<figure><img src="image_1.png" /></figure>

HAL
open science

# Ab Initio Study of Electronic, Structural, Thermal and Mechanical Characterization of Cadmium Chalcogenides

Devi Prasadh P S, B K Sarkar

► To cite this version:

Devi Prasadh P S, B K Sarkar. Ab Initio Study of Electronic, Structural, Thermal and Mechanical Characterization of Cadmium Chalcogenides. Mechanics, Materials Science & Engineering Journal, 2017, 9, 10.2412/mmse.32.38.817. hal-01500551

HAL Id: hal-01500551

https://hal.science/hal-01500551

Submitted on 3 Apr 2017

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Ab Initio Study of Electronic, Structural, Thermal and Mechanical Characterization of Cadmium Chalcogenides

Devi Prasadh P.S.¹,ª, B.K. Sarkar²,ᵇ

1. Department of Physics, Dr. Mahalingam College of Engineering & Technology, Pollachi, Coimbatore, India

2. Department of Physics, Galgotias University, Greater Noida 201308, India

a. psdprasadh@gmail.com

b. bks@physics.org.in

<figure><img src="image_3.png" /></figure>

DOI 10.2412/mmse.32.38.817 provided by [Seo4U.link](https://link.springer.com/10.2412/mmse.32.38.817)

**Keywords:** density functional theory, chalcogenides, FP-LAPW+lo.

**ABSTRACT.** Based on Density Functional Theory, we have applied Full Potential Augmented Plane Wave plus local orbital method (FAPW+lo)to study the electronic, structural, optical, thermal and mechanical properties of some semiconducting materials. In this paper we discuss the Zinc blende, CdX (X = S, Se and Te) compounds with the full-potential linear-augmented plane wave (FP-LAPW) method within the framework of the density functional theory (DFT) for electronic, structural, thermal and mechanical properties using the WIEN2k code. For the purpose of exchange-correlation energy (Exc) determination in Kohn-Sham calculation, the standard local density approximation (LDA) formalism is utilized. Murnaghan's equation of state (EOS) is used for volume optimization by minimizing the total energy with respect to the unit cell volume. The calculated lattice parameters and thermal parameters are in good agreement with other theoretical calculations as well as available experimental data.

**Introduction.** Cadmium Chalcogenides family is one of the II-VI wide band gap compound semiconductors. In that family CdS, CdSe and CdTe are some of the main materials. These materials have various scientific applications, such as solar cells, high efficiency thin film transistors, high density optical memories, light emitting diodes, laser diodes, photovoltaic devices, etc. The recent innovation of the blue-green laser diode based on the CdX compounds has changed consideration in their physical properties. CdX compounds are having different phases or crystal structures (Zinc blende, wurtzite). For our convenience we have preferred the zinc blende phase for all three compounds. Because this structure has fewer atoms in unit cell so it is easier for computational treatment. In fact for CdTe, the zinc blende structure is the standard crystal structure or phase, but for the other two compounds CdS and CdSe have wurzite phase. In the past decades numerous experimental and theoretical investigations were carried out for CdX. Many computational methods based on DFT [1] have been studied. But the calculations carried out by using conventional DFT produce disagreeable electronic properties. There is a big variance between experimentally calculated and theoretical data. The variation in energy gap is completely based on the method to calculate the band structure. Some theoretical reports are in good agreement with the measured one. They were calculated based on Local Density Approximation (LDA). The modern *ab-inito* calculation solves the discrepancies. We have used FP-LAPW+lo to calculate the band structure. The band structure of CdX binary compounds have been calculated by using Full Potential Linearized Augmented Plane Wave method Plus local orbits (FP-LAPW+lo) within the Generalized Gradient Approximation (GGA). There are several methods and theoretical reports available to calculate the band structure and optical properties but some controversies are at there. But the FP-LAPW+lo gives the closer values with the experimental data. In this paper we have presented the structural, elastic, electronic and thermal properties of CdX binary compounds. FP-LAPW+lo is the method used to
investigate the properties and the values are compared with the experimental and other theoretical
works for these compounds. Our values are in good agreement with the earlier reports.

