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[13], hRef. [5]. Fig. 2. Pressure dependent (a) lattice constants and (b) bulk moduli for ZnS, ZnSe and ZnTe. C11 C 2C12 > 0Œ46Н are well satisfied. Furthermore ...
Vol. 35, No. 7

Journal of Semiconductors

July 2014

First principle studies of structural, elastic, electronic and optical properties of Zn-chalcogenides under pressure Muhammad Bilal, M. Shafiq, Iftikhar Ahmad, and Imad KhanŽ Department of Physics, University of Malakand, Chakdara, Pakistan

Abstract: Structural, elastic, electronic and optical properties of zinc-chalcogenides (viz. ZnX, X D S, Se and Te) are studied in zinc-blende structure under hydrostatic pressure using the full-potential linearized augmented plane wave method. Generalized gradient approximation is used for exchange correlation potentials. Pressure-dependent lattice constants and bulk moduli are obtained using the optimization method. Young’s modulus, Poisson’s ratio, internal strain parameter and anisotropy are also calculated. The higher values of Young’s modulus in comparison to the bulk modulus show that these materials are hard to break. Poisson’s ratio is computed for the first time for these materials to the best of our knowledge and its values show higher ionic contribution in these materials. Modified Becke and Johnson (mBJ) method is used to study band gaps, density of states, dielectric function and refractive index. Electronic study shows direct band gaps convert to indirect band gaps with increasing pressure in the case of ZnS and ZnTe. We compared our results with other theoretical and experimental results. Our results are far better than other theoretical results because mBJ is the best technique to treat II–VI semiconductors. Key words: semiconductors; elastic properties; electronic band structures DOI: 10.1088/1674-4926/35/7/072001 EEACC: 2520

1. Introduction Enormous industrial applications of the wide and direct band gap zinc-chalcogenide (ZnS, ZnSe and ZnTe) semiconductors have attracted much attention in the last few decades. These compounds are used in many established commercial electronic and optoelectronic devices operating in blue to ultraviolet spectral regions such as visual displays, high-density optical memories, transparent conductors, solid-state laser devices, photo detectors, and solar cells. They crystallize in zincblende (B3) structuresŒ1 4 at ambient pressure. The highpressure study of II–VI semiconductors has revealed polymorphic structural transformation in these materials. These materials have extensively been studied for their applications in optoelectronic devices in the blue and green spectral regions. ZnS is an ideal semiconductor for applications in ultraviolet laser devices, electronic image display, high-density optical memory, solar cells, etcŒ5 . ZnSe is suited for the fabrication of bluelight-emitting diodes in quantum well devicesŒ6 8 , whereas ZnTe is used in many technological applications, such as photovoltaic devices, thin-film transistors, THz emitters, detectors and imaging systemsŒ9 . The knowledge of the elastic and electronic properties of these materials can play a crucial role in the understanding of their fundamental solid-state phenomena. Elastic stiffness coefficients are used for different applications regarding mechanical properties of materials such as internal strain parameter, thermo-elastic stress and load deflection. The elastic constants of a material evaluated under high pressures, are essential to determine and understand material response, strength, mechanical stability and phase transitionsŒ5 . Similarly, electronic band structure of a material is important in understanding most of the

physical properties, like optical properties and transport propertiesŒ10 . The elastic and electronic properties of ZnX (X D S, Se, Te) have been extensively studied experimentally as well as theoretically, and extensive information on the subject is available in the literature. The results of these theoretical studies differ from experimental values in one or other parameter. The elastic constants of these compounds have been investigated by pseudo potentialŒ6; 12 , linear muffin-tin orbitalŒ8 , linear combination atomic-orbitalsŒ5 , full-potential augmented plane wave plus local orbitalsŒ13 , to evaluate the mechanical properties of these compounds under pressure. Similarly, the linear combination of Gaussian orbitalsŒ14; 15 , SIC-LDAŒ16 , GW techniqueŒ17 and first principle plane-wave pseudo potentialŒ18 are used to study band gaps and optical properties of these materials. In the present letter, we have investigated the elastic properties of ZnX, (X D S, Se and Te) under different hydrostatic pressures using GGA. Our calculated results are in agreement with the availableŒ5; 6; 8; 9 experimental and theoretical data. The elastic parameters like Poisson ratios, Young’s moduli and anisotropy factors have been evaluated under high pressures for the first time for ZnSe and ZnTe. The variation of the band gaps, density of states (DOS) and optical properties with pressure of these materials are also calculated using the recently developed modified Becke Johnson (mBJ) method, which is declared as the best techniqueŒ10; 19 22 for the calculation of band gap of II–VI semiconductors.

