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Structural, electronic and optical properties of the wide-gap Zn1−x Cdx Te ternary alloys H. Rozale a,∗ , A. Lazreg a , A. Chahed a , P. Ruterana b a

Modelling and Simulation in Materials Science Laboratory, Physics Department, University of Sidi Bel-Abbes, 22000 Sidi Bel-Abbes, Algeria b

CIMAP, CNRS-ENSICAEN-CEA-UCBN, 6 Boulevard Maréchal Juin, Caen 14050, France

article

info

Article history: Received 18 October 2008 Received in revised form 16 June 2009 Accepted 20 July 2009 Available online 11 August 2009 Keywords: II–IV Zn1−x Cdx Te Band gap energy

abstract The II–VI compounds CdTe and ZnTe form a complete series of solid solutions with a cubic Zinc Blende structure. The room temperature band gap of these materials can be tuned from 1.5 eV in CdTe to 2.3 eV in ZnTe by controlling the alloy composition. This material is used as the window layer in thin-film solar cells. Using first-principles calculations, we investigated the structural and electronic properties of two binary CdTe and ZnTe for several compositions with various ordered structures (Cu3 Au, luzonite) of Zn1−x Cdx Te alloys using the theory of order–disorder transformation. An investigation was also conducted using the first-principles total-energy formalism based on the hybrid full potential augmented plane wave plus local orbital (APW + lo) method, within the local-density approximation (LDA) for the exchange and correlation potential. The 3d orbitals of the Zn atoms and 4d orbitals of the Cd atoms were treated as valence bands in every case. We analyzed the effect of alloying a small amount of ZnTe with CdTe; the fundamental direct band gap energy of the alloys was found to decrease per atomic percent of cadmium. © 2009 Elsevier Ltd. All rights reserved.

1. Introduction Band gap energy is one of the most important parameters that characterize a semiconductor and determines many gross electronic and optical properties. II–VI semiconductors with energy gaps covering the visible spectral range are compatible candidates for optoelectronic devices. Recently,

∗

Corresponding author. Tel.: +213 48557022; fax: +213 48544344. E-mail address: [email protected] (H. Rozale).

0749-6036/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.spmi.2009.07.026

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there have been many studies on the properties of wide-gap II–VI semiconductors and their ternary alloys [1–7] in response to the industrial demand for short-wavelength optoelectronic devices. The promising advantages of II–VI materials, compared with other semiconductors, are their high photochemical stability and size-dependent optical properties due to the quantum confinement effect [8,9]. The II–VI compounds CdTe and ZnTe form a complete series of solid solution with a cubic Zinc Blende structure [10]. The room temperature band gap of these materials can be tuned from 1.5 in CdTe to 2.3 in ZnTe by controlling the alloy composition [11]. The large band gap of solar cells is either used in fluorescent plastic concentrators [12] or in high-efficiency thin films in tandem solar cells [13]. For instance, in the last application the importance of the variation of Eg with (x) lies to the possibility of growing layers of Znx Cd1−x Te with different (x) values, in the entire range 0 ≤ x ≤ 1. This stratified arrange allows a tandem solar cell to absorb a large fraction of the solar spectrum energy. Znx Cd1−x Te is the basic element in the fabrication of the solid-state detectors for x-ray, beta ray, gamma ray, cosmic ray, and infrared electromagnetic radiation detection observed in medicine [14], astronomy [15], and high energy physics [16]. Znx Cd1−x Te has commonly been prepared for characterization as a single crystal grown by the Bridgman method [17–20] and the travelling heater technique [21]. The optical and magnetic properties of Znx Cd1−x Te alloys have also been experimentally studied [22,23]. For the calculation of the band energy structure of Gax Al1−x N, an approach was proposed by Kityk [24]; this approach can be extended on the different binary wide-gap semiconductor solid alloys during estimation of the band energy structure. However, for the perfect crystalline components, the better agreement between experimental and calculated data is achieved for the FLAPW method. Thus, the use of the proposed procedure may be useful only for the disordered crystals like binary semiconducting solid alloys. In the following, we report on a theoretical analysis of the structural and electronic properties of the binary semiconductor compounds (ZnTe, CdTe) in Zinc Blende structures, which constitute the ternary alloy of Znx Cd1−x Te at different concentrations in order to see the effect of cadmium on the band gap energy. 2. Calculations The calculations were performed using the nonscalar relativistic full potential linearized augmented plane wave (FP-LAPW) method [25] within the framework of the density-functional theory (DFT) using the ab initio WIEN2K package [26]. The exchange-correlation energy of the electrons is described in the local-density approximation (LDA) [27]. Basis functions were expanded in combinations of spherical harmonic functions inside non-overlapping spheres at the atomic sites (muffin-tin MT spheres) and in Fourier series in the interstitial region, with a cutoff of K∗max RMT = 9 (where RMT is the average radius of the MT spheres and Kmax is the magnitude of the largest K vector). In order to achieve the convergence of energy eigenvalues, a large number of integration points over the irreducible Brillouin Zone (BZ) were used: 30 for both ZnTe and CdTe in the Zinc Blende structure, 30 for luzonite, and 41 k points for chalcopyrite structures. The systems we will consider consist of two isovalent semiconductors AC and BC (especially ZnTe and CdTe) and their ternary ordered alloys. The choice of modelling units is based on the Landau–Lifshitz theory of order–disorder transformations [28,29]. There are eight Landau–Lifshitz structures [30] including, for the structure ABC2 the chalcopyrite (I-42d), as well as for structures A3BC4 and AB3C4, a luzonite; the lattice is simple cubic, and the space group is P-43m. We compute lattice constants and bulk moduli by minimizing the total energy versus volume; the equilibrium values are extracted by fitting the calculated data with Murnaghan’s equation of state [31]. 3. Results and discussion For the binary structures ZnTe, and CdTe in the Zinc Blende structure where the anions are arranged in a cubic compact structure, and the cations occupy one half of the tetrahedral sites between the anions, the lattice constants a, and the bulk modulus B are listed and compared in Table 1. As can be seen, for the structural properties, the results are in good agreement with other theoretical and experimental reports [32–39].

