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First-principles investigation of the electronic and magnetic properties of ZnO nanosheet with intrinsic defects
Computational Materials Science xxx (2013) xxx–xxx
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
First-principles investigation of the electronic and magnetic properties of ZnO nanosheet with intrinsic defects Guoping Qin a,b, Xinqiang Wang a,⇑, Ji Zheng a, Chunyang Kong b, Bing Zeng a a b
College of Physics, Chongqing University, Chongqing 400030, People’s Republic of China Key Laboratory of Optoelectronic Functional Materials, Chongqing Normal University, Chongqing 400047, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 23 March 2013 Received in revised form 10 August 2013 Accepted 12 August 2013 Available online xxxx Keywords: ZnO nanosheet Intrinsic defects Ferromagnetism First-principles
a b s t r a c t We studied the electronic and magnetic properties of ZnO nanosheet with intrinsic defects using the firstprinciples method based on the density functional theory. The ZnO nanosheet with VO does not exhibit magnetism. However, the ZnO nanosheet with a single VZn has the magnetic ground state and the calculated total magnetic moment is 1.60 lB that mainly originates from the unpaired O 2p electrons. Formation energy calculation directly indicates that the V0Zn plays a critical role of the magnetism. Furthermore, the ground magnetic coupling between the Zn vacancies is ferromagnetic. Ó 2013 Published by Elsevier B.V.
1. Introduction The non-magnetic semiconductor doped with transition metal (TM) elements shows semiconductor and magnetic properties, which can be applied in the spintronics [1–3]. Since Dietl et al. [4] predicted that TMs doped ZnO might realize diluted magnetic semiconductors (DMS) for room temperature, considerable studies have focused on the DMS based on ZnO. It is reported that ZnO:TM systems with the high-temperature ferromagnetism (FM) are fabricated using different techniques [5–12]. The room temperature antiferromagnetism (AFM) and paramagnetism are also observed [13–17]. In addition, the introduced defect in ZnO:TM systems can couple with the magnetic TM ions, inducing the ferromagnetic behavior [18–22]. However, the origin of magnetism moment is still controversial. Nonmagnetic ions and intrinsic defects, such as Zn vacancy (VZn), O vacancy (VO), doped ZnO can provide a possible approach to obtain the room temperature ferromagnetism and explore new areas of ZnO based DMSs. Some groups have found the ferromagnetism in nonmagnetic ions-doped ZnO systems. H. Pan et al. reports ferromagnetism in carbon-doped ZnO at room temperature by first-principles calculations and pulsed-laser deposition [23,24]. ZnO doped with nitrogen is also theoretically predicted to be ferromagnetic. A p–d exchange-like p–p coupling interaction is proposed to explain the FM state of ZnO:N or ZnO:C [25]. Meanwhile, the magnetic property of Cu doped ZnO has been ⇑ Corresponding author. Tel.: +86 023 65362230; fax: +86 023 65910179. E-mail address: [email protected] (X. Wang).
investigated intensely. The O-deficient ZnO:Cu films show roomtemperature ferromagnetic ordering evidenced by soft X-ray magnetic circular dichroism and X-ray absorption [26,27]. Several firstprinciples calculations suggest that the spontaneous spin polarization originates from indirect double-exchange model between bound magnetic polarons (BMPs) mediated by the Cu ions. And the p-type ZnO:Cu (Cu+2 or Cu+3) could have ferromagnetic property [28,29]. Additionally, the intrinsic defects in ZnO nanomaterials also attract researchers’ attention. M. Khalid et al. have investigated the magnetic properties of pure ZnO thin films grown by pulsed-laser deposition. The reproducible ferromagnetism is obtained at 300 K in ZnO films grown on c-plane Al2O3 [30]. And density-functional theory calculations suggest that the ferromagnetism in ZnO is related to Zn vacancies which make the unpaired 2p electrons at the nearest surrounding O sites spin-polarized. [31,32] ZnO nanosheet (ZnONS) is a promising nanomaterials in the possible applications of size and geometry dependent magnetoelectrical and magneto-optical effects because of its favorable semiconductor properties [33,34]. In order to explore the electronic and magnetic properties of the ZnO monolayer material, considerable effort is made. It is reported that Co doped graphenelike ZnONS presents ferromagnetic coupling due to the system topology within the monolayer graphenelike structure [35]. On the other hand, the graphene-like ZnO monolayer doped with some nonmetal species is found to be ferromagnetic using the first-principles calculations [36]. In this study, we perform a comprehensive first-principles study of the structural, electronic, and magnetic properties of ZnO nanosheet with intrinsic defects.
