Structural and electronic properties of Eu and Pddoped ZnO
 Mohammad Hussein Naseef Assadi^{1, 2},
 Yuebin Zhang^{2},
 RongKun Zheng^{1},
 Simon Peter Ringer^{1} and
 Sean Li^{2}Email author
DOI: 10.1186/1556276X6357
© Assadi et al; licensee Springer. 2011
Received: 27 September 2010
Accepted: 21 April 2011
Published: 21 April 2011
Abstract
Doping ZnO with rare earth and 4d transition elements is a popular technique to manipulate the optical properties of ZnO systems. These systems may also possess intrinsic ferromagnetism due to their magnetic moment borne on 4f and 4d electrons. In this work, the structural, electronic, and magnetic properties of Eu and Pddoped ZnO were investigated by the ab initio density functional theory methods based on generalized gradient approximation. The relative stability of incorporation sites of the doped elements in the ZnO host lattice was studied. The ground state properties, equilibrium bond lengths, and band structures of both the ZnO:Eu and ZnO:Pd systems were also investigated. The total and partial densities of electron states were also determined for both systems. It was found that in the ZnO:Eu system, ambient ferromagnetism can be induced by introducing Zn interstitial which leads to a carriermediated ferromagnetism while the ZnO:Pd system possesses no ferromagnetism.
PACS 31.15.E, 75.50.Pp, 75.30Hx
Introduction
Semiconductor metal oxides, with applications in the photoelectrochemical cells, diluted magnetic semiconductors (DMS), field effect transistors, and photoluminescence devices, have recently initiated dynamic research activities [1–3]. In particular, ZnO has a significant advantage for applications in optical [4] and spintronic [5] devices. As a result, doping ZnO with various elements has been a popular technique to manipulate and control ZnO's extrinsic properties for device applications [6]. Specially rare earth (RE) and transition metal (TM)doped ZnO systems exhibit interesting optical and magnetic properties, which do not exist in undoped ZnO. Optically, ZnO systems doped with RE ions have been intensively investigated as electroluminors with wide technological applications [7]. In REdoped ZnO, the intraionic 4f transitions of RE ions form luminescent centers which generate narrow and intense emission lines [8]. While the enhancement in the optical absorption of TMdoped ZnO can transfer these materials to efficient photocatalysts [9].
Magnetically, the intrinsic magnetic moment, borne by the RE and TM ions, makes the RE and TMdoped ZnO systems to be potential diluted magnetic semiconductors with applications in spintronic devices. Over the past decade or so, a considerable amount of effort has been made on searching for ZnObased DMSs with ferromagnetism at ambient. This goal is meant to be achieved by doping ZnO with mainly the first row TMs, such as Co, Mn, and Fe [10]. However, most recently, interesting magnetism has been observed in other metal oxides doped with the second row TMs, namely in Sn_{2}O:Pd system [11]. This stimulated further search for possible ferromagnetism [12] and functional optical properties [13] in ZnO:Pd. The realization of magnetism in the ZnO:Pd system is motivated by a previous theoretical prediction [14] and experimental observation [15] of ferromagnetism in Pd clusters. In addition to systems containing TM ions, Eudoped ZnO (ZnO:Eu) has also shown room temperature ferromagnetic ordering [16] which is partially caused by the high magnetic moment of the Eu ions. In this work, the structural and electronic properties of the ZnO:Pd and ZnO:Eu systems are investigated by a density functional approach. Furthermore, the effects of ZnO's two dominant point defects [17], Zn interstitial (Zn_{I}) and O vacancy (V_{O}), on the functional properties of these materials are studied. The results of theoretical investigations presented here will shed light on the origin of the functional properties of this relatively new family of materials.
Computational details
Ab initio calculations were performed with a density functional theorybased DMol3 package developed by Accelrys [18, 19]. Geometry optimization and partial density of states (PDOS) calculations were performed with "doublenumeric plus polarization" (DNP) basis set while generalized gradient approximation (GGA) based on PerdewWang formalism was applied for correlation functional [20]. Realspace global cutoff radii were set for all elements at 5 Å. Since only valence electrons would affect the physical properties, the nuclei and core electrons were replaced by DFT semicore pseudopotentials with a relativistic correction [21]. A Brillouin zone sampling was carried out by choosing the 2 × 2 × 2 kpoint set using the MonkhorstPark scheme with a grid spacing of approximately 0.04 Å^{1} between k points. The convergence thresholds for energy, Cartesian components of internal forces acting on the ions, and displacement were set to be 10^{5} eV/atom, 0.05 eV/Å, and 0.001 Å, respectively. A convergence testing was performed, first by increasing the k point mesh to 3 × 3 × 3; it was found that the total energy differs less by 10^{5} eV/atom. Then, the kpoint mesh was fixed at 2 × 2 × 2, and the cutoff radii were set for all elements to be 5.5 Å. Once again, no significant change in the total energy was obtained. Thus, the results were well converged.
The formation enthalpy and bandgap for undoped ZnO was calculated to be 3.5 and 2.0 eV, respectively. The formation enthalpy is in good agreement with the experimental value of 3.64 eV [22]. However, the bandgap is underestimated by 1.4 eV which is attributed to the GGA intrinsic error. The calculated lattice constants for undoped and fully optimized ZnO were found to be 3.279 Å for a and 5.281 Å for c, which are in good agreement with the experimental data [23], overestimated by only 0.9% and 1.5%, respectively. The ZnO bond lengths in the relaxed structure were 2.005 and 1.997 Å along the c direction and ab plane, respectively. In order to avoid the artificial hydrostatic stress in the doped structures, the lattice parameters were fixed to the calculated values of the undoped ZnO while only the internal atomic coordinates were relaxed.
in which E ^{t}, μ, and E _{F} represent total energy, chemical potential for respective elements, and Fermi energy, respectively. μ _{Zn} and μ _{M} are set to be the calculated energies of metallic Zn and the dopants (Pd or Eu) per element. n represents the number of Zn atoms removed from the supercell, which is zero in the case of the interstitial dopant and one for the substitutional dopant. q stands for the net number of electrons transferred from the defect to the conduction band. Since only neutral supercells were adapted for the calculations, q is zero for all configurations.
The ZnO:Eu system
The E ^{f}, Eu's spin number, and the magnetic ground state of the ZnO:Eu_{Zn}, ZnO:Eu_{I}, ZnO:Eu_{Zn} + V_{O} and ZnO:Eu_{Zn} + Zn_{I} are presented.
Configuration  E ^{f}(eV)  Eu's spin ([ℏ]/2)  Magnetic ground state 