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Table 1 Calculated LDA properties for ZnTe and CdTe in the Zinc Blende structure along with experimental and other theoretical data.

ZnTe This work Other Calculation Exp. CdTe This work Other Calculation Exp.

a

B

B0

Eg

Ed

6.00 6.0832 6.0133

39 5433 4435 4736 5237 5038

3.98

1.24 1.3332 1.034 1.434 2.3937 2.3939

−7.26 −6.534 −1334 −10.834 −9.837

34 4633 7934

5.32

0.6 0.8032 0.534 0.834 1.6037 1.6039

−8.44 −7.834 −12.234 −11.034 −10.537

6.0837 6.1039 6.40 6.4333 6.2634 6.4034 6.4837 6.4739

4437

Zn1-xCdxTe

Lattice parameter(A°)

6.4

6.3

6.2

6.1

6.0

0.0

0.2

0.4

0.6

0.8

1.0

X

Fig. 1. Equilibrium lattice parameter as a function of composition (x) for Zn1−x Cdx Te.

For the electronic structure, we treat the Zn 3d, 4s, Cd 4d, 5s, and Te 5s, 5p orbital as valence states and all lower-lying states as part of the core. The band structure for each compound has been reported by using both experimental and theoretical calculations [32,34,37,39,40] and [41]. According to Table 1, the band gap energy Eg and average d-band energies Ed are slightly underestimated in comparison with the experimental results [37,39], which is typical for LDA using the Perdew–Wang [27] exchange-correlation energy; the latter confirm the presence of the strong p–d coupling. This effect is responsible for a reduction in the band gap energy. For the ternary compounds, Fig. 1 shows the calculated equilibrium lattice parameter versus cadmium concentration in the Zn1−x Cdx Te; the quadratic equation for the dependence of lattice parameter with (x) is a(Ax B1−x C ) = xaAC + (1 − x)aBC − x(1 − x)b. In our case, xaAC represents the lattice parameter, when x = 0 (CdTe) and the quadratic term b stands for the bowing parameter. A small deviation from Vegard’s law is clearly visible for these compounds with bowing parameter equal to 0.03; it is assumed that the atoms are located at the ideal lattice sites. The band structure and the density of one-electron energy states (DOS) have been computed for the luzonite cubic structure (Zn0.25 Cd0.75 Te, Zn0.75 Cd0.25 Te) and the chalcopyrite structure Zn0.5 Cd0.5 Te with mesh of 30 and 41 points in the irreducible part of the Brillouin zone, respectively, as shown in Figs. 2–4. The top of the valence band (VB) and that of the bottom conduction band (CB) are mainly composed of the Te 5p banding levels and Cd 5p, Zn 4p antibinding levels, respectively. The middle of the VB is composed of Cd 4d and Zn 3d bands. There are Cd 4d and Zn 3d bands centred around

