Many-Body electronic structure calculations of Eu doped ZnO
aa r X i v : . [ c ond - m a t . m t r l - s c i ] F e b Many-Body electronic structure calculations of Eu doped ZnO
M. Lorke ∗ and T. Frauenheim Bremen Center for Computational Materials Science,University of Bremen, Am Fallturm 1, 28359 Bremen, Germany
A. L. da Rosa
Universidade Federal de Minas Gerais, Dept. of Physics,Av. Antˆonio Carlos, 6627, 31270-901 Belo Horizonte, MG, Brazil (Dated: June 12, 2018)The formation energies and electronic structure of europium doped zinc oxide has been deter-mined using DFT and many-body GW methods. In the absence of intrisic defects we find thatthe europium- f states are located in the ZnO band gap with europium possessing a formal chargeof 2+. On the other hand, the presence of intrinsic defects in ZnO allows intraband f − f tran-sitions otherwise forbidden in atomic europium. This result coorroborates with recently observedphotoluminescence in the visible red region [1]. PACS numbers:
I. INTRODUCTION
Doping has been widely used to tailor the electronic,magnetic and optical properties of semiconductors. Wideband-gap semiconductors such as ZnO are attractive forultraviolet light-emitting diodes, lasers and high-powerphotonic applications. In ZnO, rar-earth elements canbe incorporated in the material and the long life times ofthe excited states allow for an easy realization of popu-lation inversion with promising applications in optoelec-tronic applications [1–5]. ZnO has a large band gap of3.4 eV and a high thermal conductivity, enabling newelectroluminescent devices.Channeling experiments [6, 7] indicate, that rare-earthelements in ZnO are preferentially incorporated at cationsites. More recent photoluminescence (PL) and pho-toluminescence excitation (PLE) investigations on ZnOnanoparticles corroborate this finding [8, 9]. PL inves-tigations of Eu-doped ZnO nanoneedles showed sharpemission lines from Eu , suggesting the emission arisesfrom intra-4 f transitions, in addition to the ZnO inter-band emission [10]. The f to f transitions are forbid-den in the isolated atom. However the spherical sym-metry is broken when the impurity is incorporated intothe ZnO matrix. Besides Eu, optical emission from rare-earth orbitals has been achieved in ZnO nanowires im-planted with erbium and ytterbium [5] and thin ZnOfilms doped with erbium, samarium and europium [11–14]. The above experimental investigations have sug-gested explanations for the optical activation of rare-earths in ZnO [15, 16] by means of substitutional hydro-gen incorporation [15] or formation of defect complexes[8, 16, 17].Theoretical investigations using density functional the-ory (DFT) in the generalized-gradient approximation ∗ Electronic address: [email protected] (GGA) have performed for Eu doped ZnO [18, 19], butwere unable to ascertain the origin of the experimentallyobserved emission in ZnO. The main challenge here is thecorrect description of both ZnO band edges and defectstates. It is common understanding that the use of localexchange-correlation functionals wrongly described theZnO band gap, which could lead to misleading conclu-sions on the location of the impurity rare-earth f -states.It has been shown that the correct description of the bandgap is of paramount importance for the understanding ofimpurity and defect states in semiconductors[20–24]. Be-sides, intrinsic defects may also play an important role,since during ion implantation they are often introducedin ZnO. Jiang et al. [25] have shown that for many open d - or f -shell compounds the GW approach can provide aconsistent and accurate treatment for both localized anditinerant states.Using DFT calculations and the GW technique, wehave previously shown that a complex containing a sin-gle oxygen interstitial defect and an europium atom sub-stituting a zinc atom is a probable candidate to explainthe observed emission in the red region of the spectrumin europium doped ZnO nanowires,[1]. Note that GWcalculations do not include excitonic electron-hole inter-actions.In this work we show GW calculations, as imple-mented in VASP, for Eu-doped ZnO. Besides the workreported in Ref.