ZnO:Eu_{Zn}  2.391  6.800  Paramagnetic 
ZnO:Eu_{I}  1.429  6.859  Paramagnetic 
ZnO:Eu_{Zn} + V_{O}  1.772  6.907  Paramagnetic 
ZnO:Eu_{Zn}:Z_{I}  2.776  6.879  Ferromagnetic 
Next, the E ^{f} of Eu_{Zn} in the nonstochiometric ZnO was studied by considering two distinct situations that lead to Zn excess: first by including a V_{O} in the ZnO:Eu_{Zn} + V_{O} system and then by including a Zn_{I} in the ZnO:Eu_{Zn} + Zn_{I} system. The E ^{f} of the Eu_{Zn} + V_{O} and Eu_{Zn} + Zn_{I} complexes in the ZnO lattice was found to be 1.772 and 2.776 eV, respectively. The local geometry of the Eu ion in the ZnO:Eu_{Zn} + V_{O} and ZnO:Eu_{I} + V_{O} are presented in Figure 1c, d respectively. In the ZnO:Eu_{Zn}:V_{O} system, the length of the EuO bond is 2.280 along the c direction and 2.260 within the ab plane, which is identical to the bond length in the ZnO:Eu_{Zn} system without V_{O}. However, in the ZnO:Eu_{Zn}+Zn_{I} system, the length of the EuO bond expanded to 3.517 Å along the c direction and 3.344 Å within the ab plane. Such an expansion corresponds to a 75% and 67% increase in the length of the EuO bonds along the c direction and within the ab plane, respectively compared to the unrelaxed structure. As a result, the Eu_{Zn} + Zn_{I} complex has the highest E ^{f} and lattice distortion.
The ZnO:Pd system
The E ^{f}, Pd's spin number, and the magnetic ground state of the ZnO:Pd_{Zn}, ZnO:Pd_{I}, ZnO:Pd_{Zn} + V_{O}, and ZnO:Pd_{Zn} + Zn_{I} are presented.
System  E ^{f}(eV)  Pd's spin ([ℏ]/2)  Magnetic ground state 

ZnO:Pd_{Zn}  0.776  0.000  Nonmagnetic 
ZnO:Pd_{I}  1.612  0.000  Nonmagnetic 
ZnO:Pd_{Zn} + V_{O}  6.289  0.000  Nonmagnetic 
ZnO:Pd_{Zn}:Z_{I}  3.831  0.000  Nonmagnetic 
Similar to the previous section, the effect of V_{O} and Zn_{I} on the ZnO:Pd systems was investigated by calculating the E ^{f} of the Pd_{Zn} + V_{O} and Pd_{Zn} + Zn_{I} complexes in ZnO, which was found to be 6.289 and 3.831 eV, respectively. In the ZnO:Pd_{Zn} + V_{O} system, the PdO bond is 2.300 and 2.358 Å along the c direction and the ab plane, respectively, having 15% (18%) expansion in bond lengths with respect to the unrelaxed structure. In the ZnO:Pd_{Zn} + Zn_{I} system, the lengths of the PdO bond along the c direction and within the ab plane are 3.332 and 3.398 Å, respectively which comprise an expansion of 66% along the c direction and an expansion of 70% within the ab plane compared to the unrelaxed structure.
Conclusion
The structural and electronic properties of the ZnO:Eu and ZnO:Pd systems were investigated by ab initio techniques. It was found that both Eu and Pd ions substitute Zn sites in the ZnO host lattice favorably. With Zn excess in the ZnO:Eu system, the carriermediated ferromagnetism can be induced by Zn_{I}. In the ZnO:Pd system, the Pd ions prefer to substitute Zn sites, forming substitutional Pd. Additionally, the Pd ions are isovalent to Zn ions and, consequently, their 4d shell remains fully occupied with no magnetization per Pd ion.
Abbreviations
 DFT:

density functional theory
 DMS:

diluted magnetic semiconductors
 DNP:

double numerical polarized
 DOS:

density of states
 GGA:

generalized gradient approximation
 PDOS:

partial density of states.
Declarations
Acknowledgements
This work was supported by the Australian National Computational Facility and the Australian Research Council Discovery Programs DP1096769 and ARC DP0770987.
Authors’ Affiliations
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