0927-0256/$ - see front matter Ó 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.commatsci.2013.08.018
Please cite this article in press as: G. Qin et al., Comput. Mater. Sci. (2013), http://dx.doi.org/10.1016/j.commatsci.2013.08.018
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G. Qin et al. / Computational Materials Science xxx (2013) xxx–xxx
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2. Computational method
Ef ðDÞ ¼ Etot ðDÞ Etot ðZnONSÞ þ
The total energy and electronic structure calculations are carried out based on the density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP) [37]. The exchange and correlation functional are treated by generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE). The projector-augmented plane wave (PAW) potentials are used to describe the electron–ion interactions. The wave functions are expanded in plane waves up to a cutoff energy of 520 eV to ensure a convergence better than 1 meV per atom for the total energy. In all calculations, Brillouin zone integrations are performed with the 4 4 1 C centered K-point grid, and the conjugated gradient method is used for geometry optimizations. Meanwhile, the energy change, maximum force are set as 1 10–4 eV/atom, 0.02 eV/Å, respectively. Moreover, it is reported that the GGA underestimates the band gap of ZnO. In this work the on-site Coulomb repulsion U is taken into account as a result of the strong correlation effect of Zn 3d states (U = 7 eV for Zn atoms) to correct for the band-gap underestimation [38]. The periodic 4 4, 5 5, 6 6 unit cell ZnO single nanosheets (0 0 0 1) which are cleaved from the bulk phase are considered with the 12 Å vacuum region. The defect formation energy is calculated by the following formalism:
where Etot ðDÞ and Etot ðZnONSÞ are the total energies of the defected and perfect host, ni and li are the change in number and the chemical potential of species i, respectively. Dq is the number of electrons added or removed for the charged defect, and lF is the Fermi level which is a variable in the formalism. The chemical potentials depend on specific experimental growth conditions. It is possible to place bounds on the chemical potential in thermodynamic equilibrium. For the lZn, the upper limit is set by the energy of a single Zn atom in the metallic bulk Zn (Etot(Zn)). Simultaneously, the Zn chemical potential should satisfy the stability condition of ZnO, e.g. lZn þ lO ¼ DHðZnOÞ; where DH(ZnO) is the formation enthalpy of the ZnO. Our calculated formation enthalpy of ZnO is 3.41 eV, compared to the experimental value of 3.6 eV [39]. The lower limit for lZn is set by the formalism: Etot ðZnÞ þ DHðZnOÞ. For the lO, the upper limit and the lower bound are set by the energy of a single O atom in an O2 molecule (Etot(O)) and the formalism: Etot ðOÞ þ DHðZnOÞ. The extreme Zn-rich or O-rich conditions can be considered by use of the bounds on lZn and lO.
ni li þ DqlF
3. Results and discussion For checking the validity of our computational approaches, a tentative calculation is performed on a perfect 4 4 ZnONS. A bor-
Fig. 1. The perfect 4 4 ZnONS supercell (a), the 5 5 ZnONS with a VO supercell (b), the 5 5 ZnONS with a VZn supercell (c), and the near (d) and far (e) configurations of 6 6 ZnONS with a VZn pair supercell. The big (red) and small (grey) balls denote O sites and Zn sites, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Total DOS for the ZnONS with a single VO (a); the right channel represents the corresponding calculation with GGA + U (b). Fermi level is set to 0 eV and indicated by the dotted vertical line.
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G. Qin et al. / Computational Materials Science xxx (2013) xxx–xxx
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Fig. 3. Isosurface of the charge density distribution surrounding the perfect ZnONS (a) and the ZnONS with a single VO (b).