**Computational method:** All the calculations of the structural, thermal and electronic properties were performed in the frame work of Density Funtional Theory (DFT). To calculate these properties, we employed the full potential linearized augmented plane wave plus local orbitals (FP-LAPW+lo) as executed in the WIEN2k code [2-3].We have used the generalized gradient approximation (GGA) as parameterized by Perdew, Burke and Ernzerhof (PBE) to explain the exchange and correlation effects [4].CdX compounds crystallize in the zinc-blende structure with space group F-43 m. The Cd atom is set at (0, 0, 0) whereas the X atom is set at (0.25, 0.25, 0.25). We have employed Murnaghan's equation of state [5] for the optimization of the total energy with respect to the unit cell volume. Thus the equilibrium structural parameters have been calculated. The calculations were done with RMTkmax = 9, to attain energy Eigen value convergence. RMT is the smallest radius of the muffin-tin (MT) spheres and kmax is the maximum value of the wave vector. The corresponding values of muffin-tin radii (RMT) for Cd, S, Se and Te were taken to be 2.37, 1.73, 1.91 and 2.35 a.u. (atomic units) for all the calculations. The Gmax parameter was taken to be 14.0 Bohr⁻¹. The wave function has been expanded inside the atomic spheres with the maximum value of the angular momentum lmax as 10. The irreducible Brillouin zone (BZ) of the zinc-blende structure has been decomposed into a matrix of 10×10×10 Monkhorst-Pack k-points [6]. The iteration procedure is continued with total energy and charge convergence to 0.0001Ry and 0.001e, respectively.

**Results & discussions**

**Structural and elastic properties:** To find the elastic constants of CdX compounds with cubic structure we have used the numerical firstprinciple calculation by calculating the compounds of the stress tensor δ for small stains. Proper strains δ (-0.02-0.02) have been arranged to prevent primitive lattice vectors and then appropriately strained states were analysed. It is well known that for a cubic crystal it has only three independent elastic constants C₁₁, C₁₂ and C₄₄ as we have studied the theory in a detailed manner in previous chapter. With the Murnaghan's equation of state [5], the variation of the total energy versus unit cell volume yields to the equilibrium lattice parameter (a₀), bulk modulus B₀, and the pressure derivative of the bulk modulus B₀'. The values of a₀, B₀ and B₀' for the ZB structure of the binary CdX at zero pressure are presented in table 1. For CdS, CdSe and CdTe, the energy minima take place for a₀ = 5.805, 6.305 and 6.350 Å, our results are in good agreement with the experimental values of 5.830, 6.084 and 6.480 Å, respectively with the maximal error of 3.63% with respect to experimental values. It is clear that well defined structural properties are helpful for further study of electronic and thermal properties. The elastic constants of CdX compounds with cubic structure have been determined using the method developed by Charpinincorporated in WIEN2k code[7]. By applying appropriate lattice distortions in a cubic lattice, three independent elastic constants C₁₁, C₁₂, and C₄₄ are determined. Table 1 displays the calculated values of elastic modulus. Our calculated lattice parameters values are in good agreement with experimentally calculated and other theoretical measured values. The bulk modulus B₀ represents the resistance to fracture while the shear modulus G represents the resistance to plastic deformation. Ductility of the material can be characterized by B₀/G ratio. The B₀/G ratio for all CdX are greater than 1.75 (table 1) which tells that the compounds are ductile in nature. The peak value of B₀/G ratio is 5.2334 for CdSetelling it most ductile among all the CdX compounds. There is a correlation between the binding properties and ductility. The bond character of cubic compounds is expressed in terms of their Cauchy pressure (C₁₂–C₄₄). With increase in positive Cauchy pressure, compound is likely to form metallic bond. Hence, the ductile nature of all CdX compounds can be correlated to their positive Cauchy pressure having the metallic character in their bonds. As represented in table 1, the CdS and CdSe have a highest positive Cauchy pressure resulting strong metallic bonding (ductility) in it as compared to other compounds. The calculated value of Young's modulus (Y) is shown in table 1. It provides the degree of stiffness of the solid, i.e., the stiffer material has the larger value of Y and such materials have covalent bonds. The highest value of Y occurs for CdS demonstrating to be more covalent in nature as compared to other CdX compounds. Value of Poisson's ratio (σ), as a measure of
compressibility for CdX compounds are between 0.39 and 0.41 which predict that all the compounds are compressible. Also the Poisson's ratios having values between 0.25 and 0.5 represent central force solids. In our case, the Poisson's ratios are around 0.4, which reveals that the interatomic forces in the CdX compounds are central forces. The structural properties results are compared with other theoretical results [13].

