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Journal of Alloys and Compounds 705 (2017) 828e839

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Journal of Alloys and Compounds

journal homepage: http: / /www.elsevier .com/locate/ ja lcom

Structural, electronic and optical properties of CsPbX3 (X¼Cl, Br, I) forenergy storage and hybrid solar cell applications

Murad Ahmad a, b, Gul Rehman a, b, Liaqat Ali a, b, M. Shafiq a, c, R. Iqbal a, b,Rashid Ahmad d, Tahirzeb Khan e, S. Jalali-Asadabadi f, Muhammad Maqbool g, *,Iftikhar Ahmad a, c, **

a Center for Computational Materials Science, University of Malakand, Pakistanb Department of Physics, University of Malakand, Chakdara, Pakistanc Department of Physics, Abbottabad University of Science & Technology, Pakistand Department of Chemistry, University of Malakand, Chakdara, Pakistane Department of Physics, Abdul Wali Khan University Mardan, Pakistanf Department of Physics, Faculty of Sciences, University of Isfahan, HezarGerib Avenue, Isfahan, 81744-73441, Irang Department of Physics & Astronomy, Ball State University, Muncie, IN, 47306, USA

a r t i c l e i n f o

Article history:Received 14 December 2016Received in revised form9 February 2017Accepted 13 February 2017Available online 20 February 2017

Keywords:Structural analysisOptical constantsBandgapSolar cellPerovskite

* Corresponding author. Department of Physics & Asity, Muncie, IN, 47306, USA. Tel: (1)7652858870** Corresponding author. Abbottabad UniversityPakistan. Tel: þ92-3329067866.

E-mail addresses: mmaqbool@bsu.edu (M. Maq(I. Ahmad).

http://dx.doi.org/10.1016/j.jallcom.2017.02.1470925-8388/© 2017 Elsevier B.V. All rights reserved.

a b s t r a c t

Organic-Inorganic perovskites CsPbX3 (X ¼ Cl, Br, I) are investigated for their potential ability and use assolar cells and energy storage materials, using density function theory, generalized gradient approxi-mation and modified Becke-Johnson (TB-mBJ) exchange potential. Structural analysis shows that thelattice constant and unit cell volume varies when CsPbX3 (X ¼ Cl, Br, I) change from cubic phase totetragonal and orthorhombic structures. The electronic properties show that CsPbCl3, CsPbBr3 and CsPbI3all are semiconductor in with bandgap between 0.79 eV and 2.54 eV. It is also observed that the bandgapchanges when the structure changes. Optical properties show that these materials have a good ab-sorption ability of photons due to their narrow bandgaps. The real ε1(u) and imaginary ε2(u) parts oftheir dielectric functions show that CsPbCl3, CsPbBr3 and CsPbI3 also possess a great ability of retainingthe energy it absorbs. These properties make them very suitable for solar cells and energy storage ap-plications. These materials also behave as superluminescent material at high photon energy.

© 2017 Elsevier B.V. All rights reserved.

1. Introduction

One of the most attractive renewable energy sources across theglobe is solar energy. It is an alternative source of energy that canovercome the crises of energy and can replace the conventionalenergy resources [1]. This energy can be utilized through a solarcell, which directly converts sunlight into electrical energy withminimum losses and greenhouse gas emission [2]. Organic-Inorganic perovskites are of considerable interest for the designof electronic devices, such as light emitting diodes and solar cells,due to their low cost and applications feasibility. In the recent years

stronomy, Ball State Univer-

of Science & Technology,

bool), ahma5532@gmail.com

hybrid organic-inorganic perovskites (HOIPs) have gained sub-stantial attraction in the solar cell community [3e9]. The HOIPs areidentified with a structural formula ABX3 where A-site is occupiedby a small organic ion, B site is occupied by a divalent metallic atomand halogens are on the x-sites.Weber [10,11] replaced cesiumwithmethylammonium (CH3NH3) cations and generated the first three-dimensional (3D) organic-inorganic hybrid solar cell. HOIPs alsoexhibit good semiconducting and light absorption properties whichmake them promising candidates for opto-electronic devices ap-plications and especially in photovolatic devices as power conver-sion efficiency beyond 20% [12e18].