on nitride hexagonal crystal structure which the Zn and O atoms are in the same plane is obtained as shown in Fig. 1(a). The Zn–O bonding length is 1.876 Å, which is shorter than that of the wurtzite ZnO bulk (1.973 Å). The spin-polarized calculations based on the GGA and GGA + U schemes indicate that the perfect ZnONS is a kind of non-magnetic semiconductor. And the calculated band gaps are 1.56 eV (GGA) and 2.4 eV (GGA + U) which are wider than that of the wurtzite ZnO bulk, in agreement with previous theoretical study [40]. It is shown that the calculation method is suitable for the studied systems. Firstly, we consider the ZnONS with a single VO in the 5 5 supercell, corresponding to the defect concentration of 2%. After the structure relaxation, the corresponding Zn–O bond lengths around the VO are lengthened by 0.3 ± 0.05 Å after introducing the Vo. And the corresponding O–Zn–O bond angles are decreased to 104.9° (120° for the perfect ZnONS), which causes the three Zn atoms around the VO to approach mutually (Fig. 1(b)). Furthermore, both the spin-unpolarization state and the spin-polarization state of the ZnONS with a single VO are calculated. We found that the energies of the spin-unpolarization state and the spin-polarization state are same. Obviously, the spin-polarization of atoms does not exist in this system. As shown in Fig. 2(a), the symmetrical spin-up and spin-down total density of states (DOS) confirms the nonmagnetic property of the ZnONS with VO. The same nonmagnetic result is obtained by the GGA + U calculation (Fig. 2(b)). The increased Zn–O bond lengths make the interaction of corresponding Zn and O atoms weaker and the mutual interaction of three Zn atoms stronger. However, the inter-Zn atoms direct interaction would not lead to the spin-polarization of Zn 3d. In addition, according to the charge densities of the perfect ZnONS and the ZnONS with a single VO (Fig. 3(a) and (b)), there is no distribution of electrons at the site of VO. The calculated results indicate that 2þ ZnONS with V1þ O =VO is also nonmagnetic. So the VO would not induce the local magnetic moment of atoms due to the delocalized character as well as in the ZnO thin films with oxygen vacancies. Secondly, the ZnONS with a single VZn in the 5 5 supercell is considered as shown in Fig. 1(c), leading to the defect concentration of 2%. It is shown that the three O atoms surrounding the VZn move outwards the same as the ZnO films with a single VZn after the structure relaxation. The Zn–O bond lengths are shortened to 1.82 Å compared with the Zn–O bond lengths of the perfect ZnONS. The corresponding O–Zn–O bond angles are increased to 127.9°. It is indicated that the covalent component of the Zn–O bonds around the VZn is increased. The similar results are obtained in the TiO2 or BN nanosheet with the VZn. [41,42] Both the spinunpolarization state and the spin-polarization state are also calculated for the ZnONS with a single VZn. The spin-polarization energy DEspin is defined to signify the magnetic stability by the difference between the spin-unpolarization state and the spin-polarization state (DEspin = Eunpolarization Epolarization). The positive DEspin means that the spin-polarization state is lower in energy than the spinunpolarization state, and vice versa. The DEspin of ZnONS with a
single VZn is 89 meV that means the ground state is magnetic. The calculated total magnetic moment is 1.60 lB, which mainly comes from the three neighboring O atoms (0.26 lB per atom, correspondingly, about 0.45 lB in the ZnO films). as shown in the spin density (Fig. 4). The Zn and O atoms which are the next nearest neighbor to the VZn contribute to the rest of total magnetic moment (0.048 lB, 0.043 lB , respectively). To further examine the origin of this magnetism moment and the electronic property of the system, we calculated the total DOS and partial DOS self-consistently by GGA and GGA + U. For the GGA calculation, Fig. 5(a) shows that the total DOS of the system has the 1.64 eV band gap which is also a little wider than that of the perfect ZnONS, and the system exists the spin-polarization. According to the calculated magnetic moment of the system, the partial DOS of the nearest neighboring O atom is drawn (Fig. 5(b)). The spin-polarization of the O atom comes from the O 2p orbitals which introduce new states near the Fermi level in the gap region. We also perform the GGA + U calculation. The energies of partial DOS of Zn 3d are shifted 1.9 eV to the left. The states of the O 2p are more local compared with the GGA calculation. But the spins of O 2p are still polarized (Fig. 5(d)). The obtained band gap is 2.42 eV. Consequently, the spin-polarization at the top of the valence band is confirmed (Fig. 5(c)). Furthermore, the Zn–O bond lengths around the VZn are decreased due to the large electronegativity of O atoms and the unpaired 2p electrons, which make the interaction of corresponding Zn and O atoms stronger. Therefore, the O 2p is spin-polarized with the modulation of VZn. To study the effect of the valence state of the VZn on the magnetic property of the ZnONS with a single VZn, the structures of 2 the system with the charged VZn are relaxed, e.g. V1 Zn ; VZn . And the electronic and magnetic properties are also calculated. For the V1 Zn , the DEspin is 3 meV which means that the magnetic state is energetically nearly degenerate. For the V2 Zn , the DEspin is zero, suggesting that the spin-polarization of atoms does not exist. Subsequently, the formation energy results for the single VZn under the O-rich situation are calculated and plotted as a function of Fermi level in Fig. 6. It is shown that the 1-/0 transition level of VZn is
Fig. 4. Isosurface of the spin density distribution surrounding the ZnONS with a single VZn.
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Fig. 5. Total DOS (a) and partial DOS of O 2p (b) for the ZnONS with a single VZn; The right channel total DOS (c) and partial DOS of O 2p (d) represent the corresponding calculation with GGA + U. Fermi level is set to 0 eV and indicated by the dotted vertical line.
