Ab initio study of structural parameters and optical properties of ZnTe1−xOx

Superlattices and Microstructures 53 (2013) 155–162

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Ab initio study of structural parameters and optical properties of ZnTe1xOx S. Zerroug a,b, A. Gueddim c, M. Ajmal Khan d, N. Bouarissa d,⇑ a

Département des Troncs Communs, Faculté des Sciences de la Nature et de la Vie, Université Mira – Bejaia, Bejaia 6000, Algeria Laboratoire d’optoélectronique et composants, Département de Physique, Université Ferhat Abbes, Sétif, Algeria Materials Science and Informatics Laboratory, Faculty of Science, University of Djelfa, 17000 Djelfa, Algeria d Department of Physics, Faculty of Science, Science and Technology Unit, King Khalid University, Abha, P.O. Box 9004, Saudi Arabia b c

a r t i c l e

i n f o

Article history: Received 5 September 2012 Accepted 14 September 2012 Available online 13 October 2012 Keywords: Structural properties Optical properties ZnTeO alloys Solar cell materials Ab initio

a b s t r a c t The present work employs the full potential linearized augmented plane wave (FP-LAPW) technique to investigate the structural and optical properties of zinc-blende-structured ZnTe1xOx with oxygen concentration in the range 0–1. Features such as lattice constant, bulk modulus and its pressure derivative have been reported. In agreement with X-ray diffraction measurement, it is found that the lattice constant of ZnTe1xOx does not follow Vegard’s law. In addition, the spectral dependence of the dielectric functions of the material system of interest for various oxygen concentrations at energies below and above the fundamental absorption edge are examined and discussed. The calculated static and high-frequency dielectric constants are found to agree reasonably well with those reported in the literature. Other case, our results are predictions. The information derived from the present study may be useful for optical emitters/converters or intermediate/ defect band solar cells. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Highly mismatched alloys (HMAs) are a new class of semiconductors that has emerged, whose fundamental properties are dramatically modified through the isoelectronic substitution of a relatively small fraction of host atoms with an element of very different electronegativity [1–4], for example ⇑ Corresponding author. Present address: Department of Physics, College of Science and Arts and Centre for Advanced Materials and Nano-Research (CAMNR), Najran University, P.O. Box 1988, Najran 11001, Saudi Arabia. E-mail address: [email protected] (N. Bouarissa). 0749-6036/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.spmi.2012.09.015

