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The electronic properties of native interstitials in ZnO
Physica B 325 (2003) 157–163
The electronic properties of native interstitials in ZnO Yuming Sun*, Hezhou Wang The State Key Laboratory of Optoelectronic Materials and Technologies, Institute of Physics, Sun Yat-Sen University, Guangzhou 510275, China Received 22 August 2002; accepted 23 August 2002
Abstract To investigate the role of interstitial geometry, we reported ab initio calculations of octahedrally and tetrahedrally native interstitials in ZnO, using the full-potential linear muffin-tin orbital method. The results show that both zinc interstitials could contribute to the native n-type conduction in ZnO, meanwhile, the zinc vacancy and octahedral oxygen interstitial may contribute to the p-type conduction in ZnO. We also suggest that the 31 and 61 meV donors found by temperature-dependent Hall experiment originate from tetrahedral- and octahedral zinc interstitials, respectively, based on their charge distribution. It is noticeable that tetrahedral interstitials cause stronger interaction between interstitials and its neighboring atoms than that of octahedral interstitials. r 2002 Published by Elsevier Science B.V. PACS: 61.72.Bb; 61.72.Ji Keywords: ZnO; Interstitials
1. Introduction Zinc oxide (ZnO) is a I–IV compound semiconductor with a wide direct band gap of 3:3 eV at room temperature, its bulk material excels in electrical properties and has low point-defect concentration [1]. ZnO has been extensively used as piezoelectric tranducers, varistors [2], phosphors, and transparent conducting films, which mainly involved polycrystalline material. Recently, large-area ZnO single crystals have been successfully grown [3] and its strong UV emission at room temperature has been reported [4,5]. Although *Corresponding author. Tel.: +86-2084038887; fax: +862084037423. E-mail address: sun [email protected] (Y. Sun).
ZnO-based photonic and electronic devices show great promise for the future, still there are some severe problems to be overcome. That is, the ZnO material is strongly n-type, usable and reproducible p-type ZnO has not yet been reported, even though several laboratories have measured weak p-type conduction in acceptor-doped materials [6,7]. To identify the contribution of native defects to the strong n-type conduction of ZnO, the highenergy electron radiation experiments were performed on O and Zn face of ZnO, respectively [8], which shows that zinc interstitial (ZnI ) is the best candidate. The first-principle calculations of formation energy gave incompatible results, Kohan [9] predicted that zinc and oxygen vacancies are dominant defects, however, zinc interstitials are assigned to main donors by Zhang [10]. So it is
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necessary to identify the native defects in ZnO in further studies. The octahedral and tetrahedral defect configuration lead to different formation energy [9], this paper will investigate their difference in charge distribution and density of states (DOS). Our results also shed light on the identification of 30 and 60 meV donors [1] in ZnO.
2. Calculational method The band structures were calculated fully selfconsistently using the local density approximation (LDA) to density function theory (DFT) [11]. The exchange-correlation potential was represented according to Barth and Hedin [12]. Basic functions and matrix elements were constructed using a full-potential linear muffin-tin orbital method (FPLMTO) with a GGA correction [13]. Multiplekappa LMTO basis technique was used. The values of kappa were 0:1; 1:0 and 1.0. zinc sites centered 3d, 4s and 4p were treated as valence states, and 2s, 2p functions centered on oxygen sites. The spheres were non-overlapping, and the tails of the basis functions outside their parent spheres were represented in plane waves. A 32atom super-cell was used. The sphere radius for lattice zinc and oxygen is 1.987 and 1:692 a:u:; respectively; the zinc interstitial’s radius is 1:49926 a:u: for tetrahedral geometry and 2:069 a:u: for octahedral geometry, and 1.3793 and 1:97 a:u for two kind of oxygen interstitial configurations. The Brillouin zone integration was performed using 110 k-points.