0.28 eV (GGA) which is larger than that of the ZnO bulk. The reason maybe is the larger band gap of ZnONS. Through adding the Hubbard U on the Zn 3d by the GGA + U, the band gap is partly corrected. The 1-/0 transition level of VZn are corrected as 0.66 eV which is deepened. Consequently, the neutral VZn ðV0Zn Þ play a critical role of the magnetism of system. Next, the magnetic coupling of the VZn–VZn will be studied. We generate a VZn–VZn pair in the 6 6 supercell, leading to the defect concentration of 2.8% which is increased by 0.8% comparing with the ZnONS with a single VZn. The near and far vacancy-vacancy distances are set to 11.29 Å, 16.78 Å, respectively. (Fig. 1(d), (e)) The FM state is a combination of a spin-up VZn and a spin-up VZn, while the AFM state is a combination of a spin-up VZn and a spin-down VZn. DE = EFM EAFM is defined for determining the magnetic stability (DE < 0 indicates FM to be favorable, and vice versa). The calculated results for the systems under consideration are listed in Table 1, which the energy of FM, AFM phase is compared to the energy of FM of near configuration.
Table 1 Total energy of the FM and AFM phase in near and far configurations calculated relative to that with lowest FM energy in the near configuration, DE = EFM EAFM is defined for determining the magnetic stability, Mtot denotes the magnetic moment of the FM state.
Fig. 6. Defect formation energies of VZn as a function of Fermi level, resulting from GGA and GGA + U calculations.
Fig. 7. Isosurface of the spin density distribution surrounding the ZnONS with a VZn pair.
Configuration
FM (meV)
AFM (meV)
DE (meV)
Mtot (lB)
Near Far
0 67
84 37
84 30
3.82 –
It is shown that the energy of near configuration is the lowest and favors the FM ground state, while the far configuration favors the AFM ground state, indicating the VZn pair prefers to cluster and the FM coupling should be stable with DE = 84 meV. The system exhibits magnetism with a total magnetic moment of 3.82 lB. The spin density isosurface indicates that the spin-polarization mostly extends throughout the O ions of the ZnONS. (Fig. 7) The magnetic moments at the nearest neighboring O atom of VZn are found to be 0.251, 0.250, 0.251 lB, respectively. These results suggest that the robust room-temperature FM, half-metallicity of ZnONS with VZn is a promising dilute magnetic semiconductor and imply potential applications in the field of spintronics.
Please cite this article in press as: G. Qin et al., Comput. Mater. Sci. (2013), http://dx.doi.org/10.1016/j.commatsci.2013.08.018
G. Qin et al. / Computational Materials Science xxx (2013) xxx–xxx
4. Conclusions The electronic and magnetic properties of ZnONS with intrinsic defects are investigated by density-functional theory. Both VO and VZn are considered in our study. The ZnONS with VO is not magnetic. It is suggested that VO will not lead to magnetism in ZnONS. On the other hand, the ZnONS with a single VZn exhibits the magnetic ground state and the calculated total magnetic moment is 1.60 lB. We concluded that the total magnetic moment mainly originates from unpaired O 2p electrons which introduce new states near the Fermi level in the gap region. The formation energy of ZnONS with the charged VZn are also calculated. It is indicated that the neutral VZn ðV0Zn Þ plays a critical role of the magnetism of system. Finally, the magnetic coupling between the VZn is calculated. The FM coupling should be stable in the near configuration. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 61274128), the Nature Science Foundation of Chongqing City (Grant Nos. CSTC, 2011BA4031 and 2013jjB0023), Education Commission of Chongqing (Grant No. KJ120608) and Chongqing Normal University (Grant No. 09XLS04). References [1] C.G. Van de Walle, J. Appl. Phys. 95 (2004) 3851. [2] M. Sluiter, Y. Kawazoe, P. Sharma, A. Inoue, A. Raju, C. Rout, U. Waghmare, Phys. Rev. Lett. 94 (2005) 187204. [3] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. von Molnar, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488. [4] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science 287 (2000) 1019. [5] H.J. Lee, S.Y. Jeong, C.R. Cho, C.H. Park, Appl. Phys. Lett. 81 (2002) 4020. [6] C. Song, K. Geng, F. Zeng, X. Wang, Y. Shen, F. Pan, Y. Xie, T. Liu, H. Zhou, Z. Fan, Phys. Rev. B 73 (2006) 024405. [7] C. Song, F. Zeng, K. Geng, X. Liu, F. Pan, B. He, W. Yan, Phys. Rev. B 76 (2007) 045215. [8] M. Gacic, G. Jakob, C. Herbort, H. Adrian, T. Tietze, S. Brück, E. Goering, Phys. Rev. B 75 (2007) 205206. [9] N.A. Theodoropoulou, Soli. Stat. Electro. 47 (2003) 2231. [10] K. Potzger, S.Q. Zhou, H. Reuther, A. Mücklich, F. Eichhorn, N. Schell, W. }rfer, T.P. Papageorgiou, Appl. Skorupa, M. Helm, J. Fassbender, T. Herrmannsdo Phys. Lett. 88 (2006) 052508. [11] S.W. Jung, S.J. An, G.C. Yi, C.U. Jung, S.I. Lee, S. Cho, Appl. Phys. Lett. 80 (2002) 4561.
