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Electronic, Structural, and Optical Properties of Zinc Blende and Wurtzite Cadmium Sulfide (Cds) Using Density Functional Theory

Electronic, Structural, and Optical Properties of Zinc Blende and Wurtzite Cadmium Sulfide (Cds) Using Density Functional Theory

Hindawi Advances in Condensed Matter Physics Volume 2020, Article ID 4693654, 8 pages https://doi.org/10.1155/2020/4693654

Research Article Electronic, Structural, and Optical Properties of Blende and (CdS) Using Density Functional Theory

Teshome Gerbaba Edossa 1 and Menberu Mengasha Woldemariam 2

1Department of Physics, Wollega University, P. O. Box 395, Nekemte, Ethiopia 2Department of Physics, Jimma University, P. O. Box 378, Jimma, Ethiopia

Correspondence should be addressed to Teshome Gerbaba Edossa; [email protected] and Menberu Mengasha Woldemariam; [email protected]

Received 28 May 2020; Revised 26 June 2020; Accepted 29 June 2020; Published 20 August 2020

Academic Editor: Charles Rosenblatt

Copyright © 2020 Teshome Gerbaba Edossa and Menberu Mengasha Woldemariam. )is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Zinc blende (zb) and wurtzite (wz) structure of cadmium sulfide (CdS) are analyzed using density functional theory within local density approximation (LDA), generalized gradient approximation (GGA), Hubbard correction (GGA + U), and hybrid functional approximation (PBE0 or HSE06). To assure the accuracy of calculation, the convergence test of total energy with respect to energy cutoff and k-point sampling is performed. )e relaxed atomic position for the CdS in zb and wz structure is obtained by using total energy and force minimization method following the Hellmann–Feynman approach. )e structural optimization and electronic band structure properties of CdS are investigated. Analysis of the results shows that LDA and GGA underestimate the bandgap due to their poor approximation of exchange-correlation functional. However, the Hubbard correction to GGA and the hybrid functional approximation give a good bandgap value which is comparable to the experimental result. Moreover, the optical properties such as real and imaginary parts of the dielectric function, the absorption coefficient, and the energy loss function of CdS are determined.

