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First principles study of structural, optical, and electronic properties of zinc mercury chalcogenides
Materials Science in Semiconductor Processing 30 (2015) 462–468
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Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
First principles study of structural, optical, and electronic properties of zinc mercury chalcogenides G. Murtaza a,n, Naeem Ullah b, Abdur Rauf c, R. Khenata d, S. Bin Omran e, M. Sajjad c, A. Waheed a a
Materials Modeling Lab, Department of Physics, Islamia College University, Peshawar, Pakistan Department of Physics, G.D.C. Darra Adam Khel, F.R. Kohat, KPK, Pakistan Department of Physics, Kohat University, KPK, Pakistan d LPQ3M Laboratory, Faculty of Science and Technology, University of Mascara, Algeria e Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia b c
a r t i c l e in f o
Keywords: First principle calculations Optical properties Electronic structure
abstract First-principles calculations using the full potential linearized augmented plane wave method within the framework of density functional theory are performed to investigate the compositional dependence of the structural, electronic and optical properties of Zn1 xHgxE (E ¼ S, Se, Te). It is observed that except the lattice constant, the variation of the bulk modulus and the band gap versus mercury composition does not obey Vegard's law. The alloys at all concentrations have direct band gap ðΓ ΓÞ which decreases with increasing the concentration of Hg. Optical properties like complex dielectric function and reflectivity are discussed comprehensively. The properties of these materials such as the direct band gap and high absorption in the infrared to ultraviolet regions demonstrate the significant optical activity of these materials. & 2014 Elsevier Ltd. All rights reserved.
1. Introduction The increasing needs of technology enhanced semiconductor processing for optoelectronic devices operating in the visible and far-infrared regions, including lightemitting diodes (LEDs), photo-detectors and solar cells [1–3]. The II–VI semiconductor family contains various wide band gap semiconductors and narrow band gap mercury chalcogenides semiconductors and semimetals exhibiting a large spectrum of properties and making them chief candidates for modern optoelectronic applications [4,5]. A solid solution of two or more semiconductors forms a semiconductor alloy, which has significant technological
n
Corresponding author. Tel.: þ 92 321 6582416. E-mail addresses: [email protected] (G. Murtaza), [email protected] (R. Khenata). http://dx.doi.org/10.1016/j.mssp.2014.10.048 1369-8001/& 2014 Elsevier Ltd. All rights reserved.
applications, particularly in the fabrication of electronic and optoelectronic devices [6]. Ternary alloy solid solutions of II–VI semiconductors have been studied in numerous investigations [7–13]. The gas-source molecular beam epitaxy technique has been used by Hara et al. [7] to control the light emission in the visible range while increasing the Hg contents in Zn1 x HgxSe. Ternary Zn1 xHgxSe and quaternary Zn1 xHgxSySe1 y alloy layers have been grown on GaAs substrates using molecular beam epitaxy (MBE) and characterized using optical techniques [8]. Electrodepositing studies on Zn1 xHgxSe and Zn1 xHgxTe have been performed to explore their structural, electronic and optical properties [9,10]. Mahalingam et al. [11] prepared thin alloy films of Cd1–xHgxTe, MnxHg1–xTe, and ZnxHg1–xTe and studied the effect of biaxial stresses in these compounds. Deibuk et al. [12] further used experimental data and mathematical models to study the band gap and optical properties of quaternary
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CdxHg1 x yZnyTe alloy epitaxial layers. A complete solid solution was obtained throughout the entire range for the ZnHgS system [13]. Because of the importance of zinc and mercury chalcogenides in the modern optoelectronic devices industry, the present work intended to explore the structural, electronic and optical properties of Zn1 xHgxE (E¼ S, Se, Te) in the zinc blende (B3) structure. The modified Becke–Johnson (mBJ) [14] potential approximation was used to overcome the anomaly between the experimental and theoretical when common LDA and GGA approximations [15] are used. The adaptation of mBJ improves the band gap value and the optical spectra that are found in variety of investigations [15,16–18] and the references therein. The mBJ predicts better energy band gaps because it is able to accurately reproduce the exchange potential. It is used for the highly correlated systems with f and d orbitals. The calculations were performed in the framework of density functional theory (DFT) to treat the electronic band gap, contribution from the different energy levels, optical dielectric constants and refractive indices as a function of composition and energy. Section 2 covers the computational details, Section 3 is devoted to the results and their discussion and in Section 4, the main conclusions are summarized.
2. Computational details In this work, the calculations were performed employing the full-potential linearized augmented plane wave (FP-LAPW) method as implemented in the Wien2K code [19]. The exchange and correlation effects were treated using the mBJ approximation [14]. Inside the nonoverlapping spherical region of the Muffin–Tin radius (RMT) around each atom, a linear combination of the radial solution of the Schrödinger wave equation times the spherical harmonics is used, and in interstitial region, a plane wave basis set was used. The wave function expansion inside the sphere was confined to lmax ¼10, while for the expansion of the wave function in the interstitial region, the plane wave cut-off Kmax ¼8/RMT was used. Here, Kmax provides the magnitude of the largest K vector in the plane wave expansion. The integrals over the Brillouin
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zone are performed up to 1000 k-points in the full Brillouin zone. 3. Results and discussions 3.1. Structural properties The structural properties of the binary compounds (ZnS, ZnSe, ZnTe, HgS, HgSe and HgTe) were examined in the zinc blende structure using the generalized gradient approximation of Wu and Cohen (WC-GGA) [20]. Ternary Table 2 Present calculated equilibrium lattice constant and bulk modulus for Zn1 xHgxE along with experimental data and other calculations. x
B0 (GPa)
a0 (Å) Present Exp.