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Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
First-principles investigation of the electronic and magnetic properties of ZnO nanosheet with intrinsic defects Guoping Qin a,b, Xinqiang Wang a,⇑, Ji Zheng a, Chunyang Kong b, Bing Zeng a a b
College of Physics, Chongqing University, Chongqing 400030, People’s Republic of China Key Laboratory of Optoelectronic Functional Materials, Chongqing Normal University, Chongqing 400047, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 23 March 2013 Received in revised form 10 August 2013 Accepted 12 August 2013 Available online xxxx Keywords: ZnO nanosheet Intrinsic defects Ferromagnetism First-principles
a b s t r a c t We studied the electronic and magnetic properties of ZnO nanosheet with intrinsic defects using the firstprinciples method based on the density functional theory. The ZnO nanosheet with VO does not exhibit magnetism. However, the ZnO nanosheet with a single VZn has the magnetic ground state and the calculated total magnetic moment is 1.60 lB that mainly originates from the unpaired O 2p electrons. Formation energy calculation directly indicates that the V0Zn plays a critical role of the magnetism. Furthermore, the ground magnetic coupling between the Zn vacancies is ferromagnetic. Ó 2013 Published by Elsevier B.V.
1. Introduction The non-magnetic semiconductor doped with transition metal (TM) elements shows semiconductor and magnetic properties, which can be applied in the spintronics [1–3]. Since Dietl et al. [4] predicted that TMs doped ZnO might realize diluted magnetic semiconductors (DMS) for room temperature, considerable studies have focused on the DMS based on ZnO. It is reported that ZnO:TM systems with the high-temperature ferromagnetism (FM) are fabricated using different techniques [5–12]. The room temperature antiferromagnetism (AFM) and paramagnetism are also observed [13–17]. In addition, the introduced defect in ZnO:TM systems can couple with the magnetic TM ions, inducing the ferromagnetic behavior [18–22]. However, the origin of magnetism moment is still controversial. Nonmagnetic ions and intrinsic defects, such as Zn vacancy (VZn), O vacancy (VO), doped ZnO can provide a possible approach to obtain the room temperature ferromagnetism and explore new areas of ZnO based DMSs. Some groups have found the ferromagnetism in nonmagnetic ions-doped ZnO systems. H. Pan et al. reports ferromagnetism in carbon-doped ZnO at room temperature by first-principles calculations and pulsed-laser deposition [23,24]. ZnO doped with nitrogen is also theoretically predicted to be ferromagnetic. A p–d exchange-like p–p coupling interaction is proposed to explain the FM state of ZnO:N or ZnO:C [25]. Meanwhile, the magnetic property of Cu doped ZnO has been ⇑ Corresponding author. Tel.: +86 023 65362230; fax: +86 023 65910179. E-mail address: [email protected] (X. Wang).
investigated intensely. The O-deficient ZnO:Cu films show roomtemperature ferromagnetic ordering evidenced by soft X-ray magnetic circular dichroism and X-ray absorption [26,27]. Several firstprinciples calculations suggest that the spontaneous spin polarization originates from indirect double-exchange model between bound magnetic polarons (BMPs) mediated by the Cu ions. And the p-type ZnO:Cu (Cu+2 or Cu+3) could have ferromagnetic property [28,29]. Additionally, the intrinsic defects in ZnO nanomaterials also attract researchers’ attention. M. Khalid et al. have investigated the magnetic properties of pure ZnO thin films grown by pulsed-laser deposition. The reproducible ferromagnetism is obtained at 300 K in ZnO films grown on c-plane Al2O3 [30]. And density-functional theory calculations suggest that the ferromagnetism in ZnO is related to Zn vacancies which make the unpaired 2p electrons at the nearest surrounding O sites spin-polarized. [31,32] ZnO nanosheet (ZnONS) is a promising nanomaterials in the possible applications of size and geometry dependent magnetoelectrical and magneto-optical effects because of its favorable semiconductor properties [33,34]. In order to explore the electronic and magnetic properties of the ZnO monolayer material, considerable effort is made. It is reported that Co doped graphenelike ZnONS presents ferromagnetic coupling due to the system topology within the monolayer graphenelike structure [35]. On the other hand, the graphene-like ZnO monolayer doped with some nonmetal species is found to be ferromagnetic using the first-principles calculations [36]. In this study, we perform a comprehensive first-principles study of the structural, electronic, and magnetic properties of ZnO nanosheet with intrinsic defects.