2. Computational method In the present work we study the structural and elastic properties of ZnX (X D S, Se, Te) compounds in the zinc-

† Corresponding author. Email: [email protected] Received 11 October 2013, revised manuscript received 23 January 2014

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Muhammad Bilal et al. Table 1. Calculated lattice constants a (Å) and bulk moduli B (GPa) for ZnX (X D S, Se and Te) at ambit pressure are compared with experimental and other theoretical results. Compound ZnS

ZnSe

ZnTe

Reference Present ExperimentŒ31 LDAŒ8 LDAŒ13 LDAŒ36 Present ExperimentŒ32 LDAŒ6 GGAŒ35 LDAŒ8 Present ExperimentŒ33 GGAŒ34 LDAŒ13 LDAŒ37

a (Å) 5.383 5.412 5.335 5.342 5.328 5.630 5.667 5.582 5.571 5.618 6.078 6.089 6.158 6.000 6.027

B (GPa) 82.37 75 83.7 89.67 83.8 63.34 69.3 70.8 72.7 67.6 51.23 52.80 47.70 55.21 55.67

ensured. For wave function in the interstitial region the plane wave cut-off value of Kmax D 7/RMT was taken and fine k mesh of 2000 was used in the Brillouin zone integration and convergence was checked through self-consistency. The convergence was ensured for less than 1 mRy/a.u. The details of elastic coefficient can be found in Refs. [24–29]. The Zincblende structures of ZnX (X D S, Se and Te) are shown in Fig. 1. Zn atom in the unit cell is at (0, 0, 0) while X atom is at (0.25, 0.25, 0.25).

3. Results and discussions 3.1. Structural and elastic properties

Fig. 1. Crystal structures of zinc-blende (a) ZnS, (b) ZnSe and (c) ZnTe.

blende using generalized gradient approximation (GGA). The electronic and optical properties are investigated using the modified Becke Johnson (mBJ) exchange potential as implemented in the WIEN2K packageŒ23 . For the calculations, RMT’s were chosen in such a way that there was no charge leakage from the core and hence total energy convergence was

For investigation of structural properties of zincchalcogenides we optimize each unit cell so that the most stable ground state energy is obtained. The calculated energies and optimized volume are fitted in Murnaghan’s equationŒ30 in order to calculate other structural parameters such as lattice constants and bulk moduli. The obtained lattice parameters and bulk moduli for ZnX (X D S, Se, and Te) using GGA approximation, are compared with the available experimental and theoretical results in Table 1, and are found in good agreement with the experimental data, whereas the variations in lattice constants and bulk moduli with increasing pressure are shown in Figs. 2(a) and 2(b). It can be seen from the graphs that lattice constants decrease and bulk moduli increase for all three materials as pressure increases, which shows that hardness of these materials increases with increasing pressure. Zinc-chalcogenides exist in cubic zinc-blende structure at ambit pressure and undergo phase transition at high pressures, e.g. ZnSŒ16; 38 42 , ZnSeŒ40; 43; 44 and ZnTeŒ45 show phase transition at 15 GPa, 13.7 GPa and 8.9 GPa respectively. We investigate elastic constants under pressure in the zinc-blende structure only. The calculated elastic constants at ambient pressure are compared with the available data in Table 2 and calculated elastic constants under pressure are shown in Table 3. It can be seen from both tables that the mechanical stability conditions in the cubic structures i.e. C11 – C12 > 0, C44 > 0,

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Table 2. Calculated pressure-dependent elastic constants (C11 , C12 and C44 / for ZnX (X D S, Se and Te). Compound Elastic constants 0 GPa 3 GPa 6 GPa 9 GPa 12 GPa 15 GPa ZnS C11 110.15 120.26 130.14 142.73 143.95 153.501 C12 63.71 80.11 94.99 103.56 119.23 132.19 C44 60.41 87.55 94.17 105.54 108.95 116.107 ZnSe C11 82.45 98.88 124.23 146.65 177.38 C12 42.71 69.05 74.75 84.14 102.42 C44 35.5 73.02 89.13 90.27 117.07 ZnTe C11 62.95 81.109 117.92 C12 40.62 56.17 59.76 C44 43.16 59.01 80.63

Table 3. Comparison of elastic constants of ZnX (X D S, Se and Te) with available data at ambit pressure. Compound Elastic constants Present Experiment Theory ZnS

ZnSe

ZnTe

a Ref.