**Calculation of Debye Temperature.** The Debye temperature ($\theta_D$) is considered as a fundamental parameter for many physical properties of solids, such as specific heat, elastic constants and melting temperature. At low temperature, only the acoustic branches of phonons are active and the vibrational excitations take place exclusively from acoustic vibrations. Hence, the estimate of Debye temperature based on elastic constants at low temperature is consistent with the same as that determined from specific heat measurements. Once we have determined the elastic constants, we may obtain the Debye temperature ($\theta_D$) by using the average sound velocity $V_m$. We have calculated the density, sound velocities and Debye's temperature by using the calculated elastic constants which are produced in table 1.

**Electronic Properties.** The electronic band structure of Cd chalcogenides has been calculated. The calculated band structure for CdX at equilibrium is shown in Fig. 1. The band profiles are almost similar for all the three components, with some minute difference.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Shows the Band Structure and Density of States of CdTe.</figcaption></figure>

Each member of CdX demonstrates the existence of the valence band maximum and conduction band minimum at the same symmetry point. This confirms the direct energy gap between the top of the valence band and the bottom of conduction band at Γ point. With the increase of the lattice parameters starting from the sulphide to the telluride, the X atom p bands shift up in energy as a common feature of II–VI compounds [14]. This is the regular performance related to the increase of the lattice parameters, which was also found for other II-VI compounds. Our results for the direct band gaps are represented in table1 with the experimental and other theoretical values. The calculated band gap is underestimated in contrast with experimental results, because of the simple form of GGA which cannot account the quasi particle self-energy. The density of states (DOS) for CdTe is shown in Fig.
1. The first structure in the total DOS is small and centered at around -10.8 eV for CdTe. This structure arises from the chalcogen s states and it corresponds to the lowest lying band with the dispersion in the region around the r point in the Brillouin zone. The next structure appears at -8.6 eV. It is an attribute of Cd d states with some p states of the chalcogen atoms.

