Journal of Alloys and Compounds 621 (2015) 423–427
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Electronic structure and optical properties of V- and Nb-doped ZnO from hybrid functional calculations Wei Zhou, Yanyu Liu, Junfu Guo, Ping Wu ⇑ Department of Applied Physics, Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Institute of Advanced Materials Physics, Faculty of Science, Tianjin University, Tianjin 300072, China
a r t i c l e
i n f o
Article history: Received 23 July 2014 Received in revised form 2 October 2014 Accepted 3 October 2014 Available online 14 October 2014 Keywords: ZnO Density functional Optical property Visible light absorptions
a b s t r a c t The electronic structure and optical properties of multiple donors V and Nb doped ZnO were systematically investigated using the hybrid functional calculations. The localized states form near the Fermi level and decrease with the doping concentration of V, while Nb doping gives an opposite trend. Signiﬁcant visible light absorptions were obtained from both V and Nb doping, while the variation trend of optical properties with the doping concentration shows obvious difference. Additionally, V doped ZnO prefers to absorb the polarized light along (0 0 1) direction, while Nb doping enhance the absorption along (1 0 0) direction. These results provide useful predictions to design doping strategy for ZnO materials in photoelectric and photocatalytic applications. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction ZnO is a wide band-gap semiconductor with a direct band gap of 3.2–3.4 eV [1–2]. Advantages, such as an abundance of resources, high chemical stabilizations and nontoxicity, make it widely used in blue/UV light-emitting diodes, photocatalysts and transparent conducting layers [3–7]. Therefore, the ZnO-based semiconductors have been extensively investigated experimentally and theoretically. V and Nb show the most stable oxidation state X+5 ([email protected]
or Nb) in natural environment. Thus, as multielectron donors, V and Nb are able to improve the electrical conductivity of ZnO-based semiconductors, which are the potential candidates for replacing the single electron donor of Al. And the good electrical conductivity has been observed in both V and Nb doped ZnO [8–10]. Furthermore, the optical properties of V and Nb doped ZnO also attract much attention. It is well known that the visible light not only is decisive for our visual sense but also includes a large component of solar energy (45%). Previous experimental results indicate that both V and Nb doped ZnO have signiﬁcant absorption in visible light range [11–14]. These imply V and Nb doped ZnO will be promising multi-functional materials for optoelectronic applications. Although V and Nb are adjacent elements of the VB group in the periodic table, previous studies show that the relationships ⇑ Corresponding author. Tel.: +86 02227403488; fax: +86 02227406852. E-mail address: [email protected]
(P. Wu). http://dx.doi.org/10.1016/j.jallcom.2014.10.022 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.
between the doping content and the variation of optical properties for V and Nb doping are much different. Therefore, it is crucially important to explore the origin of doping effect in V and Nb doped ZnO system. Unfortunately, the research focus of V and Nb doped ZnO are mainly on their magnetic properties till now [15–20]. Detailed theoretical studies have rarely been reported on the optical properties of V and Nb doped ZnO systems . Especially, the dependences of the optical properties on doping content and crystal direction are still unclear. In this paper, the electronic structure and optical properties of V and Nb doped ZnO were systematically investigated using the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional which can well correct the underestimation of band gap for the standard local density approximation and generalized gradient approximation [22– 26]. Although the HSE results still underestimate the orbital energy of Zn-3d electrons , the more accurate GW calculation is much time consuming for the doped system with large supercell size [28,29]. Thus, the HSE method was chosen in this work. Our calculation results show that the HSE hybrid functional is needed, rather than the scissors operator for standard DFT functionals, to obtain accurate and reliable optical properties for ZnO system. The absorption of visible light is enhanced in both V and Nb doped ZnO materials, but the variation trend with doping concentration is different. Additionally, the absorption coefﬁcient in different crystal direction is also dependent on the doping elements. These give crucial and useful predictions for these materials in different industrial applications.
