Electronic properties and stability of ZnO from computational study

ARTICLE IN PRESS Physica B 403 (2008) 3154– 3158

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Review

Electronic properties and stability of ZnO from computational study Y. Azzaz, S. Kacimi, A. Zaoui , B. Bouhafs Modelling and Simulation in Materials Science Laboratory, Physics Department, University of Sidi Bel-Abbes, 22000 Sidi Bel-Abbes, Algeria

a r t i c l e in f o

a b s t r a c t

Article history: Received 15 February 2008 Received in revised form 25 March 2008 Accepted 26 March 2008

The ground-state properties of ZnO in the rock-salt (B1), CsCl (B2), zinc-blende (B3), wurtzite (B4), cinnabar, cmcm, d-b-tin, NiAs, Immm, and Imm2 structures were investigated using an accurate firstprinciples total-energy calculations based on the full-potential augmented plane-wave plus local orbitals ðAPW þ loÞ method. The local density approximation was used for the exchange and correlation energy density functional. The ground state properties such as lattice parameter, bulk modulus and its pressure derivative as well as the structural phase stability were calculated and compared to the available experimental data and previous theoretical works. & 2008 Elsevier B.V. All rights reserved.

Keywords: Density functional theory Local density approximation Total energy Pressure transition Semiconductor

Contents 1. 2. 3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3154 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3155 Results and discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3156 3.1. Structural stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3156 3.2. Phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3156 3.3. Charge densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3158 3.4. Density of states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3158 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3158 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3158

1. Introduction The zinc oxide semiconductor ZnO is a promising material for various technological applications, for example, ceramics, piezoelectric, transducers, chemical sensors, varistors, thyristors, catalysis, optical coating, and photovoltaics [1]. At ambient conditions, the thermodynamically stable phase of ZnO is wurtzite. The zinc-blende ZnO structure can be stabilized only by growth on cubic substrates, and the rock-salt (NaCl) structure may be obtained at relatively high pressures [2]. Due to its technological importance in various applications domains, the properties of ZnO have been the subject of several experimental and theoretical studies [3–33]. The high-pressure behavior of ZnO presented a great interest for fundamental materials physics. It

 Corresponding author.

E-mail address: [email protected] (A. Zaoui). 0921-4526/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2008.03.026

occurs naturally as a mineral and its high-pressure phase may be geologically important as a component of the lower mantle [20]. The high-pressure behavior of ZnO has also attracted theoretical interest [10,13,16,17]. The first indication of a transition from the low pressure wurtzite phase of ZnO to a high pressure NaCl phase at  10 GPa was reported by Bates et al. [4] and later confirmed by Jamieson [5], and by Yu et al. [7] at 8.0 GPa. Recent EDX studies by Decremps et al. [8,9] indicate that the transition occurs at  9:8 GPa at room temperature. The high-pressure structural calculations were mostly limited to the same pressure range as the experiments, and did not consider any possible structures of ZnO except B1 (rock-salt), B3 (zinc blende), and B4 (wurtzite). In this work, we present the results of quantum mechanical first principle calculations on the ground state properties of zinc oxide, the calculated structural properties of B1(Fm3m), B2(Pm3m), B3(F43m), B4(P63 mc), cinnabarðP31 21Þ, NiAsðP63 =mmcÞ, cmcm (Cmcm), Imm2(Imm2), Immm (Immm), and d-b-tinðI4m2Þ structures are particulary used to explain the sequence of these

ARTICLE IN PRESS Y. Azzaz et al. / Physica B 403 (2008) 3154–3158

structures as a function of pressure. Compounds II–VI were generally examined in these structures and ZnO be part of this family, then we prefer to follow the same way. These various crystal structures are selected in order to make sure that no other structures than the fcc and bcc ones could be stable at high pressure and to check if they can be intermediate structures. The chemical bonding mechanism of zinc oxide is studied on the basis of electronic charge density. The plan of the present paper is as follows. Section 2 gives a description of the method as well as some details of the calculations. The calculated structural and electronic charge density of ZnO are presented and discussed in Section 3. Finally, the conclusion is given in Section 4.