Others
Present Exp.
Others
Zn1 xHgxS 0 5.38 0.25 5.545 0.50 5.67 0.75 5.79 1 5.90
5.41a 5.30b, 5.34c 81.10 71.37 68.56 65.68 5.85a 5.97d 60.67
76.90a 77.30d
Zn1 xHgxSe 0 5.65 0.25 5.80 0.50 5.94 0.75 6.05 1 6.14
5.67a 5.59a, 5.69c 75.68 62.12 57.41 58.09 a b c 6.07 6.19 , 6.10 56.36
62.50a 83.8d
Zn1 xHgxTe 0 6.10 0.25 6.22 0.50 6.33 0.75 6.43 1 6.55
6.09a 6.02b, 6.04c 56.11 52.55 46.25 46.74 a b 6.46 5.53 43.80
68.60a 55.30d
57.50a 41.80d 50.09a 49.20d, 52.1b
47.60a
47.10d, 46.10b
a
Ref. [27]. Ref. [28]. Ref. [29]. d Ref. [30]. b c
Table 1 Atomic positions for Zn1 xHgxTe alloys. x
Atom Positions
0.25 Zn Hg Te
(0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0) (0, 0, 0) (0.25, 0.75, 0.75), (0.75, 0.25, 0.75), (0.75, 0.75, 0.25), (0.25, 0.25, 0.25)
0.50 Zn Hg Te
(0, 0, 0), (0.5, 0.5, 0) (0.5, 0, 0.5), (0, 0.5, 0.5) (0.25, 0.25, 0.25), (0.75, 0.75, 0.25), (0.75, 0.25, 0.75), (0.25, 0.75, 0.75)
0.75 Zn Hg Te
(0, 0, 0) (0.5, 0.5, 0), (0, 0.5, 0.5), (0.5, 0, 0.5) (0.25, 0.25, 0.25), (0.75, 0.75, 0.25), (0.75, 0.25, 0.75), (0.25, 0.75, 0.75)
Fig. 1. Composition dependence of calculated lattice constant and bulk moduli of Zn1 xHgxE alloys.
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alloys were patterned at selected compositions (x ¼0.25, 0.50, 0.75) using the construction of eight atoms supercell, used by Agrawal et al. [21]. Many researchers have used this method to investigate various properties of alloys [22–24]. As a prototype, the atomic positions of Zn1 xHgxTe are given in Table 1. To determine the equilibrium lattice constants and bulk moduli, the unit cell energy was fitted against the unit cell volume by the Murnaghan equation [25]. The calculated equilibrium lattice constant and bulk moduli along with previous experimental data and theoretical calculations are summarized in Table 2. Our calculated results for binary compounds are in close agreement with the experimental data. The lattice constant and bulk moduli are traced out as a function of the dopant atom concentration “x” in Fig. 1. The calculated lattice constant varies almost linearly with increase in the concentration “x” with bowing parameters equal to 0.13 Å, 0.21 Å and 0.11 Å.
For the bulk modulus, a large deviation from Vegard's law [26] was observed with bowing of 10.68, 33.2 and 9.17 GPa for Zn1 xHgxE. 3.2. Electronic properties Calculations of the band structure of the binary compounds and ternary alloys were performed at the optimized lattice constant within the mBJ-approximation, as depicted in Fig. 2 (Zn1 xHgxTe (x ¼0, 0.25, 0.50, 0.75, 1) as a prototype). It is obvious from the figure that the valence band maximum (VBM) and conduction band minimum (CBM) lie at the Γ-symmetry point, resulting in the direct ðΓ ΓÞ band gap for all these materials (x ¼0, 0.25, 0.50, 0.75, 1). The band gap decreases with an increase in the concentration “x” of Hg in Zn1 xHgxTe. The present calculated band gaps along with their available experimental
Fig. 2. Band structure for Zn1 xHgxTe (x¼ 0, 0.25, 0.50, 0.75, 1).
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and theoretical data are also listed in Table 3. The predicted band gaps for the binary compounds ZnS, ZnSe, ZnTe and HgTe are in close agreement with the experimentally measured data and offer an improvement over the previous theoretical investigations, while the band gaps for HgS and HgSe are slightly overestimated compared with previous experimental and theoretical calculations. For the ternary alloys, theoretical data are only available for Zn1 xHgxTe, while there is a lack of data for Zn1 xHgxS and Zn1 xHgxSe alloys. In addition, we traced the variations in the band gap as a function of the composition “x” as illustrated in Fig. 3. The variation of the experimental band gap versus mercury composition up to 0.44 taken from Mahalingam and co-workers [9] is also displayed in Fig. 3. From the figure, it is apparent that the band gap decreases and varies non-linearly as a function of the composition “x”, where 1.04, 0.86 and 1.95 eV bowing is observed for Zn1 xHgxS, Zn1 xHgxSe and Zn1 xHgxTe, respectively. The density of states (DOS) was calculated to explore the contributions of different electronic states to the valence and conduction bands. Fig. 4 shows the DOS for Zn1 xHgxTe as an example because the electronic state contributions for the other two alloys are similar. For both the binary compounds ZnTe and HgTe, the Te-4p state dominates the upper conduction band with a small contribution from cation-s near the Fermi level. A band with high DOS with cation-d character can be observed at approximately 6.3–7.2 eV and 6.3–8 eV in ZnSe and HgSe, respectively. The lower valence band centered on 4.7 eV in Table 3 Band gap energy of Zn1 xHgxE alloys (values are in eV). x
Band gap (eV) Present
Zn1 xHgxS 0 3.86 0.25 2.90 0.50 1.92 0.75 1.33 1 0.62 Zn1 xHgxSe 0 2.81 0.25 1.96 0.50 1.22 0.75 0.64 1 0.10 Zn1 xHgxTe 0 2.36 0.25 1.05 0.50 0.65 0.75 0.34 1 0.16 a
Ref. [30]. Ref. [28]. c Ref. [31]. d Ref. [32]. e Ref. [33]. f Ref. [34]. g Ref. [27]. h Ref. [36]. i Ref. [12]. b
Exp.