3. Results and discussion ZnO belongs to wurtzite structure, both zinc and oxygen sublattice have a set of own tetrahedral and octahedral interstices. The biggest interstice in ZnO is the common space of the nearest zinc and oxygen interstices along c-axis, so it is rational to choose the common part as the interstitial positions in calculation. The relaxation is neglected since we are only interested in the tendency of changes in electronic structure caused by native interstitials. The tetrahedral and octahe-
dral interstitial atoms are both caged in triple prisms, three zinc atoms at the top and three oxygen atoms at the bottom along c-axis. In case of tetrahedral interstice, the cage is closed by an oxygen atom above the top and a zinc atom below the bottom; instead, in case of octahedral interstice, the cage is open along c-axis. It is also noticeable that those three zinc and oxygen atoms constructing cage are the first neighbors for octahedral interstitial; however, they are second neighbors for tetrahedral interstitial. Naturally, different interstitial geometry, space and symmetry lead to different electronic properties. This section is to reveal electronic structure of zinc and oxygen interstitials in ZnO. The calculated DOS for perfect ZnO and four types of native interstitials are presented in Fig. 1, where subplots 1a–e present the DOS of perfect ZnO, ZnO with native tetrahedral oxygen interstitial (OtI ), octahedral oxygen interstitial (OoI ), tetrahedral zinc interstitial ðZntI Þ and octahedral zinc interstitial ðZnoI Þ; respectively. The vertical dashed-line in Fig. 1 marks the valence band edge, and the short vertical dotted-lines in subplots 1b–e mark the Fermi levels caused by corresponding interstitials. The binding energy is measured relative to the valence band edge. Based on the site-decomposed and l-projected state densities, we observe two groups in the valence band of perfect ZnO (subplot 1a): (1) from 6:5 to 5:0 eV (called down valence band), there are bands with a strong d character originating mostly from 3d states centered at Zn sites. (2) The upper valence bands located approximately 5:0 eV below valence band edge originate mainly from the O2p states. The valence bandwidth is in good agreement with GW calculation [14], and the calculated line shape of the total DOS is in good agreement with that of experiment [15]. The lowest conduction bands have a strong Zn4s contribution. There is charge transferred from Zn4s to O2p due to the mixing between the s and p states at O sites, and the s and p states of the surrounding Zn shifts the center of gravity of the local DOS at the O sites toward lower-energy regions. The calculated band gap of a perfect ZnO is about 1:2 eV: In general, the values of the band gap calculated using the ab initio LDA method are less than half the values obtained in
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Binding Energy (eV) Fig. 1. Total density of states (DOS) for bulk ZnO, and its four types of native interstitials. Subplot a–e present the DOS of bulk ZnO, ZnO with tetrahedral oxygen interstitial (OtI ), ZnO with octahedral oxygen interstitial (OoI ), ZnO with tetrahedral zinc interstitial (ZntI ) and ZnO with octahedral Zn interstitial ðZnoI Þ: The long vertical dashed-line presents the valence band edge, and the short vertical dotted-lines in subplots b–e present the Fermi levels caused by corresponding interstitial.
optical experiments. Inaccuracy in the determination of the optical band gap has little influence in the present discussion since we only discuss the electronic property of ground states. Subplots 1b,c show that both OtI and OoI generate defect states centered at 0:5 eV above the valence band edge. It is noticeable that the defect states caused by OtI is fully occupied, while that of OoI is half occupied. Comparing the total DOS in subplots 1b,c, there are more new features caused by OtI (subplot 1b), two bands below the bottom of valence band centered at 9 and 7:5 eV; and a band above the top of valence band centered at 2 eV: The site-decomposed and l-projected state densities show that these new bands mainly originate from the bonding between
the oxygen interstitial and its first neighboring oxygen and zinc; meanwhile pz and d3z2 1 dominate the bands centered at 9 and 2 eV; and the bands centered at 0.5 and 7:5 eV are dominated by px;y and dyz;zx : As for OoI (subplot 1c), except the band gap states, the line shape is well consistent with that of ZnO indicating poor interaction between the interstitial and its neighbor. The bands of defect states are mainly dominated by the p character. Similar with the case of OtI ; ZntI also caused more defect bands centered at 10:5; 8:3; 7:5 and 2:5 eV (subplot 1d). Based on site-decomposed and l-projected state densities, we find that the bands centered at 10:5 eV exactly consist of a broadband characteristic of d3z2 1 of ZnI and pz of