3155

l ¼ 12. A plane wave expansion with RMT  K MAX equal to 9, and the dependence of the total energy on the number of k points in the irreducible wedge of the first Brillouin zone has been explored within the linearized tetrahedron scheme by performing the calculation for 75 k points and extrapolating to an infinite number of k point. We take the Perdew–Wang local density approximations (LDA) [37] for the exchange correlation potentials. We have adopted the values of 1.8 and 1.6 bohr for Zn and O, as MT radii.

Table 1 Calculated structural parameters V0 Wurtzite (B4)

2. Calculations 10

The electronic configurations are Ar3d 4s2 for Zn and He2s2 p4 for O. The equilibrium structural parameters were calculated using the Vienna package WIEN2k [34]. This is an implementation of a hybrid full-potential (linear) augmented plane-wave plus local orbitals ðL=APW þ loÞmethod [35] within the density-functional theory [36]. The APW þ lo method expands the Kohn–Sham orbitals in atomic-like orbitals inside the atomic muffin-tin (MT) spheres and plane waves in the interstitial region. The details of the methods have been described elsewhere [35]. The basis set inside each MT sphere is split into core and valence subsets. The core states are treated within the spherical part of the potential only and are assumed to have a spherically symmetric charge density totally confined inside the MT spheres. The valence part is treated within a potential expanded into spherical harmonics up to l ¼ 4. The valence wave functions inside the spheres are expanded up to

a

22.86 23.810a 23.796b 22.874c 24.570d 22.882e 22.8f Zinc blende (B3) 22.88 22.914c 22.841e CsCl (B2) 17.90 18.073c Rock-salt (B1) 18.83 19.60a 19.484b 18.904c 18.856e 18.70f NiAs 19.18 Cinnabar 20.87 cmcm 19.13 d-b-tin 19.51 Immm 19.45 Imm2 19.41

3.25 3.2498a 3.2496b 3.199c 3.290d 3.198e 3.198f 4.51

3.29 3.306c 4.22 4.283a 4.271b 4.229c 4.225e 4.213f 3.10 3.28 4.41 3.43 4.91 4.99

b=a

B0

c=a

u

v

1.59 1.6021a 1.6018b 1.6138c 1.593d 1.615e 1.61f

0.38 0.3832a 0.3819b 0.3790c 0.3856d 0.379e 0.38f

165.92 142.6a 183b 162.3c 154.4d 159.5e 1.62f 164.41 161.7c 160.8e 200.98 194.3c 208.56 202.5a 228b 205.7c 209.1e 210f 202.50 0.54 173.96 0.27 216.98 168.26 175.30 147.88

1.45 2.24 1.11 0.80 0.96 0.61 0.54 0.60 0.52

0.25 0.49 0.72

0.44

B0

4.74 3.6a 4.0b 4.05c 3.6d 4.5e 4.73 3.95c 3.72e 4.57 3.99c 4.86 3.54a 4.0b 3.90c 2.70e 3.54 5.70 7.44 5.41 4.96 4.45

Equilibrium volumes (in A3 ), lattice constants (in A˚), bulk moduli (in GPa) and their first derivatives, and the internal structural parameters for different phases of ZnO compound. a Ref. [14]. b Ref. [13]. c Ref. [17]. d Ref. [16]. e Ref. [20]. f Ref. [24].