Others
3.82f, 3.84g
2.15a, 2.0b, 2.37c, 3.99d
0.50f, 0.11e
0.69a, 0.28d, 0.62h
2.87f, 2.82g
1.39a, 1.6b, 1.45c, 2.68d
0.10f, 0.20g
1.2a, 0.4d, 0.07h
2.39f,g
1.32a, 1.02b, 1.33c, 2.27d, 2.28i 1.30i 0.70i 0.38i 0.84a, 0.45d, 0.20h, 0.16i
0.30f,g
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Fig. 3. Variations in the band gap energy as a function of concentration “x”.
ZnSe and 5 eV in HgSe has a mixed chalcogen-p and cation-s character. For the alloys (x ¼0.25, 0.50, 0.75), the upper valence band is still dominated by the chalcogen-p state with a small contribution from the Hg-d state. The lower cation-d band consists of both Hg-d and Zn-d electronic states. The lower conduction band has a mixed character of chalcogen-p and cation-s empty states. The results for the existence of Zn-d state in the energy range 6.3–7.2 eV are in agreement to photoemission experimental results [35]. 3.3. Optical properties Understanding the optical nature of materials over a spectral range provides insight into their usage in the fabrication of optoelectronic devices. The electronic properties indicate that these materials are direct band gap semiconductors and hence are optically active. This finding motivated us to calculate the important optical properties such as the real, ε1 ðωÞ, and the imaginary, ε2 ðωÞ, parts of the complex dielectric function, εðωÞ ¼ ε1 ðωÞ þ iε2 ðωÞ, using the approach of Ehrenreich and Cohen [37]. The calculated optical spectra for Zn1 xHgxS, Zn1 xHgxSe and Zn1 xHgxTe are presented in Fig. 5 (the real part in left panel and the imaginary part in right panel). The calculated spectra of ε1 ðωÞ revealed that the zero frequency limit ε1(0) increases with an increase in the concentration of Hg-atoms in all three alloys, while the band structure calculation revealed a decrease in the band gap with increasing concentration. This inverse relationship between the band gap and optical dielectric constants is a general behavior observed in semiconductor alloys [38] and is also consistent with the Penn model [39]. The zero frequency dielectric constant ε1(0) results are listed in Table 4. The static dielectric constants for ZnS, ZnSe and ZnTe are 4.7, 5.23 and 7.13, respectively, which are closer to the experimental measurements (5.2, 5.9 and 7.30, respectively) [40] compared with other calculations [41]. The calculated values of ε1(0) were 6.9, 11.24 and 14.05 for binary HgS, HgSe and HgTe, respectively, which were lower than the values obtained in other theoretical calculations [42]. The dielectric constant for HgSe was also underestimated compared with experimental measurements (15.7) [43]. Similarly, the calculated zero frequency refractive indicesnð0Þ are given in Table 4. The value of this index increases with an increase in the concentration “x”. A comparison of the nð0Þ values for binary ZnS, ZnSe and ZnTe reveals a close agreement with the experimental
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Fig. 4. Density of states for Zn1 xHgxTe (x ¼0, 0.25, 0.50, 0.75, 1). Fermi level is set at 0 eV.
