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Core-level excitation in polymorph of AS2S3 and β -In2S3
Accepted Manuscript Title: Core-level excitation in polymorph of AS2 S3 and -In2 S3 Authors: Lawal Mohammed., Muhammad A. Saeed, Qinfang Zhang, Auwalu Musa PII: DOI: Reference:
S1877-7503(17)30935-3 https://doi.org/10.1016/j.jocs.2018.07.001 JOCS 896
To appear in: Received date: Revised date: Accepted date:
9-9-2017 9-6-2018 1-7-2018
Please cite this article as: Mohammed. L, Saeed MA, Zhang Q, Musa A, Core-level excitation in polymorph of AS2 S3 and -In2 S3 , Journal of Computational Science (2018), https://doi.org/10.1016/j.jocs.2018.07.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Core-level excitation in polymorph of AS2S3 and -In2S3 Lawal Mohammed.* 1,2,3, Muhammad A. Saeed3, Qinfang Zhang1, Auwalu Musa4 1
School of Material Science and Engineering, Yancheng Institute of Technology, Yancheng 224051, P. R. China 2 Physics Department Ahmadu Bello University, Zaria 833201, Nigeria 3 Physics Department Universiti Teknologi, Johor 81310, Malaysia
Highlights
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Similarities in the shift of the optical band-gap in β-In2S3 and orpiment. Striking comparisons in Arsenic L3 (s, d)-edges peaks for the polymorph of As2S3 crystals. Optical absorption increases due to core-hole for S K (p) and As L3-edges in orpiment. This work provides a better quality crystal for optical evaluation.
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Physics Department Bayero University Kano 3011, Nigeria
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Abstract X-ray absorption near-edge structure (XANES) is one of the most widespread spectroscopies for studying the chemical properties of materials. It is a sensitive probe of the atomic environment, because it can be used to effectively measure the transition probability between core electrons and unoccupied states. In this paper, single level excitonic effects on the core state of the polymorph of As2S3 and tetragonal In2S3 were studied using X-ray absorption spectroscopy. Our results for the first time show striking similarities in Arsenic L3 (s, d)-edges peaks for the two phases of As2S3 orpiment and anorpiment crystals. Optical absorption increases mostly due to core-hole for S K (p) and As L3-edges in orpiment as compared to the other structures. The core-level calculations for these orbitals show good agreement with the experimental ones thus validating the approach used in this study. In orpiment and anorpiment, an indirect energy band gap which has been improved by the mBJ potential to about 1.03 eV and 0.65 eV respectively was observed. We have calculated the imaginary dielectric function and the absorption coefficient with the mBJ potential and core-hole, the optical excitations, is observe to be enhance by core level spectroscopy for all the crystals. Furthermore, the bond length and angles of monoclinic and triclinic As2S3 as well as the betaphase In2S3 compared well with the experimental results. Structural optimization and total energies of all structures are computed using the all electrons full potential linearized augmented plane wave plus local orbitals (FP-LAPW + lo) within the framework of DFT.
1. Introduction
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Keywords: chalcogenide; core hole; X-ray absorption; optical properties; electronic structure *Corresponding author. E-mail address: [email protected]
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Chalcogenide semiconductors have many interesting optical and electronic properties [1-3]. Although these properties for arsenic chalcogenide [4] glasses have been studied extensively as materials for optoelectronic devices [5,34] however, the electronic structure of these materials is obtained from the study of their crystalline phases not amorphous. Anorpiment, As2S3 is a newly discovered mineral that exist in triclinic symmetry [6], it composed of layers of As2S3 macromolecules similar to that of orpiment. There are many striking similarities between the two phases, yet a little is known about the electronic and optical properties of anorpiment. Therefore, it is difficult to compare these properties with that of more stable monoclinic phase As2S3. There are few theoretical studies available on crystalline orpiment As2S3 [7] by employing GGA energy functional to investigate and compare some repulsive forces between As2S3 and As2Se3. Furthermore, electronic structure of monoclinic phase was investigated using multiple scattering approximations for clusters in real space [8]. However, none of these studies provide detail insight on the similarities and differences between the polymorph of As2S3. Therefore, for the first time as per as we know the electronic structure of the triclinic anorpiment is presented. On the other hand, the β-phase Indium sulfide is the only stable crystallized spinel among the existing three phases that shows potential photovoltaic properties, [9-11] 1
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for example, it exhibit luminescence properties in infra-red and optical regions, [10]. It is reported as an absorber material [12,26], and as buffer layer in C-In-Ga-S (CIGS) based thin film solar cells, due to its exceptional photoelectric properties, it has demonstrated impressively high sub-bandgap absorption [13,30]. Additionally, Indium sulfide semiconductors have certain structural defects, β-phase, in particular, has point defects, of sulphur, and indium vacancy, which slightly affects the properties of this compound [9], which is why it has attracted a new interest in the study of defect engineering [14]. The electrical and optical properties of beta phase In2S3 are stable at normal temperature, and it has energy bandgap between 1.98 eV and 2.1 eV, which make it a suitable material for intermediate band solar cells [1517]. Moreover, the β-In2S3 has potential applications in the preparation of green and red phosphors, manufacture of picture tubes for color television, and in infrared optical technology [18]. However, the treatment of the optical properties at the level of inducing external perturbation and the modified TB-mBJ potential for β-In2S3 is not reported as far as we know.
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Moreover, the theoretical information available on the crystalline sulfur-based chalcogenide is inadequate. Hence, there is need for comprehensive study using core level spectroscopy, and modified Becke-Johnson (mBJ) potential, to investigate X-ray absorption and electronic properties of these compounds. The mBJ potential allowed calculation of band gap with accuracy similar to the very expensive GW calculations. Hence, our analysis for the electronic properties and optical properties based on these calculations will provide a good insight on these materials.
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2. Methodology
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We have carried out a detail study of structural, electronic, and optical properties using density functional theory (DFT) [19], within full potential linearized augmented plane wave plus local orbitals (FP-LAPW+lo) as implemented in WIEN2K code [20, 21]. The exchange-correlation potential is treated using the generalized gradient approximation [22], and mBJ potential [23]. In this approach, the unit cell is partition into non-overlapping muffin-tin spheres around the atomic sites as explained somewhere in the literature.