Table 2 Transition pressure P t and corresponding transition volume from B4 to B1 and B1 to B2 structures for ZnO Phase ðB4!B1Þ P T1 (GPa) V B4 ðP T1 Þ ðA3 Þ 3

V B1 ðP T1 Þ ðA Þ ðB1!B2Þ P T2 (GPa)

Other calculations

Present work

9.5a, 9.0b, 9.1c 8.7g, 10.0h 22.77g

8.57d, 6.60e, 8.22f 22.029e, 21.8f

9.8 9.8 22.709

18.802g

18.341e, 18.0f

18.05

V B1 ðP T2 Þ ðA3 Þ

260e 11.977e

265 12.55

V B2 ðP T2 Þ ðA3 Þ

11.377e

11.69

a

Ref. [4]. Ref. [5]. Ref. [14]. d Ref. [16]. e Ref. [17]. f Ref. [24]. g Ref. [13]. h Ref. [23]. b c

Fig. 1. Computed total energy versus unit-cell volume for the rock-salt (B1), CsCl (B2), zinc-blende (B3), wurtzite (B4), cinnabar, cmcm, d-b-tin, NiAs, Immm, and Imm2 structures of zinc oxide.

Experiment

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We compute lattice constants and bulk moduli by fitting the total energy versus volume according to Murnaghan’s equation of state [38]. The total density of states (DOS) was obtained using a modified tetrahedron method of Blo¨chl et al. [39].

3. Results and discussion 3.1. Structural stability Firstly, the LDA calculations have been used to determine the optimized structures of zinc oxide. We computed the equation state of B1, B2, B3, B4, cinnabar, NiAs, cmcm, Imm2, Immm, and d-b-tin structures at zero temperature. The calculated total energies are fitted to the Murnaghan [38] to obtain the equilibrium lattice constant and other structural properties. The energy–volume curves calculated with the FP-LAPW method are shown in Fig. 1 while Table 1 summarizes the calculated structural properties, together with some theoretical results and the available experimental data. Overall, a good agreement is found. From the graph, it is seen that wurtzite (B4) phase is the most stable structure at ambient conditions of zinc oxide, consistently with experiment. The energy ordering of the phases predicted by the FP-LAPW method is EB4 oEB3 oEB1 oENiAs oEcinnabar oEcmcm oEB2 oEImm2 o EImmm oEd-b-tin which tends to support the previous ab initio results. Furthermore, we find that the ordering of the total energies follows the one suggested by their temperature and pressure ordering. Thus, our calculated values are in excellent agreement with experiment. It is clearly seen that the cmcm structure has the highest bulk modulus value. Therefore, we can expect that this phase should exhibit higher hardness than the other ZnO, assuming that the hardness scales with the bulk modulus.

3.2. Phase transitions

Fig. 2. The variation of the Gibbs free energies DG for the different phases of ZnO. The reference Gibbs free energy in set for the wurtzite phase.

ZnO compound thermodynamically stable in the B4 phase tends to undergo a B4!B1 phase transition when increasing the pressure. The Gibbs free energies ðGÞ as a function of pressure

Fig. 3. Contour plot of the total valence charge density in the (11 0) plane for ZnO.

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given by the expression: " # ðB0 1Þ=B0 B0 V 0 B0 1þ P 1 GðPÞ ¼ E0 þ 0 B0 B 1

(3.1)

The value of the phase transition pressure ðPt Þ is determined by calculating Gibbs free energies ðGÞ for two phases B4 and B1: G ¼ Etotal þ PV þ TS

(3.2)

Since we are considering only the zero temperature limit in our calculations, Gibbs free energy becomes equal to the enthalpy ðHÞ H ¼ Etotal þ PV

(3.3)

At a given pressure a stable structure is one for which enthalpy has its lowest value and the transition pressures are calculated at which the enthalpies for the phases are equal. The calculated transition pressures ðP t Þ are also given in Table 2. It has been known experimentally that under increasing hydrostatic pressure, the B4 (hexagonal wurtzite) low pressure phase transforms to the cubic B1 (rock-salt or NaCl) structure at a pressure P T ¼ 9:1 GPa [14]. Previous experimental work has probed the B1 phase of ZnO by synchrotron X-ray diffraction [10,14] and by combined X-ray diffraction and Mossbauer spectroscopy [13]. The volume of rock-salt phase is decreased by 17.6% compared to wurtzite one. Indeed, the wurtzite phase appears to be stable above P T1 ¼ 9:8 GPa, which tends to support the experimental values (9.5 and 9.1 GPa) for Refs. [4,14], respectively.