[1] we have considered the presence ofthe most common defects in ZnO, such as oxygen andzinc vacancies and interstitials. The wave functions arekept fixed to the GGA level, whereas the eigenvalues areupdated in the Green’s function only. Here we show thatthis kind of defect has a relatively low formation energyand suggest possible mechanisms for the formation ofsuch defect. Besides, we investigate other defects andcalculate their formation energies and electronic struc-ture. II. COMPUTATIONAL DETAILS
In this work we have employed density functional the-ory (DFT) [26, 27] and many-body GW techniques [28]to investigate the formation energies and electronic struc-ture of Eu doped ZnO. The projected augmented wavemethod (PAW) [29] has been used as implemented in theVienna Ab-initio Package (VASP) [30, 31]. A 3 × × × × k -pointsampling and a cutoff of 500 eV is used to calculate allisolated intrinsic defects and complexes. For Eu O wehave used (2 × ×
2) k-points. For Eu metal we adopteda bcc structure with a (6 × × k -point mesh. A. Thermodynamic properties
To verify the thermodynamic stability of the investi-gated defect complexes, we follow the approach derivedby van de Walle and Neugebauer[32]. The formation en-ergy of a neutral defect or impurity is defined as: E f = E ZnO − defecttot − E ZnO − bulktot − X i n i µ i + q(E v − E F ) , (1)where E tot (ZnO-defect) is the total energy of a defec-tive supercell and E tot ZnO-bulk is the total energy forthe supercell of pure ZnO. n i is the number of atoms oftype i (defects or impurities) that have been added to orremoved from the supercell and µ i is the correspondingchemical potential of each species, q is the charge of thedefect. The Fermi level E F is referenced with respect tothe valence band maximum E v of the host.The lower bound of the chemical potential correspondsto the total absence of impurities/defects in the material.An upper bound on the chemical potential is given by theenergy of the elemental bulk phase or other solubility-limiting phases. Formation of Eu clusters (metal) can beavoided by imposing the europium chemical potential toobey to: µ Eu µ Eu(Eu-bulk) (2)where Eu-bulk is the total energy of europium bulkin a bcc structure. Formation of europium precipitatesare avoided by considering the bound for Eu O , a verystable phase of europium: µ Eu µ Eu(Eu O ) (3)The oxygen and zinc chemical potential are not inde-pendent, but related by µ ZnO = µ Zn + µ O , where µ Zn , µ O and µ ZnO are the zinc, oxygen and zinc oxide chemical po-tentials, respectively. ∆ H ZnO is the formation enthalpyof ZnO. Combining Eq.2 and 3 and these conditions, weobtain the following relations: µ O = µ O − mol + λ ∆ H ZnO (4)The chemical potential of europium oxide can bewriten as: µ Eu O = ∆ H Eu O + 2 µ Eu-bulk + 3 µ O − mol (5)where ∆ H Eu O is the enthalpy of formation of eu-ropium oxide and µ Eu − bulk and µ O − mol are the europiumbulk and oxygen molecule chemical potentials, respec-tively. This results in µ Eu
12 ∆ H Eu O + µ Eu bulk − λ ∆ H ZnO (6)Here λ =0 for oxygen rich and λ =1 for oxygen poorconditions. B. Electronic structure