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In this work, tetrahedron method of integration is used in the irreducible Brillouin zone on a grid of 460, 231, and 159 k-point for orpiment, anorpiment, and β-In2S3 respectively, which give the minimum ground state energy, as depicted in Fig. 1(a). In order to achieve energy convergence, the wave functions in the interstitials region are expanded in terms of plane waves with cut-off parameter of RMT*Kmax= 7.5, 7.0, and 8.0 for orpiment, anorpiment and β-phase In2S3 respectively. Where RMT is the smallest atomic sphere radius and Kmax denotes the largest k vector in the plane wave expansion.
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The Muffin-tin radii (RMT) for orpiment are set to 2.15a.u and 1.85a.u for arsenic and sulfur, while for anorpiment RMT=2.21a.u and 1.9a.u, for arsenic and sulfur respectively. In the case of β-phase In2S3, RMT=2.43a.u for indium and RMT=1.99a.u for sulfur. The matrix size and local orbital used are 3,955 and 240 for orpiment, 3,206, and 240 for anorpiment and 6,896 and 408 for β-In2S3 respectively in each case. The calculations were iterated until energy convergence was achieved, the convergence tolerances set at 10 -4Ry for all the crystals. In our calculations, the ground state energy, volume of the unit cell and lattice parameters for three crystal systems are in good agreement with the experimental values as shown in Table 1, indicating that the parameters used in this calculation can give accurate and reliable results. 2
The β-In2S3 crystal information is obtained from the X-ray diffraction experiment data to generate the Crystallographic Information File (CIF) [24], which is used for this study. This information is provided to remove related inconsistency in literature that reported β-In2S3 as monoclinic structure. The calculations of X-ray absorption were performed using the XANES extension of the Wien2k. In order to minimize the unscreened effect on the nucleus, a 2*2*1 supercell are considered for each phases of As2S3, orpiment and anorpiment, whereas, 2*1*1 supercell was used for the β-In2S3.
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The optical properties are studied through the dielectric functions. The optical response is described by a frequency dependent dielectric function [27]. The imaginary part arises from the intraband and interband transitions, which depends on density of states and the momentum matrix. In the limits of linear optics, dielectric tensor contains all the optical properties. The Eqs. (1) and (2) below define the imaginary and real parts of the complex dielectric function (1)
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In the above Eq., 〈 | | 〉and〈 | | 〉are the dipole matrix elements corresponding to j and i directions of the crystal, and correspond to initial and final state respectively, and are the energy in initial and final state respectively. The Kramers-Kronig relation obtains the real part of the elements of the dielectric tensor in Eq. (2) )
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Where P is the principal value of the integral, all other frequency dependent optical constants can be calculated from above components of the dielectric function. For example total absorption coefficient ( )is calculated using Eq. (3) ( )
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In the above Eq, ( )is extinction coefficient and c is the speed of light. In core level spectroscopy, the dynamical form factor that describes the excitation of a system from its initial state to final state is giving by Eq. (4). The two states are approximated to one-particle states that obey the Fermi golden rule.
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( , )=∑ 〈
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Where q is the momentum transfer, and the absorption cross section can be expressed in terms of Fermi golden rule as
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In this case ε are the electric field polarization vector and α is the fine-structure constant. is the frequency of the X-ray, and are energy of the initial and final state respectively. Therefore, X-ray absorption near edge structures spectra (XANES) is correlated with the unoccupied density of states of the excited atom projected on the proper symmetries allowed by the dipole selection rules [28]. 3. Results and Discussion
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3.1. Structural and Electronic Properties
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The crystal structures of arsenic sulfide polymorphs, orpiment, and anorpiment together with β-In2S3 have been optimized to obtain the lowest ground state energies and the corresponding volumes of the unit cells of these structures is shown in Fig. 1(a). This was achieved by using energy versus volume curve fitted to the Birch-Murnaghan Equation of state [25]. The calculated ground state energy and bulk moduli for the As2S3 polymorphs are almost the same, even though they belong to different crystal systems.
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In the present calculation, the mean bond lengths for anorpiment are found to be AsS=2.29Ao, As-As=3.55Ao, S-S=3.40Ao, and the mean angle is calculated as As-SAs=100.96o, S-As-S=94.11o, which is in good comparison with the mean experimental bond length of 2.27Ao, and angles for As-S-As=100.95o, and S-AsS=93.74o [6]. For orpiment, the calculated mean bond distances are As-S=2.26Ao, AsAs=3.58Ao, S-S=3.35Ao, and mean angles are calculated as As-S-As=93.05o, S-AsS=105.97o, which are close to the mean experimental bond length of As-S=2.24Ao [8, 26], and angles for As-S-As=100.95o, and S-As-S=93.74o. The bands structure of polymorphs of As2S3 and β-phase In2S3 calculated by LAPW +lo method using PBEGGA and mBJ potential are shown in Fig. 2. The energy bands along some high symmetry point in the irreducible Brillouin zone are plotted. In Table 1, we have calculated some important parameters and compared with both experimental and theoretical studies. Our calculations shows good agreement with the experiment, which further confirmed the precision of LAPW+lo basis implementation in the WIEN2K code [31].
The 4s, 4p, 3d, electrons of arsenic and 3s, 3p electrons of sulphur are treated as part of valence states for both orpiment and anorpiment crystals. While 4p, 4d, 5s, 5p, electrons of indium and 3s, 3p electrons of sulphur are treated as part of valence states for the β-phase In2S3. The band structure in the conduction region appears from 1.50eV, 2.03eV, and 0.64eV onwards for orpiment, anorpiment and β-phase In2S3 respectively with PBE energy functional. Whereas for the mBJ potential, these 4
energies corresponding to 2.40eV, 2.37eV and 1.57eV respectively, as shown in Fig. (2). Furthermore, the band structure of polymorphs of As2S3 shows an indirect bandgap as given in Table 1. Dispersion of bands in the direction ZX, TS, and RZ are observed for orpiment and anorpiment respectively, which correspond to the localization of electrons in reciprocal space.
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The effect of phase transformation is clear from the energy bands. For example, the bands along the high symmetry directions for the monoclinic are less disperses compared to energy bands of triclinic phase. The bands closest to the Fermi level in the valence and conduction state may allow multiple optical transitions, which make it a useful optoelectronic material. Another direct transition is observed at about 1.83 eV at the X symmetry point for the β-In2S3. The mBJ approach gives an energy band gap larger than GGA, which is in close agreement with the experimental value. This is an expected result since GGA usually underestimate the energy gap.