1. Introduction values of 3.0 GPa and 4.3 GPa [4–6]. )e rock salt structure is only observed under high pressure [6, 7]. is a chemical compound consisting of at least Cadmium CdX (X � S, Se, and Te) and one anion and one more electropositive element. their combinations are widely studied members of group Hence, the term chalcogenide is more commonly reserved II–VI family [8, 9]. )in films of cadmium for sulfides, selenides, and tellurides rather than oxides [1]. chalcogenides have received intensive attention due to their Cadmium chalcogenides are monochalcogenides having the application in solar cells, photoelectrochemical cells, IR formula CdX (X = S, Se, and Te). )ey typically crystallize in detectors, lux meters, switching devices, and Schottky one of the three motifs, zinc blende (zb) (face-centered barriers [10, 11]. )e experimental bandgap of wz-CdS thin cubic), wurtzite (wz) (hexagonal), and rock salt (cubic) film is 2.42 eV using a chemical bath technique [12]. Pho- structures [2]. )e experimentally stable crystal phase of CdS toluminescence measurements of zb-CdS lead to a bandgap is a wurtzite structure [3]. Furthermore, the CdS can of 2.4 eV [13]. )e spectroscopic ellipsometry study of zb- crystallize in either zinc blende (zb) with CdS gives a bandgap of 2.4 eV [14]. However, the bandgap space group F-43m or wurtzite (wz) crystal structure with calculated using DFT is 1.05 eV [15], 1.2 eV [16], and 1.22 eV P63mc space group under ambient conditions [4]. Moreover, [17] which is underestimated compared with the experi- in a recent experimental measurement report, CdS phase mental value. )e challenging issue with semilocal func- transition occurs from zb to wz phase between pressure tional such as LDA and GGA is that they consist of spurious 2 Advances in Condensed Matter Physics electron self-interaction energy [18]. )is interaction results 3. Result and Discussion with considerable errors in reaction energies for which electrons are transferred between significantly different 3.1. Electronic Structure of CdS in zb and wz Phases. environments such as a metal and a transition metal oxide. Crystal structure is the most important aspect to understand One popular approach that used to overcome this problem is many properties of materials. CdS is group IIB–VI semi- to use a so-called Hubbard U parameter that will cancel part conductor which exists in zb and wz phases [4]. )e wz of the self-interaction energy orbitals on the most prob- crystal structure is a member of the hexagonal crystal system, lematic orbitals such as localized −d or −f orbitals which consists of two interpenetrating hexagonal close- [10, 19, 20]. Moreover, hybrid density functional which packed (HCP) sublattices, one of atom A and the other of incorporates a certain amount of Hartree–Fock (HF) ex- atom B, displaced from each other by 3/8 c along the c-axis. change has further improved upon PBE results [21]. )is )e zb phase of CdS consists of two interpenetrating face- improvement apparently comes in the inclusion of non- centered cubic (FCC) sublattices, one of atom A and the dynamical correlation which effectively delocalizes the PBE other of atom B, located from each other along the body exchange hole. Successful hybrid calculations of solids are diagonal by a/4, where a is the lattice constant. possible using Gaussian-type orbitals and periodic boundary )e equilibrium lattice constants of CdS for both phases conditions. To obtain an appropriate bandgap of CdS, were calculated using plane-wave self-consistent field DFT + U approach and the exchange-correlation functional (PWSCF). )e calculated values of lattice parameters using with hybrid functions are natural choices for open shell LDA and PBE methods are shown in Table 1 and compared d-block metals. )e optical bandgaps of these materials lie with the previous theoretical and experimental results. It close to the range of optimum theoretically achievable en- shows that our calculations in accordance with LDA and PBE ergy conversion efficiency [22]. In this study, we carefully are in good agreement with the previous theoretical and examined the structural, electronic, and optical properties of experimental results. LDA underestimates the lattice constant CdS in zinc blende and wurtzite structures using density by 1% whereas PBE overestimates it. Moreover, the graph of functional theory. lattice constant versus total energy is displayed in Figure 1.

2. Computational Method 3.2. Band Structure and Total Density of States of CdS. )e electronic band structures are calculated along the high )e computations are carried out using Quantum symmetry direction of the Brillouin zone using LDA, PBE, ESPRESSO (QE) package that is based on DFT and plane- PBE + U, and hybrid functions (PBE0). )e band structures wave pseudopotential method [23, 24]. In Kohn–Sham for all potential approximations are demonstrated in Figure equations, the exchange-correlation potential is unknown 2. From the calculations, the obtained bandgap values in eV and a challenging term in DFT. To approximate this po- with respect to LDA, PBE, PBE+U, and PBE0 are given in tential, LDA [25], PBE [26], GGA + U [27], and hybrid Table 2 and comparision is made with existing theoretical (PBE0) [28] functionals are adopted. While approximating and experimental results. this potential, the core electrons which do not participate in From Table 2 and Figures 2(a) and 2(b), one can observe the chemical bonding of the system are frozen and only that DFT method based on the exchange-correlation func- valence electrons are considered. )e electron configuration 10 2 2 4 tional of LDA and GGA provides underestimated value of of cadmium is [Kr] 4d 5s and that of is [Ne] 3s 3p . the energy bandgap (∼0.741–1.04 eV) compared to the ex- In order to treat the strong electron-electron correlation perimental energy bandgap. However, the energy bandgap among the d-electrons of cadmium, introducing the Hub- values obtained with respect to LDA + U and hybrid func- bard correction U term improves the approximation. For tional (PBE0) is in good agreement with the experimental convergence tests, the electronic wave functions are ex- value for zb and wz phases. panded in a plane-wave basis set with trial cutoff energy. )e )e density of states for both phases was calculated within k-point sampling of the Brillouin zone was constructed using LDA, PBE, and DFT + U as shown in Figures 3(a) and 3(b). Monkhorst and Pack mesh scheme [29]. Convergence test of Density of states (DOS) helps to understand the behavior of state total energy with respect to energy cutoff and k-point occupancy over specific energy interval. It provides detail of the sampling is performed to ensure the accuracy of the cal- states which are unoccupied and the states which are occupied. culations until the change in energy is equal to 0.01 eV. It is A high DOS at a specific energy level describes the states × × × × observed that 5 5 5 and 6 6 6 k-point samplings for available for occupation. However, there is no state occupied at Brillouin zone integration yield accurately converged total DOS equal to zero. For both phases, the density of states is energy of zb-CdS for DFT + U and LDA, PBE, and PBE0, discontinuous for the width from the top of the valence band to respectively. )e obtained value of cutoff energy for total the bottom of the conduction band which is normally the energy convergence of zb-CdS is 60 Ry with respect to LDA, bandgap of the system. PBE, PBE0, and DFT + U approximations. In case of wz- CdS, the total energy converged at 6 × 6 × 6 k-point sampling for Brillouin zone integration in relation to LDA and 3.3. Optical Properties of CdS. CdS is a semiconductor which 5 × 5 × 5 in relation to PBE, PBE0, and DFT + U. Moreover, has wide application in recent technology due to its ex- the total energy converged at 55 Ry for LDA and PBE and at ceptional physical properties. It has applications in the field 60 Ry for DFT + U and PBE0, respectively. of photonics, energy device, and light sensing. )e dielectric Advances in Condensed Matter Physics 3