W. Zhou et al. / Journal of Alloys and Compounds 621 (2015) 423–427
2. Calculation details All calculations in our work were performed within the projector augmented wave method as implemented in the Vienna Ab-initio Simulation Package (VASP) code [30,31]. The expression for the HSE exchange–correlation energy is given as HF;SR EHSE ðxÞ þ ð1 aÞEPBE;SR ðxÞ þ EPBE;LR ðxÞ þ EPBE XC ¼ aEX X X C
where EXHF;SR is the short-range Hartree–Fock (HF) exchange, EPBE;SR X and EPBE;LR are the short-range (SR) and long-range (LR) components X of the PBE exchange functional obtained by integration of the model PBE exchange hole, and EPBE is the PBE correlation energy . The C screening parameter x deﬁnes the separation range and is set to 0.207 Å1 which is called HSE06 . As for ZnO based systems, the HF mixing constant a is set to 0.375 to produce an accurate value of the band gap . It is known that hybrid functional calculation is much time consuming. Thus, the spin un-polarized calculation, which also has been employed in previous reports of transition metal doped ZnO [35,36], was chosen in this work. The plane wave energy cutoff is set to 420 eV with total energy converging to lower than 1 105s eV/atom. The crystal structure and the atomic coordinates of pure and doped ZnO are fully relaxed until the residual force on each atom is less than 0.01 eV/Å using the Conjugate-Gradient algorithm . A grid of 9 9 6 k points is used for the unit cell. For impurities doped ZnO, three different conﬁgurations of ZnO supercell (2 2 2, 3 2 1 and 2 2 1) are considered, which correspond to the doping concentration x = 6.25%, 8.3% and 12.5%. Monkhorst–Pack grids of 4 4 2, 3 4 5 and 4 4 5 are used for Brillouin zone sampling. For the formation energy calculations, spin polarized calculations were used for referenced materials. 3. Results and discussion The optimized lattice constants are a = 3.254 Å and c = 5.238 Å for pure ZnO, which are in good agreement with the experimental data (a = 3.253 Å, c = 5.213 Å). The band structures of pure ZnO using standard PBE and HSE hybrid functional are presented in Fig. 1. Both the PBE and HSE results yield qualitatively correct band characters. The valence band maximum (VBM) and the conduction band minimum (CBM) locate at the same C point, indicating the pure ZnO is a direct band gap semiconductor . Compared with PBE result, the conduction band from HSE exhibits slight localization, while the position of conduction band shifts towards to the higher energy which increases the band gap Eg from 0.79 eV (PBE) to 3.34 eV (HSE). This value is very close to the experimental results [39,40]. It indicates the underestimated band gap in the standard PBE could be appropriately corrected by HSE hybrid functional. Meanwhile, the less pronounced interaction between Zn 3d and O 2p results in that the Zn-3d band position from HSE calculation (6.3 eV) is lower than that from PBE calculation (4.8 eV), which is much closer to the experimental values (7.5 7.8 eV) . That is to say, the high energy region in valance band, which is erroneously occupied and unduly hybridized by the PBE approximation (0.40 4.42 eV), is also corrected by HSE hybrid functional (0.56 5.78 eV). More details about the electronic structure can be observed from the calculated density of states (DOS), as shown in Fig. 2(a). Both PBE and HSE results indicate that the conduction band mainly originates from the Zn 4s states which strongly hybridize with O 2p orbitals and has a slight contribution from Zn 3d orbitals. As for the valance band, the high energy region near the VBM is composed of O 2p orbitals, whereas the low energy region originates from the Zn 3d (lower than 5 eV and not presented in the ﬁgure). Different from PBE results, the bottom of conduction band from HSE shifts
Fig. 1. The band structure of pure ZnO using (a) standard PBE and (b) HSE06 hybrid functional. The Fermi level is set to 0 eV.
up to a higher energy level consistent with the band structure. Nevertheless, the most obvious change is that the excessively hybridized Zn 3d, Zn 4s and O 2p orbitals in the valence band are more extended in energy range (broadening from 3.9 to 4.7 eV) from the HSE functional. The Zn 3d and 4s states are distinctly weakened due to the delocalization, while the O 2p states are enhanced especially in the low energy region. Consequently, the HSE results give much better agreement with the experimental values for the width (position) of the valence p-band and d-band [41–43]. In a word, the hybridization between O 2p and Zn 3d states is less pronounced and the band gap is appropriately corrected through the HSE hybrid functional calculations. To investigate the doping effect of V or Nb on the electronic structures, total and partial DOS were calculated for the systems with a doping concentration of 6.25%, as shown in Fig. 2(b). Compared with un-doped ZnO, the most remarkable feature is that the Fermi level shifts into the CBM for both V and Nb doping cases, which indicates a typical n-type doping behavior. The formation energy of charged states as a function of the chemical potential of electrons were also calculated with the method proposed by Van de Walle et al. 