The many-body methodology that is underlying the GW approximation goes back to pioneering work byKadanoff and Baym [33, 34] and Hedin [28]. In GW -based approximations, the screening of the Coulomb in-teraction, that enters the non-local self-energy operator,is calculated microscopically. This description of thescreened potential W is a main advantage of many-bodymethods over other approaches, like hybrid functionalDFT, where screening is only included phenomenologi-cally.The single shot G W approximation starting fromGGA calculations often yields too small band gaps. Itwas suggested [31, 35] that partially or fully selfconsis-tent schemes, in which either Green’s function G ( GW )or both the Green’s function and the dielectric matrix( GW ) are updated can improve the agreement with ex-periments. We should mention that the implementationof selfconsistent GW or GW in VASP has the shortcom-ing, that only calculations that maintain a quasi-particlepicture are possible, i.e. satellite peaks can not be ac-counted for. Even though this means that these are tech-nically not ”full” GW calculations, we will for simplicityadopt the notation to call them GW and GW in the fol-lowing. For detailed information on the implementationwe refer the reader to Refs. [31, 36–40]. III. RESULTSA. Thermodynamic properties
It is in principle possible to calculate GW total energiesby using the Galitskii-Migdal formula [41]. In Ref. [42]it was found that for the electron gas, the total energiescan be well described using GW schemes. Alternativeapproaches to tackle the formation energy in connectionwith GW methods have been proposed [43, 44]. In VASP,the calculation of formation energies at GW level is notreadily possible. Therefore, we have decided to calculatethe formation energies at GGA level. This can be justi-fied taking into account that the GGA calculations areused as starting point for more accurate calculations us-ing the GW method. We would like to mention that wehave performed PBE0 calculations for some defects andwe note that the location of Eu- f -states are strongly de-pendent on the amount of HF included in the functional.For europium oxide, the formation enthalpy is calcu-lated to be ∆ H f (Eu O )=-14.43 eV compared with theexperimental value of -16.51 eV [45]. For zinc oxide theformation enthalpy is ∆ H f (ZnO)=-2.90 eV, which is ingood agreement with other GGA values [46] and evenGGA+U calculations [22]. This discrepancy is proba-bly due to the wrong description of the oxygen molecule,as has been discussed in Ref.[47]. Using these values, wecan obtain the binding energy of the defect complexes,which are defined asE binding = E complexf − X i E isolatedf (7)where E complexf is the formation energy of the defectsand E isolatedf is the formation energy of isolated defectscalculated according to Eq.(1). The calculated valuesare shown in Table I and a negative value means that thecomplex is stable. Calculations for intrinsic defects canreproduce well previous calculations reported using localfunctionals [46, 48, 49]. Neutral oxygen vacancies havea low formation energy under oxygen poor-conditions.On the other hand, zinc vacancies can be formed underZn-poor preparation conditions. Oxygen and zinc inter-stitials, as expected, have high formation energies, dueto their size [49]. For Eu doped ZnO at cation site weobtain a formation energy of 2.42 eV under O-rich con-ditions. Incorporation of Eu at interstitial positions ishighly unfavorable, due to the strain Eu causes in theZnO, leading to a strongly distorted lattice. Similar re-sults have been reported in Ref. [50]. Complex formationwith zinc and oxygen vacancies and zinc interstitials havea much higher formation energy. This can be understoodby considering size effects, which causes a large strain inthe lattice. As the defect complexes are formed in exper-iments under extreme non-equilibrium conditions (like,e.g.,ion-implantation) we find it more appropriate to re-port the binding energies of the defect complexes andhence their stability against dissociation.As we can see the most stable neutral defect is underO-rich conditions the Eu-O i (o) complex. It is interestingto point out that the formation of neutral oxygen defectsat interstitial sites in pure ZnO has a high formation en-ergy under thermodynamic equilibrium. However, as hasbeen shown in Ref. [49] the