Table 1: Comparison of the calculated and experimental lattice constants. LDA PBE GGA + U PBE0 Phase Present a � 5.819 a � 5.979 a � 5.847 a � 5.983 zb )eory a � 5.81 [9], 5.85 [30], 5.80 [31] Experiment a � 5.82 [32] a � 4.158 a � 4.226 a � 4.37 a � 4.160 Present c � 6.752 c � 6.863 c � 7.10 c � 6.756 a � 4.097 [9], a � 4.160 [30] wz )eory c � 6.752, c � 6.70 a � 4.136 [32] Experiment c � 6.756

–448.16 –448.17 –448.18 –448.19 –448.2

Energy (Ry) –448.21 –448.22 –448.23 –110.76 –110.78 –110.8 –110.82 –110.84 –110.86 Energy (Ry) –110.88 –110.9 10 11 12 13 11 10.5 11.5 12.5 13.5 10.6 10.8 11.2 11.4 11.6 Lattice constant (Bohr) Lattice constant (Bohr)

GGA + U PBE0 GGA LDA (a) –896.32 –896.34 –896.36 –896.38 –896.4

Energy (Ry) –896.42 –896.44 –896.46 –221.64 –221.66 –221.68 –221.7 –221.72

Energy (Ry) –221.74 –221.76 8 8 7.4 7.6 7.8 8.2 8.4 8.6 8.8 7.4 7.6 7.8 8.2 8.4 Lattice constant (Bohr) Lattice constant (Bohr)

GGA + U PBE0 GGA LDA (b)

Figure 1: Lattice constant versus total energy of CdS in zb (a) and wz (b) phases. 4 Advances in Condensed Matter Physics

LDA method PBE method

5 5

0 0.86eV 0 1.15eV

–5 –5 Energy (eV) Energy (eV)

–10 –10

ΓXWKΓLWU L ΓXWKΓLWU L

DFT + U method PBE0 method 8 6 4 5 2 2.45eV 2.48eV 0 0 –2 –4

Energy (eV) –6 Energy (eV) –5 –8 –10 –10 ΓXWKΓLWU L ΓXWKΓLWU L

(a) LDA method PBE method

5 5

0 0.88eV 0 1.17eV

–5 –5 Energy (eV) Energy (eV)

–10 –10

ΓMK ΓLA AH ΓMK ΓLA AH

DFT + U method PBE0 method 6 4 5 2 0 2.41eV 0 2.47eV –2 –4 –5

Energy (eV) –6 Energy (eV) –8 –10 –10 –12 ΓMK ΓLA AH ΓMK ΓLA AH

(b)

