Hybrid functional study of structural, electronic and magnetic properties of S-doped ZnO with and without neutral vacancy

Accepted Manuscript Hybrid Functional Study of Structural, Electronic and Magnetic Properties of S-doped ZnO With and Without Neutral Vacancy M. Debbichi, T. Sakhraoui, L. Debbichi, M. Said PII: DOI: Reference:

S0925-8388(13)01519-3 http://dx.doi.org/10.1016/j.jallcom.2013.06.121 JALCOM 28854

To appear in: Received Date: Revised Date: Accepted Date:

9 March 2013 19 May 2013 19 June 2013

Please cite this article as: M. Debbichi, T. Sakhraoui, L. Debbichi, M. Said, Hybrid Functional Study of Structural, Electronic and Magnetic Properties of S-doped ZnO With and Without Neutral Vacancy, (2013), doi: http:// dx.doi.org/10.1016/j.jallcom.2013.06.121

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Hybrid Functional Study of Structural, Electronic and Magnetic Properties of S-doped ZnO With and Without Neutral Vacancy M. Debbichi1 ,∗ T. Sakhraoui1 , L. Debbichi2 , and M. Said1 1

Laboratoire de la mati`ere condens´ee et nanosciences, D´epartement de Physique, Facult´e des Sciences de Monastir, 5019 Monastir, Tunisia 2

Institut Carnot de Bourgogne, UMR 6303,

Universit´e de Bourgogne-CNRS, 21078 Dijon, France

Abstract The structural and electronic properties of S-doped ZnO are investigated by density functional theory (DFT)and empirical pseudopotential method (EPM). Using the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional with an adjusted mixing coefficient α, we obtain a good agreement on lattice parameters and band gap energy with the available experimental data. We have also investigate the Zn-vacancy effects on the electronic and magnetic properties of S-doped ZnO. Our calculations demonstrate that S impurity prefers to be close to the cation vacancy in the apical position. The magnetic analysis with the HSE functional shows a triplet state character with a total magnetic moment of 1.81 µB , which is mainly arises from the p-orbitals of the atoms around the Zn-vacancy (15% from S,12% from Zn and 73% from O-atoms). The substitution of S by an isovalent atom decreases the total magnetic moments of the system and weakens the local triplet state without destroying it.

∗

Electronic address: [email protected]

1

I.

INTRODUCTION

Wide-band-gap II-VI alloys containing oxide have undergone rapid development in the past few years. They have been investigated due to their potential applications in spintronics, chemical sensors, piezoelectric and optoelectronic devices [1, 2]. Clearly, they offer a new opportunity in a number of technologically important areas. As a wide-band-gap II-VI semiconductor, ZnO has recently been considered the base material for realizing transparent dilute magnetic semiconcductors (DMSs)system [3]. Wurtzite ZnO has an energy band-gap in the ultraviolet region (3.37 eV) and large exciton binding energy (60 meV at 300 K) and can be made highly conductive by appropriate doping[4– 6], and it can be grown on selected patterned substrates[7] . Additionally, ZnO has novel applications in optoelectronics, sensors, transducers, biomedical devices, etc.[8–10] Modification of ZnO properties by impurity incorporation is currently another important issue for possible applications in ultraviolet optoelectronics and spin electronics [11, 12]. In fact, it is well-known that for a wide-band gap semiconductor, the addition of impurities often induces crucial changes in its electrical and optical properties, especially if large differences exist in electronegativity and covalent radii between the host atoms and the replacing elements. As a member of ZnO family, the ternary semiconductor ZnO1−x Sx is believed to be a promising material for optoelectronic devices because its band gap can be tuneled from ultraviolet (UV) to visible regimes. Thermodynamically, ZnO1−x Sx alloy is difficult to grow, owing to the formation of sulfates or sulphur dioxide which is energetically favoured compared to a mixing of O2− and S2− on the anion sublattice of ZnO[6]. Due to the large electronegativity and size differences between O and S one can expect that the bowing parameters of ZnOS is large and thus comparable to the deep isovalent center systems such as: GaPN, GaAsN, ZnTeS, CdTeS[13]. Meyer et al [14] prepared thin films of ZnO1−x Sx over a broad range of compositions using radio frequency reactive sputtering. They found that Egap goes through a minimum for x = 0.45 with the value Egap ≃ 2.6eV . This results were confirmed by Locmelis et al[15]. In the meantime theoretical studies have shed some light onto the unusual electronic situation. Persson et al [16] found that the isovalent anion alloy ZnO1−x Sx exhibited a strong valence-band (VB) offset bowing, caused by local ZnS-like bonds in the ZnO host. This strong VB offset bowing can be utilized to enhance 2