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557

10.0

5.0

EF 50 Cd 4d

Zn 3d

Zn0.25Cd0.75Te

45 -5.0 40

Dos (arb. units)

Energy (eV)

0.0

-10.0

-15.0

Te 5s

35 30 25 20

Te 5p

15 10 5 0

-20.0 R

T

Γ

Z

Χ

-20

S

-15

-10

-5

0

5

10

Energy (eV)

Fig. 2. The band structure and the total density of state for luzonite Zn0.25 Cd0.75 Te.

10.0

5.0

EF

Energy (eV)

0.0

40 Cd 4d

Zn0.50Cd0.50Te

Zn 3d

35

-5.0

Dos (arb. units)

30

-10.0

-15.0

Te 5s 25 20 15 Te 5p 10 5 0

-20.0 N

Γ

Χ

-20

-15

-10

-5

0

5

10

Energy (eV)

Fig. 3. The band structure and the total density of state for the chalcopyrite structure Zn0.50 Cd0.50 Te.

(−8.49, −6.92) for luzonite Zn0.25 Cd0.75 O, (−8.48, −7.17) for chalcopyrite Zn0.5 Cd0.5 Te, and (−8.15, −7.14) for luzonite Zn0.75 Cd0.25 Te; the d bands are very narrow and show very little dispersion. The position of the cation d levels is rather high and relatively close to the anion p-derived valenceband maximum (VBM). The effect of the Zn 3d and Cd 4d states is not negligible for the various properties. For example, the d state couples to the VBM and pushes it upward, narrowing the band gap. According to figures of band structures, we notice that the reduction in the band gap Eg is correlated

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10.0

5.0

EF

50

Cd 4d

Zn 3d

Zn0.75Cd0.25Te

45 40 -5.0

Dos (arb. units)

Energy (eV)

0.0

-10.0

35 30 25

Te 5s

20 15

Te 5p 10

-15.0

5 0 -20

-20.0 R

T

Z

Γ

Χ

S

-15

-10

-5

0

5

10

Energy (eV)

Fig. 4. The band structure and the total density of state for luzonite Zn0.75 Cd0.25 Te.

with increasing cadmium content and increasing in width of the valence band at gamma 0 point. The interesting feature of band spectra obtained is three upper valence bands with energy difference at the 0 -point of some meV. We found a value of 8.406 for luzonite Zn0.25 Cd0.75 O, 8.402 for chalcopyrite Zn0.5 Cd0.5 Te, and 8.147 eV luzonite Zn0.75 Cd0.25 Te for (BV), respectively. For density of state, the peak corresponding to Te 5s, Cd 4d, Zn 3d, and Te 5p is clearly visible. This later presents four main regions. The first one is predominantly Te 5s states. The remaining three up to the top of the valence band are made of Cd 4d, Zn 3d, and Te 5p; they are shifted up or down in energy due to the change in nearest-neighbour bond lengths and in the local symmetry. Energy gaps for the Znx Cd1−x Te alloy of 1.24 (x = 1), 1.00 (x = 0.75), 0.92 (x = 0.50), and 0.71 (x = 0.25) are shown in Fig. 5 as a function of composition (x). The variation of the energy gaps deviates slightly from linear dependence, displaying a downward bowing b = 0.15 eV. The extent of bowing is a measure of the degree of fluctuations in the crystal field or the nonlinear effect that arises due to the anisotropic nature of binding [42]; the bowing parameter of b = 0.15 eV for the Znx Cd1−x Te alloys in the present work is in good agreement with other experimental and theoretical calculations – 0.13, 0.11, and 0.10, respectively [22,43,44] – indicating that ZnTe and CdTe have a good miscibility. The band gap is direct for the different concentrations at the 0 point. The reduction in the Eg of the ternary compounds relative to their binary counterparts is correlated with increasing cadmium content, the existence of d bonding in the compounds, and the deformation in structural parameters [45,46]. Moreover, the use of LDA produces too small band gap values; however, it provides a qualitative picture of the concentration effects on the band gap energy. The most important measurable quantity we address in this section is the dielectric function ε(ω) of the system, which is a complex quantity. The optical properties of the three materials are determined by the dielctric function ε(ω) given by ε(ω) = ε1 (ω) + iε2 (ω). The imaginary part of ε(ω), ε2 (ω) depends on the joint density of states and the momentum matrix elements. The real part, ε1 (ω), was obtained from ε2 (ω) by the Kramers–Kronig relations. To our knowledge, there are no experimental data concerning the dielectric functions of the luzonite cubic structure (Zn0.25 Cd0.75 Te, Zn0.75 Cd0.25 Te) and the chalcopyrite structure Zn0.5 Cd0.5 Te. In Fig. 6 (A, B and C) we present the calculated imaginary parts of the dielectric functions ε2 (ω) and in Tables 2–4 our suggested assignments of structures in ε2 (ω), where peak positions are given for three materials. We have performed the calculations using 158 k-points in the irreducible Brillouin zone. One may note that the general shapes of curves for three compounds are rather similar, indicating the same frequency regions. This is due to the similarities in their underlying band structures.