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its first oxygen neighboring atoms, and a much narrower band centered at 10 eV characteristic of dyz;zx of ZnI : The bands centered at 8:3 eV are dominated by dxy;x2 y2 of ZnI ; while the bands centered at 7:5 eV are dominated by px;y of the first neighboring oxygen atoms. The bands ð2:5 eVÞ in conduction band mainly arise from the 4s of ZnI with a little combination of pz of the first neighboring oxygen atoms. As for ZnoI ; just below down valence, there is a new feature, which is dominated ZnI and its first neighboring atoms. The defect states centered at 2:5 eV in subplot 1e mainly comes from 4s of ZnoI ; and some py;z of the first neighboring oxygen atoms of ZnoI : The calculated results described above show that both interstitial configuration and interstitial atom affect the interaction between interstitials and its neighboring atoms. In tetrahedral configuration, OtI and ZntI generated similar interaction bands below the valence band bottom, though the component is different; meanwhile, ZnoI and OoI only have effect at the bottom of valence band. Thus, we could conclude that the interaction is much stronger in tetrahedral configuration than in octahedral configuration. Furthermore, the interstitial configuration also shows influence on the interacting direction; in other words, the interaction in tetrahedral configuration is stronger along c-axis than in x–y plane since the interaction bands originating from pz and d3z2 1 allocate higher binding energy. Instead, the octahedral configuration has little influence on the interacting direction. As to the origin of intrinsic n-type conduction of ZnO, many controversial results have been obtained. It has long been assumed that the dominant donor was a native defect, either the oxygen vacancy, or the zinc interstitial [16]. . Kroger [17] assigned VO and VZn as the dominant donor and acceptor, respectively. However, the VO has been identified as a deep donor in electron paramagnetic resonance (EPR) [18]. The defect physics of ZnO is quite complex, to date, theoretical studies of defects in ZnO are scarce, and their results are quite different. Kohan et al. [9] and Zhang et al. [10] have studied systematically the formation energies of various native defects in ZnO, the former suggests that VO and VZn are the dominant defects, while the latter
shows that ZnI is the most abundant donor. Both studies accounted for the band gap correction, but Kohan et al. [9] just simply shifted conduction band up, while Zhang et al. [10] took semiempirical approaches to push down the valence band. As a matter of fact, the fully occupied d band inside the valence band of I–VI semiconductor interacts with the p band, repelling the valence band upwards without affecting the bottom of the conduction band. A particularly striking example is ZnO, it has a smaller band gap B3:3 eV than ZnSB3:9 eV [14,19,20]. On the other hand, calculations based on LDA approximation tend to overestimate the energy of semicore levels like the d orbital in ZnO, enhencing the p–d interaction. Therefore, to correct the calculated band gap based on LDA, we should push down the valence band instead of shifting the conduction band up [9]. As far as our results are concerned, zinc interstitials (ZntI ; ZnoI ) generate donor levels 1:3 eV above the bottom of the conduction band (subplot 1d, e), and the donor levels are dominated by Zn4s in character of the conduction band according to the l-projected partial state density of subplot 1d e. So the defect levels of ZnI will remain unchanged, in line with the results of Zhang et al. [10]. Any donor levels above conduction band will ionize spontaneously, transferring electrons to levels near the bottom of the conduction band. Thus zinc interstitials (ZntI ; ZnoI ) are thus shallow donors. The defect levels in band gap produced by VZn and VO are dominated by O2p in character of the valence band, so they will shift down when the band gap is corrected, leading to deeper donor level of VO and shallower acceptor level of VZn [21]. The band gap states produced by OoI and OtI are also characteristic of valence band, they will become shallower acceptor levels (OoI ) and very deep donor levels (OtI ) according to subplot 1b, c. The contribution to conduction is also determined by the defect concentration. It is found that the corrected formation energies of VZn and OI are much higher than that of ZnI at several charged states. As a consequence, we can draw the conclusion that the dominant native donor in ZnO is ZnI ; and the dominat acceptors are VZn and OI ; but their concentration are much lower than that of ZnI ; leading to instinct n-type of ZnO.
