Ab initio study of electronic structure and lattice properties of ZnSe1−xOx

Optik 127 (2016) 1889–1892

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Optik journal homepage: www.elsevier.de/ijleo

Ab initio study of electronic structure and lattice properties of ZnSe1−x Ox A.S. Bouarissa a , H. Choutri a , M.A. Ghebouli a , N. Bouarissa b,∗ a b

LMSE Laboratory, University of Bordj-Bou-Arréridj, El-Anasser 34265, Bordj-Bou-Arréridj, Algeria Laboratory of Materials Physics and Its Applications, University of M’sila, 28000 M’sila, Algeria

a r t i c l e

i n f o

Article history: Received 1 May 2015 Accepted 16 November 2015 Keywords: Electronic structure Structural properties ZnSe1−x Ox Vegard’s law Solar cells materials

a b s t r a c t The results of fundamental properties of zinc-blende ZnSe1−x Ox ternary system and related binaries (i.e. ZnSe and ZnO) are reported using the ab initio pseudopotential-density-functional calculations. Features such as lattice constant, bulk modulus, energy gaps and electron effective mass have been determined and their variation as a function of oxygen concentration has been presented and discussed. A good agreement is obtained between the calculated results and existing experimental data. It is found that the lattice constant of the material of interest violates the Vegard’s law. The information gathered from the present study could be useful for solar cells technological applications. © 2015 Elsevier GmbH. All rights reserved.

PACS: 71.20.Nr 71.20.−b 71.15.Mb 77.84.Bw

1. Introduction The zinc mono-chalcogenides are promising materials for many technological applications [1,2]. ZnSe is a light yellow solid compound. It is an intrinsic semiconductor with a wide band gap. It is used to form II–VI light-emitting diodes and diode lasers. It emits blue light and is widely used for infrared components, windows and lenses. On the other hand, ZnO is an inorganic compound. It has also a wide band gap. This material has several favorable properties, including good transparency, high electron mobility, and strong room temperature luminescence. These properties are used in emerging applications in energy saving or heat protecting windows, and in electronics as thin film transistors and light-emitting diodes. By alloying, ZnSe1−x Ox with a large band gap bowing effect is a potential material for optical devices (photodetectors, solar cells, etc) owing to its wide tunable range from ultraviolet to near infrared. Recently, it has been possible to deposit ZnSeO epilayers on GaAs (0 0 1), which exhibit a red-shift of the band gap and giant optical bowing. In fact, ZnSeO was grown on GaAs by molecular beam epitaxy [3,4]. Moreover, Mayer et al. grown ZnSeO thin film

∗ Corresponding author. Tel.: +213 552624855. E-mail address: n [email protected] (N. Bouarissa). http://dx.doi.org/10.1016/j.ijleo.2015.11.120 0030-4026/© 2015 Elsevier GmbH. All rights reserved.

(200–1500 nm thick) on sapphire substrates by pulsed laser deposition [5]. New results on the ZnSeO have been reported by Sun et al. [6] who grown ZnO:Se nanorods on silicon using mixture of Se powder and Zn powder by a simple physical vapor deposition method. Characterization and properties of Zn–O–Se ternary system thin films deposited by radio-frequency-magnetron sputtering have also been presented by Pan et al. [7]. Current activities in electronic and photovoltaic devices have led to significant interest in studies of fundamental properties. In this respect and in order to provide a structural basis for an understanding of the material physical properties, we have performed a study of structural and electronic properties of the material system ZnSe1−x Ox and its related binaries, namely ZnSe and ZnO. The crystal structure of the material of interest investigated in the present paper is zinc-blende. The calculations are carried out using ab initio pseudopotential approach within the local density approximation (LDA) based on the density functional theory (DFT) under the virtual crystal approximation (VCA). 2. Computational details The calculations are performed within the LDA of Ceperley–Alder [8] form as parameterized by Perdew and Zunger [9] to the DFT, using the pseudopotential planewave method as implemented in the ABINIT code [10]. The

