001) 1317. R. Tenne, L. Margulis, M. Genut, Nature 360 (1992) 444. L. Margulis, G. Salitra, R. Tenne, M. Talianker, Nature 365 (1993) 113. J. Goldberger, R. He, Y. Zhang, S. Lee, H. Yan, H.-J. Choi, P. Yang, Nature (London) 422 (2003) 599.
[8] Qiang Wu, Zheng Hu, Xizhang Wang, Yinong Lu, Xin Chen, Hua Xu, Yi Chen, J. Am. Chem. Soc. 125 (2003) 10176. [9] H.Y. Xu, Z. Liu, X.T. Zhang, S.K. Hark, Appl. Phys. Lett. 90 (2007) 113105. [10] Dongju Zhang, R.Q. Zhang, Chem. Phys. Lett. 371 (2003) 426. [11] Mingwen Zhao, Yueyuan Xia, Dongju Zhang, Liangmo Mei, Phys. Rev. B 68 (2003) 235415. [12] P. Hohenberg, W. Kohn, Phys. Rev. B 864 (1964) 136; W. Kohn, L.J. Sham, Phys. Rev. A 1133 (1965) 140. [13] J.M. Soler, J.D. Gale, A. Garcı´a, J. Junquera, P. Ordejo´n, D. Sanche´z-Portal, J. Phys.: Condens. Matter 14 (2002) 2745. [14] A. John, P. Perdew, Kieron Burke, Mathias Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [15] D.R. Hamann, Phys. Rev. Lett. 76 (1996) 660. [16] C. Stampfl, C.G. van de Walle, Phys. Rev. B 59 (1999) 5521. [17] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. [18] H.J. Monkhorst, J.K. Pack, Phys. Rev. B 13 (1976) 5188. [19] I. Vurgaftman, J.R. Meyer, L.R. Ram-Mohan, J. Appl. Phys. 89 (2001) 518; I. Vurgaftman, J.R. Meyer, J. Appl. Phys. 94 (2003) 3675. [20] P. Jonnard, N. Capron, F. Semond, J. Massies, E. Martinez-Guerrero, H. Mariette, arXiv: cond-mat/0312245v1 [cond-mat.mtrl-sci] 10 December 2003. [21] B. Xu, B.C. Pan, Phys. Rev. B 74 (2006) 245402.
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Thickness-dependent electronic and optical properties of faceted hexagonal aluminum nitride nanotubes Karim Rezouali a,, Mohamed Akli Belkhir a, JinBo Bai b a b
Groupe de Physique du Solide, Laboratoire de Physique The´orique, De´partement de Physique, Universite´ de Bejaia, Bejaia 06000, Algeria ˆtenay Malabry Cedex, France Laboratoire MSSMAT, CNRS UMR 8579, Ecole Centrale Paris, 92295 Cha
a r t i c l e in f o
a b s t r a c t
Article history: Received 24 March 2008 Received in revised form 13 July 2008 Accepted 14 July 2008 Available online 7 September 2008
Electronic and optical properties of aluminum nitride nanotubes are studied in the framework of density-functional theory. It is found that the surface atoms attribute their electronic states near the upper valence band edge as well as the lower conduction band edge as defect states. Moreover, the absorption spectrum of a AlN nanotube is shown to be correlated with the ratios of the surface atoms to the bulk atoms. As tube thickness increases, a AlN tube is observed to have an increased tendency to show an optical absorption of bulk wurtzite AlN. Therefore, we predict that for realistic AlN nanotubes with large thicknesses (30–80 nm), the absorption spectra are most probably originating from the electronic states arising from the bulk portion. & 2008 Elsevier B.V. All rights reserved.
PACS: 72.80.Ey 73.22.–f 74.25.Gz 74.25.Jb Keywords: AlN nanotubes Hexagonal cross-sections Electronic properties Optical properties Thickness-dependence
1. Introduction One-dimensional and quasi-one-dimensional nanometer scale structures are nowadays of enormous fundamental interest, because of their broad spectrum of unique and fascinating properties [1,2], which are relevant for technological applications [3,4]. These are the reasons why significant research efforts are devoted to synthesize and to examine tubular forms of various systems ever since the discovery of carbon nanotubes [1]. Examples are the nanotubes of layered materials such as metal dichalcogenides [5,6]. There are reports of tubular structures made from materials that do not have a layered or anisotropic structure such as the III nitrides [7–9]. Unlike the case of other nonlayered materials, where template confinement is needed to obtain the corresponding nanotubes [7,9], the AlN nanotubes were synthesized without template [8]. These nanotubes are strikingly different from the nanotubes of layered materials and are faceted with hexagonal cross-sections. They are typically a few micrometers in length with the diameters from 30 to 80 nm. Most tubes
Corresponding author.