0927-0256/$ - see front matter Ó 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.commatsci.2013.08.018
Please cite this article in press as: G. Qin et al., Comput. Mater. Sci. (2013), http://dx.doi.org/10.1016/j.commatsci.2013.08.018
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G. Qin et al. / Computational Materials Science xxx (2013) xxx–xxx
X
2. Computational method
Ef ðDÞ ¼ Etot ðDÞ Etot ðZnONSÞ þ
The total energy and electronic structure calculations are carried out based on the density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP) [37]. The exchange and correlation functional are treated by generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE). The projector-augmented plane wave (PAW) potentials are used to describe the electron–ion interactions. The wave functions are expanded in plane waves up to a cutoff energy of 520 eV to ensure a convergence better than 1 meV per atom for the total energy. In all calculations, Brillouin zone integrations are performed with the 4 4 1 C centered K-point grid, and the conjugated gradient method is used for geometry optimizations. Meanwhile, the energy change, maximum force are set as 1 10–4 eV/atom, 0.02 eV/Å, respectively. Moreover, it is reported that the GGA underestimates the band gap of ZnO. In this work the on-site Coulomb repulsion U is taken into account as a result of the strong correlation effect of Zn 3d states (U = 7 eV for Zn atoms) to correct for the band-gap underestimation [38]. The periodic 4 4, 5 5, 6 6 unit cell ZnO single nanosheets (0 0 0 1) which are cleaved from the bulk phase are considered with the 12 Å vacuum region. The defect formation energy is calculated by the following formalism:
where Etot ðDÞ and Etot ðZnONSÞ are the total energies of the defected and perfect host, ni and li are the change in number and the chemical potential of species i, respectively. Dq is the number of electrons added or removed for the charged defect, and lF is the Fermi level which is a variable in the formalism. The chemical potentials depend on specific experimental growth conditions. It is possible to place bounds on the chemical potential in thermodynamic equilibrium. For the lZn, the upper limit is set by the energy of a single Zn atom in the metallic bulk Zn (Etot(Zn)). Simultaneously, the Zn chemical potential should satisfy the stability condition of ZnO, e.g. lZn þ lO ¼ DHðZnOÞ; where DH(ZnO) is the formation enthalpy of the ZnO. Our calculated formation enthalpy of ZnO is 3.41 eV, compared to the experimental value of 3.6 eV [39]. The lower limit for lZn is set by the formalism: Etot ðZnÞ þ DHðZnOÞ. For the lO, the upper limit and the lower bound are set by the energy of a single O atom in an O2 molecule (Etot(O)) and the formalism: Etot ðOÞ þ DHðZnOÞ. The extreme Zn-rich or O-rich conditions can be considered by use of the bounds on lZn and lO.
ni li þ DqlF
3. Results and discussion For checking the validity of our computational approaches, a tentative calculation is performed on a perfect 4 4 ZnONS. A bor-
Fig. 1. The perfect 4 4 ZnONS supercell (a), the 5 5 ZnONS with a VO supercell (b), the 5 5 ZnONS with a VZn supercell (c), and the near (d) and far (e) configurations of 6 6 ZnONS with a VZn pair supercell. The big (red) and small (grey) balls denote O sites and Zn sites, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Total DOS for the ZnONS with a single VO (a); the right channel represents the corresponding calculation with GGA + U (b). Fermi level is set to 0 eV and indicated by the dotted vertical line.
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Fig. 3. Isosurface of the charge density distribution surrounding the perfect ZnONS (a) and the ZnONS with a single VO (b).
on nitride hexagonal crystal structure which the Zn and O atoms are in the same plane is obtained as shown in Fig. 1(a). The Zn–O bonding length is 1.876 Å, which is shorter than that of the wurtzite ZnO bulk (1.973 Å). The spin-polarized calculations based on the GGA and GGA + U schemes indicate that the perfect ZnONS is a kind of non-magnetic semiconductor. And the calculated band gaps are 1.56 eV (GGA) and 2.4 eV (GGA + U) which are wider than that of the wurtzite ZnO bulk, in agreement with previous theoretical study [40]. It is shown that the calculation method is suitable for the studied systems. Firstly, we consider the ZnONS with a single VO in the 5 5 supercell, corresponding to the defect concentration of 2%. After the structure relaxation, the corresponding Zn–O bond lengths around the VO are lengthened by 0.3 ± 0.05 Å after introducing the Vo. And the corresponding O–Zn–O bond angles are decreased to 104.9° (120° for the perfect ZnONS), which causes the three Zn atoms around the VO to approach mutually (Fig. 1(b)). Furthermore, both the spin-unpolarization state and the spin-polarization state of the ZnONS with a single VO are calculated. We found that the energies of the spin-unpolarization state