Figure 2: Band structure of (a) zb-CdS structure and (b) wz-CdS structure along high symmetry points with respect to LDA, PBE, PBE + U, and PBE0 approximations. constant and extinction coefficient are the optical properties electrostatic charge, and Ω is the unit cell volume. )e of a medium which can be derived from its complex di- superscripts c and v represent the conduction and valence electric function, ε � ε1(ω) + iε2(ω). Direct computation of band wave functions. Using the Kramers–Kronig relation many-body wave function yields the imaginary part of di- [36], the real part of the dielectric function is given by electric function [38]: ∞ 4 ϖε (ω) ( ) � + P � 2 d . ( ) 2 � � � � ε1 ω 1 2 2 ϖ 2 2e π � c � � v �2 k k π ϖ − ω ε2(ω) � � �〈φk�rσ�� φk〉� δ�Ec − Ev − Zω�, (1) 0 Ωε0 k,v,c )e absorption coefficient and the loss function in terms where σ� is the vector defining the polarization of incident of the real and imaginary parts of dielectric function are electric field, ω is the incident photon frequency, e is the given by Advances in Condensed Matter Physics 5

16 35 EF E 14 30 F 12 25 10 20 8 15 6 4 10 DOS cell)) (state/(ev 2 cell)) DOS (states/(eV 5 0 0 –5 0 5 10 15 20 –5 0 5 10 15 20 Energy (eV) Energy (eV) LDA LDA PBE PBE DFT + U DFT + U (a) (b)

Figure 3: Total density of states of (a) zb-CdS and (b) wz-CdS.

Table 2: Comparison of the calculated and experimental bandgap. Methods LDA PBE DFT + U PBE0 Phase Present 1.15 zb 0.86 1.37 [33] 2.45 2.48 Exper. 2.37 [34] )eory 1.24 [35] 2.58 [36] Present 1.17 wz 0.88 1.20 [16] 2.41 2.47 Exper. 2.48 [37] )eory 1.15 [35] 2.55 [35]

√� �������������� 1 the real part of the dielectric function has its maxima, when 2 2 2 β(ω) � 2ω� ε1(ω) + ε2(ω) − ε1(ω)� , the imaginary part of the dielectric function has its minima. (3) From Figure 4(a), one can see that the real part of di- ε (ω) electric function ε (ω) of zb-CdS structure has a maximum L(ω) � 2 . 1 ε (ω)2 + ε (ω)2 peak of 14.52 at a photon energy of 0.44 eV using LDA 1 2 approximation. According to PBE approximation, it has )e frequency-dependent real (ε1(ω)) and imaginary maxima at 10.41 for a photon energy of 0.88 eV. Moreover, (ε2(ω)) parts of the dielectric constant of zb- and wz-CdS the static dielectric constant ε(0) is equal to 12.30 and 7.96 compounds are studied using TD-DFPT with a help of the using LDA and PBE approximations, respectively, for zb- Lanczos chain as demonstrated in Figure 4. CdS crystal. )e peak magnitudes of the imaginary part of Several peaks corresponding to different electronic the dielectric function for zb-CdS is 12.07 at a photon energy transitions were observed in the spectra of real and imag- of 0.66 eV using the LDA method. However, it has a peak inary parts of the dielectric constant. )e real part of the value of 9.76 at a photon energy of 5.94 eV using the PBE dielectric function ε1(ω) describes the strength of dynamical method. screening and the polarization effects. However, the imag- From Figure 4(b), it can be demonstrated that the real inary part of the dielectric function ε2(ω) is related to the part of dielectric function ε1(ω) of wz-CdS structure has energy absorption due to charge excitations. )e optical maxima of 7.61 for a photon energy of 0.22 eV based on LDA properties of the dielectric function of zb- and wz-CdS are approximation. However, it has a peak value of 7.64 at a calculated for energy ranging from 0 to 20 eV. )e peaks photon energy of 0.22 eV with respect to the PBE method. In seen in the optical spectra are described based on transitions addition, our calculation shows that the static dielectric from the occupied to unoccupied bands in the electronic constant ε(0) of wz-CdS is 7.96 in LDA and 7.3160 in PBE energy band structure, particularly at high symmetry points approximation. )e maximum value of the imaginary part of in the Brillouin zone. )e oscillatory trend in this spectrum dielectric function ε2(ω) of wz-CdS is 6.04 at a photon represents the presence of many-body interactions and it is energy of 0.88 eV using the LDA method. However, its value dependent on the strength of transition. )is may be due to is 6.50 at a photon energy of 1.10 eV in accordance with PBE the random orientation of transition dipoles with respect to approximation. )e figures clearly confirm that when the the exciting electromagnetic field direction. For both phases, real part of the dielectric function has its maxima, the 6 Advances in Condensed Matter Physics