A.S. Bouarissa et al. / Optik 127 (2016) 1889–1892

Hartwigsen–Goedecker–Hutter scheme [11] is used so as to generate the norm-conserving non-local pseudopotentials. The plane-wave energy cutoff to expand the wave functions is set to be 80 Ha (1 Ha = 27.211396 eV) in order to reach an accuracy of 10−5 Ha. The special points sampling integration over the Brillouin zone is realized using the Monkhorst-Pack method [12] with a 8 × 8 × 8 special k-point mesh for both compounds ZnSe and ZnO. The Broyden–Fletcher–Goldfarb–Shanno minimization technique [13], which provides a fast way of finding the lowest energy structure, is used in the geometry optimization. For the treatment of the ternary alloy system, we used LDA calculations on ZnSe1−x Ox in the zinc-blende phase within the VCA. The VCA allows creating a virtual chemical element which mixes the pseudo-potentials of the elements within the framework of DFT. In this regard, elemental ionic pseudo-potentials of ZnSe and ZnO are combined to construct the virtual pseudo-potential of the alloy system of interest. 3. Results and discussion The present computed lattice constants of ZnSe and ZnO binary compounds obtained from the minimization of the energy are ˚ respectively. The lattice constants found to be 5.27 and 4.04 A, of ZnSe and zinc-blende structured ZnO reported by Adachi are 5.6692 and 4.47 A˚ [14], respectively. Note that our results regarding the lattice constant of both compounds of interest are underestimated with respect to those reported in Ref. [14]. Generally, the LDA overestimates the crystal cohesive and molecular binding energies which results in an underestimation of the lattice constant. The compositional dependence of the lattice constant of ZnSe1−x Ox system in the composition range 0–1 is displayed in Fig. 1 using both the DFT–LDA scheme and Vegard’s law. As can be seen from Fig. 1 in both cases the lattice constant decreases monotonically with increasing the oxygen concentration x on going from x = 0 (ZnSe) to x = 1 (ZnO). However, the use of DFT–LDA scheme shows a nonlinear behavior of the lattice constant with respect to x whereas the use of Vegard’s law gives a linear variation of the lattice constant versus the oxygen content x. As a matter of fact, in the treatment of alloy problems, usually it is assumed that the atoms are located at the ideal lattice sites and the lattice constants of semiconductor alloys obey Vegard’s law which assumes that the lattice constant of an alloy is a compositional linear interpolation of those of the end members (binaries). Nevertheless, deviation from Vegard’s law has been reported in semiconductor alloys both experimentally and theoretically [15–19]. This is consistent with the present results where violation of Vegard’s rule can be clearly seen in Fig. 1. The

5.4

DFT-LDA Vegard's Law

5.0

0

Lattice constant (A )

5.2

4.8 4.6 4.4

ZnSe1-xOX

4.2 4.0 3.8 0.0

0.2

0.4

0.6

0.8

1.0

Oxygen concentration X Fig. 1. Lattice constant versus oxygen concentration in ZnSe1−x Ox . This work using DFT (solid curve with square symbols), calculated using Vegard’s law (solid curve with circle symbols).

180

160

Bulk modulus (GPa)

1890

ZnSe1-xOX

140

120

100

80

60

40 0.0

0.2

0.4

0.6

0.8

1.0

Oxygen concentration X Fig. 2. Bulk modulus versus oxygen concentration in ZnSe1−x Ox .

deviation of the lattice constant from Vegard’s law seems to be larger with the oxygen content around 0.50. The non-linear behavior of the lattice constant as a function of the oxygen concentration can be traced back to the difference in the bond-bending forces of the two constituents of ZnSe1−x Ox material system. The fit of our data by a least-squares procedure gives the following analytical expression, aalloy (x) = 5.25 + 0.28x − 1.46x2

(1)

where aalloy is expressed in angstroms. The quadratic term in Eq. (1) stands for the lattice constant bowing parameter. Note that the value of this parameter confirms the non-linear behavior of the lattice constant with respect to the oxygen content. The bulk modulus is a measure of the volume compressibility of a material. In the present contribution, the bulk modulus of the system under load has been calculated for various oxygen concentrations ranging from 0 to 1 using the stress–strain method [20]. Our results concerning the bulk modulus for ZnSe and zinc-blende structured ZnO are found to be 62.37 and 162.73 GPa, respectively. As regards ZnSe, our obtained bulk modulus value is in excellent agreement with the experimental one of 62.5 GPa reported in Ref. [21]. In terms of theoretical calculations, our result is closer to experiment than those reported by Qteish et al. [22], Khenata et al. [23], Saib et al. [24] and Nourbakhsh [25]. As far as the zinc-blende structured ZnO is concerned, our determined bulk modulus compares well with those of 157.86 and 160.8 GPa calculated by Saib and Bouarissa [26] and Serrano et al. [27], respectively. The variation of the bulk modulus as a function of the oxygen content x in ZnSe1−x Ox is shown in Fig. 2. We observe that by increasing the oxygen concentration x on going from ZnSe (x = 0) to ZnO (x = 1), the bulk modulus increases monotonically suggesting thus that ZnO exhibits a larger stiffness than ZnSe and that ZnSe1−x Ox material system becomes less compressible. Fig. 3 displays the calculated electronic band structures of zincblende (a) ZnSe (b) ZnSe0.50 O0.50 and (c) ZnO along representative directions of high-symmetry points in the Brillouin zone. The picture looks to be similar for all band structures of interest. The main difference between the three band structures lies in their optical and anti-symmetric gaps. Moreover, their valence bands are different in both size and dispersion. These differences can be ascribed to variations in the competing bonding mechanisms, that is, covalent versus ionic forces. This accounts for the success of Phillip’s decomposition of the bonding-antibonding gap into homopolar and ionic parts and the categorization of trends with his ionicity scale [28]. For ZnSe (Fig. 3a) and ZnO (Fig. 3c), the maximum of the valence band is formed by the triply degenerate hybridized Zn(4p,3d)–Se(4p) and Zn(4p,3d)–O(2p) like orbitals, respectively in an antibonding manner, whereas the minimum of the conduction