E-mail address: [email protected] (K. Rezouali). 1386-9477/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2008.07.008
have both ends open. The tetrahedral particles of AlN nanotubes may permit the realization of nanoscale optoelectronic devices with advanced features such as high thermal conductivity and superior stability using this system. Despite of the scientific and technological importance, the knowledge of structural, electronic and optical properties of AlN nanotubes is still lacking. Moreover, on the theoretical side, reports on these nanotubes are restricted to few studies of the physical properties of hypothetical nanotubes [10,11]. In this letter we address, for the first time, the problem of the electronic properties of faceted hexagonal AlN nanotubes in the framework of density-functional theory (DFT) [12]. It is found that the surface atoms attribute their electronic states near the upper valence band edge as well as the lower conduction band edge as defect states. Furthermore, the calculated imaginary part of dielectric functions (e2) curves showed that the optical properties of AlN nanotubes are strongly sizedependent.
2. Theoretical details We adopt an efficient ab-initio-DFT method called SIESTA [13] for the total energy calculations. The exchange-correlation
ARTICLE IN PRESS K. Rezouali et al. / Physica E 41 (2008) 254–257
potential has been approximated by the generalized gradient approximation (GGA) as parameterized by Perdew–Burke– Ernzerhof (PBE) [14]. The GGA has been successfully used in studying of ionic compounds [15,16]. The mesh cutoff, an energy which corresponds to the grid spacing, was chosen to be 80 Ry. The pseudopotentials were constructed according to the Troullier– Martins scheme [17] in order to take into account the effect of core electrons. The basis set was double zeta plus polarization orbitals. To compress the basis set, an energy cutoff of 0.02 Ry was used. Brillouin-zone integrations are done using special k-points sampling, as suggested by Monkhorst and Pack [18]. The energy is minimized using the Broyden method. We first chose a supercell of 48 atoms for ideal wurtzite AlN (Al24N24) in order to be used as a reference. Periodical boundary condition along the three directions was employed. Brillouin-zone integrations along the three axes are done using twelve special k-points sampling. The average nearest neighbour’s distance is about 1.89 A˚. The calculated band gap is found to be 4.64 eV, being smaller than that the experimental value of 6.2 eV [19]. This result is expected since DFT calculations are known to underestimate the semiconductor band gaps. The error can be corrected by using more elaborate approaches with GW approximations. These features are in good agreement with results from band structure calculations for bulk wurtzite AlN [20].
3. Results and discussions When we start to construct AlN nanotubes, it is natural for us to pay a special attention to the experimental evidence [8]. With this reference, we propose an approach to create AlN nanotubes from wurtzite AlN. That consists to isolate a hexagonal cylinder with the [0 0 1] direction in a wurtzite AlN and to remove the atoms from a coaxial cylinder with smaller diameter. The residual is a AlN nanotube with hexagonal-shaped cross-section. Following this scheme, we construct two AlN nanotubes with lateral facets in the [1 0 0] direction and composed of a double layer and a triple layer of atoms (Fig. 1). The AlN nanotubes generated this way have atomic structures match well with the structural aspects from experiment. The number of atoms in each supercell for the double and triple atomic layers nanotubes contains 96 and 180 atoms, respectively. Periodical boundary condition along each tube axis and large vacuum regions between nanotubes were employed.