and the spin-polarization state are same. Obviously, the spin-polarization of atoms does not exist in this system. As shown in Fig. 2(a), the symmetrical spin-up and spin-down total density of states (DOS) confirms the nonmagnetic property of the ZnONS with VO. The same nonmagnetic result is obtained by the GGA + U calculation (Fig. 2(b)). The increased Zn–O bond lengths make the interaction of corresponding Zn and O atoms weaker and the mutual interaction of three Zn atoms stronger. However, the inter-Zn atoms direct interaction would not lead to the spin-polarization of Zn 3d. In addition, according to the charge densities of the perfect ZnONS and the ZnONS with a single VO (Fig. 3(a) and (b)), there is no distribution of electrons at the site of VO. The calculated results indicate that 2þ ZnONS with V1þ O =VO is also nonmagnetic. So the VO would not induce the local magnetic moment of atoms due to the delocalized character as well as in the ZnO thin films with oxygen vacancies. Secondly, the ZnONS with a single VZn in the 5 5 supercell is considered as shown in Fig. 1(c), leading to the defect concentration of 2%. It is shown that the three O atoms surrounding the VZn move outwards the same as the ZnO films with a single VZn after the structure relaxation. The Zn–O bond lengths are shortened to 1.82 Å compared with the Zn–O bond lengths of the perfect ZnONS. The corresponding O–Zn–O bond angles are increased to 127.9°. It is indicated that the covalent component of the Zn–O bonds around the VZn is increased. The similar results are obtained in the TiO2 or BN nanosheet with the VZn. [41,42] Both the spinunpolarization state and the spin-polarization state are also calculated for the ZnONS with a single VZn. The spin-polarization energy DEspin is defined to signify the magnetic stability by the difference between the spin-unpolarization state and the spin-polarization state (DEspin = Eunpolarization Epolarization). The positive DEspin means that the spin-polarization state is lower in energy than the spinunpolarization state, and vice versa. The DEspin of ZnONS with a
single VZn is 89 meV that means the ground state is magnetic. The calculated total magnetic moment is 1.60 lB, which mainly comes from the three neighboring O atoms (0.26 lB per atom, correspondingly, about 0.45 lB in the ZnO films). as shown in the spin density (Fig. 4). The Zn and O atoms which are the next nearest neighbor to the VZn contribute to the rest of total magnetic moment (0.048 lB, 0.043 lB , respectively). To further examine the origin of this magnetism moment and the electronic property of the system, we calculated the total DOS and partial DOS self-consistently by GGA and GGA + U. For the GGA calculation, Fig. 5(a) shows that the total DOS of the system has the 1.64 eV band gap which is also a little wider than that of the perfect ZnONS, and the system exists the spin-polarization. According to the calculated magnetic moment of the system, the partial DOS of the nearest neighboring O atom is drawn (Fig. 5(b)). The spin-polarization of the O atom comes from the O 2p orbitals which introduce new states near the Fermi level in the gap region. We also perform the GGA + U calculation. The energies of partial DOS of Zn 3d are shifted 1.9 eV to the left. The states of the O 2p are more local compared with the GGA calculation. But the spins of O 2p are still polarized (Fig. 5(d)). The obtained band gap is 2.42 eV. Consequently, the spin-polarization at the top of the valence band is confirmed (Fig. 5(c)). Furthermore, the Zn–O bond lengths around the VZn are decreased due to the large electronegativity of O atoms and the unpaired 2p electrons, which make the interaction of corresponding Zn and O atoms stronger. Therefore, the O 2p is spin-polarized with the modulation of VZn. To study the effect of the valence state of the VZn on the magnetic property of the ZnONS with a single VZn, the structures of 2 the system with the charged VZn are relaxed, e.g. V1 Zn ; VZn . And the electronic and magnetic properties are also calculated. For the V1 Zn , the DEspin is 3 meV which means that the magnetic state is energetically nearly degenerate. For the V2 Zn , the DEspin is zero, suggesting that the spin-polarization of atoms does not exist. Subsequently, the formation energy results for the single VZn under the O-rich situation are calculated and plotted as a function of Fermi level in Fig. 6. It is shown that the 1-/0 transition level of VZn is
Fig. 4. Isosurface of the spin density distribution surrounding the ZnONS with a single VZn.
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G. Qin et al. / Computational Materials Science xxx (2013) xxx–xxx
Fig. 5. Total DOS (a) and partial DOS of O 2p (b) for the ZnONS with a single VZn; The right channel total DOS (c) and partial DOS of O 2p (d) represent the corresponding calculation with GGA + U. Fermi level is set to 0 eV and indicated by the dotted vertical line.