diffusion barrier for this kindof defect is relatively low (around 0.2 eV). Therefore, once this defect is formed under ion implantation (non-equilibrium conditions), it can rapidly diffuse in the ma-terial and form complexes with europium atoms. Thismay explain why the complex Eu-O i (o) is so stable inZnO. TABLE I: Formation energies E f and binding energies E b forneutral intrinsic defects and defect complexes in ZnO.Defect E f (eV) E b (eV)O-rich O-poor O-rich O-poorEu Zn i(split) i(oct) O Zn int Zn + Oi(split) 4.52 14.67 -0.48 1.75Eu Zn + Oi(oct) 4.4 14.55 -1.40 0.83Eu Zn + V O Zn + V Zn Zn + Zn int Now let us discuss the charged complexes. In Fig.1 weshow the formation energies of several Eu-complexes as afunction of the Fermi energy at O-rich and Zn-rich con-ditions. The top of the valence band E v for all defectscalculations was aligned with the top of the valence bandof the host ZnO using the averaged electrostatic poten-tial as described in Ref.[32]. We see that the most stablestructure at O-rich conditions is a complex of Eu-O i ( oct )in the -1 charge state. Although this is the thermody-namically most stable defect, followed by Eu-subst andEu − V O ( − i ( oct ) correponds to the experimental f-f transitionis very appealing. Obviouly we cannot rule out the co-existence of these other defects during the preparationconditions. Further calculations are needed to clarifywhether these defects also have transitions in the exper-imentally observed region. On the other hand at Zn-richthe defect Eu-subst is the most stable one for E F − E v between 0 and 0.6. For values lerger than that the de-fect Eu-V O in the -1 charge state is the most stable one.It is important to note that under Zn-rich conditions alldefects have a very high formation energy, which is anindication that they are unlikely to form at these condi-tions. B. Electronic properties
Because GW calculations can be performed using dif-ferent approximations, the results for the theoreticalband gap of ZnO has been under debate. Parameters con-trolling the calculations include the number of bands [51–53], the exchange-correlation potential for the startingwave function[22] as well as the use of approximate mod- v -E F (eV)05101520 F o r m a ti on e n e r gy ( e V ) Eu-substEu-subst(+1)Eu-subst(-1)Eu-V Zn Eu-V Zn (+1)Eu-V Zn (-1)Eu-Zn i Eu-Zn i (+1)Eu-Zn i (-1)Eu-O i(split) Eu-O split (+1)Eu-O i(split) (-1)Eu-V O Eu-V O (+1)Eu-V O (-1)Eu-O i(oct) Eu-O i(oct) (+1)Eu-O i(oct) (-1) v -E F (eV)8101214161820 F o r m a ti on e n e r gy ( e V ) Eu-substEu-subst(+1)Eu-subst(-1)Eu-V Zn Eu-V Zn (+1)Eu-V Zn (-1)Eu-Zn i Eu-Zn i (+1)Eu-Zn i (-1)Eu-O i(split) Eu-O i(split) (+1)Eu-O i(split) (-1)Eu-V O Eu-V O (+1)Eu-V O (-1)Eu-O i(oct) Eu-O i(oct) (+1)Eu-O i(oct) (-1)
O-rich Zn-rich
FIG. 1: (color online) Formation energies of several Eu-complexes as a function of the Fermi energy a) O-rich and b) Zn-richconditions . els for the screening, like plasmon pole approximations[51].Depending on the starting functional and the detailsof the calculation, values between 2.1 and 3.6 eV areobtained for G W [24, 31, 39, 40, 51–54], between 2.54-3.6 for GW0 [24, 39, 54–56] and between 3.2-4.3 for GW[24, 37].We start by validating the GW method for bulk ZnO.For this purpose we consider a four-atom wurzite ZnOunit cell and employ a 8 × × k point sampling withan energy cutoff of 500 eV. The resulting band gaps andenergetic positions of the Zn-3 d states (with respect tothe valence band maximum set at zero) for several levelsof GW calculations are a) PBE: 0.8 and -5.1 eV, b) PBE0:3.2 and -7.3 eV, c) HSE06: 2.5 and -7.1 eV, d) PBE+ GW :4.3 and -7.2 eV, e) PBE+ GW : 3.3 and -7.0 eV.For the GW calculation, a cutoff of 200 eV for theresponse functions χ , as well as 1024 bands have beenemployed. It has been shown that a large number ofbands is necessary to obtain properly converged resultsin