p-type doping with lower formation energy and shallower acceptor state in the ZnO-like alloys.Recently, Yifang et al investigated the dependences of the band gap narrowing and magnetism feature of S-doped ZnOCu[17]. The theoretical understanding of electrical and optical properties of this kind of materials is hampered by the shortcomings of the local density approximation (LDA) or generalized gradient approximation (GGA) to density functional theory (DFT). In particular, DFT/LDA and DFT/GGA severely underestimate band gaps, leading to errors in the formation energy of defects and impurities and the related position of transition levels in the band gap. This is especially in the case of wide-band-gap materials, and in semiconductor materials that are predicted to have no gap in DFT/LDA. To overcome this problem several approaches have been proposed, including LDA+U and hybrid functionals. The LDA+U improves the description of the bands related to the semicore d states, leading to a partial correction of band gaps in materials such as ZnO, CdO and InN [18]. Hybrid functionals, which include a portion of Hartree-Fock(HF) type exchange in the exchange-correlation functional(XC), provide a significant improvement over the LDA-GGA description for metal oxides and other materials [19, 20]. However, in several cases the results (Lattice parameters, bulk modul, band gaps etc...) are not yet with experiment especially for the oxides materials[21].The underestimation can be remedied by increasing the ratio of exact exchange mixed into the XC functional. In this work, we use density functional theory calculations along with the screened hybrid functional HSE and the mixing coefficient α as a variable to study the structural, electronic and magnetic properties of S-doped wurtzite ZnO, with and without neutral vacancy. The paper is laid out as follows; In section 2, we outline the computational details. The main results obtained from this study are presented and discussed in section 3. The conclusions drawn from this study are summarized in section 4.

II.

COMPUTATIONAL DETAILS AND METHODS

The starting point of our calculations is density functional theory (DFT) in the local spin density approximation (LSDA)[22] with the parameterization of Perdew and Zunger. We use a plane wave code[23] and a norm-conserving pseudopotentials with Trouiller-Martins to describe the interactions between ionic cores and valence electrons. The wave function 3

was expanded in plane waves of energy less than the cutoff energy, 50 Ry. The simulation procedure has been iterated self-consistency with a grid of 8 ×8 ×4 k-points in the reciprocal space. In all of the results the Zn 3d electrons are treated as valence. It is well known, in fact, that neglecting the 3d states would produce an heavy underestimation of the lattice constants 18% [24]. The standard DFT usually employs local (LDA) or semilocal (GGA) approximations to the exchange-correlation (XC) energy. This leads to erroneous descriptions for some real systems such as transition-metal oxides. One way of overcoming this deficiency is to use Heyd-Scuseria-Ernzerhof hybrid functionals, where a part of the nonlocal Hartree-Fock (HF) type exchange is admixed with a semilocal XC functional giving the following expression [25]: HF,SR LR EHSE (ω)+(1-α) ESR xc =α Ex x (ω)+ Ex (ω)+Ec ,

where α is the mixing coefficient and ω is the screening parameter that controls the decomposition of the Coulomb kernel into short-range (SR) and long-range (LR) exchange contributions. In this case an energy cutoff of 70 Ry on the plane-wave basis has been considered. Besides to the standard and hybrid DFT calculations, the empirical potential method (EPM) have been used, which is well discussed in our previous works[26, 27]. In order to calculate the band structure parameters of ZnO1−x Sx alloys, 16 atoms supercell are used, which correspond to a 2 × 2 × 1 conventional wurtzite supercell. In all calculations, full atomic relaxations were made using convergence parameters up ˚ for atomic forces, and self consistency was achieved with a tolerance in total to 0.01 eV/A energy of 10−4 eV through LSDA approach.