16 8

14 6 12

10 4 8 ( ω ) ( ω ) 2 2 6 2 ( ω ), ε ( ω ), ε 1 1 ε ε 4 0 2

0 −2 −2

−4 −4 0 5 10152025 0 5 10152025 ω (eV) ω (eV) ε ⇒ ε ⇒ ε ⇒ ε ⇒ 1 PBE 2 PBE 1 PBE 2 PBE ε ⇒ ε ⇒ ε ⇒ ε ⇒ 1 LDA 2 LDA 1 LDA 2 LDA (a) (b)

Figure 4: Real and imaginary parts of dielectric function for (a) zb-CdS and (b) wz-CdS.

15 5

4 10 3 α ( ω ) α ( ω ) 2 5 1

0 0 50 10 15 20 25 0 5 10152025 ω (eV) ω (eV) LDA LDA PBE PBE (a) (b) 2 5

1.5 0 1 L ( ω ) L ( ω ) 0.5 −5 0

−0.5 −10 0 5 10152025 0 510152025 ω (eV) ω (eV) LDA LDA PBE PBE (c) (d)

Figure 5: Absorption coefficients for (a) zb-CdS and (b) wz-CdS and energy loss spectrum for (c) zb-CdS and (d) wz-CdS. Advances in Condensed Matter Physics 7 imaginary part of the dielectric function has its minima as it part of the dielectric function is related to the transmission of is expected. photons within the material. However, the imaginary part of )e absorption coefficient and the energy loss function the dielectric function describes the absorption coefficient. spectrum for zb- and wz-CdS structure are calculated from )e energy loss function shows the lost energy while the frequency-dependent dielectric function using equation (3). electromagnetic wave traverses inside both phases of CdS. )e energy loss spectrum and absorption coefficient are )e absorption coefficient describes the transition of elec- shown in Figure 5. trons from the valence band to the conduction band from Figures 5(a) and 5(b) show plot for optical absorption of different orbitals. zb- and wz-CdS based on LDA and PBE approximations. Absorption traits shown in Figures 5(a) and 5(b) represent energy-dependent spectra of absorption where a viable in- Data Availability creasing and decreasing trend can be observed. Many peaks )e data used to support the findings of this study are in- correspond to different electronic transitions from the va- cluded within the article. lence band to the conduction band. Moreover, the oscillatory trend in these spectrums represents many-body interactions and is dependent on the strength of transitions. It is caused Conflicts of Interest by the random orientation of the transition dipoles with applied electromagnetic field direction. )e maximum )e authors declare that there are no conflicts of interest values of the absorption coefficient are 10.93 and 11.49 for regarding the publication of this article. zb-CdS with respect to LDA and PBE approximations, re- spectively. However, the maximum values of absorption Acknowledgments coefficients for wz-CdS are 4.54 and 4.84 using LDA and PBE approximations in that order. One of the authors Teshome Gerbaba expresses his thanks Figures 5(c) and 5(d) show the value of energy loss and appreciation to the Department of Physics, Wollega evaluated using equation (3). )e energy loss spectrum is University, for its material support during this study. important for describing the energy loss of fast electrons traversing the zb or wz phase of CdS. )e peaks that oc- References curred in both phases of CdS compound are believed to originate from the resonance of the S 2p valence electrons, [1] D. Keita, T. Yoshihiko, and M. Yoshikazu, “Physics and possibly owing to the plasmon-like collective excitation of Chemistry review of layered Chalcogenide superconductors,” the valence and semicore electrons. All the peaks ofL(ω) Science and Technology of Advanced Materials, vol. 13, no. 5, (Figures 5(c) and 5(d)) correspond to the rapid reduction in pp. 1–11, 2012. [2] S. Z. L. Abdulwahab, Y. Al-Douri, U. 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