earlier one-shot G W calculations [51–53]. We specu- late that the deviations to Ref. [54] are due to the ratherlow number of bands in that publication. The results areshown in Fig. 2. We find a band gap of 3.3 eV in reason-able agreement with the experimental value of 3.44 eV[57], as well as with other all-electron GW calculations[53, 55]. It should be pointed out that recently normconserving pseudopotentials were introduced in VASP toimprove GW calculations [53]. However, as shown inRef. [53], we expect these to only lead to minor modifica-tions of the bandstructure of up to 0.2eV, not changingthe main conclusions of this work. It should be notedthat that use of GW -based methods has been able topredict the positions of lanthanide f -states in NiO [58]and CeO [25].The center of the Zn- d orbitals is localted at -7 eV,in agreement with previous GW -calculations for ZnO[31, 55, 59]. We want to point out, that a fully-selfconsistent GW calculation results in a much too highquasi-particle gap of 4.2 eV. Again this agrees well withrecent all-electron calculations that find a quasi-particlegap of 4.3 [55]. -10 -5 0 5 10 15Energy (eV)0 DO S ( s t a t e s / e V ) totalZn s Zn d O p FIG. 2: (color online) Density of states of bulk ZnO calculatedin the PBE+ GW approximation. The vertical line denotesthe highest occupied state. From here on we show only results for GW calcula-tions. It has been shown that the position of defect statesis not strongly influenced by the number of empty bandsand the response function cutoff [24]. The relaxed geom-etry of Eu at a zinc lattice position without the presenceof intrinsic defects is shown in Fig. 3. The europium dis-tance to nearest oxygen atoms are 2.23˚A and 2.27˚A forin-plane and c -direction, respectively. These values areslightly larger than the Zn-O bond lengths in pure ZnO.This means that if Eu is incorporated at a Zn lattice po-sition, it should not disturb the lattice significantly. Wewould like to point out that in the supercell GW cal-culations, the ZnO bandgap is slightly to large, around3.6-3.9eV. We attribute this to the reduced k -point sam-pling in the supercell calculation. We also several testswith sc GW calculations, to also investigate the influenceof a selfconsistent update of also the wave-functions. Inthese tests, we find that quasi-particle energies are onlychanged by up to 0.1-0.2eV between sc GW and GW calculations, supporting the use of the GW approxima-tion in the following.In Fig. 4 the GW electronic density-of-states of sub-stitutionally incorporated Eu in this geometry is shown.The Eu- f states lie within the band gap, around 2 eVabove the VBM (valence band maximum), hybridizeweakly with the Zn- s and O- p states. As expected forsubstitutional Eu at a Zn lattice position, Eu has a for-mal charge closer to 2+. The f spin-up orbitals are fullyoccupied, giving a total magnetic moment of 7 µ B . Fur-themore, the Eu d -states lie deep in the conduction bandof ZnO, ≈ f -states of over 3eV. Therefore, ourresults explain why the 4 f − f / d optical transitionat 530 nm ( ≈ FIG. 3: (color online) Atomic structure around the europiumimpurity calculated within GGA for substitutional europiumin ZnO. Blue, red and grey spheres are Eu, O and Zn atoms,respectively. doped ZnO [5, 11]. -10 -8 -6 -4 -2 0 2 4 6 8Energy (eV)-100-50050100 DO S ( s t a t e s / e V ) totalEu fEu dZn sZn dO p FIG. 4: (color online) Total and projected density of statesfor Eu at Zn site in ZnO calculated within the PBE0+ GW approximation. The vertical dashed line denotes the highestoccupied state. Positive (negative) values of the DOS denotespin up (down). A possible way to modify the oxidation state of Euin the ZnO lattice is therefore a change of its environ-ment. It is known that during ion implantation intrinsicdefects are likely to form [5, 17]. We therefore investi-gated Eu doped ZnO in the presence of nearby oxygenand zinc vacancies as well as zinc and oxygen intersti-tials. In the presence of a neutral oxygen vacancy theEu-O distances for neighboring oxygen atoms remain al-most unchanged, compared to the case without vacancy,and increase slightly to 2.24˚A. The geometry is shownin Fig. 5. The Eu-Zn distance is 3.27˚Aand relaxation offarther neighbors is insignificant.The electronic structure for this system is shown inFig. 