measurements. For ZnS and ZnSe, the calculated values 2.17 and 2.34 are consistent with the measured values of 2.15 (at 12.4 μm) [44] and 2.32 (at 18 μm) [45], respectively. For ZnTe, our calculated value was 2.67, while the experimental measurement was 2.49 (at 18 μm) [46]. The left panel in Fig. 5 depicts the imaginary part of the complex dielectric function. The imaginary part ε2 ðωÞ shows the absorption or loss of energy by electromagnetic radiations within the medium and is directly related to the band structure. The first critical points in the spectra of ZnS, ZnSe and ZnTe occur at 3.43, 2.57 and 2.10 eV, respectively, in close agreement with experimental measurements [47,48] and offer an improvement over other theoretical calculations [41]. These points show the direct optical transition from the occupied chalcogen-p state in the valence band to the unoccupied Hg, ZnS and chalcogen-p states in the conduction band at the Γ-point and are called the fundamental absorption edge. The peaks in the spectra are attributed to various electronic transitions from the occupied states in the valence band to the unoccupied states in the conduction band. With an
increase in the concentration “x”, the peaks in the spectra shift toward lower energies in accordance with the decrease in the band gap. The shift in absorption peaks toward lower energies results in a variety of proficient materials for optoelectronic devices in the infrared and visible energy ranges. The shift of absorption edge and prominent peaks are also observed experimentally [8,9] in these materials. The present calculated frequency dependent reflectivity R(ω) spectra of these materials are presented in Fig. 5 (right panel), while the zero frequency reflectivity R(0) calculated data are listed in Table 4, as shown in Fig. 6. The R(0) values increase with increase in the concentration “x” for these materials. The present zero frequency reflectivity for ZnS is 13.2%, which is in close agreement with the experimental measurement (13.5%) [44] at 12.4 μm wavelength. For ZnSe, the calculated R(0) is approximately 15.8%, which is in agreement with the experimental value (16.8%) at 18 μm by Connolly et al. [45]. The 19.7% R(0) value for ZnTe is close to the measured value of 21% at 18 μm [46]. The maximum reflectivity occurs in the energy
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Fig. 5. Spectra of real part of dielectric function (left panel), imaginary part of dielectric function (mid panel) and reflectivity (right panel) for Zn1 xHgxE alloys. Table 4 Zero frequency limit of dielectric constant ε1(0), reflectivity R(0) and refractive index n(0). x
ε1(0)
R(0) (%)
n(0)
Zn1 xHgxS 0 0.25 0.50 0.75 1
4.72 5.05 5.92 6.03 6.90
13.4 13.7 14.9 17.0 20.0
2.17 2.24 2.43 2.45 2.62
Zn1 xHgxSe 0 0.25 0.50 0.75 1
5.51 6.87 7.15 7.79 11.24
15.8 17.1 20.0 22.2 28.3
2.34 2.62 2.67 2.79 3.27
Zn1 xHgxTe 0 0.25 0.50 0.75 1
7.13 8.98 9.47 10.15 14.05
19.7 24.0 26.0 27.5 37.4
2.67 2.99 3.07 3.18 3.74
ranges where the spectra of ε1 ðωÞ is below zero. The maximum reflectivity peaks shift toward lower energies for these alloys due to the band gap decrease. For negative
Fig. 6. Variation in zero frequency limit of real part of dielectric function “ε1(0)” as function of concentration “x” in Zn1 xHgxE alloys.
values of ε1 ðωÞ, the material possesses a metallic nature and hence maximum reflection. 4. Conclusions The structural, electronic and optical properties of Zn1 xHgxE (E ¼S, Se, Te) (x ¼0, 0.25, 0.50, 0.75, 1) were studied using the full potential linearized augmented plane wave method. The calculated equilibrium lattice constants and bulk moduli were in good agreement with earlier experimental and theoretical data. We have found
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that the variation of the bulk modulus and the band gap depends non-linearly on the mercury composition, while the variation of the lattice constant obeys Vegard's law. The electronic band structure calculations demonstrate that the incorporation of Hg in ZnS, ZnSe and ZnTe decreases the band gap. The fundamental absorption edge is due to the interband transition from the occupied E-p state in the valence band to the unoccupied Hg, Zn-s and E-p states in the conduction band at the Γ-point. This study provides wide band gap to semi-metallic material candidates covering the entire spectral range from IR to near UV. Acknowledgments The author (G.M.) acknowledges the Higher Education Commission of Pakistan for providing the funding for computational lab upgradation of Physics Department, Islamia College, Peshawar. Authors (K.R., and S.B.O.) acknowledge the financial support provided by the Deanship of Scientific Research at King Saud University for funding the work through the research group project no. RPG-VPP-088. References [1] Z. He, C. Zhong, S. Su, M. Xu, H. Wu, Y. Cao, Nat. Photon. 6 (2012) 591–595. [2] K.M. Wong, S.M. Alay-e-Abbas, A. Shaukat, Y. Fang, Y. Lei, J. Appl. Phys. 113 (2013) 014304–11 [3] E.J.W. Crossland, N. Noel, V. Sivaram, T. Leijtens, J.A. AlexanderWebber, H.J. Snaith, Nature 495 (2012) 215–219. [4] C.N.V. Huong, R. Triboulet, P. Lemasson, J. Cryst. Growth 101 (1990) 311–317. [5] T. Vasyl, Quaternary Alloys Based on II–VI Semiconductors, second edition, CRC Press, 2014. [6] K.M. Wong, S.M. Alay-e-Abbas, Y. Fang, A. Shaukat, Y. Lei, J. Appl. Phys. 114 (2013) 034901–10 [7] K. Hara, H. Machimura, M. Usui, H. Munekata, H. Kukimoto, J. Yoshino, Appl. Phys. Lett. 66 (1995) 3337–3339. [8] K. Hara, K. Yamamoto, Y. Eguchi, M. Usui, H. Munekata, H. Kukimoto, J. Cryst. Growth 159 (1996) 45–49. [9] T. Mahalingam, A. Kathalingam, S. Velumani, S. Lee, K.S. Lew, Y.D. Kim, Semicond. Sci. Technol. 20 (2005) 749–754. [10] C. Jain, J.R. Willis, R. Bullogh, Adv. Phys. 39 (1990) 127–190. [11] T. Mahalingam, A. Kathalingam, S. Velumani, S. Lee, H. Moon, Y. Deak Kim, J. New Mater. Electrochem. Syst. 10 (2007) 33–37. [12] V.G. Deibuk, S.G. Dremlyuzhenko, S.É. Ostapov, Semiconductors 39 (2005) 1111–1116.