III. A.

RESULTS AND DISCUSSION Perfect crystal of ZnO1−x Sx ternary alloys

In order to investigate the electronic and structural properties of ternary alloys, it is essential to calculate the lattice constants and band gap parameters of related ZnO and ZnS binary alloys. The stable alloys and their corresponding symmetric groups are listed in Table I. In our case we are interested only to the hexagonal symmetry. The obtained lattice parameters (a,c ˚ A) from LSDA, HSE(α) and EPM calculations are compared in Table II, in

4

which also experimental data are given as reference. Calculated values are in agreement with those obtained experimentally within 2% and 1% for LSDA and hybrid DFT respectively. The lattice parameters a and c calculated by LSDA for ZnO1−x Sx are ploted in Fig. 1. Significant increase of the lattice parameters upon replacing oxygen by sulfur was observed with a basically linear evolution of the lattice parameters in accordance with Vegard’s law as indicated by the experimental results[14]. Following this, the lattice constants using the other methods (HSE, EPM) are linearly interpolated between the calculated parent compound lattice constants taken from Table II. As a fundamental property of the optoelectronic materials, the fundamental energy gap of ZnO1−x Sx is calculated. In table III calculated band gaps of the pure compounds ZnO and ZnS are compared with experimental values . LSDA-calculated band gaps of ZnO and ZnS are 0.81 and 2.23 eV respectively. These values are in good agreement with the available LDA-theoretical data, but significantly smaller than those obtained experimentally. This large error is typical for LDA calculations. In fact, the underestimation of the band gap might result from the self-interaction problem, the discontinuity of the exchange-correlation potential, and incorrect description of the asymptotic behaviour by LSDA exchange-correlation potentials. To overcome the band gap problem we have tested the effect of varying the HSE exact exchange mixing coefficient(α). The crystal structures are reoptimized whenever α is changed (see Table II). Using the standard value of α = 0.25, we obtained for Eg the following values 3.380 and 2.968 eV for ZnS and ZnO respectively. These values are underestimated of 0.22 and 0.402 eV respectively, compared to those obtained experimentally. The last value is in good agreement with that obtained by Sohee and al [21]. This discrepancy can be reduced by increasing the relative weight of the HF term. Note that the HF method overestimates the energy gap value. As can be seen in Table III that the mixing coefficient required to acheive the ZnO and ZnS experimental band gap is 0.28≤ α and 0.25 ≤ α ≤ 0.28, respectively. This shows clearly the dependence of the mixing coefficient on the material. Consequently, we have fixed the value of α to 0.28 to study the electronic properties of the alloy. Figure 2 shows the calculated fundamental energy gaps of ZnO1−x Sx using, HSE(α = 0.28), LSDA functionals and EPM, in comparison with the experimental data reported by Meyer and al [14]. For the EPM calculation, the adjusted form factors for wurtzite ZnO and ZnS are listed in Table IV. 5

Calculations reveal that the reduction in the band gap of O-rich and S-rich ZnO1−x Sx arises mainly from the upward movement of the valence band and the downward of the conduction band , respectively. Figure 2 shows that the values obtained by LSDA are underestimated by 25-60% compared to those obtained experimentally. In contrast, the HSE functional with the adjusted coefficient α = 0.28 significantly improves the band gap values, the discrepancy with experiment and EPM results is less than 5% on average. Moreover, HSE predicts a large band gap bowing effect, in qualitative agreement with the experiment (bExp = 3.0 eV). The band gap can be fitted by the quadratic form: Egalloy = xEgZnS + (1 − x)EgZnO − x(1 − x)b, from which the bowing coefficient bHSE = 2.78 eV is deduced, somewhat smaller to the value, 3.22 eV obtained by the EPM with the improved virtual crystal approach (VCA) for a compositional disorder coefficient, p = 0.93. This value is smaller than that obtained by LSDA, bLSDA = 4.39 eV, likely because of the band gap behaviour for O-rich region. Our results show, that HSE emerges as an appropriate method for the study of electronic properties of semiconducting alloys.