6. The states due to the oxygen vacancy lie 1 eVabove the VBM. This is in good agreement with calcu-lations for pure ZnO (see e.g. Refs. [23, 46, 48]). The
FIG. 5: (color online) Atomic structure around the Eu − V O complex calculated within GGA. Blue, red and gray spheresare Eu, O and Zn atoms, respectively. -10 -5 0 5Energy (eV)-100-50050100 DO S ( s t a t e s / e V ) totalEu fEu dZn sZn dO p FIG. 6: (color online) Total and projected density of statesfor Eu incorporated at Zn position in ZnO next to a oxygenvacancy calculated within the PBE0+ GW approximation.The vertical line denotes the highest occupied state. Positive(negative) values of the DOS denote spin up (down). Eu f -states are located now at 2.5 eV above the VBM.Moreover, we observe a small splitting of the Eu- f statesas well as a small hybridization with the Eu- d and O- p states. The splitting is caused by a shift of one ofthe seven Eu- f states that we assume to be induced bychanges in the local environment that affect the interac-tion matrix elements and therefore the charge distribu-tion around the impurity.Our GW results are in strong contrast to the find-ings of Ref. [18], where the Eu- f states are energeti-cally located directly above the V O states. We attributethis discrepancy to the choice of the GGA functional inRef. [18], predicting a much too narrow band gap. Onthe other hand, the presence of the V O does not signif-icantly change the formal charge around the Eu atom.Moreover, the positions of the Eu- f spin down and Eu d -states remain practically unchanged. Again this defectscannot explain the experimental observed f − f transition FIG. 7: (color online) Atomic structure around the Eu − Zn i complex calculated within GGA. Blue, red and gray spheresare Eu, O and Zn atoms, respectively. in ZnO.The relaxed geometry of the Eu+Zn i defect is shownin Fig. 7. The bond lengths between the Eu atom andthe nearest oxygen atoms are 2.19˚A, 2.19˚A and 2.24˚Ain the in-plane direction, and 2.41˚A in the c -direction.This is because Eu atom relaxes away from the Zn atom.The Eu-Zn distance is 2.72˚A, while the distances to Znsecond neighbors are 3.29˚A. -10 -5 0 5Energy (eV)-100-50050100 DO S ( s t a t e s / e V ) totalEu fEu dZn d Zn sO p FIG. 8: (color online) Density of states of Eu doped ZnOin the presence of a nearby zinc interstitial calculated withinthe PBE0+GW0 approximation. The vertical line denotesthe highest occupied state. Positive (negative) values are thespin up (down) components.
The electronic structure of this system is shown inFig. 8. The location of the Eu f -states lies close to theconduction band minimum (CBM), around 2.9 eV abovethe VBM. We can infer a weak hybridization with bothZn- s and Zn- d states of the Zn interstitial atom. Sim-ilarly, a very small hybridization with the O- p states isfound. Here, the formal charge of the Eu atom remainsclose to 2+ with the spin-up f -states occupied. FIG. 9: (color online) Atomic structure around theEu − O splitint complex calculated within GGA. Blue, red andgray spheres are Eu, O and Zn atoms, respectively. -10 -5 0 5Energy (eV)-100-50050100 DO S ( s t a t e s / e V ) totalEu fEu dZn sZn dO p FIG. 10: (color online) Density of states of Eu doped ZnO inthe presence of a nearby split oxygen interstitial calculatedwithin the PBE0+GW0 approximation. The vertical line de-notes the highest occupied state. Positive (negative) valuesare the spin up (down) components.