H. Rozale et al. / Superlattices and Microstructures 46 (2009) 554–562 1.3 Zn1-xCdxTe 1.2

Energy Gap (ev)

1.1 1.0 0.9 0.8 0.7 0.6 0.0

0.2

0.4

0.6

0.8

1.0

X

Fig. 5. Direct band gap at point 0 as a function of composition (x).

A

30

D

Zn0.25Cd0.75Te 25 20 C

2

15

F

B

10 A

5 0 0

2

4

6

8

10

12

Photon energy(eV)

B 30

Zn0.50Cd0.50Te

D 25 20

B 2

F C

15 10

A 5 0 0

2

4

6

8

10

12

Photon energy(eV)

C 30

D

Zn0.75Cd0.25Te

25 20

E

B 2

F

15

C A

10 5 0 0

2

4

6

8

10

12

Photon energy(eV)

Fig. 6. Calculated ε2 (ω) for Zn1−x Cdx Te (A) 0.25–0.75, (B) 0.50–0.50, and (C) (0.75–0.25.

559

560

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Table 2 Main peak position (in eV) and the calculated origins obtained from the band structure calculation of contributions to the structure in ε2 (ω) for the luzonite Zn0.25 Cd0.75 Te. The valence bands are labeled 1–12 and the conduction bands being from 13. Transitions using these notations are given in parentheses. Peaks

Main peak positions (eV)

Major contributions transitions Transitions

Energy

A B C

2.1 2.8 4.07

R(11, 12) → R(13) 0 (4, 5, 6) → 0 (13) 0 (7, 8, 9) → 0 (14, 15, 16)

2.18 2.82 4.05

D

4.43

0 (7, 8, 9) → 0 (17, 18) 0 (4, 5, 6) → 0 (14, 15, 16) 0 (10, 11, 12) → 0 (20, 21, 22)

4.44 4.47 4.48

E

5.8

X(6) → X(15) R(8, 9, 10) → R(17, 18) X(3) → X(14)

5.79 5.80 5.80

Table 3 Main peak position (in eV) and the calculated origins obtained from the band structure calculation of contributions to the structure in ε2 (ω) for the luzonite Zn0.5 Cd0.5 Te. The valence bands are labeled 1–12 and the conduction bands being from 13. Transitions using these notations are given in parentheses. Peaks

Main peak positions (eV)

Major contributions transitions Transitions

Energy

A

2.26

0 (12) → 0 (14) 0 (10, 11) → 0 (14) 0 (12) → 0 (15) 0 (10, 11) → 0 (15)

2.20 2.21 2.23 2.24

B C

2.78 3.81

T(7, 8) → T(13, 14) 0 (4) → 0 (13)

2.74 3.77

D

4.43

0 (19) → 0 (12) 0 (19) → 0 (10, 11)