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In the partial DOS plot, shown in Fig. 3, the valence band and conduction band mainly consist of the S-3s, 3p states and In-5s, 5p states for all the crystals. This might indicate probable application in solar water splitting [33], especially since the band gaps match to the absorption of visible light. There is only small contribution of In -4d states from the mBJ scheme in the VB, because it is the inner-shell electronic states that are under the screen effect of the outer-shell electronic states. The VB region near the Fermi level is mainly dominated by S-3p for both GGA and mBJ in all the cases, except for orpiment in which case As-5p show strong contribution. Therefore, the highest occupied crystal orbitals (HOCO) are constructed with these orbitals. While, the lowest unoccupied crystal orbitals, (LUCO) composed of In-5s and some S-3p in all the compounds. Hence, in all the cases the band gap depends on the energy of the In-5p anti-bonding level, while the overall shape of the DOS for both cases looks same except for energy shift in the mBJ calculations. Here, we can deduced that, within a framework of mBJ-GGA approach, the spectral energy shift of In-s and S-p states have strong effect in opening the gap keeping the valence bands unchanged as shown in Fig. 2.
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3.2. Optical Properties
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Both phases of As2S3 and β-phase In2S3 were reported to have promising applications in photo-conduction and high-performance solar cells. Optical calculations are carried out using mBJ-GGA potential because it yields a better band gaps than PBE-GGA as shown in Fig. 2. The total imaginary part of the dielectric functionsℑ ( )with and without core-hole calculations in Fig. 4(b), highlight the significant of the corelevel shift calculations. The peaks that appear in Fig. 4(b) for all the structures are attributed to certain energy transition between some orbitals corresponding to some energy spectrum of the respective crystal system. In the case of the β-In2S3, the threshold for direct optical transition from the upper valence band to lower conduction band starts around 1.57 eV as shown in the inset of Fig. 4(b) lower panel. These correspond to transitions from S-3p valence states to conduction band, or from occupied indium 4d to S-3p orbitals of Fig. 3(f).
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Beyond this energy, the curve increases rapidly and reaches a maximum at about 6 eV. For the core-hole calculation, theℑ ( )curve described by equation (1) shows a similar trend, except for the energy shift of about 1.4 eV along the direction of the curve. This shift is similar for the anorpiment structure but for orpiment, it is about 2.5 eV. The threshold for the indirect optical transition for the polymorph of As2S3 is ~2.40 eV and 2.18 eV for anorpiment and orpiment respectively. These energies correspond to the VB and CB splitting at Гv-Yc and Zv-Wc as shown in Fig. 2(a and b) respectively. Therefore, high-energy photons can be utilized for the overall performance of the crystals as solar cell materials. Other structures at 4.29 eV, 4.88 eV and 5.40 eV and 6.88 eV in Fig. 4(b) are due to transition between S-3p and As-4d orbitals in both crystals.
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Total absorption coefficients with and without core hole are calculated for the monoclinic, triclinic, and tetragonal crystals as depicted in Fig. 4(a). The absorption edge is shifted in all of the three crystals due to the core-hole inclusion and is more pronounced in orpiment. However, at high energy above ~6.3 eV, and ~6.8 eV for anorpiment and β-In2S3 respectively, the spectral variation is not large. The absorption increase for orpiment is around 0.4μm-1 within the energy range of 7.0 eV and 8.40 eV, which shows that orpiment, has high optical absorption than the triclinic dimorph. A similarity was observed in the shift of the optical band gap in β-In2S3 and orpiment due to the core-hole effect. Indicating that orpiment can also be used for solar cells application.
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The X-ray absorption spectroscopy allows scanning the unoccupied electronic states separately for different states symmetries, for example, s, p, and d separately for each element. By recording spectra at different absorption edges that correspond to the atomic orbitals transitions. Since the core states are defined as the derivative of the total energy with respect to the occupation of the corresponding state. Here Z+1 approximation are used, which involve removing one core electron from the valence band, and add one electron to conduction band to induce the perturbation. Core-level spectroscopy calculations in Fig. 5, were used to study X-ray absorption near edge structures for the core orbitals of indium, arsenic, and sulfur in each of the three structures studied here. The purpose is to induce excitation of the localized states in order to study the absorption spectra from these structures. With the corehole calculations, the screening function show similar trend to that of ground state calculation above 6.0 eV in anorpiment and β-In2S3. However, below this energy significant changes can be observed, the localization of the core hole has an impact below 6.0 eV for all the structures, as shown in Fig. 4(b). 7
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The effect of the perturbation induced by the presence of core hole is shown in Fig. 4and 5. It is clear from the plot of Fig. 5 that the core-hole effect is more pronounce on the sulphur K edge of orpiment structure than on the sulphur K edge of anorpiment and β-In2S3. It is shown to have shifted by about 2 eV. Energy positions of labelled peaks are chosen to represent maxima of the core absorption spectrum (dash line) for the three crystal systems. Our theoretical model in Fig. 5(b) with core-level shift shows the good agreement with the experiment [8] for S K-edge and As K-edge of monoclinic orpiment. Therefore, our optical absorption analysis would provide a good insight into the use of these compounds for photocatalysis [32] and solar cell applications. In Fig. 5(c), the core-hole calculation for the S K-edge of β-In2S3 also shows good agreement with the experiment [29], with energy different of 0.4 eV. At energies between 3.5 to 5 eV and 6.7 to 9 eV, the core-hole effect is completely negligible for the sulphur K edge. Furthermore, this has been observed for the sulphur K edge in 8
Conclusions The optical absorption enhancement induced by a core-shift spectroscopy has been investigated within Z+1 approximation. High effect of core excitation is observed in monoclinic As2S3, which shows increase absorption of low energy photons in the visible range of solar spectrum of about 0.4μm-1 as compared to other structures. The calculated electronic structure shows indirect band gap for the two phases of As2S3, whereas βIn2S3 reveals both direct and indirect energy gap. Our results for the band structure, DOS and PDOS have shown that LUCO constituted mainly by In-5s and S-3p orbitals for all the studied structures. Whereas S-3p dominates the HOCO for all the systems except for the orpiment. Our calculations show similarities in the shift of the optical band-gap in βIn2S3 and orpiment, and striking comparisons in Arsenic L3 (s, d)-edges peaks for the polymorph of As2S3 crystals was observed, which indicates small effect due to localization of the core hole.