C11 C12 C44 C11 C12 C44 C11 C12 C44

104a 65a 46.2a 82.8b 46.2b 41.2b 73.7c 42.3c 32.1c

110.15 63.71 60.41 82.45 42.71 35.5 62.95 40.62 43.16

122d , 123.7f , 118g , 92.2h 68d , 62.1f , 72g , 56.4h 57d , 59.7f , 75g , 64.2h 91.2d , 95.9f , 94g 58.2d , 53.6f , 61g 42d , 48.9f , 64g 51.36e 36.71e 38.65e

[47], b Ref. [48], c Ref. [11], d Red. [6], e Ref. [9], f Ref. [8], g Ref. [13], h Ref. [5]

Fig. 2. Pressure dependent (a) lattice constants and (b) bulk moduli for ZnS, ZnSe and ZnTe.

C11 C 2C12 > 0Œ46 are well satisfied. Furthermore, the calculated elastic moduli also satisfy the cubic stability condition i.e. C12 < B < C11 Œ12 . Table 3 also shows that elastic constants increase with increasing pressure for all three compounds.

In Table 4 variations of the anisotropy factor, Young modulus (Y ), internal strain parameter (/ and Poisson ratio (/ for ZnS, ZnSe and ZnTe are presented. Young’s modulus is the measure of stiffness of an elastic material. The table shows a gradual increase in Young’s modulus for these materials as pressure is increased which shows that stiffness of these materials increases with pressure. For ZnS, Y decreases at 12 GPa, which can be related to the conversion of material from direct to indirect band gap nature because Y decreases due to micro structural inhomogeneitiesŒ49 . The higher values of Young’s modulus in comparison to the bulk modulus show that these materials are hard to breakŒ50 . The nature of the bond can be predicted using Poisson ratio , which is usually between 0 and 0.5. For covalent bonded materials the value of Poisson ratio is of the order of 0.1 while in ionic compounds the value of Poisson ratio is usually 0.25Œ51 . In present calculations the values of Poisson ratio are  D 0.254, 0.223, 0.352 for ZnS, ZnSe and ZnTe respectively at zero pressure, which shows that the ionic contribution is dominant in these compounds which makes them useful for high electro-optical and electromechanical coupling. Poisson ratios for these compounds are calculated for the first time to the best of our knowledge. Pressure dependent studies reveal ionic behavior of these materials strengthens with increasing pressure where its value increases for ZnS and stays around 0.25 for ZnSe and ZnTe. KleinmanŒ29 introduced an important parameter called internal strain parameter (/, which explains relative tendency of bond bending to bond stretching. Its value usually lies between 0, showing minimum bond bending, and 1, showing minimum bond stretchingŒ52 . The pressure dependent study of internal strain parameter  presented in Table 4 shows that bond bending is preferred in these materials. The results are compared

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Table 4. Pressure-dependent Anisotropy factor (A), Young’s Modulus (Y ), Internal strain parameter (/ and Poisson ratio (/ for ZnX (X D S, Se and Te). Compound Parameter 0 GPa 3 GPa 6 GPa 9 GPa 12 GPa 15 GPa ZnS A 2.6 4.36 5.35 5.388 8.81 10.9 Y 105.28 125.10 127.34 141.96 128.79 130.80  0.68 0.759 0.808 0.8051 0.88 0.904 0.297 0.3316 0.3435  0.27 0.277 0.3011 ZnSe A 1.78 4.89 3.602 3.01 3.12 Y 72.25 106.09 133.38 149.17 186.53  0.64 0.784 0.708 0.686 0.689  0.284 0.287 0.246 0.263 0.255 ZnTe A 3.86 4.7323 5.772 Y 64.42 82.37 131.16  0.743 0.779 0.63  0.276 0.287 0.223