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Since ZntI and ZnoI differ in configuration and interactions with neighboring atoms, there should be a difference in defect formation energies. Kohan et al. [9] studied the formation energy of various native defects in ZnO, where Fermi level, relaxation, and chemical potential are involved. Their results indicate that whether ZnoI and ZntI are neutral or charged, ZnoI has less formation energy than ZntI at various conditions, indicating that less concentration for ZntI : To understand the n-type conduction of ZnO, temperature-dependent Hall measurements [3] were applied, and energies of 31 and 61 meV were found for two donors of concentration 1 1016 and 1 1017 cm3 ; respectively. The larger donor energy is consistent with the hydrogenic model; however, the shallower one is not. According to Ref. [8], the shallower one is also a native defect, but is not identified. Here we suggest that the 31 and 61 meV donors originate from tetrahedral and octahedral zinc interstitial, respectively, based on the charge distribution around the ZntI and ZnoI defects. In order to show the changes in charge distribution, we show the difference charge density
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in Figs. 2, 3 for ZnoI and ZntI ; respectively. They are contour plots obtained by subtracting the charge density of bulk ZnO from that of ZnoI and ZntI for the same cuts through the super-cell, the cutting plane is (1 0 1% 0) through zinc interstitials. These two figures are drawn at the same contour range and step to show the difference in changes caused by ZnoI and ZntI clearly. We find that ZnoI interacts with its first neighboring zinc and oxygen atoms through weak covalency and anti-bonding, respectively (Fig. 2). The change of charge distribution around ZnoI defect appears almost as spherical symmetry indicating a spherical potential after ionization; thus, the donor energy can be expected by ED ¼ 13:6m% =e20 ¼ 66 meV; here polaron effective mass is m% ¼ 0:318m0 ; and the relative static dielectric constant is e0 ¼ 8:12 [22]. This is right for an approximately spherical defect potential, when the defect potential derives much from spherical symmetry, we cannot expect the donor energy by this hydrogenic model. The ZntI defect interacts strongly with neighboring atom as shown in Fig. 3, resulting in apparently non-spherical charge distribution, or potential after ionization,
Zn
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Fig. 2. Contour plot of difference charge density in (1 0 1% 0) plane, this is obtained by subtracting the charge density of bulk ZnO in the same plane from that of ZnO with octahedral zinc interstitial. The values of contours range from 0.004 to 0.04 stepped by 0.004. The units are e=a:u3 : Zni represents the position of octahedral zinc interstitial, and Zn, O represent the position of the first neighboring zinc and oxygen.
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O
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Fig. 3. Contour plot of difference charge density in (1 0 1% 0) plane, this is obtained by subtracting the charge density of bulk ZnO in the same plane from that of ZnO with tetrahedral zinc interstitial. The values of contours range from 0.004 to 0.04 stepped by 0.004. The units are e=a:u3 : Zni represents the position of tetrahedral zinc interstitial, and Zn, O represent the position of first neighboring zinc and oxygen.
then its donor energy cannot be explained in terms of hydrogenic model.
4. Conclusion In conclusion, we have reported the FP-LMTO calculations of zinc and oxygen interstitials in ZnO. We suggested that zinc interstitials dominate the shallow donors in ZnO, and native donors with energy 31 meV might come from the tetrahedral zinc interstitials, while the native donors with energy 61 meV come from octahedral zinc interstitials. The native defects VZn and OoI may contribute to acceptors in ZnO. Our calculations also present the influence of interstitial configuration on the interaction between the interstitial atom and its neighboring atoms, that is, there is stronger interaction in tetrahedral configuration than in octahedral configuration; on the other hand, the tetrahedral interstitials cause stronger interaction along z-direction than any other direction.
Acknowledgements The calculations were performed on the super server Dawn2000-II located at Computer Network Information Center of Chinese Academy of Science. This work is supported by the National Natural Science Foundation of China, the National Key Basic Research Special Foundation, the Natural Science Foundation of Guangdong Province, and the Natural Science Foundation of Education Ministry of China.
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Y. Sun, H. Wang / Physica B 325 (2003) 157–163 [6] K. Minegishi, Y. Koiwai, Y. Kikuchi, Jpn. J. Appl. Phys. 36 (1997) L1453. [7] M. Joseph, H. Tabata, T. Kawai, Jpn. J. Appl. Phys. 38 (1999) L1205. [8] D.C. Look, J.W. Hemsky, J.R. Sizelove, Phys. Rev. Lett. 82 (1999) 2552. [9] A.F. Kohan, G. Ceder, D. Morgan, Chris G. Van de Walle, Phys. Rev. B 61 (2000) 15,019. [10] S.B. Zhang, S.H. Wei, Alex Zunger, Phys. Rev. B 63 (2001) 075,205. [11] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 846. [12] U. Von Barth, L. Hedin, J. Phys. C 5 (1972) 1629. [13] S.Y. Savrasov, Phys. Rev. B 54 (1996) 16,470. [14] S. Massidda, R. Resta, M. Posternak, A. Baldereschi, Phys. Rev. B 52 (1995) R16,977.