The efficiency of solar cell materials varies with its band gap,while band gap depends on different physical parameters as well asphase transition [19]. To understand the efficiency of a solar cell thecomplete knowledge of those parameters that effects band gap aswell as all phases of the compound are necessary to be known.Moller [20] reported that cesium lead halides have a perovskitestructure, as mentioned above, with the general formula CsPbX3

M. Ahmad et al. / Journal of Alloys and Compounds 705 (2017) 828e839 829

(X ¼ Cl, Br, I). He also investigated that these materials are semi-conductors and contribute to photoconductivity [21]. CsPbX3(X¼Cl, Br, I) are direct band gap semiconductors that absorb visibleand ultraviolet light [22]. Hence these compounds are used inphotovoltaic and optoelectronic devices such as solar cells, pho-tonic crystals [19,22], radiation detectors [2,23], and light emittingdiodes (LEDs) [24,25].

These compounds show flexibility to changing crystallinestructures at different temperatures [20,26]. The range of temper-ature for the phase transition in CsPbX3 (X¼ Cl, Br, I) depends uponthe nature of halogen atom attached. Moller [21] investigated thestructural properties of CsPbX3 (X¼Cl, Br, I) by x-ray diffraction andreported that these compounds exist in three different phases.CsPbCl3 exists in orthorhombic phase below 315 K, in tetragonalstructure in the range of 315 K up to 320 K and in cubic phase above320 K [27,28]. CsPbBr3 exist in orthorhombic phase at room tem-perature, transforms to tetragonal phase at 373 K, followed by cubicphase at 403 K [27,29]. CsPbI3 occurs in orthorhombic structure atroom temperature [30], then changes to tetragonal phase but thereis no clearly define temperature range in the literature and at 634 Kit transforms to cubic structure. With a cubic structure its bandgapreduces and it becomes highly luminescent [31,32].

Gesi et al. [33] reported the phase transition in CsPbCl3 andCsPbBr3 under hydrostatic pressure. At high temperature, struc-tural phase transition was reported in CsPbI3 by Trots et al. [30].Heidrich [34] and Eperson [19] reported the electronic, optical andstructural properties of CsPbCl3, CsPbBr3 and CsPbI3 for photovol-taic application. The structural, electronic and optical properties ofcubic CsPbX3 are studied by Murtaza et al. [23] using densityfunctional theory (DFT). Chang et al. [35] calculated the structuraland electronic properties of the cubic CsPbX3 (X ¼ Cl, Br, I) by first-principles study. Ma et al. investigated that CsPbF3 has indirectbandgap nature and has a bandgap of 5.344 eVwhich is in the rangeof insulators [36]. Ghebouli et al. used density functional for theCalculation of the bandgap energy and optical properties of CsCdF3which verified the experimental and theoretical results of Vai-theeswaran et al. [37,38], according to their results CsCdF3 is indi-rect bandgap insulator which are not suitable for solar cellapplications. The detailed literature on these compounds showsthat most of the theoretical works are focused on the cubic phase ofthese compounds.

The understanding of the structural, electronic and opticalproperties of these materials for the use in energy storage appli-cations and hybrid solar cells CsPbX3 (X ¼ Cl, Br, I) are highlydesirable and are investigated in this research work.

2. Computational details

In the present work, all calculations are carried out with the fullpotential linearized augmented plane wave's method within theframe work of density functional theory (DFT). The exchange-correlation energy is treated with the generalized gradientapproximation (GGA) [39] and local density functional approxi-mation (LDA) within WIEN2k code [40]. For the accurate band gapcalculations of CsPbX3 (X ¼ Cl, Br, I) perovskites, modified Becke-Johnson (TB-mBJ) exchange potential in addition to GGA is used[41]. However, the experimental band gap is accurately calculatedby using nTB-mBJ (non-regular Tran and Blaha's modified.

BeckeeJohnson approach). For semiconductors, the TB-mBJprovides smaller band gaps than the experimental values,because of the smaller c factor in it. Since the band gap dependsupon electron density of a material and this density can be properlycontrolled by the c-factor, therefore, c-factor will be optimized forthe optimization of the electron density of every compound, whichis done in non-regular TB-mBJ (nTB-mBJ) calculations [42].