Fig. 3. Calculated pressure-dependent band structures of ZnS at (a) 3, (b) 6, (c) 9, (d) 12, (e) 15 and (f) 18 GPa pressure.

with other theoretical results in Table 5. Anisotropy of a material is another important parameter used to determine whether the structural properties remain the same in all directions or not. For A D 1, material is isotropic otherwise its properties change along different directions. The pressure dependent studies of ZnS, ZnSe and ZnTe presented

in Table 4 reveal that all these materials are anisotropic. Chen et al.Œ53 worked on anisotropy of ZnS and found A D 2.9 at ambit pressure, while no data is found for anisotropic study of ZnSe and ZnTe. The table shows the anisotropy of ZnS increases with pressure, as ZnS transformsŒ54 into a distortion of rock salt under high pressures, while in the case of ZnSe,

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Fig. 4. Calculated pressure-dependent band structures of ZnSe at (a) 0, (b) 3, (c) 6, (d) 9, (e) 12 and (f) 15 GPa pressure.

Table 5. Comparison of Internal strain parameter  for ZnX (X D S, Se and Te) at ambit pressure. Compound Reference  ZnS Present 0.68 LDAŒ8 0.651 TheoryŒ56 0.723 ZnSe Present 0.64 LDAŒ8 0.63 TheoryŒ56 0.736 ZnTe Present 0.743 TheoryŒ56 0.706 LDAŒ7 0.58

anisotropy initially increases up to 3 GPa and then shows very small variation with pressure because it remains cubic during transformationŒ55 from fourfold coordination zinc-blende to six-fold coordination rock salt structure. In contrast, the anisotropy of ZnTe shows little increase because at a pressure of 9 GPa after transforming into cinnabar phase it keeps the same coordination numberŒ45 as in the initial zinc-blende

phase. 3.2. Electronic properties The band structures of ZnS, ZnSe and ZnTe under various pressures are presented in Figs. 3, 4 and 5 respectively. The relation between the band gaps with pressure is presented in Fig. 6. It is clear from Figs. 3, 4, and 5 that band gaps initially increase with the increasing pressure, which is a commonly observed behavior in binary tetrahedral semiconductorsŒ57 59 . It is observed that the band gaps of ZnS and ZnTe converts from direct to indirect band gap materials at 12 GPa and 6 GPa respectively, while increasing pressure beyond these points the indirect band gap decreases in these two materials and the direct band gap of ZnSe keeps increasing and does not convert to indirect band structure till 15 GPa. Band structures for these materials clearly show the top of the valance band and bottom of conduction band occur at point for all three materials at ambit pressure, which shows direct band gap. Table 6 shows the calculated band gaps for all three zinc chalcogenides and they are compared with available experimental and theoretical results. The comparison with the available experimental results

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Fig. 5. Calculated pressure-dependent band structures of ZnTe at (a) 0, (b) 3, (c) 6, (d) 9 GPa pressure.

Compound ZnS ZnSe ZnTe a Present

Table 6. Calculated pressure-dependent elastic constants (C11 , C12 and C44 / for ZnX (X D S, Se and Te). Band gap 0 GPa 3 GPa 6 GPa 9 GPa 12 GPa 15 GPa Eg Eg Eg

3.6a , 3.7b , 2.2e , 2.18f 2.8a , 2.7c , 3.1g , 1.45h 2.4a , 2.39d , 1.16i , 2.57h

3.8 2.9 2.7

3.9 3 2.6 (indirect)

4 3.1 2.5

4 (indirect) 3.3

3.9 3.4

18 GPa 3.8

work. b ExpŒ60 . c ExpŒ61 . d ExpŒ62 . e GWŒ4 , f GGA-PBEŒ18 , g GWŒ63 , h GWŒ64 , i LDAŒ65

confirms that our theoretical results are consistent with the experiments. The calculated densities of states (DOS) at different pressures for ZnS are shown in Fig. 7. The DOS for the other compounds is similar to ZnS with minor differences in detail. The peaks in semi-core states are observed at –5.3 eV and are occupied by Zn d states while the peaks in the upper valance states are occupied by S-p states. The peaks shift towards low

energies as pressure is increased. Further, it is observed that peaks decrease with increasing pressure. The range of the upper valance band is –5 to 0 eV. The wide gap, between valance and conduction band, can also be seen from the density of states graph. The conduction band starts from 3.6 eV, 2.8 eV and 2.4 eV for ZnS, ZnSe and ZnTe respectively. The conduction states are dominated by p and d states of S atoms and s and p states of Zn. The overlapping of the Zn-s states and S-p states reveals

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Fig. 6. Pressure-dependent band gaps for ZnS, ZnSe and ZnTe.