B.

Magnetic properties of S-doped ZnO with Zn-vacancy

Several defects can appear during the growth of ternary alloys. Among them, the most common defects are cation/anion vacancy. It has been proved that the magnetic properties in Ax Zn1−x O may be controled by the amount of defects, in particular Zn-vacancy, where A (Li, Mg, Al etc...) is nonmagnetic elements [37]. Whereas cation doping of ZnO has been extensively investigated, anion substitution is rather rare. However, unlike the cation, few works have been have been focused on anion substitution in zinc chalcogenides[38] Firstly, we underlook the magnetic properties of ZnO with neutral vacancy which consist in removing a Zn (VZn ) or O (VO ) atom from the bulk ZnO supercell as shown in Figure 3. Calculation were performed using 32-atom 2 × 2 × 2 ZnO supercell. Our results indicate that ZnO with and without neutral O vacancy show a nonmagnetic behaviour. LSDA calculated total magnetic moments for one neutral VZn induces a value 1.74 µB , similar to that obtained by Wang et al[37]. While, with HSE functional, VZn induces a total magnetic moment equal 2µB , in good agreement with that obtained by Haowei and al [39]. The calculated total energy difference between antiferromagnetic (AFM) and ferromagnetic (FM) spin configuration ∆EAF M −F M is equal to 5.44 meV, indicating that the ground state 6

is FM, in agreement with experiments [39]. The same magnetic calculations have also carried out with a 2 × 2 × 1 supercell, which confirmed our calculated magnetic properties for the single Zn vacancy in the larger supercell. Figure 4 display the spin resolved density of states (DOS) of ZnO containing VZn (Zn15 VZn O16 ) obtained by LDA and HSE functionals. As can be seen, the magnetic state is assessed by the asymmetrical DOSs for majority and minority electrons below the Fermi level, which mainly arise from the p-orbitals of the oxygen around VZn . Using HSE functional, the local magnetic moment for each neighbouring O sites is about 0.52µB and only 0.02µB from the nearest Zn atoms. It is well known that the oxygen atoms in terms of their relative positions to the Zn-vacancy (VZn ) in wurtzite structure are classed into three groups[40]: one oxygen (O) atom bonded to VZn along the c-axis, which is called apical oxygen (V1 ), three O atoms bonded laterally to VZn (V2 ) and the remaining O atoms in the supercell labeled (V3 ) (see Fig. 3). The calculated local magnetic moment (MX ) of oxygen atom in the position V1 , V2 and V3 are respectively 0.52, 0.49 and 0.06µB . Next, we considered the combination of Zn-vacancy and one S-doped atom in ZnO supercell, where S is located in the position of V1 , V2 or V3 . The substitution of one O by S-atom in the tetrahedral molecule VZn O4 reduces the symmetry. Without neutral vacancy (x = 0.0625), the band gap reduction compared to ZnO is 0.13 eV and 0.11 eV for LSDA and HSE, respectively, in relatively agreement with both experimental data[14] and GGAcalculation[17]. The calculated values of total local magnetic moments as well as the energy difference between nonmagnetic and magnetic solutions are listed in Table V. The substitution of O by S-atom in the position V1 , V2 or V3 using LSDA, leads to a total magnetic moment of 1.45, 1.06 and 1.42µB and a local S magnetic moment of 0.21, 0.17 and 0.01µB , respectively. Whereas the HSE functional hybrid, induces a decrease of these values between 15% and 20%. Fig. 5 shows the band structure of the minority and majority spin states of Zn15 VZn O15 S. As can be seen the spin-majority bands are completely filled, only the minority-spin bands can be responsible for the magnetic interactions. We find that the p bands are crossing the Fermi level mostly along the A-L, Γ-M, A-H and Γ-K directions (ab plane), while along M-L, Γ-A and K-H (c-axis) the Fermi energy lies in the gap between the occupied and the 7