0.28 eV (GGA) which is larger than that of the ZnO bulk. The reason maybe is the larger band gap of ZnONS. Through adding the Hubbard U on the Zn 3d by the GGA + U, the band gap is partly corrected. The 1-/0 transition level of VZn are corrected as 0.66 eV which is deepened. Consequently, the neutral VZn ðV0Zn Þ play a critical role of the magnetism of system. Next, the magnetic coupling of the VZn–VZn will be studied. We generate a VZn–VZn pair in the 6 6 supercell, leading to the defect concentration of 2.8% which is increased by 0.8% comparing with the ZnONS with a single VZn. The near and far vacancy-vacancy distances are set to 11.29 Å, 16.78 Å, respectively. (Fig. 1(d), (e)) The FM state is a combination of a spin-up VZn and a spin-up VZn, while the AFM state is a combination of a spin-up VZn and a spin-down VZn. DE = EFM EAFM is defined for determining the magnetic stability (DE < 0 indicates FM to be favorable, and vice versa). The calculated results for the systems under consideration are listed in Table 1, which the energy of FM, AFM phase is compared to the energy of FM of near configuration.
Table 1 Total energy of the FM and AFM phase in near and far configurations calculated relative to that with lowest FM energy in the near configuration, DE = EFM EAFM is defined for determining the magnetic stability, Mtot denotes the magnetic moment of the FM state.
Fig. 6. Defect formation energies of VZn as a function of Fermi level, resulting from GGA and GGA + U calculations.
Fig. 7. Isosurface of the spin density distribution surrounding the ZnONS with a VZn pair.
Configuration
FM (meV)
AFM (meV)
DE (meV)
Mtot (lB)
Near Far
0 67
84 37
84 30
3.82 –
It is shown that the energy of near configuration is the lowest and favors the FM ground state, while the far configuration favors the AFM ground state, indicating the VZn pair prefers to cluster and the FM coupling should be stable with DE = 84 meV. The system exhibits magnetism with a total magnetic moment of 3.82 lB. The spin density isosurface indicates that the spin-polarization mostly extends throughout the O ions of the ZnONS. (Fig. 7) The magnetic moments at the nearest neighboring O atom of VZn are found to be 0.251, 0.250, 0.251 lB, respectively. These results suggest that the robust room-temperature FM, half-metallicity of ZnONS with VZn is a promising dilute magnetic semiconductor and imply potential applications in the field of spintronics.
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G. Qin et al. / Computational Materials Science xxx (2013) xxx–xxx
4. Conclusions The electronic and magnetic properties of ZnONS with intrinsic defects are investigated by density-functional theory. Both VO and VZn are considered in our study. The ZnONS with VO is not magnetic. It is suggested that VO will not lead to magnetism in ZnONS. On the other hand, the ZnONS with a single VZn exhibits the magnetic ground state and the calculated total magnetic moment is 1.60 lB. We concluded that the total magnetic moment mainly originates from unpaired O 2p electrons which introduce new states near the Fermi level in the gap region. The formation energy of ZnONS with the charged VZn are also calculated. It is indicated that the neutral VZn ðV0Zn Þ plays a critical role of the magnetism of system. Finally, the magnetic coupling between the VZn is calculated. The FM coupling should be stable in the near configuration. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 61274128), the Nature Science Foundation of Chongqing City (Grant Nos. CSTC, 2011BA4031 and 2013jjB0023), Education Commission of Chongqing (Grant No. KJ120608) and Chongqing Normal University (Grant No. 09XLS04). References [1] C.G. Van de Walle, J. Appl. Phys. 95 (2004) 3851. [2] M. Sluiter, Y. Kawazoe, P. Sharma, A. Inoue, A. Raju, C. Rout, U. Waghmare, Phys. Rev. Lett. 94 (2005) 187204. [3] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. von Molnar, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488. [4] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science 287 (2000) 1019. [5] H.J. Lee, S.Y. Jeong, C.R. Cho, C.H. Park, Appl. Phys. Lett. 81 (2002) 4020. [6] C. Song, K. Geng, F. Zeng, X. Wang, Y. Shen, F. Pan, Y. Xie, T. Liu, H. Zhou, Z. Fan, Phys. Rev. B 73 (2006) 024405. [7] C. Song, F. Zeng, K. Geng, X. Liu, F. Pan, B. He, W. Yan, Phys. Rev. B 76 (2007) 045215. [8] M. Gacic, G. Jakob, C. Herbort, H. Adrian, T. Tietze, S. Brück, E. Goering, Phys. Rev. B 75 (2007) 205206. [9] N.A. Theodoropoulou, Soli. Stat. Electro. 47 (2003) 2231. [10] K. Potzger, S.Q. Zhou, H. Reuther, A. Mücklich, F. Eichhorn, N. Schell, W. }rfer, T.P. Papageorgiou, Appl. Skorupa, M. Helm, J. Fassbender, T. Herrmannsdo Phys. Lett. 88 (2006) 052508. [11] S.W. Jung, S.J. An, G.C. Yi, C.U. Jung, S.I. Lee, S. Cho, Appl. Phys. Lett. 80 (2002) 4561.
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