255
Brillouin-zone integrations are done using eleven special k-points sampling, respectively. The convergence in force was set to 0.001 eV/A˚. We find that the optimal structures are almost identical to the initial ones. The optimized Al–N bond length is about 1.87 and 1.88 A˚ for the double and triple atomic layers tubes, respectively. These bond lengths are smaller than that of wurtzite AlN (1.89 A˚). It is noted that the bond length increases as the thickness of the nanotube increases showing a thickness effect clearly. Such a size dependence of structural properties of AlN nanotubes has not been reported elsewhere. Therefore, we predict that for a realistic AlN nanotube with large thickness, the Al–N bond length will approach that of the wurtzite AlN. In these nanotubes there are both threefold- and fourfold-coordinated atoms. The fourfold-coordinated atoms have the same bonding character as that of the wurtzite AlN. In addition, it is noted that there is dangling bond on each surface atoms for all of the nanotubes. These dangling bonds should have a major effect on the electronic structures of the tubes. Mulliken population analysis show that the charge transfer difference from aluminum to nitrogen between the tubes and wurtzite AlN is minor. The main features of the calculated electronic densities of states (DOS) curves (Fig. 2) are quite distinct for all tubes and also different to that of the wurtzite AlN. The DOS (Fig. 2(a)) of the double-layer tube is characterized, at the valence band edge, by a sharp peak (T1) mainly formed by the p states of threefold-coordinated N atoms. So the peak is surface states. This is following, at the lower energy, by others formed by hybridized of the electronic states of fourfold- and threefoldcoordinated atoms. In the conduction band edge, there is a peak (T2) at about 7 eV above the Fermi level which arises from atomic orbitals of threefold-coordinated Al atoms at lateral facets. This peak is also surface states and is essentially formed by hybridized of Al s and Al p states. Apart from these states; the others in the conduction band are formed by hybridized of electronic states arising from the surface atoms and bulk atoms. One can conclude that the threefold-coordinated atoms give rise to surface states near the band edges in the energy gap. In the case of a triplelayer nanotube, the surfaces states arising from the threefoldcoordinated atoms arranging at the inner and outer shells form subbands within the energy gap. The band structures curves (not shown here) around the Fermi energy show the nanotubes as semiconductors with direct band gaps at the G point. The calculated band structures have not been reported elsewhere.
Fig. 1. The fully relaxed geometries of (a) double-layer, and (b) triple-layer faceted hexagonal nanotubes of aluminum nitride. The smaller ball and the larger ball represent Al and N, respectively.
ARTICLE IN PRESS 256
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B1
Total B2
T2
DOS (arb. units)
T1
Surface atoms
Bulk atoms
Total
B1 T1
B2
DOS (arb. units)
T2
Surface atoms
Bulk atoms
-20
-15
-10
-5
0
5
10 15 Energy (eV)
20
25
30
35
40
Fig. 2. The calculated DOS for (a) double-layer, and triple-layer AlN nanotubes. Solid lines stand for the Al s states, the dashed lines for the Al p states, the dash–dot lines for N s, and the short-dashed lines for the N p states. The Fermi level is shifted to zero.
The band gaps are evaluated to be about 5.17 and 4.99 eV, respectively. It is noted that the gap size decreases with increasing tube thickness, but still being larger than the gap of wurtzite AlN (4.46 eV), showing a size-dependence clearly. Similar behavior has been reported for GaN nanotubes with different thicknesses [21]. Furthermore, that the gap size vanishes results from the downward shift of conduction band minimum, while the top of the valence band seems to be insensitive to a change of tube thickness. The imaginary parts of e2 are calculated so as to determine the optical absorption of AlN nanotubes. We also calculate e2 for the wurtzite AlN for comparison. Fig. 3 shows the dispersion of e2 as a function of photon energy (hn) of all tubes, as well as the wurtzite AlN. The main features of the calculated e2 curves are quite distinct for all tubes and also different to that of the wurtzite AlN. Such a difference in the absorption spectra is expected since the AlN nanotubes concerned have different electronic DOS. The e2 curves (Fig. 3) also show that the longitudinal components eL2 (solid lines) are different from the transversal components eT2(dashed lines) indicating that the calculated e2 is anisotropic for each tube. Here the focus is on the calculated eL2 curves. From Fig. 3(a), we find that the eL2 curve of the double-layer nanotube is characterized by several peaks which stem from the transition of electrons between related peaks in the DOS (Fig. 2(a)). The major peaks labelled with S and B are evaluated at about 7.98 and