One of the relativistic effects is the spin-orbit coupling (SOC)that makes spectacular impact on the separation energy of com-pound or molecules containing heavy atoms. The SOC effect is dueto the interacting particles that depends on their values, mutualorientations, orbital and spin angular momenta of these particles.Here we include the GGA along with spin-orbit coupling (SOC)calculations using variational method [43] programmed inWIEN2Kcode.

3. Results and discussion

3.1. Structural properties

CsPbX3 (X ¼ Cl, Br, I) perovskites exist in different phases atdifferent temperatures as they are sensitive to temperature. In thecurrent studies we focus only on the three different phases (cubic,tetragonal, orthorhombic) by using DFT method. These perovskitespossess simple cubical structure at high temperature. There struc-ture orientation is PbX6 make octahedral with Pb at the center andsix halogens, Cs exists at the corner of the cubic as shown in Fig. 1.At room temperature CsPbX3 (X ¼ Cl, Br, I) exists in orthorhombicphase. When temperature is increased, a structural distortion oc-curs and it converts to tetragonal phase [27,30e32]. The structuralproperties such as lattice constant, volume and bulkmodulus of thecubic CsPbX3 are obtained from the volume optimization of eachunit cell of CsPbX3 (X ¼ Cl, Br, I).

In the process of optimization, the equation of state of Birch-Murangan is used to plot the calculate total energy (Ry) of eachunit cell in a compound against the corresponding calculated vol-umes [33,43]. There lattice parameters in orthorhombic, tetragonalphases are calculated through 3D and 2D optimization respectively.The calculated ground state parameters with the comparison ofexperimental and other calculated DFT parameters are given inTables (1)e(3), showing that the results of PBEsol have goodagreement with the experimental results as compared to the re-sults obtained by other methods. The calculated bond lengths andbond angles are also given in the mentioned three tables, high-lighting the idea of structural orientation and information aboutband gap of the compounds. The bonding nature of.

these compounds is explained by electron charge density plots.The electron charge density plots for (100) plane are represented bythe circles which show that the atoms of the compound are notoverlapped with each other, clarifies that bonding between Cs andX (X ¼ Cl, Br, I) is ionic. On the other hand, the (110) plane plotsshow that the bonding between Pb and X (X¼Cl, Br, I) is covalent innature due to overlap of the circles of the atoms in the compounds.Therefore, the compounds CsPbX3 (X¼ Cl, Br, I) have both ionic andcovalent nature.

3.2. Electronic properties

The electronic properties are calculated, using two differentpotentials (GGA, nT-mBJ), to achieve the band gap of all phases ofCsPbX3 (X ¼ Cl, Br, I) Pervoskite compounds experimentally. Fromexperimental and our calculated results, it is clear that thesecompounds are direct band gap materials in all phases. Therevalence bands maxima and conduction band minima are separatedby RdR symmetric points in Brillouin zone. The calculated bandgap energies by GGA are underestimated, while the nT-mBJ resultsaccurately agree with the experimental results given in Table 4.Therefore, it can be concluded that nT-mBJ potential is a goodapproach to calculate the electronic properties especially the bandgap of the compounds as compare to the other potentials. Thepredicted energy band gap of CsPbCl3 orthorhombic is 2.7 eV, andthat of CsPbBr3 and CsPbI3 tetragonal are 2.3 eV, 1.7 eV respectively.

Fig. 1. Structural view of (a) cubic, (b) tetragonal, and (c) orthorhombic CSPbX3, (X ¼ Cl, Br, I).

M. Ahmad et al. / Journal of Alloys and Compounds 705 (2017) 828e839830

Good agreement of the results of other phases of these compoundswith the experimental results supports the predicted bandgaps. It isclear from calculated band gap that when Cl is gradually replacedby I atoms the band gap decreases because of increase in the atomicsize. The bigger atomic size of I containmore number of nucleons ascompared to the smaller Cl atom. As a result, the increasing atomicsize causes a decrease in the electrostatic attractive force of nucleuson the outermost shell electrons. This reduced hold of nucleus onthe outermost shell electrons lowers the bonding energy and sep-aration between conduction bands (CB) and valance band (VB). Onthe other hand, when we go from cubic to orthorhombic phase theband gap decreases due to the increasing electronic charge densityand lattice constants in the crystals. Therefore, in orthorhombicphase the number of atoms and the number of electrons in thecrystal increase. Eventually, the valance band shifts up to the Fermilevel due to the occupation of electrons in the position near theFermi level, causing a decrease in the energy gap between the va-lance and conduction bands.