For the oxygen interstitial plus Eu defect, we have con-sidered two geometries. The first consists of an Eu atomat substitutional Zn site next to an oxygen interstitial indumbbell configuration [60]. This configuration is shownin Fig. 9. In this case the lattice ralaxations are morepronounced, The Eu atom is shifted away from the in-terstitial complex, decreasing the Eu-O bond lengths to2.21˚A. The Eu-Zn distance is also slightly increased to3.29˚Aand the distances to the oxygen atoms of the inter-stitial are 2.31˚Aand 2.33˚A, respctively.The electronic structure is presented in Fig. 10. Weobserve a splitting of the Eu- f states that we attributeto a combination of the changed symmetry in the localenvironment. This affects both the interaction matrixelements as well as their screening, so that different Eustates are influences differently. While 6 of the Eu- f arelocated closer to the VBM, the remaining occupied Eu- f state lies about 1 eV higher in energy. We find contribu-tions to the localized states from both O int − p and O host states. However, also in this case, the Eu atom pos-sesses a formal charge of 2+ with all Eu- f spin-up statesfully occupied. The oxygen interstitial atom possesses amagetic moment of 0 µ B , a further confirmation, that noelectron is transfered from the Eu atom to the oxygensite. FIG. 11: (color online) Atomic structure around the Eu − V Zn complex within GGA. Blue, red and gray spheres are Eu, Oand Zn atoms, respectively. -5 0 5Energy (eV)-100-50050100 DO S ( s t a t e s / e V ) totalEu fEu dZn sZn dO p FIG. 12: (color online) Density of states of Eu doped ZnOin the presence of a nearby zinc vacancy calculated withinthe PBE0+GW0 approximation. The vertical line denotesthe highest occupied state. Positive (negative) values are thespin up (down) components.
The geometry of Eu doped ZnO in the presence ofa neutral Zn vacancy (V Zn ) is shown in Fig. 11. TheEu atom shifts towards the vacancy, increasing the in-plane Zn-Eu distance to 3.49˚A and 3.40˚A in comparisonto 3.3˚A that would correspond to Eu exactly on Zn lat-tice position. Consequently, the in-plane Eu-O distancesalso change, asymmetrically, to 2.09˚A, 2.19˚A and 2.24˚A,respectively. Along the c -direction the Eu-O distance is2.22˚A. The corresponding electronic structure is shown inFig. 12. We find no occupied Eu- f states in the band gap.These states lie within the VB, close to the O- p statesand hybridize both with with O- p and Zn- d states. Thelocal projected moment on the V Zn site is 1 µ B , whichis aligned anti-parallel to the magnetic moment on theEu which is 6 µ B . However the fact that the Eu- f statesare energetically located inside the VB and the unoccu-pied Eu- f state is energetically located at 2 eV above theVBM, does not fit with experimentally observed transi-tion.The other defect complex including an oxygen inter-stitial consists of an oxygen at a octahedral interstitialsite next to an Eu at Zn lattice position. The corre-sponding atomic structure is shown in Fig. 13. We findmuch more pronounced lattice relaxations in this case,also involving second nearest neighbors. The Eu-Zn dis-tance is 3.2˚A, while the Eu-O bond lengths are 2.2˚A tothe oxygen atoms in the basal plane and 2.25˚A to theoxygen along the c -direction. The distance between theEu atom and the oxygen interstitial is 2.24˚A. This can beexplained by looking at the coordination Eu adopts. TheEu-O distance to the nearest neighbors is very similar toEu O , which possess a coordination number of 6 ± ± .
015 ˚A according to Ref[61].
FIG. 13: (color online) Atomic structure around the Eu+O octint complex within GGA. Blue, red and gray spheres are Eu, Oand Zn atoms, respectively.