<table><caption>Table 1. Calculated lattice constant (in Å), bulk modulus $B_0$ (in GPa), pressure derivative $B'_0$, elastic constants ($C_{ij}$ in GPa), elastic modulus (in GPa), Sound velocities, Debye temperatures and energy gap ($E_g$) in eV for CdX compounds.</caption><thead><tr><th>Properties</th><th>CdS</th><th>CdSe</th><th>CdTe</th></tr></thead><tbody><tr><td>a<sub>0</sub> (Present Study)</td><td>5.805</td><td>6.305</td><td>6.350</td></tr><tr><td>a<sub>0</sub> (Other works)</td><td>5.820<sup>a</sup>, 5.840<sup>b</sup>, 5.948<sup>c</sup>, 5.810<sup>d</sup></td><td>6.050<sup>a</sup>, 6.050<sup>d</sup></td><td>6.480<sup>a</sup>, 6.624<sup>c</sup>, 6.480<sup>d</sup></td></tr><tr><td>B<sub>0</sub> (Present Study)</td><td>64.90</td><td>58.93</td><td>42.70</td></tr><tr><td>B<sub>0</sub> (Other works)</td><td>62.00<sup>a</sup>, 61.69<sup>b</sup>, 53.838<sup>c</sup>, 72.42<sup>d</sup></td><td>53.00<sup>a</sup>, 54.948<sup>c</sup>, 65.12<sup>d</sup></td><td>42.00<sup>a</sup>, 37.44<sup>c</sup>, 48.94<sup>d</sup></td></tr><tr><td>B'<sub>0</sub> (Present Study)</td><td>4.25</td><td>4.13</td><td>4.39</td></tr><tr><td>B'<sub>0</sub> (Other works)</td><td>4.57<sup>a</sup>, 4.72<sup>c</sup>, 4.31<sup>d</sup></td><td>4.67<sup>a</sup>, 1.584<sup>c</sup>, 4.20<sup>d</sup></td><td>3.00<sup>a</sup>, 3.87<sup>c</sup>, 4.47<sup>d</sup></td></tr><tr><td>C<sub>11</sub> (Present Study)</td><td>92.3</td><td>81.2</td><td>59.9</td></tr><tr><td>C<sub>11</sub> (Other works)</td><td>75.2<sup>e</sup>, 104.62<sup>b</sup>, 67.6<sup>f</sup>, 97.8<sup>d</sup></td><td>65.0<sup>e</sup>, 55.4<sup>f</sup>, 88.1<sup>d</sup></td><td>56.5<sup>e</sup>, 53.2<sup>f</sup>, 68.1<sup>d</sup></td></tr><tr><td>C<sub>12</sub> (Present Study)</td><td>51.2</td><td>47.8</td><td>34.1</td></tr><tr><td>C<sub>12</sub> (Other works)</td><td>55.0<sup>e</sup>, 46.25<sup>b</sup>, 46.3<sup>f</sup>, 59.7<sup>d</sup></td><td>49.0<sup>e</sup>, 37.7<sup>f</sup>, 53.6<sup>d</sup></td><td>32.1<sup>e</sup>, 23.2<sup>f</sup>, 39.3<sup>d</sup></td></tr><tr><td>C<sub>44</sub> (Present Study)</td><td>26.3</td><td>22.9</td><td>20.1</td></tr><tr><td>C<sub>44</sub> (Other works)</td><td>39.1<sup>e</sup>, 77.28<sup>b</sup>, 29.5<sup>f</sup>, 30.6<sup>d</sup></td><td>36.8<sup>e</sup>, 18.9<sup>f</sup>, 27.4<sup>d</sup></td><td>31.8<sup>e</sup>, 13.01<sup>f</sup>, 22.1<sup>d</sup></td></tr><tr><td>G (GPa) (Present Study)</td><td>13.48</td><td>11.26</td><td>9.18</td></tr><tr><td>G (GPa)</td><td>21.25<sup>b</sup></td><td></td><td></td></tr><tr><td>B<sub>0</sub>/G (Present Study)</td><td>4.8145</td><td>5.2334</td><td>4.6514</td></tr><tr><td>C<sub>12</sub>-C<sub>44</sub> (GPa) (Present Study)</td><td>24.9</td><td>24.9</td><td>14.0</td></tr><tr><td>Y (GPa) (Present Study)</td><td>55.76</td><td>45.77</td><td>35.15</td></tr><tr><td>Y (GPa) (Other works)</td><td>25.68<sup>b</sup></td><td></td><td></td></tr><tr><td>σ (Present Study)</td><td>0.4029</td><td>0.4102</td><td>0.3997</td></tr><tr><td>σ (Other works)</td><td>0.34<sup>b</sup></td><td></td><td></td></tr><tr><td>A (Present Study)</td><td>1.2798</td><td>1.3713</td><td>1.5581</td></tr><tr><td>ρ(Kg/m<sup>3</sup>)</td><td>4870</td><td>5655</td><td>5860</td></tr><tr><td>V<sub>t</sub>(m/s)</td><td>2219</td><td>1900</td><td>1714</td></tr><tr><td>V<sub>l</sub>(m/s)</td><td>4460</td><td>3903</td><td>3347</td></tr><tr><td>V<sub>m</sub>(m/s)</td><td>2490</td><td>2137</td><td>1920</td></tr><tr><td>θ<sub>D</sub>(K)</td><td>255</td><td>210</td><td>177</td></tr><tr><td>E<sub>g</sub> (eV) (Present Study)</td><td>1.35</td><td>0.77</td><td>0.80</td></tr><tr><td>E<sub>g</sub> (eV) (Other works)</td><td>2.55<sup>a</sup>, 1.45<sup>d</sup>, 2.66<sup>c</sup></td><td>1.90<sup>a</sup>, 1.08<sup>d</sup>, 1.89<sup>c</sup></td><td>2.55<sup>a</sup>, 1.88<sup>d</sup>, 1.56<sup>c</sup></td></tr></tbody></table>

It is found that a wide spread in DOS in the energy range from -4.8 eV to zero energy for CdTe. The peaks in this energy interval arise from the chalcogen p states partially mixed with Cd s states and

<footnote><sup>a</sup>Madelung O<sup>8</sup>, <sup>b</sup>Al Shafaay<sup>9</sup>,<sup>c</sup>HakanGurel<sup>10</sup>,<sup>d</sup>Deligoz<sup>11</sup>,<sup>e</sup> Kitamura<sup>12</sup>,<sup>f</sup> Ouendadji<sup>13</sup></footnote>
they subsidize to the upper valence band. Above the Fermi level, the feature in the DOS create mainly from the s and p states of Zn somewhat mixed with little of chalcogen d states. Band width of valence band as determined from the width of the peaks in DOS dispersion below Fermi level equal to 11.5 eV. The results showing valence band width minimum for CdTe, clearly indicate that the wave function for CdTe is more localized than that for CdS. This is in consistence with the fact that when the atomic number of the anion increases, a material becomes non-polar covalent with valence band states being more localized.