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anorpiment below 2.3 eV, and in orpiment above 15 eV. Thus, in these energy regions the screening function is equivalent to that of the ground-state calculation. But, for L2,3 edge in all the structures, significant changes can be observed within the energy range. Hence, the localization of the core hole has an impact on the indium L2,3 edge. These results clearly indicate that a core-hole effect is significant in indium L3-edge forwide range of energies. However, In L3 (s, d) the curves with and without core shift shows no reasonable agreement with the experimental reported values. So far, we could not find the experimental result to compare with the indium K-edge for the βIn2S3. Nevertheless, our result shows a peak at 2.23 eV for the calculation with core hole. The X-ray spectra for two polymorphs of As2S3 show a similar trend in Fig. 5(a and b). The peaks with core and without core occur nearly at the same energies for both structures similar to the reported PXRD pattern in[6].
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Acknowledgements
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Lawal Mohammed, PhD is an academic staff of the Ahmadu Bello University, Zaria, Nigeria for more than ten years. He got his PhD in Computational Physics and Material Science from the Universiti Teknologi Malaysia (UTM). He is a member of the Material Research Society of Singapore (MRS) He was an ICTP (Italy) scholar during his MSc and PhD program. Currently, he is a Postdoc Research Scientist at the School of Material Science and Engineering, Yancheng Institute of Technology, Yancheng P. R. China. His research interests include material prediction in Nano technology for energy storage and solar cells application.
The authors would like to thank for the financial support by the Ministry of Higher Education (MOHE) Malaysia and Universiti Teknologi Malaysia (UTM) under Grant No Q.J130000.2526.06H14.
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Table 1. The calculated data is compared to the experimental and theoretical data available in the literature.
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This work
7.50 [1], 7.77[2], 7.63[3], 7.585[4], 7.757[5] 32.20[1], 32.94[2], 32.22[3], 32.349[4], 32.956[5] 906.50[1]
7.60[6],7.62[6],7.62[6], 7.594[6], 7.621[5] 32.35[6],32.33[6],32.46[6], 32.352[6], 32.360[5] 937.93[6], 1875.86[6], 1880.90[5]
7.54
1.02 b[1], 0.68[2], 80a, 0.61b[3], 0.9[5], 0.86[7] -207,392.42[3]
2.1[8], 1.90[9], 2.0[5], 2.1[7]
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Crystals β-In2S3 a (Ao)
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ETotal (Ry) Orpiment a (Ao) b(Ao) c (Ao) Vo (Ao)3 B (GPa) Eg (eV) ETotal (Ry)
11.475[10], 11.46[11] 9.577[10], 9.57[11] 4.256[10], 4.22[11] 467.7[10] 1.59b[12]
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33.02 1875.91 65.03 0.64a,c, 1.57a,c, 1.83b,c 2.54b,d -207,427.33
11.68 9.76 4.30 490.40 55.60 1.50b,c, 2.37b,d -45758.452
Anorpiment a (Ao) b(Ao) c (Ao) Vo (Ao)3 B (GPa) Eg (eV) ETotal (Ry)
5.7577[10] 8.7169[10] 10.2682[10] 488.38[10]
517.65 55.99 2.03a,c, 2.40b,d -45758.448
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Figure:
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a = direct, b = indirect, c = PBE, d = mBJ
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Fig. 1 (a) the optimized volume curves as total energy versus unit cell volume of monoclinic and triclinic phases of Arsenic sulfide and β-In2S3 crystal (inset) (b) Pictorial diagram showing excitation of a core-level electron (filled circles) from the core energy level (solid horizontal line down) into an unoccupied state leaving a hole (empty circles) in the shifted energy level (dash horizontal line down). The dash horizontal line up represent shifted Fermi level.
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(b)
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Fig. 2 Electronic band structure of (a) anorpiment (b) orpiment and (c) β-In2S3 calculated with GGA (red color) and mBJ potential (black color).
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Fig. 3 Total and Partial density of state (DOS) calculated with GGA and mBJ potential of (a-b) anorpiment (c-d) orpiment and (e-f) β-In2S3
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Fig. 4. Comparison between calculations with and without core hole (a) Calculated absorption coefficient (b) Calculated Imaginary part of dielectric function, the inset in each case highlight the fundamental absorption edge highlighted by the green bar.
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Fig. 5 Comparison between calculations of X-ray spectra with and without core hole at the S K and In L3 absorption edges (a) Anorpiment (b) Orpiment (c) β-In2S3
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S1877-7503(17)30935-3 https://doi.org/10.1016/j.jocs.2018.07.001 JOCS 896
To appear in: Received date: Revised date: Accepted date:
9-9-2017 9-6-2018 1-7-2018
Please cite this article as: Mohammed. L, Saeed MA, Zhang Q, Musa A, Core-level excitation in polymorph of AS2 S3 and -In2 S3 , Journal of Computational Science (2018), https://doi.org/10.1016/j.jocs.2018.07.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Core-level excitation in polymorph of AS2S3 and -In2S3 Lawal Mohammed.* 1,2,3, Muhammad A. Saeed3, Qinfang Zhang1, Auwalu Musa4 1
School of Material Science and Engineering, Yancheng Institute of Technology, Yancheng 224051, P. R. China 2 Physics Department Ahmadu Bello University, Zaria 833201, Nigeria 3 Physics Department Universiti Teknologi, Johor 81310, Malaysia
Highlights
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Similarities in the shift of the optical band-gap in β-In2S3 and orpiment. Striking comparisons in Arsenic L3 (s, d)-edges peaks for the polymorph of As2S3 crystals. Optical absorption increases due to core-hole for S K (p) and As L3-edges in orpiment. This work provides a better quality crystal for optical evaluation.