unoccupied bands. It is found that the difference energy between the nonmagnetic and magnetic configurations ∆E as well as the total magnetic moment MT are reduced by doping with S impurity. This reduction is very strong when S atom is coordinated in the position V2 . This can be explained as follows; the effective radius of S is large to that of O-atom and the bond length dVZn −S is less than that from dVZn −O , this causes more overlap between the valence S 2p states and O 2p states. This feature leads to a merging of VZn impurity band with the main valence band for spin down causing a metallic behaviour which reduces the magnetic moments in the supercell. To further examine the distribution of this moment around the VZn , we have calculated the spin-density iso-surface for Zn15 VZn O15 S (Fig. 6). It can be seen that the strong interaction between the p electrons at O and S sites surrounding the VZn appears to be the source of the magnetism in the system. In fact these p-states have an extended tail and they are expected to interact efficiently with VZn . In order to understand the origin of the decrease of magnetic moment of S-doped Zn15 VZn O16 , we have investigated the magnetic properties of Zn15 VZn O15 X, where X is an isovalent S atom, such as Se, Te and Po. All the calculations have been performed for the X atom in the position V1 , which corresponds to the most stable structure. Our results show that X-doped ZnO without VZn defect are nonmagnetic. However the creation VZn favors energetically the FM configuration compared to that of AFM, yielding a triplet ground state. Fig. 7 shows a comparison of total and partial DOSs of X-doped ZnO with Zn-vacancy. It can be seen that the DOS is shifted up going from S to Po comparing with that from ZnO with VZn defect. The LSDA and HSE calculated total and local magnetic moments of Zn15 VZn O15 X are listed in Table VI. We observe that the total magnetic moment value decreases when the substitutional defect X going from S to Po. This weakening is attended by an increase of VZn -X and a decrease of O-X bond lengths. One can note that the effective radius increases from S to Po (r(Po)> r(Te)> r(Se)> r(S)). These effects induce more overlap between the valence p states of X atom and the 2p states of the oxygen atoms. In the opposite, the overlap of Xp and Zn3d states decreases, leading to a reduction of the magnetic interaction from S to Po (p-d hybridation). To highlight the decrease of the total magnetic moment of the system when substituting X-atom, we plot in Fig. 8 the ˚3 . It is apparent that the presence spin density difference with isosurface value of 0.005 e/A 8

of a substitute going from O to Po causes significant delocalization of spin polarization of the dopant and its nearest neighbours Zn-atms. The spin density decreases going from O to Po, and is negligible for the radioactive element Po. This result reflects the total and local magnetic moments in the corresponding system.

IV.

CONCLUSION

In summary, using DFT and EPM we systematically studied the structural and electronic properties of wurtzite ZnO1−x Sx . With HSE functional and an optimized mixing coefficient (α =0.28), we demonstrate that the lattice parameters and the band gap energy are in good agreement with experiment compared to standard DFT results. The effects of S-doped on electronic and magnetic properties of ZnO with Zn vacancy are also investigated by LSDA and HSE functionals. Our results show that, S-dopant prefer the opical position V1 near the Zn vacancy and can induces a magnetic moment of 1.81 µB with HSE functional, which mainly comes from the 2p states of S and O atoms nearest to the Zn vacancy. In addition, the doping with S-atom weakens the total and local magnetic moments, and the energy differences between nonmagnetic and magnetic solutions. These enfeebling effects are particularly pronounced for V2 position. The isovalent atoms of oxygen tend to weakens the ferromagnetic state of the ZnO with Zn vacancy but does not destory it. Overall, the present work demonstrates that the optimized mixing coefficient α from the hybrid functional can be used as a tool in studying the oxides materials.

V.

ACKNOWLEDGMENTS

We acknowledge the R´egion Bourgogne for the provision of computer facilities.