DHf ðqÞ ¼ Etotal ða; qÞ Etotal ðZnOÞ þ
qðeF þ Ev þ DVÞ
where Etotal(a,q) it the total energy of a supercell with dopant, ni is the number of atoms of species i that have been added to or remove from the supercell. li is the chemical potential of element i. Ev is the VBM of the bulk system. A correction term DV of the difference between the electrostatic potentials of the defected and
W. Zhou et al. / Journal of Alloys and Compounds 621 (2015) 423–427
Fig. 2. The total DOS and PDOS of (a) pure ZnO (PBE and HSE results) and (b) 6.25% (V or Nb) doped ZnO (HSE results only). The color ﬁlled areas represent the PBE results in (a) and the V doping case in (b), respectively. The Fermi level is set to 0 eV. (XAZn 4s indicates the Zn 4s state in X doped ZnO, and XAZn 3d indicates the Zn 3d state in X doped ZnO (X is Nb or V).).
un-defected systems is used to align the band structure. And a jellium background was used for charged system as charge correction. Beside the stable bulk phases of Zn, V and Nb, O2, V2O5 and Nb2O5 were also chosen as the references for calculations. Following relationships were used to calculate chemical potentials:
lZnO ¼ lZn þ lO ¼ lZn ðbulkÞ þ lO ðO2 Þ þ DHf ðZnOÞ lX2O5 ¼ 2lX þ 5lO ¼ 2lX ðbulkÞ þ 5lO ðO2 Þ þ DHf ðX2 O5 Þ
ðX ¼ V or NbÞ
The calculated formation energies of ZnO, V2O5 and Nb2O5 are 3.67 eV, 15.23 eV and 20.14 eV, which is close to the previous experimental and theoretical data [35,45,46]. Similar with the report by Zhou et al. for In doped ZnO, the growth conditions of O-rich and Zn-rich was considered . As for the O-rich condition, the up limit of lO was given as one-half of the total energy of a single oxygen molecule (4.86 eV), while the lower limit (8.53 eV) was determined from the formation of ZnO. The same with oxygen, the chemical potentials of Zn, V and Nb can be calculated with Eqs. (2) and (3). Our calculated results (Fig. 3(a)) show that the V3+ Zn and Nb3+ Zn states are dominant over the whole range of the chemical potential of electron at both O-rich and Zn-rich conditions, which indicates both V and Nb in ZnO are shallow donors. And the dopants prefer to be introduced into the crystal at Zn-rich condition which has lower formation energy. From the DOS, the impurity bands of V 3d states exhibit two extremely localized peaks
near the Fermi level (0.95 eV and 0.14 eV), while some other bands locate above the Fermi level in the energy range from 1.86 to 3.70 eV. Our calculated impurity band is much higher than that reported by Wang et al. using GGA + U functional , which is due to the different description of orbital interaction from hybrid functional. As the dominant states in the conduction band, O 2p and Zn 4s states slightly hybridize with the V 3d orbitals. And due to the partially occupied impurity bands crossing the Fermi level, the band gap decreases from 3.34 eV of pure ZnO to 3.18 eV. The similar behavior is also observed in the case of Nb doping. However, the Nb 4d states are less localized, and the peaks in the conduction band are weaker but wider than those of the V doping (1.10 2.54 eV). And the remained Nb 4d bands hybridize with Zn 3d and O 2p orbitals, where the V 3d states contribute a little in V doping cases. Moreover, the relatively delocalized Nb impurity bands result in a small band gap of 2.76 eV. In order to show the effect of doping content on the electronic properties, the total DOS of ZnO with different concentrations are shown in Fig. 3. The peaks near the Fermi level become weaker and wider as V doping concentration increases. The case for Nb doping is similar with V doping except a slight increase at energy around 2 eV. The position of valence-band maximum (VBM) moves to the low energy region in both cases, which gives an agreement with our previous calculation results . Then, the optical properties of V and Nb-doped ZnO will be discussed with the dielectric function. Since ZnO ﬁlm usually grows along the (0 0 1) orientation, the polarization vectors of incident light was set perpendicular to the c axis (E\c) in this work. The imaginary part of the dielectric function (e2(x)), which determines the optical properties of materials, is shown in Fig. 4. For pure ZnO, the PBE results have a good agreement with the previous reports . While for the HSE results, the shift of dielectric function to the higher energy can be observed which is consistent with the DOS results. Three intrinsic peaks move to 4.92, 9.76, and 15.74 eV resulting in the decrease of values in low energy region . The line shape for V- or Nb-doped ZnO from HSE calculations is similar with pure ZnO in UV energy region. The peak at 4.92 eV shifts upward to 6.19 eV because the VBM moves to the lower energy. Hence, a higher energy will be needed when transition occurs from VBM to the states above Fermi level. The slightly enhanced peak at 9.76 eV may be attributed to the impurity states. On the other hand, with respect to the obvious change in low energy region, the emerging peak at 0.8 eV originates from the electronic intraband transition of impurity d states and Zn 4s states in the conduction band, which is similar with previous reports for V doped ZnO . Compared with the PBE results, it also implies that the scissors operator , which simply shifts the host conduction band minimum to higher energies, may not correctly produce the optical properties of transition metal doped ZnO. In the case of V doping, this peak weakens with increasing the doping concentration. This phenomenon may be deduced from the less localization of the impurity band as shown in Fig. 3(b). While for the case of Nb doping, this peak just increases with the doping concentration. For the promising photoelectric and photocatalytic applications, the optical absorption in visible light region should be taken into account. Hence, the absorption coefﬁcients of doped ZnO are plotted in Fig. 5. Different from the PBE result, the absorption coefﬁcient of un-doped ZnO calculated by HSE is extremely small in the visible region which is consistent with the experimental result that the pure ZnO has a considerable transparency of over 90% in this region. For V-doped ZnO, both PBE and HSE results show the 6.25% doping has the strongest absorption in visible region which is beneﬁt for the photocatalytic process. The typical peaks at 0.95 and 2.27 eV origin from the intraband transition from 0.93 to 0.12 eV and 0.12 to 2.64 eV (Fig. 2(b)). It’s worth noting that for
W. Zhou et al. / Journal of Alloys and Compounds 621 (2015) 423–427
Fig. 3. (a) The formation energy of charged states at O-rich (solid line) and Zn-rich (dashed line) conditions, and (b) the total DOS for both V and Nb doping (HSE results only). The Fermi level is set to 0 eV.