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Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
First principles study of structural, optical, and electronic properties of zinc mercury chalcogenides G. Murtaza a,n, Naeem Ullah b, Abdur Rauf c, R. Khenata d, S. Bin Omran e, M. Sajjad c, A. Waheed a a
Materials Modeling Lab, Department of Physics, Islamia College University, Peshawar, Pakistan Department of Physics, G.D.C. Darra Adam Khel, F.R. Kohat, KPK, Pakistan Department of Physics, Kohat University, KPK, Pakistan d LPQ3M Laboratory, Faculty of Science and Technology, University of Mascara, Algeria e Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia b c
a r t i c l e in f o
Keywords: First principle calculations Optical properties Electronic structure
abstract First-principles calculations using the full potential linearized augmented plane wave method within the framework of density functional theory are performed to investigate the compositional dependence of the structural, electronic and optical properties of Zn1 xHgxE (E ¼ S, Se, Te). It is observed that except the lattice constant, the variation of the bulk modulus and the band gap versus mercury composition does not obey Vegard's law. The alloys at all concentrations have direct band gap ðΓ ΓÞ which decreases with increasing the concentration of Hg. Optical properties like complex dielectric function and reflectivity are discussed comprehensively. The properties of these materials such as the direct band gap and high absorption in the infrared to ultraviolet regions demonstrate the significant optical activity of these materials. & 2014 Elsevier Ltd. All rights reserved.
1. Introduction The increasing needs of technology enhanced semiconductor processing for optoelectronic devices operating in the visible and far-infrared regions, including lightemitting diodes (LEDs), photo-detectors and solar cells [1–3]. The II–VI semiconductor family contains various wide band gap semiconductors and narrow band gap mercury chalcogenides semiconductors and semimetals exhibiting a large spectrum of properties and making them chief candidates for modern optoelectronic applications [4,5]. A solid solution of two or more semiconductors forms a semiconductor alloy, which has significant technological
n
Corresponding author. Tel.: þ 92 321 6582416. E-mail addresses: [email protected] (G. Murtaza), [email protected] (R. Khenata). http://dx.doi.org/10.1016/j.mssp.2014.10.048 1369-8001/& 2014 Elsevier Ltd. All rights reserved.
applications, particularly in the fabrication of electronic and optoelectronic devices [6]. Ternary alloy solid solutions of II–VI semiconductors have been studied in numerous investigations [7–13]. The gas-source molecular beam epitaxy technique has been used by Hara et al. [7] to control the light emission in the visible range while increasing the Hg contents in Zn1 x HgxSe. Ternary Zn1 xHgxSe and quaternary Zn1 xHgxSySe1 y alloy layers have been grown on GaAs substrates using molecular beam epitaxy (MBE) and characterized using optical techniques [8]. Electrodepositing studies on Zn1 xHgxSe and Zn1 xHgxTe have been performed to explore their structural, electronic and optical properties [9,10]. Mahalingam et al. [11] prepared thin alloy films of Cd1–xHgxTe, MnxHg1–xTe, and ZnxHg1–xTe and studied the effect of biaxial stresses in these compounds. Deibuk et al. [12] further used experimental data and mathematical models to study the band gap and optical properties of quaternary
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CdxHg1 x yZnyTe alloy epitaxial layers. A complete solid solution was obtained throughout the entire range for the ZnHgS system [13]. Because of the importance of zinc and mercury chalcogenides in the modern optoelectronic devices industry, the present work intended to explore the structural, electronic and optical properties of Zn1 xHgxE (E¼ S, Se, Te) in the zinc blende (B3) structure. The modified Becke–Johnson (mBJ) [14] potential approximation was used to overcome the anomaly between the experimental and theoretical when common LDA and GGA approximations [15] are used. The adaptation of mBJ improves the band gap value and the optical spectra that are found in variety of investigations [15,16–18] and the references therein. The mBJ predicts better energy band gaps because it is able to accurately reproduce the exchange potential. It is used for the highly correlated systems with f and d orbitals. The calculations were performed in the framework of density functional theory (DFT) to treat the electronic band gap, contribution from the different energy levels, optical dielectric constants and refractive indices as a function of composition and energy. Section 2 covers the computational details, Section 3 is devoted to the results and their discussion and in Section 4, the main conclusions are summarized.
2. Computational details In this work, the calculations were performed employing the full-potential linearized augmented plane wave (FP-LAPW) method as implemented in the Wien2K code [19]. The exchange and correlation effects were treated using the mBJ approximation [14]. Inside the nonoverlapping spherical region of the Muffin–Tin radius (RMT) around each atom, a linear combination of the radial solution of the Schrödinger wave equation times the spherical harmonics is used, and in interstitial region, a plane wave basis set was used. The wave function expansion inside the sphere was confined to lmax ¼10, while for the expansion of the wave function in the interstitial region, the plane wave cut-off Kmax ¼8/RMT was used. Here, Kmax provides the magnitude of the largest K vector in the plane wave expansion. The integrals over the Brillouin
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zone are performed up to 1000 k-points in the full Brillouin zone. 3. Results and discussions 3.1. Structural properties The structural properties of the binary compounds (ZnS, ZnSe, ZnTe, HgS, HgSe and HgTe) were examined in the zinc blende structure using the generalized gradient approximation of Wu and Cohen (WC-GGA) [20]. Ternary Table 2 Present calculated equilibrium lattice constant and bulk modulus for Zn1 xHgxE along with experimental data and other calculations. x
B0 (GPa)
a0 (Å) Present Exp.