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nitrogen in GaAs and oxygen in ZnTe. On the other hand, ZnTeO, in which O concentrations are high enough to form ternary alloys, show large band gap bowing [3,5,6]. According to Nabetani et al. [5], the large band gap bowing is due to the interaction between the localized energy level originating from the electronegative atoms and the energy band of the host materials. Much interest has recently been focused on ZnTe1xOx semiconductor alloys because of their potential applications in optoelectronic devices [5,7,8–11]. These materials are attractive for several device applications including light emitters and detectors operating in the visible/ultraviolet spectral region, and transparent electronics. Besides, ZnTe1xOx is a candidate material system for intermediate band solar cells [10,11] since the incorporation of oxygen into ZnTe results in electronic states within the band gap with highly radiative properties, and long carrier lifetimes [12]. In fact the incorporation of oxygen leads to the formation of a narrow oxygen-derived band of extended states located well below the conduction band edge of the ZnTe [11]. The technological importance of this material system requires the knowledge of the band parameters such as the structural and optical properties. In the present work, we address the question of these properties which are important for modeling quantum structures. Our calculations are performed using the full potential linearized augmented plane wave (FP-LAPW) method based on the density functional theory (DFT) within the generalized gradient approximation (GGA). Results regarding the lattice constant, bulk modulus and pressure derivative of the bulk modulus, as well as the real and imaginary parts of the dielectric function are reported. Comparison is made, when possible, with experimental and previous theoretical data and shows generally satisfactory agreement. 2. Computational method The calculations are performed using the FP-LAPW method based on the DFT [13] as implemented in the WIEN 2k code [14]. The exchange–correlation potential for the structural properties is calculated by the GGA based on Perdew et al. [15] form, while for the optical properties, the exchange–correlation functional of Engel and Vosko (EV-GGA) [15] is applied. In the FP-LAPW method, the wave function and potential are expanded in spherical harmonic functions inside non-overlapping spheres surrounding the atomic sites (muffin-tin spheres) and a plane wave basis set in the remaining space of the unit cell (interstitial region) is employed. In the present contribution, a cubic super cell which is composed of eight atoms (four Zn atoms and four shared out between Te and O) is considered. For a concentration of 50%, a super cell with layer wise is used in order to arrange Te and O atoms. In this case, the structure undergoes a tetragonal deformation. The effect of the tetragonalization on the determined parameters is estimated and the tetragonal distortion is given in terms of a c/a ratio that is found to be 1.24 (a and c are found to be 4.14 and 5.12 Å, respectively). A plane wave cut-off of RMTkmax = 7 (where RMT is the smallest muffin-tin radius in the unit cell) is used. RMT’s are chosen to be 1.8, 1.9 and 1.7 a.u. for Zn, Te and O, respectively. 56 special k-points are used in the irreducible part of the Brillouin zone for all concentrations of ZnTe1xOx, except that of 50% where 40 special k-points are used. 3. Results and discussion In the present study, the zinc-blende structure (B3) is assumed for ZnTe1xOx (0 6 x 6 1). The variation of the total energy as a function of the volume has been calculated for x = 0, 0.25, 0.50, 0.75 and 1. Our results are displayed in Fig. 1. The curves of Fig. 1 have been fitted to the Murnaghan’s equation of state so as to determine the equilibrium structural parameters. Our results regarding the equilibrium lattice constant for ZnTe and ZnO parent compounds are 6.16 and 4.61 Å, respectively. The lattice constants of ZnTe and zinc-blende structured ZnO reported by Jaffe and Hess are 6.1037 and 4.6 Å [16], respectively. Note that while our calculated lattice constant for ZnTe is larger than that reported in Ref. [16], our result for zinc-blende ZnO agrees well with that of Ref. [16]. On the other hand, the calculations of Schleife et al. [17] and Serrano et al. [18] showed that the value of the lattice constant of zincblende ZnO is 4.627 and 4.504 Å, respectively. In comparison with the results of Refs. [17,18] we find reasonably good agreement with Ref. [17] which is not the case with Ref. [18] where our calculated value is overestimated with respect to that reported in Ref. [18]. This can be traced back to the use

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-17185,862

(a)

-17185,864

ZnTe0.75O0.25 Energy (eV)

-17185,866

Energy (eV)

(b) -55300,24

ZnTe B3

-17185,868 -17185,870

-55300,26

-55300,28

-17185,872 -55300,30

-17185,874 -55300,32

-17185,876 340

360

380

400

420

440

460

1150

1200

1250

3

1300

1350

1400

1450

1500

1550

1600

3

Volume ((au) )

Volume ((au) )

-28413,76 -41856,6

(c)

ZnTe0.25O0.75

-28413,80

-41856,7

ZnTe0.5O0.5

Energy (eV)

Energy (eV)

(d)

-28413,78

-41856,8

-41856,9

-28413,82 -28413,84 -28413,86 -28413,88

-41857,0

-28413,90 -41857,1 800

900

1000

1100

1200

1300

1400

750

1500

800

850

3

950

1000

1050

1100

1150

Volume ((au) )

(e)

-3742,760

ZnO B3

-3742,765

Energy (eV)

900

3

Volume ((au) )

-3742,770

-3742,775

-3742,780

-3742,785 140

150

160

170

180

190

3

Volume ((au) )

Fig. 1. Total energy versus volume for (a) ZnTe, (b) ZnTe0.75O0.25, (c) ZnTe0.50O0.50, (d) ZnTe0.25O0.75 and (e) ZnO.