Fig. 9. Pressure-dependent real part of dielectric function "1 (!/ for ZnS, ZnSe and ZnTe.

Table 7. Dielectric function "1 (0) for ZnX. Compound Reference "1 (0) ZnS Present 4.59 ExpŒ66 5.2 LDAŒ13 6.18 ZnSe Present 5.36 ExpŒ66 5.9 LDAŒ13 7.4 ZnTe Present 6.69 ExpŒ66 7.3 LDAŒ13 9.02 Fig. 7. Pressure-dependent density of states for ZnS.

Fig. 8. Pressure-dependent real part of dielectric function "1 .!/ for ZnS.

strong ionic bonding between these atoms. Further, it is observed that at zero pressure the bottom of the conduction band, which occurs at symmetry point, is due to Zn-s states. Meanwhile at 12 GPa, where material converts into indirect nature, the bottom of the conduction band, which occurs at X symmetry point, is due to Zn-p states and these Zn-p states are being pressed by S-d and Zn-d states.

vices and optical communication applications. Therefore, the real part of dielectric function, as all the optical properties depend on dielectric function, is also investigated. The real part of dielectric function for ZnS is shown in Fig. 8. Pressure dependent study of band structures of ZnSe and ZnTe reveals that band gaps vary in the visible energy range; therefore, tuning the band gaps on the required range, these materials can be used for making optoelectronic devices in the visible range. It is clear from the figure that for energy 5 eV, a sharp increase in "1 .!/ is observed in ZnS and reaches the peak at energy 6 eV. Then it starts to decrease with some variations and beyond 7.5 eV goes below zero. It reaches the minimum at energy 9.32 eV and beyond 17 eV it raises above zero and becomes constant. Increasing pressure also causes a shift of peak towards higher energies. The variation of static dielectric function "1 (0) with increasing pressure is presented in Fig. 9. It can be seen from the plot that the value of "1 (0) increases with pressure. This is due to the fact that the band gaps increase with pressure up to 9 GPa and 6 GPa for ZnS and ZnTe respectively but then band gaps decrease with increasing pressure as it converts into indirect materials. In the case of ZnSe, "1 (0) approximately remains constant with a very small positive gradient. For the three materials the values of zero frequency limit, "1 (0), which is the electric part of "1 .!/ at 0 GPa are shown in the Table 7. Zero frequency limits "1 (0), are 4.59, 5.36 and 6.69 for ZnS, ZnSe and ZnTe respectively.

3.3. Optical properties Due to wide and direct band gaps of ZnX, optical properties of these materials are of great importance in photonic de-

4. Conclusion

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properties of zinc-chalcogenides ZnS, ZnSe and ZnTe in zincblende structure are investigated under hydrostatic pressure. Results show that lattice constants for these materials decrease while bulk moduli and Young’s moduli increase as we increase pressure. This shows hardness of these materials increases with increasing pressure. Elastic constants C11 , C12 and C44 also increase with pressure and satisfy mechanical stability conditions in the cubic structures i.e. C11 – C12 > 0, C44 > 0, C11 C 2C12 > 0. The pressure dependent study of internal strain parameter  shows bond bending is preferred in these materials. Poisson’s ratio  is computed for the first time for these materials to the best of our knowledge and its values show higher ionic contribution in these materials. Anisotropy increases for ZnS and decreases for ZnTe with increasing pressure, whereas it remains approximately constant for ZnSe. Electronic and optical properties are studied using modified Becke and Johnson (mBJ) method. Band structure studies reveal these materials have direct band gaps. With increasing pressure the band gap of ZnS and ZnTe converts to an indirect band gap at 12 GPa and 6 GPa respectively and then this indirect band gap decreases with pressure while the band gap of ZnSe increases steadily with pressure. For their optical importance, dielectric function and refractive index are also calculated.

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