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Physics Department Bayero University Kano 3011, Nigeria
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Abstract X-ray absorption near-edge structure (XANES) is one of the most widespread spectroscopies for studying the chemical properties of materials. It is a sensitive probe of the atomic environment, because it can be used to effectively measure the transition probability between core electrons and unoccupied states. In this paper, single level excitonic effects on the core state of the polymorph of As2S3 and tetragonal In2S3 were studied using X-ray absorption spectroscopy. Our results for the first time show striking similarities in Arsenic L3 (s, d)-edges peaks for the two phases of As2S3 orpiment and anorpiment crystals. Optical absorption increases mostly due to core-hole for S K (p) and As L3-edges in orpiment as compared to the other structures. The core-level calculations for these orbitals show good agreement with the experimental ones thus validating the approach used in this study. In orpiment and anorpiment, an indirect energy band gap which has been improved by the mBJ potential to about 1.03 eV and 0.65 eV respectively was observed. We have calculated the imaginary dielectric function and the absorption coefficient with the mBJ potential and core-hole, the optical excitations, is observe to be enhance by core level spectroscopy for all the crystals. Furthermore, the bond length and angles of monoclinic and triclinic As2S3 as well as the betaphase In2S3 compared well with the experimental results. Structural optimization and total energies of all structures are computed using the all electrons full potential linearized augmented plane wave plus local orbitals (FP-LAPW + lo) within the framework of DFT.
1. Introduction
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Keywords: chalcogenide; core hole; X-ray absorption; optical properties; electronic structure *Corresponding author. E-mail address: [email protected]
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Chalcogenide semiconductors have many interesting optical and electronic properties [1-3]. Although these properties for arsenic chalcogenide [4] glasses have been studied extensively as materials for optoelectronic devices [5,34] however, the electronic structure of these materials is obtained from the study of their crystalline phases not amorphous. Anorpiment, As2S3 is a newly discovered mineral that exist in triclinic symmetry [6], it composed of layers of As2S3 macromolecules similar to that of orpiment. There are many striking similarities between the two phases, yet a little is known about the electronic and optical properties of anorpiment. Therefore, it is difficult to compare these properties with that of more stable monoclinic phase As2S3. There are few theoretical studies available on crystalline orpiment As2S3 [7] by employing GGA energy functional to investigate and compare some repulsive forces between As2S3 and As2Se3. Furthermore, electronic structure of monoclinic phase was investigated using multiple scattering approximations for clusters in real space [8]. However, none of these studies provide detail insight on the similarities and differences between the polymorph of As2S3. Therefore, for the first time as per as we know the electronic structure of the triclinic anorpiment is presented. On the other hand, the β-phase Indium sulfide is the only stable crystallized spinel among the existing three phases that shows potential photovoltaic properties, [9-11] 1
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for example, it exhibit luminescence properties in infra-red and optical regions, [10]. It is reported as an absorber material [12,26], and as buffer layer in C-In-Ga-S (CIGS) based thin film solar cells, due to its exceptional photoelectric properties, it has demonstrated impressively high sub-bandgap absorption [13,30]. Additionally, Indium sulfide semiconductors have certain structural defects, β-phase, in particular, has point defects, of sulphur, and indium vacancy, which slightly affects the properties of this compound [9], which is why it has attracted a new interest in the study of defect engineering [14]. The electrical and optical properties of beta phase In2S3 are stable at normal temperature, and it has energy bandgap between 1.98 eV and 2.1 eV, which make it a suitable material for intermediate band solar cells [1517]. Moreover, the β-In2S3 has potential applications in the preparation of green and red phosphors, manufacture of picture tubes for color television, and in infrared optical technology [18]. However, the treatment of the optical properties at the level of inducing external perturbation and the modified TB-mBJ potential for β-In2S3 is not reported as far as we know.
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Moreover, the theoretical information available on the crystalline sulfur-based chalcogenide is inadequate. Hence, there is need for comprehensive study using core level spectroscopy, and modified Becke-Johnson (mBJ) potential, to investigate X-ray absorption and electronic properties of these compounds. The mBJ potential allowed calculation of band gap with accuracy similar to the very expensive GW calculations. Hence, our analysis for the electronic properties and optical properties based on these calculations will provide a good insight on these materials.
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2. Methodology
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We have carried out a detail study of structural, electronic, and optical properties using density functional theory (DFT) [19], within full potential linearized augmented plane wave plus local orbitals (FP-LAPW+lo) as implemented in WIEN2K code [20, 21]. The exchange-correlation potential is treated using the generalized gradient approximation [22], and mBJ potential [23]. In this approach, the unit cell is partition into non-overlapping muffin-tin spheres around the atomic sites as explained somewhere in the literature.
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In this work, tetrahedron method of integration is used in the irreducible Brillouin zone on a grid of 460, 231, and 159 k-point for orpiment, anorpiment, and β-In2S3 respectively, which give the minimum ground state energy, as depicted in Fig. 1(a). In order to achieve energy convergence, the wave functions in the interstitials region are expanded in terms of plane waves with cut-off parameter of RMT*Kmax= 7.5, 7.0, and 8.0 for orpiment, anorpiment and β-phase In2S3 respectively. Where RMT is the smallest atomic sphere radius and Kmax denotes the largest k vector in the plane wave expansion.
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The Muffin-tin radii (RMT) for orpiment are set to 2.15a.u and 1.85a.u for arsenic and sulfur, while for anorpiment RMT=2.21a.u and 1.9a.u, for arsenic and sulfur respectively. In the case of β-phase In2S3, RMT=2.43a.u for indium and RMT=1.99a.u for sulfur. The matrix size and local orbital used are 3,955 and 240 for orpiment, 3,206, and 240 for anorpiment and 6,896 and 408 for β-In2S3 respectively in each case. The calculations were iterated until energy convergence was achieved, the convergence tolerances set at 10 -4Ry for all the crystals. In our calculations, the ground state energy, volume of the unit cell and lattice parameters for three crystal systems are in good agreement with the experimental values as shown in Table 1, indicating that the parameters used in this calculation can give accurate and reliable results. 2
The β-In2S3 crystal information is obtained from the X-ray diffraction experiment data to generate the Crystallographic Information File (CIF) [24], which is used for this study. This information is provided to remove related inconsistency in literature that reported β-In2S3 as monoclinic structure. The calculations of X-ray absorption were performed using the XANES extension of the Wien2k. In order to minimize the unscreened effect on the nucleus, a 2*2*1 supercell are considered for each phases of As2S3, orpiment and anorpiment, whereas, 2*1*1 supercell was used for the β-In2S3.
