Theoretical Exploration of the Structural, Electronic, and Magnetic

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Theoretical Exploration of the Structural, Electronic, and Magnetic Properties of ZnO Nanotubes with Vacancies, Antisites, and Nitrogen Substitutional Defects D. Q. Fang,†,‡ A. L. Rosa,§ R. Q. Zhang,*,†,| and Th. Frauenheim§ Nano-organic Photoelectronic Laboratory, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100101, China, Graduate UniVersity of Chinese Academy of Sciences, Beijing 100190, China, BCCMS, UniVersita¨t Bremen, 28359 Bremen, Germany, and Center of Super-Diamond and AdVanced Films (COSDAF) and Department of Physics and Materials Science, City UniVersity of Hong Kong, Hong Kong SAR, China ReceiVed: October 16, 2009; ReVised Manuscript ReceiVed: January 13, 2010

We investigated vacancies, antisites, and nitrogen substitutional defects in ZnO single-walled zigzag and armchair nanotubes using spin-polarized density-functional calculations. We found that all defects introduced defect levels in the band gap. Among the investigated defects, oxygen vacancy had the lowest formation energy under zinc-rich conditions, but induced no magnetism in the tubes. A Zn vacancy induced a magnetic moment of 2.0 µB/cell in the tubes, resulting from the oxygen dangling-bond states. On the other hand, while a ZnO antisite defect induced a magnetic moment of 2.0 µB/cell in the zigzag tube, we found no magnetism in the armchair tube. An important prediction is that antisite defects, with high formation energies in bulk, could have relatively low formation energies in ZnO tubes. Finally, we report on the nitrogen-doped ZnO tubes. Most interestingly, we found a magnetic moment of 1.0 µB/cell for the N substitution on both the oxygen and zinc sites. I. Introduction Zinc oxide (ZnO) is an important semiconductor material with a direct wide band gap (3.37 eV) and a large exciton binding energy (60 meV), having numerous potential applications in optoelectronics and gas sensors. The recent synthesis of nanostructured ZnO-like nanowires, nanotubes, and nanobelts1-5 expands the possible applications of ZnO. One-dimensional tubular nanostructures have attracted extensive attention in experimental and theoretical studies, benefiting also from the finding of carbon nanotubes by Iijima in 1991.6 Though carbon nanotube is one of the promising candidates for nanoelectronics and spintronics, ZnO nanostructures have also arisen as potential materials in these fields in view of their novel electrical, mechanical, and optical properties. Although ZnO is most commonly found in the nanowire form, Tusche et al.7 showed that ultrathin ZnO (0001) films deposited on Ag(111) provide direct evidence for the presence of hexagonal ZnO sheets in which Zn and O atoms are 3-fold coordinated, thus demonstrating the feasibility of single-walled ZnO nanotubes (SWZnONTs). The demonstration that ZnO can be grown in a sheet-like form makes ZnO worth investigating for electronics, spintronics, and sensing applications. Another interesting theoretical prediction based on density-functional theory calculations is that both zigzag and armchair ZnO nanotubes are found to be semiconducting,8-12 which may be an advantage compared to carbon nanotubes, whose electrical properties depend on the nanotube chirality, which is difficult to control. * To whom correspondence should be addressed. E-mail: aprqz@ cityu.edu.hk. † Technical Institute of Physics and Chemistry, Chinese Academy of Sciences. ‡ Graduate University of Chinese Academy of Sciences. § Universita¨t Bremen. | City University of Hong Kong.