Others
Present Exp.
Others
Zn1 xHgxS 0 5.38 0.25 5.545 0.50 5.67 0.75 5.79 1 5.90
5.41a 5.30b, 5.34c 81.10 71.37 68.56 65.68 5.85a 5.97d 60.67
76.90a 77.30d
Zn1 xHgxSe 0 5.65 0.25 5.80 0.50 5.94 0.75 6.05 1 6.14
5.67a 5.59a, 5.69c 75.68 62.12 57.41 58.09 a b c 6.07 6.19 , 6.10 56.36
62.50a 83.8d
Zn1 xHgxTe 0 6.10 0.25 6.22 0.50 6.33 0.75 6.43 1 6.55
6.09a 6.02b, 6.04c 56.11 52.55 46.25 46.74 a b 6.46 5.53 43.80
68.60a 55.30d
57.50a 41.80d 50.09a 49.20d, 52.1b
47.60a
47.10d, 46.10b
a
Ref. [27]. Ref. [28]. Ref. [29]. d Ref. [30]. b c
Table 1 Atomic positions for Zn1 xHgxTe alloys. x
Atom Positions
0.25 Zn Hg Te
(0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0) (0, 0, 0) (0.25, 0.75, 0.75), (0.75, 0.25, 0.75), (0.75, 0.75, 0.25), (0.25, 0.25, 0.25)
0.50 Zn Hg Te
(0, 0, 0), (0.5, 0.5, 0) (0.5, 0, 0.5), (0, 0.5, 0.5) (0.25, 0.25, 0.25), (0.75, 0.75, 0.25), (0.75, 0.25, 0.75), (0.25, 0.75, 0.75)
0.75 Zn Hg Te
(0, 0, 0) (0.5, 0.5, 0), (0, 0.5, 0.5), (0.5, 0, 0.5) (0.25, 0.25, 0.25), (0.75, 0.75, 0.25), (0.75, 0.25, 0.75), (0.25, 0.75, 0.75)
Fig. 1. Composition dependence of calculated lattice constant and bulk moduli of Zn1 xHgxE alloys.
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alloys were patterned at selected compositions (x ¼0.25, 0.50, 0.75) using the construction of eight atoms supercell, used by Agrawal et al. [21]. Many researchers have used this method to investigate various properties of alloys [22–24]. As a prototype, the atomic positions of Zn1 xHgxTe are given in Table 1. To determine the equilibrium lattice constants and bulk moduli, the unit cell energy was fitted against the unit cell volume by the Murnaghan equation [25]. The calculated equilibrium lattice constant and bulk moduli along with previous experimental data and theoretical calculations are summarized in Table 2. Our calculated results for binary compounds are in close agreement with the experimental data. The lattice constant and bulk moduli are traced out as a function of the dopant atom concentration “x” in Fig. 1. The calculated lattice constant varies almost linearly with increase in the concentration “x” with bowing parameters equal to 0.13 Å, 0.21 Å and 0.11 Å.
For the bulk modulus, a large deviation from Vegard's law [26] was observed with bowing of 10.68, 33.2 and 9.17 GPa for Zn1 xHgxE. 3.2. Electronic properties Calculations of the band structure of the binary compounds and ternary alloys were performed at the optimized lattice constant within the mBJ-approximation, as depicted in Fig. 2 (Zn1 xHgxTe (x ¼0, 0.25, 0.50, 0.75, 1) as a prototype). It is obvious from the figure that the valence band maximum (VBM) and conduction band minimum (CBM) lie at the Γ-symmetry point, resulting in the direct ðΓ ΓÞ band gap for all these materials (x ¼0, 0.25, 0.50, 0.75, 1). The band gap decreases with an increase in the concentration “x” of Hg in Zn1 xHgxTe. The present calculated band gaps along with their available experimental
Fig. 2. Band structure for Zn1 xHgxTe (x¼ 0, 0.25, 0.50, 0.75, 1).
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and theoretical data are also listed in Table 3. The predicted band gaps for the binary compounds ZnS, ZnSe, ZnTe and HgTe are in close agreement with the experimentally measured data and offer an improvement over the previous theoretical investigations, while the band gaps for HgS and HgSe are slightly overestimated compared with previous experimental and theoretical calculations. For the ternary alloys, theoretical data are only available for Zn1 xHgxTe, while there is a lack of data for Zn1 xHgxS and Zn1 xHgxSe alloys. In addition, we traced the variations in the band gap as a function of the composition “x” as illustrated in Fig. 3. The variation of the experimental band gap versus mercury composition up to 0.44 taken from Mahalingam and co-workers [9] is also displayed in Fig. 3. From the figure, it is apparent that the band gap decreases and varies non-linearly as a function of the composition “x”, where 1.04, 0.86 and 1.95 eV bowing is observed for Zn1 xHgxS, Zn1 xHgxSe and Zn1 xHgxTe, respectively. The density of states (DOS) was calculated to explore the contributions of different electronic states to the valence and conduction bands. Fig. 4 shows the DOS for Zn1 xHgxTe as an example because the electronic state contributions for the other two alloys are similar. For both the binary compounds ZnTe and HgTe, the Te-4p state dominates the upper conduction band with a small contribution from cation-s near the Fermi level. A band with high DOS with cation-d character can be observed at approximately 6.3–7.2 eV and 6.3–8 eV in ZnSe and HgSe, respectively. The lower valence band centered on 4.7 eV in Table 3 Band gap energy of Zn1 xHgxE alloys (values are in eV). x
Band gap (eV) Present
Zn1 xHgxS 0 3.86 0.25 2.90 0.50 1.92 0.75 1.33 1 0.62 Zn1 xHgxSe 0 2.81 0.25 1.96 0.50 1.22 0.75 0.64 1 0.10 Zn1 xHgxTe 0 2.36 0.25 1.05 0.50 0.65 0.75 0.34 1 0.16 a
Ref. [30]. Ref. [28]. c Ref. [31]. d Ref. [32]. e Ref. [33]. f Ref. [34]. g Ref. [27]. h Ref. [36]. i Ref. [12]. b
Exp.