11.26 eV, respectively. The former corresponds to the transition of electrons between T1 and T2 originating from the surface atoms, whereas the latter is associated with the transition of electrons from B1 to B2 arising from the bulk atoms (Fig. 2(a)). For the case of triple-layer tube, these two main peaks are at 7.8 and 10.79 eV (Fig. 3(b)). From eL2 curves (Fig. 3), it is observed that the relative intensities of these peaks decrease with increasing tube thickness. Furthermore, the peak S and B show an infrared shift as the tube thickness increases. One can conclude that the positions as well as the relative intensities of these peaks are dependent on the thickness of the AlN nanotubes, showing a thickness effect clearly. Therefore, we predict that when the thickness of a AlN nanotube is very large (realistic nanotubes), the intensity of the peak S vanishes nearly and the position of the peak B will approach that of the wurtzite AlN. In other words, the optical absorption of a realistic AlN nanotube stems from the bulk atoms. In summary, we have studied the electronic and optical properties of AlN nanotubes by means of ab-initio supercell calculations. It is found that the surface atoms attribute their electronic states near the upper valence band edge as well as the lower conduction band edge as defect states. Moreover, the imaginary part of e2 curves; exhibit two main peaks originating from the surface atoms and bulk atoms, respectively. The former as well as the latter peak show an infrared shift as the tube thickness increases. Furthermore, their relative intensities are
ARTICLE IN PRESS K. Rezouali et al. / Physica E 41 (2008) 254–257
257
0.9 B
S 0.6
Imaginary part of dielectric function
0.3
0.0 1.5 B 1.0
S
0.5
0.0 12 B
9 6 3 0
4
6
8
10
12 14 16 Photon energy (eV)
18
20
22
24
Fig. 3. The calculated imaginary part of dielectric functions for (a) double-layer, (b) triple-layer AlN nanotubes, and (c) bulk wurtzite AlN. The solid lines and the dashed lines show the longitudinal components (along the z direction) and the transverse components (in the xy plane), respectively.
strongly dependent upon tube thickness showing a thickness effect clearly.
Acknowledgment We thank Anne-Sophie Mouronval for her computational assistance. References [1] [2] [3] [4] [5] [6] [7]
S. Iijima, Nature (London) 56 (1991) 354. C. Lieber, P. Yang, Nature 319 (2002) 553. P. Kim, C.M. Lieber, Science 286 (1999) 2148. A. Bachtold, P. Hadley, T. Nakanishi, C. Decker, Science 294 (2001) 1317. R. Tenne, L. Margulis, M. Genut, Nature 360 (1992) 444. L. Margulis, G. Salitra, R. Tenne, M. Talianker, Nature 365 (1993) 113. J. Goldberger, R. He, Y. Zhang, S. Lee, H. Yan, H.-J. Choi, P. Yang, Nature (London) 422 (2003) 599.
[8] Qiang Wu, Zheng Hu, Xizhang Wang, Yinong Lu, Xin Chen, Hua Xu, Yi Chen, J. Am. Chem. Soc. 125 (2003) 10176. [9] H.Y. Xu, Z. Liu, X.T. Zhang, S.K. Hark, Appl. Phys. Lett. 90 (2007) 113105. [10] Dongju Zhang, R.Q. Zhang, Chem. Phys. Lett. 371 (2003) 426. [11] Mingwen Zhao, Yueyuan Xia, Dongju Zhang, Liangmo Mei, Phys. Rev. B 68 (2003) 235415. [12] P. Hohenberg, W. Kohn, Phys. Rev. B 864 (1964) 136; W. Kohn, L.J. Sham, Phys. Rev. A 1133 (1965) 140. [13] J.M. Soler, J.D. Gale, A. Garcı´a, J. Junquera, P. Ordejo´n, D. Sanche´z-Portal, J. Phys.: Condens. Matter 14 (2002) 2745. [14] A. John, P. Perdew, Kieron Burke, Mathias Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [15] D.R. Hamann, Phys. Rev. Lett. 76 (1996) 660. [16] C. Stampfl, C.G. van de Walle, Phys. Rev. B 59 (1999) 5521. [17] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. [18] H.J. Monkhorst, J.K. Pack, Phys. Rev. B 13 (1976) 5188. [19] I. Vurgaftman, J.R. Meyer, L.R. Ram-Mohan, J. Appl. Phys. 89 (2001) 518; I. Vurgaftman, J.R. Meyer, J. Appl. Phys. 94 (2003) 3675. [20] P. Jonnard, N. Capron, F. Semond, J. Massies, E. Martinez-Guerrero, H. Mariette, arXiv: cond-mat/0312245v1 [cond-mat.mtrl-sci] 10 December 2003. [21] B. Xu, B.C. Pan, Phys. Rev. B 74 (2006) 245402.