The presence of defects has an important influence on the properties of bulk semiconductors. For the low-dimensional nanostructures, defects are expected to play a significant role, because they have a large surface-to-volume ratio. Experimental and theoretical studies in carbon nanotubes have demonstrated the presence of point defects like adatoms, monovacancies, interstitial-vacancy defects, and pentagonheptagon pairs.13-20 Investigations on pristine and defective inorganic nanotubes based on BN,21,22 SiC,23-25 AlN,26,27 and GaN28 suggest that these defects have a profound effect on the electronic, magnetic, and mechanical properties of these materials. In this paper, we investigated the structural, electronic, and magnetic properties of vacancies, antisites, and N-substitutional defects in SWZnONTs based on density functional theoretical (DFT) calculations. We found that the formation energies of the defects depend on the chemical potentials and are similar for both zigzag and armchair nanotubes; moreover, antisite defects in ZnONTs could have relatively lower formation energies than in bulk ZnO. II. Methodology We performed first-principles spin-polarized DFT calculations using the Vienna ab initio simulation package (VASP).29 We used the PW91 generalized gradient approximation (GGA)30 for the exchange and correlation potential, and the projector augmented-wave (PAW) method31,32 for the total energy calculation. The cutoff energy for the plane wave basis was 500 eV. All atoms were relaxed until the Hellmann-Feynman forces acting on them were less than 0.02 eV/Å. We investigated tubes with different chiralities as prototypes: ZnO (10,0) zigzag tube and (6,6) armchair tube. The supercells for the ZnO (10,0) and (6,6) nanotubes had two (80 atoms) and three (72 atoms) basic unit cells along the z direction, with the periodic lengths of 11.34 and 9.84 Å in the z direction, respectively. A vacuum region of 15 Å between neighboring

10.1021/jp909937u  2010 American Chemical Society Published on Web 03/15/2010

Exploration of ZnO Nanotubes

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Figure 1. Relaxed geometries for (a) zigzag (10,0) and (b) armchair (6,6) ZnONTs. The unit cell repeats along the z direction. The red (gray) spheres represent O (Zn) atoms.

tubes was used to avoid the interactions between them. To sample the Brillouin zone, we used a (1 × 1 × 4) k-point Monkhorst-Pack mesh33 for the structural relaxations. The defects in ZnONTs were constructed as follows: the oxygen (zinc) vacancy was constructed by removing one oxygen (zinc) atom in the supercell, labeled as VO (VZn); the oxygen (zinc) antisite was constructed by replacing one zinc (oxygen) atom with one oxygen (zinc) atom in the supercell, labeled as OZn (ZnO); one N atom was substituted for O (Zn) atom, labeled as NO (NZn). The formation energy of the neutral defects of the ZnONT can be defined according to the following34

Ef[D] ) Etot[D] - Etot[NT] -

∑ niµi

(1)

i

where Etot[D] is the total energy of the ZnONT with a single defect, Etot[NT] is the total energy of the pristine ZnONT, ni represents the number of atoms of type i (O, Zn, or N) that have been added to (ni > 0) or removed from (ni < 0) the supercell when the defect is created, and µi are the corresponding chemical potentials of these species. The chemical potentials for Zn (µZn) and O (µO) were constrained by the thermodynamic equilibrium condition tube µZn + µO ) µZnO

(2)

where µtube ZnO is the energy of one ZnO pair in ZnONT. We neglect the entropy and the pV term, because they are small,34 the chemical potential can be replaced by the total energy of the solid/molecule per atom. We then examined two extreme conditions. Under the Zn-rich Zn , corresponding to the total energy condition, we took µZn ) Ebulk of metallic zinc in the hexagonal closed packed structure, and µO O2 is then defined by eq 2. For the O-rich case, we took µO ) 1/2Emol , corresponding to half of the total energy of an oxygen molecule including spin polarization, and eq 2 defines the remained chemical potential, µZn. For systems containing nitrogen atoms, µN is half of the total energy of a nitrogen molecule. III. Results and Discussion We first investigated the properties of bulk ZnO in the wurtzite structure. The optimized lattice parameters were the following: a ) 3.283 Å, c ) 5.300 Å, and u ) 0.379, which were in good agreement with the experimental values of a ) 3.258 Å, c ) 5.220 Å, and u ) 0.382.35 The calculation gave

Figure 2. Electronic band structures and density of states (DOS) for pristine (a) (10,0) and (b) (6,6) ZnONTs, respectively. The Fermi energy is set to zero.