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[15] R.R. Gay, M.H. Nodine, V.E. Henrich, H.J. Zeiger, E.I. Solomon, J. Am. Chem. Soc. 102 (1980) 6752. . [16] G. Heiland, E. Mollwo, F. Stockmann, in: F. Seitz, D. Turnbull (Eds.), Solid State Physics, Vol. 8, Academic Press, New York, 1959, p. 191. . [17] F.A. Kroger, The Chemistry of Imperfect Crystal, NorthHolland, Amsterdam, 1974. [18] P. Kasai, Phys. Rev. 130 (1963) 989. [19] S.-H. Wei, Alex Zunger, Phys. Rev. B 37 (1988) 8958. . P. Kruger, [20] P. Schroer, . J. Pollmann, Phys. Rev. B 47 (1993) 6971. [21] Sun Yuming, Xu Pengshou, Shi Chaoshu, Xu Faqiang, Pan Haibin, Lu Erdong, J. Electron Spectrosco. Relat. Phenom. 114–116 (2001) 1123. [22] P. Wagner, R. Helbig, J. Phys. Chem. Solids 35 (1974) 327.
The electronic properties of native interstitials in ZnO Yuming Sun*, Hezhou Wang The State Key Laboratory of Optoelectronic Materials and Technologies, Institute of Physics, Sun Yat-Sen University, Guangzhou 510275, China Received 22 August 2002; accepted 23 August 2002
Abstract To investigate the role of interstitial geometry, we reported ab initio calculations of octahedrally and tetrahedrally native interstitials in ZnO, using the full-potential linear muffin-tin orbital method. The results show that both zinc interstitials could contribute to the native n-type conduction in ZnO, meanwhile, the zinc vacancy and octahedral oxygen interstitial may contribute to the p-type conduction in ZnO. We also suggest that the 31 and 61 meV donors found by temperature-dependent Hall experiment originate from tetrahedral- and octahedral zinc interstitials, respectively, based on their charge distribution. It is noticeable that tetrahedral interstitials cause stronger interaction between interstitials and its neighboring atoms than that of octahedral interstitials. r 2002 Published by Elsevier Science B.V. PACS: 61.72.Bb; 61.72.Ji Keywords: ZnO; Interstitials
1. Introduction Zinc oxide (ZnO) is a I–IV compound semiconductor with a wide direct band gap of 3:3 eV at room temperature, its bulk material excels in electrical properties and has low point-defect concentration [1]. ZnO has been extensively used as piezoelectric tranducers, varistors [2], phosphors, and transparent conducting films, which mainly involved polycrystalline material. Recently, large-area ZnO single crystals have been successfully grown [3] and its strong UV emission at room temperature has been reported [4,5]. Although *Corresponding author. Tel.: +86-2084038887; fax: +862084037423. E-mail address: sun [email protected] (Y. Sun).
ZnO-based photonic and electronic devices show great promise for the future, still there are some severe problems to be overcome. That is, the ZnO material is strongly n-type, usable and reproducible p-type ZnO has not yet been reported, even though several laboratories have measured weak p-type conduction in acceptor-doped materials [6,7]. To identify the contribution of native defects to the strong n-type conduction of ZnO, the highenergy electron radiation experiments were performed on O and Zn face of ZnO, respectively [8], which shows that zinc interstitial (ZnI ) is the best candidate. The first-principle calculations of formation energy gave incompatible results, Kohan [9] predicted that zinc and oxygen vacancies are dominant defects, however, zinc interstitials are assigned to main donors by Zhang [10]. So it is
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necessary to identify the native defects in ZnO in further studies. The octahedral and tetrahedral defect configuration lead to different formation energy [9], this paper will investigate their difference in charge distribution and density of states (DOS). Our results also shed light on the identification of 30 and 60 meV donors [1] in ZnO.
2. Calculational method The band structures were calculated fully selfconsistently using the local density approximation (LDA) to density function theory (DFT) [11]. The exchange-correlation potential was represented according to Barth and Hedin [12]. Basic functions and matrix elements were constructed using a full-potential linear muffin-tin orbital method (FPLMTO) with a GGA correction [13]. Multiplekappa LMTO basis technique was used. The values of kappa were 0:1; 1:0 and 1.0. zinc sites centered 3d, 4s and 4p were treated as valence states, and 2s, 2p functions centered on oxygen sites. The spheres were non-overlapping, and the tails of the basis functions outside their parent spheres were represented in plane waves. A 32atom super-cell was used. The sphere radius for lattice zinc and oxygen is 1.987 and 1:692 a:u:; respectively; the zinc interstitial’s radius is 1:49926 a:u: for tetrahedral geometry and 2:069 a:u: for octahedral geometry, and 1.3793 and 1:97 a:u for two kind of oxygen interstitial configurations. The Brillouin zone integration was performed using 110 k-points.