Others
3.82f, 3.84g
2.15a, 2.0b, 2.37c, 3.99d
0.50f, 0.11e
0.69a, 0.28d, 0.62h
2.87f, 2.82g
1.39a, 1.6b, 1.45c, 2.68d
0.10f, 0.20g
1.2a, 0.4d, 0.07h
2.39f,g
1.32a, 1.02b, 1.33c, 2.27d, 2.28i 1.30i 0.70i 0.38i 0.84a, 0.45d, 0.20h, 0.16i
0.30f,g
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Fig. 3. Variations in the band gap energy as a function of concentration “x”.
ZnSe and 5 eV in HgSe has a mixed chalcogen-p and cation-s character. For the alloys (x ¼0.25, 0.50, 0.75), the upper valence band is still dominated by the chalcogen-p state with a small contribution from the Hg-d state. The lower cation-d band consists of both Hg-d and Zn-d electronic states. The lower conduction band has a mixed character of chalcogen-p and cation-s empty states. The results for the existence of Zn-d state in the energy range 6.3–7.2 eV are in agreement to photoemission experimental results [35]. 3.3. Optical properties Understanding the optical nature of materials over a spectral range provides insight into their usage in the fabrication of optoelectronic devices. The electronic properties indicate that these materials are direct band gap semiconductors and hence are optically active. This finding motivated us to calculate the important optical properties such as the real, ε1 ðωÞ, and the imaginary, ε2 ðωÞ, parts of the complex dielectric function, εðωÞ ¼ ε1 ðωÞ þ iε2 ðωÞ, using the approach of Ehrenreich and Cohen [37]. The calculated optical spectra for Zn1 xHgxS, Zn1 xHgxSe and Zn1 xHgxTe are presented in Fig. 5 (the real part in left panel and the imaginary part in right panel). The calculated spectra of ε1 ðωÞ revealed that the zero frequency limit ε1(0) increases with an increase in the concentration of Hg-atoms in all three alloys, while the band structure calculation revealed a decrease in the band gap with increasing concentration. This inverse relationship between the band gap and optical dielectric constants is a general behavior observed in semiconductor alloys [38] and is also consistent with the Penn model [39]. The zero frequency dielectric constant ε1(0) results are listed in Table 4. The static dielectric constants for ZnS, ZnSe and ZnTe are 4.7, 5.23 and 7.13, respectively, which are closer to the experimental measurements (5.2, 5.9 and 7.30, respectively) [40] compared with other calculations [41]. The calculated values of ε1(0) were 6.9, 11.24 and 14.05 for binary HgS, HgSe and HgTe, respectively, which were lower than the values obtained in other theoretical calculations [42]. The dielectric constant for HgSe was also underestimated compared with experimental measurements (15.7) [43]. Similarly, the calculated zero frequency refractive indicesnð0Þ are given in Table 4. The value of this index increases with an increase in the concentration “x”. A comparison of the nð0Þ values for binary ZnS, ZnSe and ZnTe reveals a close agreement with the experimental
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Fig. 4. Density of states for Zn1 xHgxTe (x ¼0, 0.25, 0.50, 0.75, 1). Fermi level is set at 0 eV.