9

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11

System

Symmetry E(Ry)

Lattice prameter (˚ A)

Angle(o )

Zn8 O8

P63 mc

0.00

a = b = 3.236, c = 5.210

α = β = 90, γ = 120

Zn8 O7 S1

P3m1

8.16

a = b = 3.302, c = 5.375

α = β = 90, γ = 120

Zn8 O6 S2

P63 mc

19.62

a = b = 3.392, c = 5.429

α = β = 90, γ = 120

Zn8 O5 S3

Cm

Zn8 O4 S4

P3m1

Zn8 O3 S5

Cm

Zn8 O2 S6

P63 mc

65.34

a = b = 3.615, c = 5.985

α = β = 90, γ = 120

Zn8 O1 S7

P3m1

76.73

a = b = 3.672, c = 6.095

α = β = 90, γ = 120

Zn8 S8

P63 mc

88.05

a = b = 3.782, c = 6.258

α = β = 90, γ = 120

31.09 a = 3.409, b = 3.405, c = 5.484 α = β = 90, γ = 120.016 42.55

a = b = 3.518, c = 5.680

α = β = 90, γ = 120

54.16 a = 3.529, b = 3.483, c = 5.734 α = β = 90, γ = 120.022

TABLE I: Structural parameters for the different stable configurations of ZnOS within 16 atoms supercell. E is the total energy difference between ZnO1−x Sx and ZnO, Et (ZnO1−x Sx )-Et (ZnO).

LSDA HSE(0.25) HSE(0.28) EPM a

Exp

3.175

3.249

3.252

3.242 3.258[28]

ZnO c/a 1.610

1.611

1.614

1.630 1.602[28]

a

3.757

3.808

3.806

3.800 3.822[29]

ZnS c/a 1.620

1.622

1.621

1.63 1.638[29]

TABLE II: Calculated lattice constant (a and c in ˚ A) of ZnO and ZnS wurtzite compared to experimental data. Calculations were performed using the LSDA, HSE fonctionals and the EPM method.

12

Method

ZnO

ZnS

This work Other work This work Other work LSDA

0.83

0.80[30]

2.23

1.99[31]

HSE(0.25)

2.96

2.90[32]

3.38

3.37[33]

HSE(0.28)

3.11

-

3.62

-

EPM

3.38

3.44[34]

-

3.65[35]

Exp.

-

3.37[36]

-

3.60[14]

TABLE III: Band gap energy of wurtzite ZnO and ZnS calculated by standard and hybrid DFT.

ZnO G

ZnS

G2 V s (Ry) V a (Ry) V s (Ry) V a (Ry)

100 2.66

-0.30

0.18

-0.24

0.00

002 3.00

-0.27

0.26

-0.22

0.16

101 3.41

-0.22

0.26

-0.19

0.15

102 5.66

-0.07

0.11

-0.06

0.12

210 8.00

0.04

0.02

0.02

0.00

103 9.41

0.06

0.02

0.06

0.06

200 10.66

0.07

0.00

0.07

0.00

212 11.00

0.07

0.02

0.07

0.02

201 11.41

0.07

0.02

0.07

0.02

004 12.00

0.00

0.02

0.00

0.02

202 13.66

0.04

0.01

0.04

0.01

TABLE IV: The adjusted symmetric (V s ) and antisymmetric (V a ) form factors of wurtzite ZnO and ZnS.

13

System

Method Position MT (µB ) MX (µB ) ∆E(meV ) LSDA

Zn15 VZn O16

HSE

LSDA Zn15 VZn O15 S

HSE

V1

1.73

0.41

068.02

V2

1.73

0.38

068.02

V3

1.73

0.03

068.02

V1

2.00

0.52

134.14

V2

2.00

0.49

134.14

V3

2.00

0.06

134.14

S:V1

1.45

0.21

027.21

S:V2

1.06

0.17

016.32

S:V3

1.42

0.01

043.53

S:V1

1.81

0.39

088.16

S:V2

1.79

0.31

013.40

S:V3

1.91

0.03

093.10

TABLE V: Calculated total (MT ) and local (MX ) spin magnetic moments, and the energy differences between the nonmagnetic and magnetic solutions ∆E for the three impurity positions in the Zn15 VZn O15 X (X= O, S) supercell.