a formation enthalpy of -3.01 eV/fu (fu: formula unit), in fair agreement with the experimental value of -3.61 eV/fu.36 A. Pristine ZnO Nanotubes. Figure 1 shows the structures of the pristine zigzag (10,0) and armchair (6,6) ZnONTs. The calculated electronic band structures for the (10,0) ZnONT (Figure 2a) and the (6,6) ZnONT (Figure 2b) show that both systems are semiconducting, with direct band gaps of 1.660 eV for the (10,0) ZnONT and 1.655 eV for the (6,6) ZnONT, which are larger than the calculated band gap of bulk ZnO (0.749 eV). The total density of states (DOS) for both pristine nanotubes is shown in parts a and b of Figure 2. The results indicate a nonmagnetic ground state. For both nanotubes, a strong hybridization of Zn 3d and O 2p states in the valence band is observed; the top of the valence bands has a main contribution from the O 2p states, while the bottom of the conduction bands is mainly contributed by the Zn 4s states. The calculated formation energies are -2.50 eV/fu for the zigzag (10,0) ZnONT and -2.51 eV/fu for the armchair (6,6) ZnONT, in good agreement with previous calculations.8-12 B. Vacancy Defects. Vacancies are important native defects commonly found in semiconductor materials. In bulk ZnO, O and Zn vacancies are the dominant defects, together with Zn interstitials. The O vacancy (VO) is a donor-like defect, while

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Figure 3. Relaxed structures of the defects: (a) VO, (b) VZn, (c) OZn, (d) ZnO, (e) NO, and (f) NZn in the zigzag (10,0) ZnONT and (g) VO, (h) VZn, (i) OZn, (j) ZnO, (k) NO, and (l) NZn in the armchair (6,6) ZnONT. The red (gray, blue) spheres represent O (Zn, N) atoms.

TABLE I: Local Bond Lengths near the Defects in ZnONTsa nanotube

defect bond length (Å)

(10,0)

VO VZn OZn ZnO NO NZn

(6,6)

VO VZn OZn ZnO NO NZn

a

Zn1-O1 1.934 Zn1-O1 1.837 Zn1-O1 2.003 Zn1-O1 1.901 Zn1-N1 1.913 N1-O1 1.404 Zn1-O1 1.925 Zn1-O1 1.842 O1-O2 1.514 Zn1-O1 1.929 Zn1-N1 1.922 N1-O1 1.419

Zn1-Zn2 2.688 Zn2-O2 1.835 O1-O2 1.479 Zn1-Zn2 2.453 Zn2-N1 1.913 N1-O2 1.404 Zn1-Zn2 2.574 Zn2-O1 1.825 O1-O3 1.451 Zn1-Zn2 2.337 Zn2-N1 1.908 N1-O2 1.376

Zn1-Zn3 2.688 Zn3-O2 1.825 O2-O3 1.479 Zn2-Zn3 2.475

Zn2-Zn3 2.551

Zn2-O2 1.913

Zn2-O3 1.930

O2-O4 3.032 Zn2-Zn4 2.475

Zn2-O1 1.977 Zn3-Zn4 4.070

Zn3-O4 1.830 Zn3-O2 1.898

Zn1-O3 1.845 Zn1-Zn3 2.574 Zn3-O3 1.828 Zn1-O3 2.008 Zn2-Zn3 2.639

Zn2-Zn3 2.830

Zn2-O2 1.943

Zn2-O4 1.823 Zn2-Zn4 2.639

Zn3-O4 1.836 Zn3-Zn4 2.846

Zn1-O2 2.053

Zn2-O3 1.818

Zn3-O3 1.834

Zn3-O2 1.978

The notation for different cases follows Figure 3.

the Zn vacancy (VZn) is an acceptor-like defect.37-39 Recently, Chanier et al. found that a single VZn in bulk ZnO yields a total

spin of ST ) 1, which could lead to interesting magneto-optical effects.40 Wang et al. further showed that VZn in ZnO thin films



Figure 4. Electronic band structures (black for spin-up bands, red for spin-down bands) and density of states (only spin-up atom-projected DOS are shown for the nonmagnetic defects) for (a) VO, (b) VZn, (c) OZn, and (d) ZnO in the zigzag (10,0) ZnONT, respectively. The Fermi energy is set to zero.