of different schemes in the calculations. Generally, the DFT-GGA scheme we used here tends to underestimate slightly the bonding which results in an overestimation of the lattice constant. The compositional dependence of the lattice constant of ZnTe1xOx system in the composition range 0–1 is shown in Fig. 2. We observe that the lattice constant decreases monotonically with increasing the oxygen concentration x on going from x = 0 (pure ZnTe) to x = 1 (pure ZnO). Conventionally, the lattice constants of ternary semiconductor alloys obey Vegard’s law that gives the lattice constant of an alloy as a compositional linear interpolation of those of the end members. Nevertheless, deviation from Vegard’s law has been reported in semiconductor alloys both experimentally and theoretically [19–22]. For that purpose, the composition dependence of the lattice constant of zinc-blende ZnTe1xOx has also been drawn following the Vegard’s law (Fig. 2, solid curve with circle symbols). It is clearly seen from Fig. 2 that the change of the lattice constant does not follow Vegard’s law (violation of Vegard’s

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law). This is consistent with the X-ray diffraction measurements reported by Nabetani et al. [7]. The deviation of the lattice constant from the Vegard’s law becomes larger with O concentration around 0.50. Nabetani et al. [7] reported that the O concentration dependence of the lattice constant measured by X-ray diffraction suggested that O atoms are incorporated as interstitials as well as Te substitutions. The fit of our data by a least-squares procedure gives the following analytical expression,

aalloy ðxÞ ¼ 6:15  0:55x  0:98x2

ð1Þ

where aalloy is expressed in angstroms. The quadratic term in Eq. (1) represents the lattice constant bowing parameter. The value of this bowing indicates that the lattice constant of ZnTe1xOx exhibits a non-linear behavior versus the composition x confirming thus the deviation from Vegards rule, i.e. from the linearity. The bulk modulus (B) is a measure of the volume compressibility of a material. In the present paper, B has been calculated for various oxygen concentrations x in ZnTe1xOx material system. Our results concerning the compositional dependence of B for zinc-blende ZnTe1xOx are drawn in Fig. 3. The values of B calculated in the present contribution for x = 0 (pure ZnTe) and x = 1 (pure zinc-blende structured ZnO) are 43.06 and 135.03 GPa, respectively. The known data regarding B for ZnTe as reported in Ref. [23] is 51.0 GPa. Our value is underestimated with respect to that one. This is not surprising, the results are consistent with the general trend of the DFT-GGA approach [24,25]. As far as the B for zincblende ZnO is concerned, our result is compared with those of 131.6, 160.8 and 135.3 GPa reported by Schleife et al. [17], Serrano et al. [18] and Jaffe et al. [26], respectively. Our computed B for the zincblende ZnO shows excellent agreement with the result of Jaffe et al. [26]. These authors also used a DFT-GGA scheme but expand the wave functions in localized orbitals of Gaussian form. However, note that while our B agrees to within a few per cent with that reported in Ref. [17], it is too small as compared with that reported by Serrano et al. [18]. By inspection of Fig. 3, one can note that as the oxygen concentration increases from x = 0 to x = 1, the bulk modulus increases as well. The increase is monotonic. This suggests that as the oxygen concentration increases, the ZnTe1xOx material system becomes less compressible. Our calculated data for B are fitted by a least-squares procedure. The analytical expression obtained from the fit is as follows:

BðxÞ ¼ 45:80  44:33x þ 130:58x2

ð2Þ

The large value of the bulk modulus bowing parameter suggests a non-linear behavior of B versus x. We have also calculated the pressure derivative of the bulk modulus (B0 ) for zinc-blende structured ZnTe1xOx for various compositions x in the range 0–1. The predicted values of B0 for zinc-blende ZnTe and ZnO are 5.48 and 5.42, respectively. Our computed B0 for the zinc-blende ZnO is compared with

6.4

ZnTe1-xOx

0

Lattice constant (A )

6.0

5.6

5.2

4.8

4.4 0.0

This work Using Vegard's law

0.2

0.4

0.6

0.8

1.0

Oxygen concentration (x) Fig. 2. Lattice constant versus oxygen concentration in ZnTe1xOx. This work (solid curve with square symbols), calculated using Vegard’s law (solid curve with circle symbols).