Further explanation of the nature of electronic band gap energyof CsPbX3 (X ¼ Cl, Br, I) compounds is carried out through thedensity of state. The total density of state (DOS), explaining thenature of the materials, are plotted in Figs. 2, 4 and 6. The plots oftotal DOS for CsPbX3 (X ¼ Cl, Br, I) compounds and their differentphase structures show that these materials exhibit semiconductingproperties. The total and partial DOS graphs for all three phases of

CsPbX3 (X¼Cl, Br, I) are plotted by using GGA and nT-mBJ. From theplots it is clear that none of them cross the Fermi level which jus-tifies that these materials are not conductors. The graphs of thetotal DOS obtained from GGA shows that its resultant band gapenergies do not match with the experimental results as shown inTable 4. On the other side, the results of nT-mBJ have good agree-ment with it. In tetragonal phase CsPbX3 (X¼ Cl, Br, I) the total DOSplot the nearest left side of Fermi level (valence band) and its rightside (conduction band) are very slightly shifted towards the Fermilevel. Similarly, in orthorhombic phase the valence and conductionbands are shifted more than tetragonal phase towards the Fermilevel. These results show reduction in the band gap energy movingfrom cubic to orthorhombic phase structures. The same trend in thereduction of band gap energy is shown by the CsPbX3 (X ¼ Cl, Br, I)compounds moving from Cl to I.

The partial density of state (DOS) plots show the contribution ofatoms and there different states in band gap energy ofCsPbX3(X ¼ Cl, Br, I) compounds. The distribution of total DOS andpartial DOS plots in the range of �10 to 10 eV and �10 to 20 eVrespectively for CsPbX3 (X ¼ Cl, Br, I) are shown in three regions onthe basis of bands which are given in Figs. 2e7. The range of firstregion around �8 eV shows a narrow band which is due to Cs-5Pstate while the second one is the valance band ranging from �5to 0 eV (VB). In this band, the Halogens (Cl, Br, I) contribute mainlywith 3p, 4p, 5p states respectively in the CsPbX3 (X ¼ Cl, Br, I)

Table 1Comparison of calculated lattice parameters of cubic ScPbX3(X ¼ Cl, Br, I) with experimental and other DFT values.

Parameters CsPbCl3 CsPbBr3 CsPbI3

This work (Exp) Others This work (Exp) Others This work (Exp) Others

PBEsola (Å) 5.62 5.732b 5.87 6.009b 6.242 6.383b

(5.605)a 5.49d (5.87)a 5.74d (6.289)c 6.05d

5.73e 5.99e 6.39e

6.38g

Volume(Å)3 177.940 202.262 243.256 260.42f

(176.558)a (202.262)a (248.78)c

Error% 0.78 0 2.22 4.67Bond length (Å)Cs_X 6.883 e 4.150 e 4.137 e

Pb_X 2.810 2.865h 2.935 2.996h 3.121 3.196h

Cs_Pb 4.867 e 5.170 e 5.406 e

Bond angleCs-X2-X1 60� e 60� e 60� e

X1-Pb-X2 90� e 90� e 90� e

Pb-Cs-X1 35.26� e 35.26� e 35.26� e

GGA096a (Å) 5.7387 e 6.0051 e 6.3824 e

V (Å)3 188.993 e 216.551 e 259.988 e

Error% 7.0 e 7.0 e 4.5 e

LDAa (Å) 5.5312 e 5.7700 e 6.1329 e

Volume(Å)3 162.516 e 192.100 e 230.672 e

Error% 7.9 e 5.0 e 7.3 e

a Ref. [21].b Ref. [44].c Ref. [31].d Ref. [35].e Ref. [50].f Ref. [51].g Ref. [56].h Ref. [45], [47].

Table 2Calculated Lattice parameters of orthorhombic CsPbX3(X ¼ Cl, Br, I) with experimental and other DFT calculated values.