**Summary.** This chapter reports a systematic study of the structural, electronic, elastic and thermal properties of zinc blende Cd-chalcogenides (CdS, CdSe and CdTe) have been studied with FP-LAPW+ lo method in the framework of density functional theory (DFT). The quantities such as elastic constant and band structure were obtained. The generalized gradient approximation (GGA) was considered for the exchange and correlation effects calculations. The results from FP-LAPW + lo method were generally satisfactory with the experimental data in comparison to other calculation methods. The calculated lattice parameters, bulk modulus, Young's modulus and Poisson's ratio of binary compounds CdX are in good agreement with the experimental data. The elastic constants maintain all conditions to be satisfied for mechanical stability of the compound. The profound ductility in CdX compound was observed with the increase in chalcogen atomic number. The metallic character in their bonds is well demonstrated from the positive Cauchy pressure ($C_{12}-C_{44}$) values. The band structure of all Cd-chalcogenides confirms the direct energy gap between the top of the valence band and the bottom of conduction band at Γ point.

## References

[1] P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136, B864-B871 (1964). doi: 10.1103/PhysRev.136.B864

[2] G. K. H. Madsen, P. Blaha, K. Schwarz, E. Sjöstedt, L. Nordström, Efficient linearization of the augmented planewave method. Phys. Rev. B 64, issue 19, 195134 (2001). doi: 10.1103/PhysRevB.64.195134

[3] K. Schwarz, P. Blaha, G.K.H. Madsen, Electronic structure calculations of solids using the WIEN2k package for material science, *Comp. Phys. Commun.*, Vol. 147, Issue 1, pp. 71–76 (2002). doi: 10.1016/S0010-4655(02)00206-0

[4] J. P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996). doi: 10.1103/PhysRevLett.77.3865

[5] F.D. Murnaghan, On the Theory of the Tension of an Elastic Cylinder, *Proc. Natl. Acad. Sci.*, Vol. 30, No. 12, pp. 382–384 (1944), USA. PMID:16588670 PMCID:PMC1078732

[6] H.J. Monkhorst, J. D. Pack, Special points for Brillouin-zone integrations, *Phys. Rev. B.* 13, No. 12, pp. 5188–5192 (1976). doi: 10.1103/PhysRevB.13.5188

[7] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An augmented plane wave plus local orbitals program for calculating crystal properties, (User's Guide), Inst. of Physical and Theoretical Chemistry, Vienna University of Technology, Austria, pp. 1-205, (2001).

[8] O. Madelung, H. Weiss, and M. Schultz, eds. *Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology. Group III: Crystal and Solid State Physics. Vol. 17, Subvolume A: Physics of Group IV Elements and III-V Compounds*. Berlin: Springer (1982).

[9] B. Al Shafaay, Structural, electronic, mechanical and thermodynamic properties of CdS compound, *J. Che., Bio. And Phy. Sci.*, Vol. 4, No. 4; pp. 3606–3618 (2014).

[10] H. HakanGurel, OzdenAkinci, HilmiUnlu, First principles calculations of Cd and Zn chalcogenides with modified Becke–Johnson density potential, *Superlattices and Microstructures*, Vol. 51, Issue 5, pp. 725–732 (2012). doi: 10.1016/j.spmi.2012.02.010
[11] E. Deligoz, K. Colakoglu and Y. Ciftci, "Elastic, Electonic, and Lattice Dynamical Properties of CdS, CdSe, and CdTe," Physica B: Physics of Condensed Matter, Vol. 373 (2006), pp. 124-130. doi:10.1016/j.physb.2005.11.099

[12] M. Kitamura, S. Muramatsu & W. A. Harrison, "Elastic properties of semiconductors studied by extended Hückel theory", Physical Review B, Vol. 46, No. 3, (1992), pp. 1351-1357. doi: 10.1103/PhysRevB.46.1351

[13] S. Ouendadji, S. Ghemid, H. Meradji, F.El Haj Hassan, Theoretical study of structural, electronic, and thermal properties of CdS, CdSe and CdTe compounds, *Comp. Mat. Sci.*, Vol. 50, pp. 1460–1466 (2011). doi: 10.1016/j.commatsci.2010.11.035

[14] M. Dadsetani, A. Pourghazi, Optical properties of strontium monochalcogenides from first principles, *Phys. Rev. B*, Vol. 73, No. 19, pp. 195102, (2006). doi: 10.1103/PhysRevB.73.195102

Cite the paper
Devi Prasadh PS, B.K. Sarkar, (2017). *Ab initio Study of Electronic, Structural, Thermal and Mechanical Characterization of Cadmium Chalcogenides*. Mechanics, Materials Science & Engineering, Vol 9. doi: 10.2412/mmse.32.38.817