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The optical properties are studied through the dielectric functions. The optical response is described by a frequency dependent dielectric function [27]. The imaginary part arises from the intraband and interband transitions, which depends on density of states and the momentum matrix. In the limits of linear optics, dielectric tensor contains all the optical properties. The Eqs. (1) and (2) below define the imaginary and real parts of the complex dielectric function (1)
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In the above Eq., 〈 | | 〉and〈 | | 〉are the dipole matrix elements corresponding to j and i directions of the crystal, and correspond to initial and final state respectively, and are the energy in initial and final state respectively. The Kramers-Kronig relation obtains the real part of the elements of the dielectric tensor in Eq. (2) )
(2)
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Where P is the principal value of the integral, all other frequency dependent optical constants can be calculated from above components of the dielectric function. For example total absorption coefficient ( )is calculated using Eq. (3) ( )
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In the above Eq, ( )is extinction coefficient and c is the speed of light. In core level spectroscopy, the dynamical form factor that describes the excitation of a system from its initial state to final state is giving by Eq. (4). The two states are approximated to one-particle states that obey the Fermi golden rule.
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( , )=∑ 〈
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Where q is the momentum transfer, and the absorption cross section can be expressed in terms of Fermi golden rule as
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In this case ε are the electric field polarization vector and α is the fine-structure constant. is the frequency of the X-ray, and are energy of the initial and final state respectively. Therefore, X-ray absorption near edge structures spectra (XANES) is correlated with the unoccupied density of states of the excited atom projected on the proper symmetries allowed by the dipole selection rules [28]. 3. Results and Discussion
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3.1. Structural and Electronic Properties
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The crystal structures of arsenic sulfide polymorphs, orpiment, and anorpiment together with β-In2S3 have been optimized to obtain the lowest ground state energies and the corresponding volumes of the unit cells of these structures is shown in Fig. 1(a). This was achieved by using energy versus volume curve fitted to the Birch-Murnaghan Equation of state [25]. The calculated ground state energy and bulk moduli for the As2S3 polymorphs are almost the same, even though they belong to different crystal systems.
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In the present calculation, the mean bond lengths for anorpiment are found to be AsS=2.29Ao, As-As=3.55Ao, S-S=3.40Ao, and the mean angle is calculated as As-SAs=100.96o, S-As-S=94.11o, which is in good comparison with the mean experimental bond length of 2.27Ao, and angles for As-S-As=100.95o, and S-AsS=93.74o [6]. For orpiment, the calculated mean bond distances are As-S=2.26Ao, AsAs=3.58Ao, S-S=3.35Ao, and mean angles are calculated as As-S-As=93.05o, S-AsS=105.97o, which are close to the mean experimental bond length of As-S=2.24Ao [8, 26], and angles for As-S-As=100.95o, and S-As-S=93.74o. The bands structure of polymorphs of As2S3 and β-phase In2S3 calculated by LAPW +lo method using PBEGGA and mBJ potential are shown in Fig. 2. The energy bands along some high symmetry point in the irreducible Brillouin zone are plotted. In Table 1, we have calculated some important parameters and compared with both experimental and theoretical studies. Our calculations shows good agreement with the experiment, which further confirmed the precision of LAPW+lo basis implementation in the WIEN2K code [31].
The 4s, 4p, 3d, electrons of arsenic and 3s, 3p electrons of sulphur are treated as part of valence states for both orpiment and anorpiment crystals. While 4p, 4d, 5s, 5p, electrons of indium and 3s, 3p electrons of sulphur are treated as part of valence states for the β-phase In2S3. The band structure in the conduction region appears from 1.50eV, 2.03eV, and 0.64eV onwards for orpiment, anorpiment and β-phase In2S3 respectively with PBE energy functional. Whereas for the mBJ potential, these 4
energies corresponding to 2.40eV, 2.37eV and 1.57eV respectively, as shown in Fig. (2). Furthermore, the band structure of polymorphs of As2S3 shows an indirect bandgap as given in Table 1. Dispersion of bands in the direction ZX, TS, and RZ are observed for orpiment and anorpiment respectively, which correspond to the localization of electrons in reciprocal space.
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The effect of phase transformation is clear from the energy bands. For example, the bands along the high symmetry directions for the monoclinic are less disperses compared to energy bands of triclinic phase. The bands closest to the Fermi level in the valence and conduction state may allow multiple optical transitions, which make it a useful optoelectronic material. Another direct transition is observed at about 1.83 eV at the X symmetry point for the β-In2S3. The mBJ approach gives an energy band gap larger than GGA, which is in close agreement with the experimental value. This is an expected result since GGA usually underestimate the energy gap.
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In the partial DOS plot, shown in Fig. 3, the valence band and conduction band mainly consist of the S-3s, 3p states and In-5s, 5p states for all the crystals. This might indicate probable application in solar water splitting [33], especially since the band gaps match to the absorption of visible light. There is only small contribution of In -4d states from the mBJ scheme in the VB, because it is the inner-shell electronic states that are under the screen effect of the outer-shell electronic states. The VB region near the Fermi level is mainly dominated by S-3p for both GGA and mBJ in all the cases, except for orpiment in which case As-5p show strong contribution. Therefore, the highest occupied crystal orbitals (HOCO) are constructed with these orbitals. While, the lowest unoccupied crystal orbitals, (LUCO) composed of In-5s and some S-3p in all the compounds. Hence, in all the cases the band gap depends on the energy of the In-5p anti-bonding level, while the overall shape of the DOS for both cases looks same except for energy shift in the mBJ calculations. Here, we can deduced that, within a framework of mBJ-GGA approach, the spectral energy shift of In-s and S-p states have strong effect in opening the gap keeping the valence bands unchanged as shown in Fig. 2.
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3.2. Optical Properties
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Both phases of As2S3 and β-phase In2S3 were reported to have promising applications in photo-conduction and high-performance solar cells. Optical calculations are carried out using mBJ-GGA potential because it yields a better band gaps than PBE-GGA as shown in Fig. 2. The total imaginary part of the dielectric functionsℑ ( )with and without core-hole calculations in Fig. 4(b), highlight the significant of the corelevel shift calculations. The peaks that appear in Fig. 4(b) for all the structures are attributed to certain energy transition between some orbitals corresponding to some energy spectrum of the respective crystal system. In the case of the β-In2S3, the threshold for direct optical transition from the upper valence band to lower conduction band starts around 1.57 eV as shown in the inset of Fig. 4(b) lower panel. These correspond to transitions from S-3p valence states to conduction band, or from occupied indium 4d to S-3p orbitals of Fig. 3(f).