A.S. Bouarissa et al. / Optik 127 (2016) 1889–1892 0.26

ZnSe

14

Energy (eV)

7 0 -7 -14 -21 -28 W

L

Γ

X WK

W

L

Γ

X WK W

L

Γ

X WK

Fig. 3. Band structures for zinc-blende (a) ZnSe (b) ZnSe0.50 O0.50 (c) ZnO.

Electron effective mass (m0 units)

ZnO0.5Se0.5

ZnO 21

1891

0.24

ZnSe1-xOX 0.22

0.20

0.18

0.16

0.14 0.0

0.2

0.4

0.6

0.8

1.0

Oxygen concentration X Fig. 5. Electron effective mass versus oxygen concentration in ZnSe1−x Ox .

contribution the electron effective mass (me * ) has been obtained for the lowest conduction band  from the second derivative of the band energy with respect to the wave vector k. Our results showed that me * for ZnSe is: 0.156 m0 whereas that for ZnO is: 0.241 m0 (m0 is the electron free-particle mass). These values agree very well with those of 0.137 (for ZnSe) and 0.234 m0 (for ZnO) reported in Ref. [14]. The compositional dependence of the me * for ZnSe1−x Ox is displayed in Fig. 5. Note that as the oxygen concentration x is increased, me * increases monotonically. The increase of me * with x will contribute to the decrease of the electron mobility in ZnSe1−x Ox when increasing the oxygen concentration x. Fig. 4. Direct (–) and indirect (–X) and (–L) band-gap energies versus oxygen concentration in ZnSe1−x Ox .

band is at the zone center  and is the antibonding Zn(4s)–Se(4s) and Zn(4s)–O(2s) singlet state, respectively. The higher conduction states arise from the hybridization of the Zn(4p,3d)- and Se(4p,3d) and Zn(4p,3d)-and O(2p,1d)-like orbitals in ZnSe and ZnO, respectively. The incorporation of an amount of 50% of O in ZnSe (Fig. 3b) leads to a formation of more dispersive bands and band crossing. Similarly to ZnTe [29], one can expect that the incorporation of a small fraction of O leads to the formation of a new intermediate band which makes the system under load useful for intermediate band solar cell. The composition energy variations of the conduction band edges at , X and L with respect to the top of the valence band for ZnSe1−x Ox are determined. The results are displayed in Fig. 4. We observe that all band gap energies being considered here vary monotonically with respect to the oxygen concentration x. The extent of the direct-to-indirect band gap transition has been examined in the present contribution. As can be seen from Fig. 4 our result implies that ZnSe1−x Ox ternary system does not show a transition between the direct to indirect structures over all the composition range 0–1. One can conclude then that the energy gap in the material under load remains direct within a whole range of the oxygen concentration x (0 ≤ x ≤ 1). The effective mass is a necessary parameter for analyzing the most carrier transport properties [30]. Its precise knowledge is also useful for the investigation of ZnSe1−x Ox quantum well structures. Values, of effective mass can often be determined by, for instance, cyclotron resonances or transport measurements [31]. On the theoretical side, the effective mass can be determined from the electronic band structure calculations [32]. In general, the effective mass is a direction dependent quantity. However, for a very idealized simple case, i.e., for the band extremum occurring precisely at k = 0 and the parabolic E(k) relationship (such as the case here), the effective mass can be considered as a scalar. In the present

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