and nanowires could induce magnetism due to polarization of the surrounding O atoms.41 With use of a (3 × 3 × 2) ZnO supercell, formation energies of 0.83 eV (3.84 eV) for VO under the Zn-rich (O-rich) conditions were calculated. On the other hand, for a single VZn we found a value of 5.37 eV (2.36 eV) under Zn-rich (O-rich) conditions, in good agreement with previous DFT calculations.37-39 We further found VZn induced a local magnetic moment of 1.68 µB in agreement with previous calculations.41 Parts a and g of Figure 3 show the relaxed structures of a VO in the zigzag (10,0) and armchair (6,6) ZnONTs, respectively. The local bond reconstruction in the vicinity of the VO occurs where atoms Zn1, Zn2, and Zn3 relax toward each other to form stable metal-metal bonds whose lengths can be compared with the calculated nearest neighbor distance of metal Zn (2.65 Å) in the hexagonal closed packed structure. The metal-metal bond near the VO can act as a catalyst and enhance the adsorption of molecules on ZnONT, which has been proposed by An et al.12 A similar reconstruction has been found for group III nitride nanotubes.26,28 Table I lists the local bond lengths for the VO. The presence of VO induces perturbations to the top of the valence band and the bottom of the conduction band, as shown in Figures 4a and 6a, and introduces occupied defect levels on the top of the valence band. We found no spin polarization resulting from the VO in the ZnONTs, similar to what has been found in bulk ZnO. For the VZn, the O atoms near the VZn relax outward, and the bond lengths between the 2-fold coordinated O atoms and the

neighboring Zn atoms become contracted, as shown in Figure 3b,h. The VZn induces acceptor levels above the valence band, and these defect levels result mainly from the 2-fold coordinated O atoms near the VZn, as shown in Figures 4b and 6b. The distribution of spin density for single VZn in the zigzag (10,0) ZnONT was shown in Figure 5a. Our calculations showed that a single VZn in the ZnONT induces a net magnetic moment of 2.0 µB. Because the VZn has a relatively low formation energy in the O-rich condition and will induce magnetism in both tubes, we considered two VZn in the (10,0) ZnONT (the vacancy sites are shown in Figure 1) for studying the spin interaction. For the coupling of the two VZn in the (10,0) ZnONT, we found that the magnetic interactions depend on the VZn-VZn distance, as shown in Table III. The localization of the defect states results in the decreasing of the exchange interaction with increasing the VZn-VZn distance. For the nanotube system, VO had the lowest formation energy (0.68 eV) under the Zn-rich condition resulting from the formation of stable metal-metal bond, as shown in Table II. The formation energy is lower than the value of 0.83 eV in bulk ZnO under the Zn-rich conditions. Our results are similar to those found in ZnO thin films and nanowires, where no magnetism induced by VO has been found.41 C. Antisite Defects. In bulk ZnO, O antisite is an acceptorlike defect and Zn antisite is a donor-like defect, but they usually have high formation energies.37-39 In ZnONTs, however, the

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Fang et al. TABLE II: Formation Energies (Ef) and Total Magnetic Moment (µS) for the Defects at the Neutral Charge State Ef (eV) nanotube

defect

O-rich

Zn-rich

µS (µB)

(10,0)

VO VZn OZn ZnO NO NZn VO VZn OZn ZnO NO NZn VO VZn

3.18 2.78 2.53 7.87 4.38 3.24 3.18 2.73 2.58 7.36 4.39 3.21 3.84 2.36

0.68 5.28 7.54 2.86 1.88 5.75 0.67 5.24 7.59 2.35 1.88 5.72 0.83 5.37

0.0 2.0 0.0 2.0 1.0 1.0 0.0 2.0 0.0 0.0 1.0 1.0 0.0 1.68

(6,6)

bulk

TABLE III: Energy Difference between the Anti-Ferromagnetic and Ferromagnetic Configurations (∆E ) EAFM - EFM) As a Function of the VZn - VZn Distance (d), Total Magnetic Moments (µS) in the Lowest Energy State, and Energy Relative to the Lowest Energy Configuration (Erel) for the (10,0) ZnONTa