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Beyond this energy, the curve increases rapidly and reaches a maximum at about 6 eV. For the core-hole calculation, theℑ ( )curve described by equation (1) shows a similar trend, except for the energy shift of about 1.4 eV along the direction of the curve. This shift is similar for the anorpiment structure but for orpiment, it is about 2.5 eV. The threshold for the indirect optical transition for the polymorph of As2S3 is ~2.40 eV and 2.18 eV for anorpiment and orpiment respectively. These energies correspond to the VB and CB splitting at Гv-Yc and Zv-Wc as shown in Fig. 2(a and b) respectively. Therefore, high-energy photons can be utilized for the overall performance of the crystals as solar cell materials. Other structures at 4.29 eV, 4.88 eV and 5.40 eV and 6.88 eV in Fig. 4(b) are due to transition between S-3p and As-4d orbitals in both crystals.
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Total absorption coefficients with and without core hole are calculated for the monoclinic, triclinic, and tetragonal crystals as depicted in Fig. 4(a). The absorption edge is shifted in all of the three crystals due to the core-hole inclusion and is more pronounced in orpiment. However, at high energy above ~6.3 eV, and ~6.8 eV for anorpiment and β-In2S3 respectively, the spectral variation is not large. The absorption increase for orpiment is around 0.4μm-1 within the energy range of 7.0 eV and 8.40 eV, which shows that orpiment, has high optical absorption than the triclinic dimorph. A similarity was observed in the shift of the optical band gap in β-In2S3 and orpiment due to the core-hole effect. Indicating that orpiment can also be used for solar cells application.
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The X-ray absorption spectroscopy allows scanning the unoccupied electronic states separately for different states symmetries, for example, s, p, and d separately for each element. By recording spectra at different absorption edges that correspond to the atomic orbitals transitions. Since the core states are defined as the derivative of the total energy with respect to the occupation of the corresponding state. Here Z+1 approximation are used, which involve removing one core electron from the valence band, and add one electron to conduction band to induce the perturbation. Core-level spectroscopy calculations in Fig. 5, were used to study X-ray absorption near edge structures for the core orbitals of indium, arsenic, and sulfur in each of the three structures studied here. The purpose is to induce excitation of the localized states in order to study the absorption spectra from these structures. With the corehole calculations, the screening function show similar trend to that of ground state calculation above 6.0 eV in anorpiment and β-In2S3. However, below this energy significant changes can be observed, the localization of the core hole has an impact below 6.0 eV for all the structures, as shown in Fig. 4(b). 7
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The effect of the perturbation induced by the presence of core hole is shown in Fig. 4and 5. It is clear from the plot of Fig. 5 that the core-hole effect is more pronounce on the sulphur K edge of orpiment structure than on the sulphur K edge of anorpiment and β-In2S3. It is shown to have shifted by about 2 eV. Energy positions of labelled peaks are chosen to represent maxima of the core absorption spectrum (dash line) for the three crystal systems. Our theoretical model in Fig. 5(b) with core-level shift shows the good agreement with the experiment [8] for S K-edge and As K-edge of monoclinic orpiment. Therefore, our optical absorption analysis would provide a good insight into the use of these compounds for photocatalysis [32] and solar cell applications. In Fig. 5(c), the core-hole calculation for the S K-edge of β-In2S3 also shows good agreement with the experiment [29], with energy different of 0.4 eV. At energies between 3.5 to 5 eV and 6.7 to 9 eV, the core-hole effect is completely negligible for the sulphur K edge. Furthermore, this has been observed for the sulphur K edge in 8
Conclusions The optical absorption enhancement induced by a core-shift spectroscopy has been investigated within Z+1 approximation. High effect of core excitation is observed in monoclinic As2S3, which shows increase absorption of low energy photons in the visible range of solar spectrum of about 0.4μm-1 as compared to other structures. The calculated electronic structure shows indirect band gap for the two phases of As2S3, whereas βIn2S3 reveals both direct and indirect energy gap. Our results for the band structure, DOS and PDOS have shown that LUCO constituted mainly by In-5s and S-3p orbitals for all the studied structures. Whereas S-3p dominates the HOCO for all the systems except for the orpiment. Our calculations show similarities in the shift of the optical band-gap in βIn2S3 and orpiment, and striking comparisons in Arsenic L3 (s, d)-edges peaks for the polymorph of As2S3 crystals was observed, which indicates small effect due to localization of the core hole.
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anorpiment below 2.3 eV, and in orpiment above 15 eV. Thus, in these energy regions the screening function is equivalent to that of the ground-state calculation. But, for L2,3 edge in all the structures, significant changes can be observed within the energy range. Hence, the localization of the core hole has an impact on the indium L2,3 edge. These results clearly indicate that a core-hole effect is significant in indium L3-edge forwide range of energies. However, In L3 (s, d) the curves with and without core shift shows no reasonable agreement with the experimental reported values. So far, we could not find the experimental result to compare with the indium K-edge for the βIn2S3. Nevertheless, our result shows a peak at 2.23 eV for the calculation with core hole. The X-ray spectra for two polymorphs of As2S3 show a similar trend in Fig. 5(a and b). The peaks with core and without core occur nearly at the same energies for both structures similar to the reported PXRD pattern in[6].
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Acknowledgements
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Lawal Mohammed, PhD is an academic staff of the Ahmadu Bello University, Zaria, Nigeria for more than ten years. He got his PhD in Computational Physics and Material Science from the Universiti Teknologi Malaysia (UTM). He is a member of the Material Research Society of Singapore (MRS) He was an ICTP (Italy) scholar during his MSc and PhD program. Currently, he is a Postdoc Research Scientist at the School of Material Science and Engineering, Yancheng Institute of Technology, Yancheng P. R. China. His research interests include material prediction in Nano technology for energy storage and solar cells application.
The authors would like to thank for the financial support by the Ministry of Higher Education (MOHE) Malaysia and Universiti Teknologi Malaysia (UTM) under Grant No Q.J130000.2526.06H14.