Fig. 4. The imaginary part of dielectric function from PBE and HSE for (a) V- and (b) Nb-doped ZnO with different concentrations in (0 0 1) direction (the main peaks are indicated by black arrows).
V doping the absorption coefﬁcient increases with small doping concentration (less than 6.25%) and decreases with heavy doping, which is in agreement with the experimental results by Wang et al. . The calculation results also imply that there is a critical doping concentration for the strongest visible light absorption. For Nb-doped system, the absorption coefﬁcients increase monotonously with the doping concentration, which is consistent with the experimental reports [9,11]. Moreover, the anisotropy of
Fig. 5. The absorption coefﬁcients for (a) V- and (b) Nb-doped ZnO with different concentrations in (0 0 1) and (1 0 0) direction. The color ﬁlled areas represent the visible light region. (PBE and HSE results). (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)
optical absorption is also taken into account in this work. The absorption coefﬁcient of incident light along (1 0 0) direction (E// c) is presented in Fig. 5. It can be found that the model with 8.3% doping concentration has the strongest absorption in (1 0 0) direction for V-doped ZnO, while Nb-doped ZnO keeps the similar pattern with that along (0 0 1) direction. This gives an agreement with the critical doping concentration of V mentioned above. Moreover, for all doping concentrations, the absorption along (0 0 1) direction
W. Zhou et al. / Journal of Alloys and Compounds 621 (2015) 423–427
resources were supported by High Performance Computing Center of Tianjin University, China. References
Fig. 6. The reﬂectivity R, refractivity n index, and energy-loss functions L of pure and 6.25% (V or Nb) doped ZnO (HSE results only).
is stronger than that along (1 0 0) direction for V-doped ZnO systems, whereas the Nb-doped ZnO systems show the opposite trend. It gives a suggestion to choose the preferred growth direction for different applications. Fig. 6 shows the reﬂectivity (R(x)), refractivity index(n(x)), and energy-loss (L(x)) spectrum (HSE results) of the pure and 6.25% doping systems. The refractivity of pure ZnO in the visible region is about 2 which shows a good agreement with the experimental value . For the V-(Nb-) doped system, the low photon-energy range below 1.93 eV (1.18 eV) presents an appreciable refractivity. When the refractivity for V doped ZnO goes to the weakest, the corresponding reﬂectivity reaches the largest value which is different from the variation of Nb doping case. The energy-loss peaks at 5.31 eV (1.74 eV) and 21.74 eV (20.89 eV) are related to the plasma oscillations where the both reﬂectivity and refractivity decrease [47,50]. 4. Conclusions In summary, the electronic structure and optical properties of V and Nb-doped ZnO are systematically investigated through ﬁrstprinciples calculations. The calculation results show that HSE hybrid functional appropriately corrects the shortcomings of standard PBE approximation for band structure. V doping will introduce strong localized impurity states into ZnO host, while the localization of impurity states in Nb doping is less pronounced. The calculated optical properties indicate low V doping concentration can enhance the absorption of visible light and high concentration will result in good transparency, whereas the absorption of Nb-doped ZnO shows a monotonous increase with the doping concentration. That is to say, the suitable doping concentration can be chosen to improve the light absorption of V or Nb doped ZnO for potential photocatalysis application. Moreover, the dependence of absorption coefﬁcients on the incident light direction show much difference for V- and Nb doped ZnO. Thus, as for the transparent application the (1 0 0) and (0 0 1) directions should be chosen for V and Nb doped ZnO, respectively. Acknowledgement This work was supported by the National Natural Science Foundation of China (51074112) (11247224), the Key Program of Tianjin Natural Science Foundation (11JCZDJC22100). The supercomputing
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