measurements. For ZnS and ZnSe, the calculated values 2.17 and 2.34 are consistent with the measured values of 2.15 (at 12.4 μm) [44] and 2.32 (at 18 μm) [45], respectively. For ZnTe, our calculated value was 2.67, while the experimental measurement was 2.49 (at 18 μm) [46]. The left panel in Fig. 5 depicts the imaginary part of the complex dielectric function. The imaginary part ε2 ðωÞ shows the absorption or loss of energy by electromagnetic radiations within the medium and is directly related to the band structure. The first critical points in the spectra of ZnS, ZnSe and ZnTe occur at 3.43, 2.57 and 2.10 eV, respectively, in close agreement with experimental measurements [47,48] and offer an improvement over other theoretical calculations [41]. These points show the direct optical transition from the occupied chalcogen-p state in the valence band to the unoccupied Hg, ZnS and chalcogen-p states in the conduction band at the Γ-point and are called the fundamental absorption edge. The peaks in the spectra are attributed to various electronic transitions from the occupied states in the valence band to the unoccupied states in the conduction band. With an
increase in the concentration “x”, the peaks in the spectra shift toward lower energies in accordance with the decrease in the band gap. The shift in absorption peaks toward lower energies results in a variety of proficient materials for optoelectronic devices in the infrared and visible energy ranges. The shift of absorption edge and prominent peaks are also observed experimentally [8,9] in these materials. The present calculated frequency dependent reflectivity R(ω) spectra of these materials are presented in Fig. 5 (right panel), while the zero frequency reflectivity R(0) calculated data are listed in Table 4, as shown in Fig. 6. The R(0) values increase with increase in the concentration “x” for these materials. The present zero frequency reflectivity for ZnS is 13.2%, which is in close agreement with the experimental measurement (13.5%) [44] at 12.4 μm wavelength. For ZnSe, the calculated R(0) is approximately 15.8%, which is in agreement with the experimental value (16.8%) at 18 μm by Connolly et al. [45]. The 19.7% R(0) value for ZnTe is close to the measured value of 21% at 18 μm [46]. The maximum reflectivity occurs in the energy
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Fig. 5. Spectra of real part of dielectric function (left panel), imaginary part of dielectric function (mid panel) and reflectivity (right panel) for Zn1 xHgxE alloys. Table 4 Zero frequency limit of dielectric constant ε1(0), reflectivity R(0) and refractive index n(0). x
ε1(0)
R(0) (%)
n(0)
Zn1 xHgxS 0 0.25 0.50 0.75 1
4.72 5.05 5.92 6.03 6.90
13.4 13.7 14.9 17.0 20.0
2.17 2.24 2.43 2.45 2.62
Zn1 xHgxSe 0 0.25 0.50 0.75 1
5.51 6.87 7.15 7.79 11.24
15.8 17.1 20.0 22.2 28.3
2.34 2.62 2.67 2.79 3.27
Zn1 xHgxTe 0 0.25 0.50 0.75 1
7.13 8.98 9.47 10.15 14.05
19.7 24.0 26.0 27.5 37.4
2.67 2.99 3.07 3.18 3.74
ranges where the spectra of ε1 ðωÞ is below zero. The maximum reflectivity peaks shift toward lower energies for these alloys due to the band gap decrease. For negative
Fig. 6. Variation in zero frequency limit of real part of dielectric function “ε1(0)” as function of concentration “x” in Zn1 xHgxE alloys.
values of ε1 ðωÞ, the material possesses a metallic nature and hence maximum reflection. 4. Conclusions The structural, electronic and optical properties of Zn1 xHgxE (E ¼S, Se, Te) (x ¼0, 0.25, 0.50, 0.75, 1) were studied using the full potential linearized augmented plane wave method. The calculated equilibrium lattice constants and bulk moduli were in good agreement with earlier experimental and theoretical data. We have found
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that the variation of the bulk modulus and the band gap depends non-linearly on the mercury composition, while the variation of the lattice constant obeys Vegard's law. The electronic band structure calculations demonstrate that the incorporation of Hg in ZnS, ZnSe and ZnTe decreases the band gap. The fundamental absorption edge is due to the interband transition from the occupied E-p state in the valence band to the unoccupied Hg, Zn-s and E-p states in the conduction band at the Γ-point. This study provides wide band gap to semi-metallic material candidates covering the entire spectral range from IR to near UV. Acknowledgments The author (G.M.) acknowledges the Higher Education Commission of Pakistan for providing the funding for computational lab upgradation of Physics Department, Islamia College, Peshawar. Authors (K.R., and S.B.O.) acknowledge the financial support provided by the Deanship of Scientific Research at King Saud University for funding the work through the research group project no. RPG-VPP-088. References [1] Z. He, C. Zhong, S. Su, M. Xu, H. Wu, Y. Cao, Nat. Photon. 6 (2012) 591–595. [2] K.M. Wong, S.M. Alay-e-Abbas, A. Shaukat, Y. Fang, Y. Lei, J. Appl. Phys. 113 (2013) 014304–11 [3] E.J.W. Crossland, N. Noel, V. Sivaram, T. Leijtens, J.A. AlexanderWebber, H.J. Snaith, Nature 495 (2012) 215–219. [4] C.N.V. Huong, R. Triboulet, P. Lemasson, J. Cryst. Growth 101 (1990) 311–317. [5] T. Vasyl, Quaternary Alloys Based on II–VI Semiconductors, second edition, CRC Press, 2014. [6] K.M. Wong, S.M. Alay-e-Abbas, Y. Fang, A. Shaukat, Y. Lei, J. Appl. Phys. 114 (2013) 034901–10 [7] K. Hara, H. Machimura, M. Usui, H. Munekata, H. Kukimoto, J. Yoshino, Appl. Phys. Lett. 66 (1995) 3337–3339. [8] K. Hara, K. Yamamoto, Y. Eguchi, M. Usui, H. Munekata, H. Kukimoto, J. Cryst. Growth 159 (1996) 45–49. [9] T. Mahalingam, A. Kathalingam, S. Velumani, S. Lee, K.S. Lew, Y.D. Kim, Semicond. Sci. Technol. 20 (2005) 749–754. [10] C. Jain, J.R. Willis, R. Bullogh, Adv. Phys. 39 (1990) 127–190. [11] T. Mahalingam, A. Kathalingam, S. Velumani, S. Lee, H. Moon, Y. Deak Kim, J. New Mater. Electrochem. Syst. 10 (2007) 33–37. [12] V.G. Deibuk, S.G. Dremlyuzhenko, S.É. Ostapov, Semiconductors 39 (2005) 1111–1116.
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