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[25] F. Birch, Physical Review, 71, 809-824, (1947). [26] N. Barreau, J. C. Bernède, S. Marsillac, C. Amory and W. N. Shafarman, Thin Solid Films, 431, 326-329, (2003). [27] C. Ambrosch-Draxl and J. O. Sofo, Computer Physics Communications, 175, 1-14, (2006). [28] S. Nufer, A. G. Marinorpo. T. Gemming, C. Elsässer, W. Kurtz, S. Köstlmeier, and M. Rühle, PHYSICAL REVIEW LETTERS, 86, (2001). [29] M. Womes, J. C. Jumas and J. Olivier-Fourcade, Solid State Communications, 131, 257-260, (2004).
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[30] M. Lawal., M. A. Saeed & A. Musa Electronic confinement for tuning optical properties in β-InxTMzSy (TM = V, Fe, and Ti): Prospects for intermediate-band materials. Solar Energy, 137, 621-627, (2016).
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[31] Kurt, L., Gustav, B., Torbjörn B., Peter, B., Stefan, B., Volker, B., Damien, C., Ivano, E., Stewart, J., Andrea, C., Stefano, G., Thierry, D., John, D., Igor, M., Claudia, D., Marcin, D., Olle, E., José, A. F., Kevin, et al F. G., Luigi, G., Paolo, G., Matteo, G., Stefan, G., Xavier, G., Oscar, G., Gross, E. K. U., Andris, G., François, G., Hamann, D. R., Phil, J. H., Holzwarth, N. A. W., Diana, I., Dominik, B. J., François, J., Daniel, J., Georg, K., Klaus, K., Emine, K., Yaroslav, O. K., Inka, L. M., Sven, L., Martijn, M., Nicola, M., Ulrike, N., Lars, N., Taisuke, O., Lorenzo, P., Chris, J. P., Ward, P., Matt, I. J. P., Keith, R., Manuel, R., Gian-Marco, R., Santanu, S., Matthias, S., Martin, S., Karlheinz, S., Sangeeta, S., Francesca, T., Patrik, T., Alexandre, T., Marc, T., David, V., Michiel, J. S., Veronique, S., John, M. W., Jonathan, R. Y., Guo-Xu, Z., Stefaan, C., Reproducibility in density functional theory calculations of solids. Science, 351 (6280), 1415-1424 (2016).
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[32] Biao Wang, A.K., Xukai Luo, Guangzhao Wang, Hongkuan Yuan, Hong Chen, Bandgap engineering and charge separation in two-dimensional-GaS-based van der Waals heterostructures for photocatalytic water splitting. Applied Surface Science, 439, 374379 (2018). Habib Ullah, A.A.T., Salma Bibi, Tapas K. Mallick, Smagul Zh. Karazhanov, Electronic properties of β-TaON and its surfaces for solar water splitting. Applied Catalysis B: Environmental, 229, 24-31 (2018). [34] Diwaker, C.S.Chidan Kumar, Ashish Kumar, Siddegowda Chandraju, Ching Kheng Quah, Hoong-Kun Fun, Synthesis, spectroscopic characterization, electronic and optical studies of (2Z)‐5,6‐dimethyl‐2‐[(4‐nitrophenyl)methylidene]‐2,3‐dihydro‐1‐benzofuran‐3‐ one. Journal of Computational Science, 10, 237-246 (2015).
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[33]
Table 1. The calculated data is compared to the experimental and theoretical data available in the literature.
c (Ao)
CC
Vo (Ao)3 B (GPa) Eg (eV)
Theory
Experiment
This work
7.50 [1], 7.77[2], 7.63[3], 7.585[4], 7.757[5] 32.20[1], 32.94[2], 32.22[3], 32.349[4], 32.956[5] 906.50[1]
7.60[6],7.62[6],7.62[6], 7.594[6], 7.621[5] 32.35[6],32.33[6],32.46[6], 32.352[6], 32.360[5] 937.93[6], 1875.86[6], 1880.90[5]
7.54
1.02 b[1], 0.68[2], 80a, 0.61b[3], 0.9[5], 0.86[7] -207,392.42[3]
2.1[8], 1.90[9], 2.0[5], 2.1[7]
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Crystals β-In2S3 a (Ao)
A
ETotal (Ry) Orpiment a (Ao) b(Ao) c (Ao) Vo (Ao)3 B (GPa) Eg (eV) ETotal (Ry)
11.475[10], 11.46[11] 9.577[10], 9.57[11] 4.256[10], 4.22[11] 467.7[10] 1.59b[12]
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33.02 1875.91 65.03 0.64a,c, 1.57a,c, 1.83b,c 2.54b,d -207,427.33
11.68 9.76 4.30 490.40 55.60 1.50b,c, 2.37b,d -45758.452
Anorpiment a (Ao) b(Ao) c (Ao) Vo (Ao)3 B (GPa) Eg (eV) ETotal (Ry)
5.7577[10] 8.7169[10] 10.2682[10] 488.38[10]
517.65 55.99 2.03a,c, 2.40b,d -45758.448
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Figure:
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a = direct, b = indirect, c = PBE, d = mBJ
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Fig. 1 (a) the optimized volume curves as total energy versus unit cell volume of monoclinic and triclinic phases of Arsenic sulfide and β-In2S3 crystal (inset) (b) Pictorial diagram showing excitation of a core-level electron (filled circles) from the core energy level (solid horizontal line down) into an unoccupied state leaving a hole (empty circles) in the shifted energy level (dash horizontal line down). The dash horizontal line up represent shifted Fermi level.
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(b)
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EF
s, p,
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Fig. 2 Electronic band structure of (a) anorpiment (b) orpiment and (c) β-In2S3 calculated with GGA (red color) and mBJ potential (black color).
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A
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Fig. 3 Total and Partial density of state (DOS) calculated with GGA and mBJ potential of (a-b) anorpiment (c-d) orpiment and (e-f) β-In2S3
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Fig. 4. Comparison between calculations with and without core hole (a) Calculated absorption coefficient (b) Calculated Imaginary part of dielectric function, the inset in each case highlight the fundamental absorption edge highlighted by the green bar.
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Fig. 5 Comparison between calculations of X-ray spectra with and without core hole at the S K and In L3 absorption edges (a) Anorpiment (b) Orpiment (c) β-In2S3
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