The corresponding electronic structure is shown inFig. 14. We find the occupied Eu f -states are locatedin the band gap, with the Eu- f orbitals being occupiedwith six electrons. The occupied and unoccupied statesare located at -0.7 eV and 1.3 eV, respectively. We find asmall hybridization with O- p i(oct) and O- p (host) . The to-tal magnetic moment of the complex is 5 µ B , determinedby a magnetic moment of 6 µ B spin up at the europiumaligned anti-parallel to the magnetic moment of 1 µ B atthe oxygen interstitial atom. Therefore, we suggest thatthe intra-4 f luminescence of the ZnO:Eu samples is mostlikely due to Eu Zn +O oct i complexes. We have also ex-plored the mechanism for optical activation of Eu in ZnOreported in Ref. [15], where substitutional hydrogen at Znlattice position next to an europium atom is suggested.However, this configuration does not change the formal -10 -5 0 5Energy (eV)-100-50050100 DO S ( s t a t e s / e V ) totalEu fEu dZn sZn dO p FIG. 14: (color online) Density of states of Eu doped ZnOin the presence of a nearby octahedral oxygen interstitial cal-culated within the PBE0+GW0 approximation. The verticaldashed line denotes the highest occupied state. Positive (neg-ative) values are the spin up (down) components. charge of Eu.In order to summarize the results discussed above weshow the position of the defect levels with respect to theband edges of ZnO. The results are shown in Table II.We show the relative position of Eu-f states for the com-plexes with respect to the top of the valence band of ZnO.The position of the Eu-f states were taken approximatelyin the middle of the f -bands, since we cannot describecorrectly with DFT the multiplets of the f-orbitals. TABLE II: Relative position of Eu-f states for the investigatedcomplexes with respect to the top of the valence band of ZnO.The position of the Eu-f states were taken approximately inthe middle of the f-bands. All values are given in eV.Complex E VB − E f Eu Zn Zn + Oi(split) 1.5/3.2Eu Zn + Oi(oct) 2.5Eu Zn + V O Zn + V Zn Zn + Zn int IV. CONCLUSIONS
In conclusion, we have investigated Eu-doped ZnO us-ing DFT and the many-body GW technique within theGW approximation. We find that the position and for-mal charge of the Eu- f states is strongly dependent onthe environment around the Eu atom. We conclude thatthe optical activity of Eu in ZnO is most likely due toEu+O octi defect complexes, possibly either in a neutralor -1 charge state or in the presence of both. Finally,we believe our results can open the pathway for a betterunderstanding of these complexes in zinc oxide. Acknowledgments
We acknowledge fruitful discussions with R. R¨oder, C.Ronning and H. Chacham and financial support from the Deutsche Forschungsgemeinschaft under the programmFOR1616. A. L. da Rosa would like to thank financialsupport from CNPq under the program “Science withoutBorders”. We also thank HLRN (Hannover/Berlin) forcomputational resources. [1] S. Geburt, M. Lorke, A. L. da Rosa, T. Frauenheim,R. Rder, T. Voss, U. Kaiser, W. Heimbrodt, and C. Ron-ning, Nano Letters , 4523 (2014).[2] A. Ishizumi, Y. Taguchi, A. Yamamoto, and Y. Kane-mitsu, Thin Solid Films , 50 (2005).[3] M. Peres, A. Cruz, S. Pereira, M. Correia,M. Soares, A. Neves, M. Carmo, T. Mon-teiro, A. Pereira, M. Martins, et al., AppliedPhysics A , 129 (2007), ISSN 0947-8396, URL http://dx.doi.org/10.1007/s00339-007-3941-9 .[4] C. Pan, C. Chen, J. Chen, P. Huang, G. Chi,C. Chang, F. Ren, and S. Pearton, Applied Sur-face Science , 187 (2009), ISSN 0169-4332, URL .[5] C. Ronning, C. Borschel, S. Geburt, R. Niepelt,S. Mller, D. 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