3. Results and discussion ZnO belongs to wurtzite structure, both zinc and oxygen sublattice have a set of own tetrahedral and octahedral interstices. The biggest interstice in ZnO is the common space of the nearest zinc and oxygen interstices along c-axis, so it is rational to choose the common part as the interstitial positions in calculation. The relaxation is neglected since we are only interested in the tendency of changes in electronic structure caused by native interstitials. The tetrahedral and octahe-
dral interstitial atoms are both caged in triple prisms, three zinc atoms at the top and three oxygen atoms at the bottom along c-axis. In case of tetrahedral interstice, the cage is closed by an oxygen atom above the top and a zinc atom below the bottom; instead, in case of octahedral interstice, the cage is open along c-axis. It is also noticeable that those three zinc and oxygen atoms constructing cage are the first neighbors for octahedral interstitial; however, they are second neighbors for tetrahedral interstitial. Naturally, different interstitial geometry, space and symmetry lead to different electronic properties. This section is to reveal electronic structure of zinc and oxygen interstitials in ZnO. The calculated DOS for perfect ZnO and four types of native interstitials are presented in Fig. 1, where subplots 1a–e present the DOS of perfect ZnO, ZnO with native tetrahedral oxygen interstitial (OtI ), octahedral oxygen interstitial (OoI ), tetrahedral zinc interstitial ðZntI Þ and octahedral zinc interstitial ðZnoI Þ; respectively. The vertical dashed-line in Fig. 1 marks the valence band edge, and the short vertical dotted-lines in subplots 1b–e mark the Fermi levels caused by corresponding interstitials. The binding energy is measured relative to the valence band edge. Based on the site-decomposed and l-projected state densities, we observe two groups in the valence band of perfect ZnO (subplot 1a): (1) from 6:5 to 5:0 eV (called down valence band), there are bands with a strong d character originating mostly from 3d states centered at Zn sites. (2) The upper valence bands located approximately 5:0 eV below valence band edge originate mainly from the O2p states. The valence bandwidth is in good agreement with GW calculation [14], and the calculated line shape of the total DOS is in good agreement with that of experiment [15]. The lowest conduction bands have a strong Zn4s contribution. There is charge transferred from Zn4s to O2p due to the mixing between the s and p states at O sites, and the s and p states of the surrounding Zn shifts the center of gravity of the local DOS at the O sites toward lower-energy regions. The calculated band gap of a perfect ZnO is about 1:2 eV: In general, the values of the band gap calculated using the ab initio LDA method are less than half the values obtained in
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Binding Energy (eV) Fig. 1. Total density of states (DOS) for bulk ZnO, and its four types of native interstitials. Subplot a–e present the DOS of bulk ZnO, ZnO with tetrahedral oxygen interstitial (OtI ), ZnO with octahedral oxygen interstitial (OoI ), ZnO with tetrahedral zinc interstitial (ZntI ) and ZnO with octahedral Zn interstitial ðZnoI Þ: The long vertical dashed-line presents the valence band edge, and the short vertical dotted-lines in subplots b–e present the Fermi levels caused by corresponding interstitial.