Figure 5. Isosurface of the spin density (∆F ) Fv - FV) at the value of 0.03 e/Å3 for (a) VZn, (b) ZnO, (c) NO, and (d) NZn defects in the zigzag (10,0) ZnONT.

change from sp3 to sp2 hybridization favors the formation of such defects, which could not be stabilized otherwise in bulk ZnO. The formation of O antisite (OZn) defects leads to a large distortion of the pristine structure. For the OZn in the (10,0) ZnONT (Figure 3c), the neighbors (O1 and O3) of the antisite atom O2 relax inward, while the atom O4 relaxes outward. Both O2 and O4 are 2-fold coordinated. For the OZn in the (6,6) ZnONT, the configuration that the antisite atom O2 bonds to the atoms O1 and O3 has the lowest energy, as shown in Figure 3i. The band structures for OZn in the (10,0) and (6,6) ZnONT show two defect levels in the gap resulting from the 2-fold coordinated O atoms, as shown in Figures 4c and 6c. For the OZn in both ZnONTs, no magnetism is found. For the ZnO antisite in the (10,0) and (6,6) ZnONTs (Figure 3d,j), the Zn atom as a substitute for O in the ZnONT relaxes out of the tube with bond lengths as listed in Table I. This radial bump is mainly the result of the greater covalent radius of Zn as compared with O. It is worth noticing that the distance between Zn3-Zn4 is 4.070 Å in the (10,0) ZnONT, while it is 2.846 Å in the (6,6) ZnONT. The pairs of atoms (Zn1 and Zn2) and (Zn3 and Zn4) in the (10,0) nanotube induce four defect levels (two spin-up levels below the Fermi energy and two spindown levels above the Fermi energy) in the gap region, as shown in Figure 4d. The distribution of spin density for single ZnO in the zigzag (10,0) ZnONT was shown in Figure 5b. On the other hand, in the (6,6) nanotube, the same atoms do not induce spinsplitting, as shown in Figure 6d. Table II lists the formation energies for OZn and ZnO in the ZnONTs. Under the O-rich condition, OZn has a formation energy with a value of 2.53 eV for the (10,0) nanotube and 2.58 eV for the (6,6) nanotube, which is lower than that of the other defects. This tendency differs from the case of bulk ZnO,

configuration

d (Å)

∆E (meV/cell)

µS (µB)

Erel (eV)

(VZn1,VZn2) (VZn1,VZn3) (VZn1,VZn4) (VZn1,VZn5) (NO6,NO8) (NO6,NO7)

5.52 6.14 8.44 9.92 3.27 3.31

79 58 -13 -14 39 11

4.0 4.0 0.0 0.0 2.0 2.0

0.040 0.000 0.023 0.042 0.000 0.037

a The same values for NO-NO defects are also given. The configurations are labeled according to Figure 1.

where VZn has a lower formation energy under the O-rich condition.37-39 This is because in single-walled nanotubes all the atoms are sitting on the surface, thus allowing more effective strain relief. D. Nitrogen Doping and Magnetic Coupling. Incorporating N into sp2 hybridized materials is a possible way to change their electronic properties.42-44 Nitrogen is the preferred dopant for p-type ZnO because it has a low p orbital energy and a similar size to O. Nitrogen can also affect the magnetic properties of ZnO, since it has one electron less than O and can then provide holes to the system, rendering hole-induced magnetism. Shen et al. recently proposed that ZnO doped by a low concentration of N is a weak ferromagnet owing to a p-d exchange-like p-p coupling interaction involving holes.45 Here we investigated N incorporation into both the zigzag and armchair ZnONTs. The formation energies for NO and NZn in the ZnONTs are listed in Table II. We found NO had lower formation energy under the Zn-rich condition with the value of 1.88 eV for both the zigzag and armchair tubes. Furthermore, our spin polarized calculation showed that for both the zigzag and armchair ZnONTs, NO induces a magnetic moment of 1.0 µB/cell. The magnetic moments are rather localized around the N atoms, being about 0.8 µB coming from the N atoms and 0.1 µB coming from the nearest neighboring Zn atoms as well as 0.1 µB from the second-nearest neighboring O atoms. The distribution of spin density for a single NO in the zigzag (10,0) ZnONT is shown in Figure 5c. This differs from what has been found for NO in ZnO bulk, where the second-nearest neighboring O atoms have a much larger contribution.45,46 NO induces a defect level in the gap coming mainly from the N 2p states, as



Figure 6. Electronic band structures (black for spin-up bands, red for spin-down bands) and density of states (only spin-up atom-projected DOS are shown for the nonmagnetic defects) for (a) VO, (b) VZn, (c) OZn, and (d) ZnO in the armchair (6,6) ZnONT, respectively. The Fermi energy is set to zero.