4.40 4.42

E

5.77

0 (23, 24) → 0 (12) 0 (23, 24) → 0 (13, 14) N(19) → N(12) N(19) → N(13, 14) T(17, 18) → T(9, 10)

5.76 5.77 5.76 5.77 5.78

Table 4 Main peak position (in eV) and the calculated origins obtained from the band structure calculation of contributions to the structure in ε2 (ω) for the luzonite Zn0.75 Cd0.25 Te. The valence bands are labeled 1–12 and the conduction bands being from 13. Transitions using these notations are given in parentheses. Peaks

Main peak positions (eV)

Major contributions transitions Transitions

Energy

A B C D E F G

2.37 2.87 3.88 4.21 4.41 5.01 6.02

R(10, 11, 12) → R(13, 14, 15) R(5, 6) → R(19, 20, 21) X(11, 12) → X(14) X(9, 10) → X(14) 0 (10, 11, 12) → 0 (20, 21, 22) X(9, 10) → X(16) R(7, 8, 9) → R(20, 21, 22)

2.34 2.88 3.80 4.20 4.43 4.95 6.01

In interpreting these results, we also remarks that the luzonite cubic structure (Zn0.25 Cd0.75 Te, Zn0.75 Cd0.25 Te) and the chalcopyrite structure Zn0.5 Cd0.5 Te spectra have some features in common. Firstly, the calculated ε2 (ω) function begins with the E0 -type transition at 0 , corresponding to the energy gap. Our calculated onset energies are 0.71, 1.00, and 0.92 eV for Zn0.25 Cd0.75 Te, Zn0.75 Cd0.25 Te, and Zn0.5 Cd0.5 Te, respectively. Secondly, there are three groups of peaks. The first group (peak A, B, and C) is in the photon energy range (2–4.1 eV) for the three materials. The A peak for Zn0.25 Cd0.75 Te

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and Zn0.75 Cd0.25 Te is due to transitions from the highest valence to the lowest conduction band at the R-point and at the 0 -point for Zn0.5 Cd0.5 Te. The B structure may originate due to transitions from the lower valence band to the highest conduction band near the 0 -point for Zn0.25 Cd0.75 Te and transitions from the lower valence band to the lower conduction band near the T-point for Zn0.5 Cd0.5 Te and Rpoint for Zn0.75 Cd0.25 Te. The C peak is also dominated by transitions at the 0 -point for Zn0.25 Cd0.75 Te, at X-point for Zn0.75 Cd0.25 Te, and at 0 -point for Zn0.5 Cd0.5 Te. The second group of peaks (peaks D and E) is in the photon energy range (4.4–5.1 eV) for the three compounds. These principally arise from regions at the 0 -point for the luzonite Zn0.25 Cd0.75 Te, at the 0 and X-point for the luzonite Zn0.75 Cd0.25 Te, and at 0 -point for the chalcopyrite Zn0.5 Cd0.5 Te. At higher energy, the last group of peaks (F peaks) comes mainly from transitions at X and R-point for the luzonite Zn0.25 Cd0.75 Te, at R-point for the luzonite Zn0.75 Cd0.25 Te, and at 0 , N, and T-point for the chalcopyrite Zn0.5 Cd0.5 Te. 4. Conclusion In conclusion, we have reported an ab-initio study of the ZnTe and CdTe compound in the Zinc Blende structure and their ternary ordered alloys Zn1−x Cdx Te as modelled using Landau–Lifshitz cubic structures. The obtained structural properties are in good agreement with other theoretical results for the binary compounds, which is a support for those of the ternary alloys that we report for the first time. In this instance, the band gaps are shown to vary strongly from ZnTe and CdTe in a nonlinear way. The bowing parameter for the Znx Cd1−x Te alloys in the present work is in good agreement with other experimental and theoretical calculations [22,43,44] indicating that ZnTe and CdTe have a good miscibility. We have also presented the dielectric tensor for the Zn1−x Cdx Te and we have given assignments for the most important transition taking into account band structure calculations and the appropriate selection rules for coupling between electronic states. Acknowledgments This work was supported by the Algerian–French Ministries of Foreign Affairs under grant no. CMEP 01/MDU/516. One of us (B.B.) acknowledges the Abdus-Salam International Center for Theoretical Physics (Trieste-Italy) for financial support and kind hospitality, where part of this work has been done. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

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