LSDA

HSE

dVZn −X

MT MX MO

˚ (A)

X:S

1.45 0.21 1.06 1.74 0.31 1.26

2.26

X:Se

1.31 0.19 0.96 1.59 0.30 1.15

2.47

X:Te

0.83 0.11 0.63 1.06 0.17 0.81

2.68

X:Po

0.54 0.05 0.43 0.74 0.08 0.61

2.81

System MT MX MO

TABLE VI: Calculated total and local magnetic moment of the system Zn15 VZn O15 X,(X= S, Se, Te and Po) with LSDA and HSE (µB ). MX and MO are respectively the local magnetic moment of X atom and the 3 oxygen atoms nearest to VZn . dVZn −X represents the relaxed VZn -X bond length.

14

6.3 6 5.7

Lattice constant (Å)

5.4 5.1

a c. c_exp. c fitting line a fitting line

4.8 4.5 4.2 3.9 3.6 3.3 3

0

0.2

0.4

0.6

0.8

1

Composition (x)

FIG. 1: Lattice Constants of ZnO1−x Sx as a function of x. Experimental data for the c-axe Lattice Constant (c exp) is shown for comparison.

15

4 Experimental EPM Calculation LDA HSE(0.28) Fit-HSE(0.28) Fit-LDA

3.5

Energy (eV)

3 2.5 2 1.5 1 0.5 0

0

ZnO

0.2

0.4

0.6

Composition (x)

0.8

1

ZnS

FIG. 2: Band gap energy of Zn O1−x Sx calculated using LSDA, EPM and HSE (α = 0.28) hybrid functional in comparison with the experimental data taken from Ref.[14].

16

c

FIG. 3: The 2 × 2 × 2 wurtzite ZnO supercell. The green balls represent O atoms and the other balls represent Zn atoms. VZn represent the Zn-vacancy. V1 and V2 are respectively the apical and lateral oxygen position.

17

60

LSDA

40 20

DOS (States/eV)

0 -20 -40 -60 60

40

HSE

20 0 -20 -40 -60 -8

-6

-4

-2

0 2 E-Ef (eV)

4

6

8

10

FIG. 4: Total DOS (black line) and the spin up minus spin down (up-down) DOS (blue line) for Zn15 VZn O16 using LSDA and HSE functional.

3

Spin down Spin up

Energy (eV)

2

1

0

-1 A

L

M

Γ

A

H

K

Γ

FIG. 5: Band structure of the minority and majority spin states of S-doped ZnO with Zn-vacancy relative to V1 position, calculated by LSDA functional.

18

˚3 . b) FIG. 6: a)Iso-surface spin density plot for VZn in S-doped ZnO at isovalue of 1.2×10−3 e/A Two-dimensional distribution of spin density for the (0001) plane.

60

2

a) x=O X=S X=Se X=Te X=Po

40 20

Xp states 1 0

0

DOS (states/eV)

b)

-20

-1 -40 -60 2

-2 60

c)

d)

O2p states 40

Zn3d states

1

20 0

0

-20 -1

-40 -2 -8

-4

0

-60 8 -8

4

-4

0

4

8

E-Ef (eV) FIG. 7: Total and partial densities of states of X-doped ZnO with Zn-vacancy, where X=O, S, Se, Te and Po, abotained from LSDA functional. a)Total DOS, b)PDOS of Xp-states, c)PDOS of the nearest O atom of Vzn , d)PDOS of Zn3d states of the system. EF is the Fermi energy level of Zn15 Vzn O16 .

19

b)

a) S

d)

c) Se

Te

FIG. 8: The spin density distribution of X-doped ZnO with Zn-vacancy, where X = O, S, Se,Te ˚3 . and Po. The isosurface value was taken as 5×10−3 e/A

20

S-doped ZnO have been investigated by density functional theory (DFT) and empirical pseudopotential method (EPM). Good agreement on lattice parameters and band gap energy with the available experimental data is obtained with HSE functional using a mixing coefficient α = 0.28. The magnetic analysis with the HSE functional shows a FM character with a total magnetic moment of 1.81 μB, which is mainly arises from the p-orbitals of the atoms around the Zn-vacancy.