optical experiments. Inaccuracy in the determination of the optical band gap has little influence in the present discussion since we only discuss the electronic property of ground states. Subplots 1b,c show that both OtI and OoI generate defect states centered at 0:5 eV above the valence band edge. It is noticeable that the defect states caused by OtI is fully occupied, while that of OoI is half occupied. Comparing the total DOS in subplots 1b,c, there are more new features caused by OtI (subplot 1b), two bands below the bottom of valence band centered at 9 and 7:5 eV; and a band above the top of valence band centered at 2 eV: The site-decomposed and l-projected state densities show that these new bands mainly originate from the bonding between
the oxygen interstitial and its first neighboring oxygen and zinc; meanwhile pz and d3z2 1 dominate the bands centered at 9 and 2 eV; and the bands centered at 0.5 and 7:5 eV are dominated by px;y and dyz;zx : As for OoI (subplot 1c), except the band gap states, the line shape is well consistent with that of ZnO indicating poor interaction between the interstitial and its neighbor. The bands of defect states are mainly dominated by the p character. Similar with the case of OtI ; ZntI also caused more defect bands centered at 10:5; 8:3; 7:5 and 2:5 eV (subplot 1d). Based on site-decomposed and l-projected state densities, we find that the bands centered at 10:5 eV exactly consist of a broadband characteristic of d3z2 1 of ZnI and pz of
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its first oxygen neighboring atoms, and a much narrower band centered at 10 eV characteristic of dyz;zx of ZnI : The bands centered at 8:3 eV are dominated by dxy;x2 y2 of ZnI ; while the bands centered at 7:5 eV are dominated by px;y of the first neighboring oxygen atoms. The bands ð2:5 eVÞ in conduction band mainly arise from the 4s of ZnI with a little combination of pz of the first neighboring oxygen atoms. As for ZnoI ; just below down valence, there is a new feature, which is dominated ZnI and its first neighboring atoms. The defect states centered at 2:5 eV in subplot 1e mainly comes from 4s of ZnoI ; and some py;z of the first neighboring oxygen atoms of ZnoI : The calculated results described above show that both interstitial configuration and interstitial atom affect the interaction between interstitials and its neighboring atoms. In tetrahedral configuration, OtI and ZntI generated similar interaction bands below the valence band bottom, though the component is different; meanwhile, ZnoI and OoI only have effect at the bottom of valence band. Thus, we could conclude that the interaction is much stronger in tetrahedral configuration than in octahedral configuration. Furthermore, the interstitial configuration also shows influence on the interacting direction; in other words, the interaction in tetrahedral configuration is stronger along c-axis than in x–y plane since the interaction bands originating from pz and d3z2 1 allocate higher binding energy. Instead, the octahedral configuration has little influence on the interacting direction. As to the origin of intrinsic n-type conduction of ZnO, many controversial results have been obtained. It has long been assumed that the dominant donor was a native defect, either the oxygen vacancy, or the zinc interstitial [16]. . Kroger [17] assigned VO and VZn as the dominant donor and acceptor, respectively. However, the VO has been identified as a deep donor in electron paramagnetic resonance (EPR) [18]. The defect physics of ZnO is quite complex, to date, theoretical studies of defects in ZnO are scarce, and their results are quite different. Kohan et al. [9] and Zhang et al. [10] have studied systematically the formation energies of various native defects in ZnO, the former suggests that VO and VZn are the dominant defects, while the latter
shows that ZnI is the most abundant donor. Both studies accounted for the band gap correction, but Kohan et al. [9] just simply shifted conduction band up, while Zhang et al. [10] took semiempirical approaches to push down the valence band. As a matter of fact, the fully occupied d band inside the valence band of I–VI semiconductor interacts with the p band, repelling the valence band upwards without affecting the bottom of the conduction band. A particularly striking example is ZnO, it has a smaller band gap B3:3 eV than ZnSB3:9 eV [14,19,20]. On the other hand, calculations based on LDA approximation tend to overestimate the energy of semicore levels like the d orbital in ZnO, enhencing the p–d interaction. Therefore, to correct the calculated band gap based on LDA, we should push down the valence band instead of shifting the conduction band up [9]. As far as our results are concerned, zinc interstitials (ZntI ; ZnoI ) generate donor levels 1:3 eV above the bottom of the conduction band (subplot 1d, e), and the donor levels are dominated by Zn4s in character of the conduction band according to the l-projected partial state density of subplot 1d e. So the defect levels of ZnI will remain unchanged, in line with the results of Zhang et al. [10]. Any donor levels above conduction band will ionize spontaneously, transferring electrons to levels near the bottom of the conduction band. Thus zinc interstitials (ZntI ; ZnoI ) are thus shallow donors. The defect levels in band gap produced by VZn and VO are dominated by O2p in character of the valence band, so they will shift down when the band gap is corrected, leading to deeper donor level of VO and shallower acceptor level of VZn [21]. The band gap states produced by OoI and OtI are also characteristic of valence band, they will become shallower acceptor levels (OoI ) and very deep donor levels (OtI ) according to subplot 1b, c. The contribution to conduction is also determined by the defect concentration. It is found that the corrected formation energies of VZn and OI are much higher than that of ZnI at several charged states. As a consequence, we can draw the conclusion that the dominant native donor in ZnO is ZnI ; and the dominat acceptors are VZn and OI ; but their concentration are much lower than that of ZnI ; leading to instinct n-type of ZnO.