Figure 7. Density of states for (a) NO and (c) NZn in the zigzag (10,0) ZnONT and (b) NO and (d) NZn in the armchair (6,6) ZnONT. The Fermi energy is set to zero.

shown in parts a and b of Figure 7. When one N atom substitutes for the O atom (NO) in the ZnONTs, the local structure around the defect remains practically unaffected. On the other hand, as an N atom substitutes for a Zn atom (NZn), the relaxed local structures are similar to the case of the OZn antisite defect. But now NZn will induce a magnetic moment of 1.0 µB per

cell in both the zigzag and armchair nanotubes. The distribution of spin density for single NZn in the zigzag (10,0) ZnONT was shown in Figure 5d. Furthermore, the DOS for NZn in the (10,0) and (6,6) nanotubes are somewhat different (see parts c and d of Figure 7) because of the different contributions of the 2-fold coordinated atom O3 to the defect levels in the gap.

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Figure 8. (a) Isosurface of the spin density (∆F ) Fv - FV) at the value of 0.03 e/Å3 for two N dopants in the zigzag (10,0) ZnONT in the ferromagnetic state and (b) the projected density of states showing the N 2p states.

We further investigated the magnetic interaction between two NO. Because NZn has a much higher formation energy than NO, we considered the magnetic coupling for the latter case only. We investigated two configurations. The dopant sites are shown in Figure 1. Our results showed that the magnetic coupling is favored by 39 and 11 meV for configurations I (6 and 8) and II (6 and 7), respectively, as shown in Table III. Those values are similar to the ones found for N-doped ZnO bulk (7, 22, and 10 meV) for N-N distances of 3.249, 6.136, and 9.252 Å, respectively.45 On the basis of these results, we can conclude that the magnetism in N-doped ZnO nanotubes is not expected to be robust. Figure 8 shows the distribution of spin density and the projected DOS of the N 2p states in the magnetic coupling for configuration I (6 and 8). Further experiments are needed to confirm our theoretical predictions on ZnONTs. IV. Conclusions On the basis of spin-polarized DFT calculations, we studied the structural, electronic, and magnetic properties of pristine as well as several defective zigzag (10,0) and armchair (6,6) ZnONTs. All calculations were shown to introduce defect levels in the band gap. The formation energies of the defects (VO, VZn, OZn, ZnO, NO, and NZn) depended on the chemical potentials and were similar for both the zigzag and armchair nanotubes. The VO defect had the lowest formation energy under the Znrich condition, while VZn induced a local magnetic moment of 2.0 µB/cell. Furthermore we found that the ZnO defects in the zigzag (10,0) nanotube had a local magnetic moment of 2.0 µB/cell, whereas there was no magnetism in the armchair (6,6) nanotube. N substitutions on the O site and Zn sites for the (10,0) and (6,6) ZnONTs induced a local magnetic moment of 1.0 µB/cell and deep levels in the band gap. In addition, magnetic coupling between two NO defects was possible, but not robust. We believe our results help to understand the role of single point defects in these systems and will open the possibility of future investigations of ZnO nanostructures for electronic and spintronic applications. Acknowledgment. The work described in this paper is supported by the City University of Hong Kong (Project No. 7002279) and National Basic Research Program of China (Grant No. 2006CB933000). We would like to thank Shanghai Supercomputer Center for the computational facilities. R.Q.Z. thanks Dr. Shuping Huang for her comments on the manuscript. References and Notes (1) Wang, J.; An, X.; Li, Q.; Egerton, R. F. Appl. Phys. Lett. 2005, 86, 201911.

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