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159

140

Bulk modulus (GPa)

120

ZnTe1-xOx

100

80

60

40

20 0.0

0.2

0.4

0.6

0.8

1.0

Oxygen concentration (x) Fig. 3. Bulk modulus versus oxygen concentration in ZnTe1xOx.

those of 3.3 [17], 5.7 [18] and 3.7 [26]. We observe that our B0 is closer to that reported in Ref. [18] than those quoted in Refs. [17,26]. The variation of B0 as a function of the oxygen concentration in ZnTe1xOx material system is plotted in Fig. 4. Note that as the oxygen concentration increases from x = 0 (ZnTe) to x = 1 (ZnO), B0 decreases up to x = 0.50, then increases up to x = 1. Our data concerning B0 are also fitted using a least-squares procedure. The obtained analytical expression can be written as,

B0 ðxÞ ¼ 5:42  3:77x þ 3:87x2

ð3Þ 0

This expression can be used to predict B for any oxygen concentration in ZnTe1xOx material system. We now turn our attention to the optical properties, such as the dielectric function. The computed optical response functions, that is, real e1(E) and imaginary e2(E) parts of the dielectric function, for ZnTe1xOx ternary alloys in the composition range 0–1 are displayed in Figs. 5 and 6, respectively. Here E is the photon energy. We observe that while the incorporation of small fractions of oxygen into ZnTe do not affect much the behavior of e1(E) and e2(E), the incorporation of large fractions of oxygen into ZnTe results in a significant change of the e1(E) and e2(E) shapes. The difference is clearly seen when comparing between the optical response functions of ZnTe (x = 0) and ZnO (x = 1). The main peak of the real part of ZnTe occurs at around E = 3 eV. The peak position decreases and is shifted towards low-

Pressure derivative of bulk modulus

5.6 5.4 5.2

ZnTe1-xOx 5.0 4.8 4.6 4.4 4.2 0.0

0.2

0.4

0.6

0.8

1.0

Oxygen concentration (x) Fig. 4. Pressure derivative of bulk modulus versus oxygen concentration in ZnTe1xOx.

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er photon energies and becomes more flat as far as the oxygen concentration increases in the ZnTe1xOx material system. This can be attributed to the interband transitions. The optical spectrum of a crystalline semiconductor is usually classified into several photon energy regions based on their own optical transition mechanisms [23]. Generally, three spectral regions are distinguished. The first one is the so-called reststrahlen region in which the radiation field interacts with the fundamental lattice vibrations [23]. Below the reststrahlen region in the optical spectra, the real part of the dielectric function asymptotically approaches the static or low-energy dielectric constant e0. The e0 for ZnTe1xOx material system determined from our calculation in the whole composition range 0–1 can be written as,

e0 ðxÞ ¼ 7:49  0:87x  3:35x2

ð4Þ

this expression gives e0 = 7.49 for x = 0 (ZnTe), and e0 = 3.27 for x = 1 (ZnO). As regards e0 of ZnTe, our result is in good agreement with that of 7.4 quoted in Refs. [27,28] and in reasonable agreement with the value of 7.04 reported by Mezrag et al. [29]. To the best of our knowledge, no data regarding e0 for zinc-blende ZnO has been reported so far. Thus, our result may serve for a reference. The optical constant connecting the reststrahlen-near infrared range is called the high-frequency dielectric constant e1. For the material system of interest in the x composition range 0–1, the compositional dependence of e1 is found to be non-linear and can be represented by the following expression:

e1 ðxÞ ¼ 6:70  0:83x  3:04x2

ð5Þ

from expression (5), one can obtain e1 for ZnTe and ZnO to be 6.70 and 2.83, respectively. The calculated value of e1 for ZnTe shows reasonable agreement with that of 6.91 reported by Mezrag et al. [29]. The calculations of Schleife et al. [17] find a value of 5.54 for e1 in zinc-blende ZnO which is too large as compared to our computed one. We can also observe in the first region (as shown in Figs. 5 and 6) the S shape of dispersion of e1 accompanied by the inverted V shape of absorption of e2. These shapes are highly affected as one proceeds from pure ZnTe to pure zinc-blende structured ZnO. As a matter of fact, the general shape of e1 is that expected for a harmonic oscillator with resonant frequencies at about 7 and 11.5 eV for zincblende ZnTe and ZnO, respectively. The resonant frequency is shifted towards higher energies as the oxygen concentration in ZnTe1xOx material system is enhanced. The resonant frequency is thought to be a fundamental property of the material system in question that represents the average bonding–antibonding energy level separation [30]. This average bonding–antibonding gap can be divided up into two parts: ionic and covalent. This suggests that relevant parameters for formulating ionicity scales can be extracted from the knowledge of the dielectric function.

Real Part of the Dielectric Function

12

ZnTe1-xOx

10

0 0.25 0.50 0.75 1

8 6 4 2 0 -2 -4 0

2

4

6

8

10

12

Energy (eV) Fig. 5. Real part of the dielectric function for ZnTe1xOx at various oxygen concentrations.

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Imaginary Part of the Dielectric Function

14

ZnTe1-xOx

12

0 0.25 0.50 0.75 1

10 8 6 4 2 0 0

2

4

6

8

10

12

Energy (eV) Fig. 6. Imaginary part of the dielectric function for ZnTe1xOx at various oxygen concentrations.

The second region is the region where the material is considered to be primarily transmitting (i.e., near or below the fundamental absorption edge) [23]. The absorption for the imaginary part of the dielectric function starts at about 1.56 and 1.41 eV for ZnTe and ZnO, respectively. As one proceeds from pure zinc-blende ZnTe to pure zinc-blende structured ZnO, the starting energy value of the absorption for e2 decreases up to the oxygen concentration x = 0.50, then increases slightly up to x = 1. These points are Uv – Uc splitting. The third region is the strongly absorbing or opaque region. In this region (Fig. 6), the curves vary rapidly. This is attributed to the fact that the number of points contributing towards e2(E) changes abruptly. Similar behavior has been reported by Bouarissa [31] for InP. The region is characterized by sharp structures associated with valence-to-conduction band transitions at the critical points.

4. Conclusion In summary, we have studied the structural and optical properties of ZnTe1xOx alloy semiconductors by using the FP-LAPW technique within DFT in the GGA, for structural properties and EV-GGA for optical properties. The crystal structure of ZnTe1xOx investigated in this study was zinc-blende. Results regarding lattice constant, bulk modulus and its pressure derivative for ZnTe1xOx at various compositions x ranging from 0 to 1 are reported and compared where possible with the available experimental and theoretical data in the literature. Generally, a reasonably good agreement is found between our results and those reported in the literature. Other case, our results are predictions and may serve for a reference. Our calculations showed that the lattice constant of ZnTe1xOx does not obey to Vegard’s rule. This result is consistent with that reported by Nabetani et al. using X-ray diffraction measurement. The spectral dependence of the real and imaginary part of the dielectric function of the material system in question for various oxygen in the range 0–1 have been also studied at energies below and above the fundamental absorption edge. It is found that by increasing oxygen concentration, all the peaks of both real and imaginary parts of the dielectric function are hardly affected, indicating the isoelectronic feature of oxygen. Thus, the advantage of the studied material system is that further optimization of solar cell performance may be achieved by varying the oxygen concentration.

Acknowledgments M.A.K. and N.B. would like to gratefully acknowledge both the Science and Technology Unit at King Khalid University (KKU) and King Abdulaziz City for Sciences and Technology (KACST), for the financial support provided through Project No. 08-NAN 157-7.

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