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Since ZntI and ZnoI differ in configuration and interactions with neighboring atoms, there should be a difference in defect formation energies. Kohan et al. [9] studied the formation energy of various native defects in ZnO, where Fermi level, relaxation, and chemical potential are involved. Their results indicate that whether ZnoI and ZntI are neutral or charged, ZnoI has less formation energy than ZntI at various conditions, indicating that less concentration for ZntI : To understand the n-type conduction of ZnO, temperature-dependent Hall measurements [3] were applied, and energies of 31 and 61 meV were found for two donors of concentration 1 1016 and 1 1017 cm3 ; respectively. The larger donor energy is consistent with the hydrogenic model; however, the shallower one is not. According to Ref. [8], the shallower one is also a native defect, but is not identified. Here we suggest that the 31 and 61 meV donors originate from tetrahedral and octahedral zinc interstitial, respectively, based on the charge distribution around the ZntI and ZnoI defects. In order to show the changes in charge distribution, we show the difference charge density
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in Figs. 2, 3 for ZnoI and ZntI ; respectively. They are contour plots obtained by subtracting the charge density of bulk ZnO from that of ZnoI and ZntI for the same cuts through the super-cell, the cutting plane is (1 0 1% 0) through zinc interstitials. These two figures are drawn at the same contour range and step to show the difference in changes caused by ZnoI and ZntI clearly. We find that ZnoI interacts with its first neighboring zinc and oxygen atoms through weak covalency and anti-bonding, respectively (Fig. 2). The change of charge distribution around ZnoI defect appears almost as spherical symmetry indicating a spherical potential after ionization; thus, the donor energy can be expected by ED ¼ 13:6m% =e20 ¼ 66 meV; here polaron effective mass is m% ¼ 0:318m0 ; and the relative static dielectric constant is e0 ¼ 8:12 [22]. This is right for an approximately spherical defect potential, when the defect potential derives much from spherical symmetry, we cannot expect the donor energy by this hydrogenic model. The ZntI defect interacts strongly with neighboring atom as shown in Fig. 3, resulting in apparently non-spherical charge distribution, or potential after ionization,
Zn
Zni
O
Fig. 2. Contour plot of difference charge density in (1 0 1% 0) plane, this is obtained by subtracting the charge density of bulk ZnO in the same plane from that of ZnO with octahedral zinc interstitial. The values of contours range from 0.004 to 0.04 stepped by 0.004. The units are e=a:u3 : Zni represents the position of octahedral zinc interstitial, and Zn, O represent the position of the first neighboring zinc and oxygen.
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O
Zni
Zn
Fig. 3. Contour plot of difference charge density in (1 0 1% 0) plane, this is obtained by subtracting the charge density of bulk ZnO in the same plane from that of ZnO with tetrahedral zinc interstitial. The values of contours range from 0.004 to 0.04 stepped by 0.004. The units are e=a:u3 : Zni represents the position of tetrahedral zinc interstitial, and Zn, O represent the position of first neighboring zinc and oxygen.
then its donor energy cannot be explained in terms of hydrogenic model.
4. Conclusion In conclusion, we have reported the FP-LMTO calculations of zinc and oxygen interstitials in ZnO. We suggested that zinc interstitials dominate the shallow donors in ZnO, and native donors with energy 31 meV might come from the tetrahedral zinc interstitials, while the native donors with energy 61 meV come from octahedral zinc interstitials. The native defects VZn and OoI may contribute to acceptors in ZnO. Our calculations also present the influence of interstitial configuration on the interaction between the interstitial atom and its neighboring atoms, that is, there is stronger interaction in tetrahedral configuration than in octahedral configuration; on the other hand, the tetrahedral interstitials cause stronger interaction along z-direction than any other direction.
Acknowledgements The calculations were performed on the super server Dawn2000-II located at Computer Network Information Center of Chinese Academy of Science. This work is supported by the National Natural Science Foundation of China, the National Key Basic Research Special Foundation, the Natural Science Foundation of Guangdong Province, and the Natural Science Foundation of Education Ministry of China.
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