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Liu and Bassett [6] have suggested that at a sufficiently high pressure, ZnO should undergo a phase transformation from the six-fold-coordinated B1 (cubic NaCl) to the eight-fold coordinated B2 (cubic cesium chloride) structure, in analogy to the alkali halides and alkaline-earth oxides. Jaffe and Hess [16] predicted the transition pressure from the B1 phase to the B2 phase at 260 GPa by employing LDA, whereas Maouche et al. [31] calculated the transition pressure at a higher value of ðP T2 Þ ¼ 260 GPa by using the Cambridge Serial Total Energy Package Software (CASTEP) code based on the plane wave basis set. At a much higher pressure, we predict a transition pressure of ZnO from B1 to B2 at ðP T2 Þ ðB1!B2Þ ¼ 260 GPa accompanied by a volume reduction of about 7.9%. This result agrees very well with the results of Maouche et al. [31]. In Fig. 2, we plot the energy of Gibbs, we consider the B4 phase like a reference, one notes that the various structures B4, B3, B2, B1, cmcm, and cinnabar are not stable in any range of pressure. However, the enthalpy of phase B3 is rather close to those of phase B4 and B1 near P T (B4/B1) and it is conceivable that the effects of temperature or improvement in the calculations could result in the emergence of a narrow field of stability for phase B3. Even if phase B3 is unstable it is possible that the B4!B3 transition could be observed at a slightly larger pressure if the B4!B1 transition were suppressed by a large activation barrier. Conversely, a B3 B1 transition could be favorable on decrease of pressure from phase B1 if the B4 B1 transition were impeded. In both cases, phase B3 would exist only as a meta stable phase. Of

Fig. 4. Total and partial densities of states (DOS) of ZnO compound in both the wurtzite and NaCl structures.

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course, to predict such possibilities for meta stable phases by decreasing the pressure one has to know the actual mechanisms of the transform from one phase to the other. 3.3. Charge densities To visualize the nature of the bond character and to explain the charge transfer and the bonding properties of zinc oxide compound, we have investigated the effect of the O states on the total charge densities in wurtzite structure see Fig. 3. We note that the large difference of the electronegativity between Zn and O appears in the difference of the charge transfer. This charge transfer between cation and anion increases when the difference in electronegativity values increases. The strong covalent interaction of the Zn–O bonds in our compound is responsible to have a high bulk modulus. 3.4. Density of states The DOS of ZnO (B4) and ZnO (B1) are presented in Fig. 4. The main features of the valence band are one peak at low energies corresponding to O(2s) states and the lower valence bands at around 6:5 to 0 eV for ZnO(B4), and 8 to 0 eV for ZnO(B1), are derived mostly from the cation Zn 3d-states hybridized with the anions O (2p). From Fig. 4, we can observe that the calculated densities of states are similar for both structures but the difference appears in the quantities of the band gap values.

4. Conclusion Ab initio calculation have been performed on the structural and electronic properties of zinc oxide. We use the full potential linearized augmented plane wave (FP-LAPW) method, in the framework of the density functional theory (DFT) with the local density approximation (LDA). The structural properties including lattice constants, bulk modulus and static pressure transitions were calculated. Our results agree with experimental data. Furthermore, the FP-LAPW calculations reproduce the correct hierarchy in the energy of the different phases. Note that we have used the Gibbs equation for examining a few high-pressure structures and comparing their enthalpies. Our key result is that ZnO will transform from rock-salt (B1) structure to the CsCl (B2) at a pressure near 265 GPa, by ensuring that no other new phase appears first.

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