Parameters CsPbCl3 CsPbBr3 CsPbI3

This work (Exp) Others This work (Exp) Others This work (Exp) Others

GGAsola (Å) 7.840 (7.902)a 8.251 (8.207)b 4.799 (4.795)c 4.909d

b (Å) 11.241 (11.247)a 8.179 (8.255)b 10.261 (10.45)c 10.80d

c (Å) 7.954 (7.899)a 11.751 (11.759)b 17.851 (17.76)c 18.26d

V (Å)3 700.927 (702.1) 790.58 (796.66) 883.393 (887.78) 968.09d

Error% 0.167 0.76 0.49Bond length (Å)Pb___X1 2.944 2.843 2.906 3.037 3.174(3.0513)c 3.239Pb___X2 2.854 2.850 2.935 3.046 3.259(3.226)c 3.253Pb___X3 3.173 2.854 2.9435 3.051 (3.277)c 3.262Cs___Pb 3.798 e 5.159 e 5.200 e

Bond angleCs-X1-X2 36.96 e 56.91 e 58.87 e

X1-Pb-X2 180.0 e 53.43 e 51.86 e

Pb-Cs-X1 35.76 e 98.35 e 30.84 e

GGA096a (Å) 8.0188 e 8.3556 e 4.9874 e

b (Å) 11.4631 e 8.4068 e 10.1343 e

c (Å) 8.0791 e 11.9196 e 18.2757 e

V (Å)3 742.63 e 837.28 e 923.72 e

Error% 5.8 e 5.1 e 4.1 e

LDAa (Å) 7.6357 e 7.9928 e 4.65110 e

b (Å) 11.0008 e 8.1480 e 10.2152 e

c (Å) 7.8876 e 11.5036 e 17.7575 e

V (Å)3 662.55 e 749.18 e 843.69 e

5.6 e 5.96 e 4.96 e

a Ref. [57].b Ref. [26].c Ref. [2].d Ref. [46], [48].

M. Ahmad et al. / Journal of Alloys and Compounds 705 (2017) 828e839 831

Table 3Calculated Lattice parameters of tetragonal CsPbX3(X ¼ Cl, Br, I) with experimental and other DFT calculated values.

Parameters CsPbCl3 CsPbBr3 CsPbI3

This work (Exp) Others This work (Exp) Others This work (Exp) Others

GGAsola (Å) 5.64 (5.590)a e 8.31 (8.48)b e 6.273 (6.15)c e

b (Å) 5.64 (5.590)a e 8.31(8.48)b e 6.273 (6.15)c e

c (Å) 5.77 (5.630)a e 14.945(15.25)b e 6.23 (6.23)c e

V (Å)3 183.54 e 1032.04 e 244.91 e

Error% (175.93) 4.3 e (1096.63) 5.8 e (235.63) 3.9 e

Bond length (Å)Pb___X1 2.85 7.778 e 2.85 e

Pb___X2 3.17 9.894 e 3.27 e

Cs1___Pb1 5.041 12.410 e 5.34 e

Bond angleCs- X1- X2 60.65� e 45� e 45� e

X1-Pb- X2 89.74� e 38.18� e 89.75� e

Pb-Cs- X1 61.59� e 60.92� e 60.92� e

GGA096a (Å) 5.7487 e 7.9779 e 6.393b (Å) 5.7487 e 7.9779 e 6.393c (Å) 5.8082 e 14.640 e 6.477V (Å)3 191.947 e 931.790 e 264.718Error% 16.02 e 15.03 e 12.34LDAa (Å) 5.7518 e 7.9779 e 6.5239 e

b (Å) 5.7518 e 7.9779 e 6.5239 e

c (Å) 5.8548 e 15.8600 6.6088 e

V (Å)3 193.487 e 1009.440 e 281.279 e

Error% 9.98 e 7.98 e 19.37 e

a Ref. [20].b Ref. [2].c Ref. [7].

Table 4Calculated band gape energy of CsPbX3(X ¼ Cl, Br, I) with Experimental and other DFT calculated values.

Compounds Phase Structure Eg (eV) Others Eg(eV) exp Eg (eV) Present work

GGA mBj GW GGA nTmBj

CsPbCl3 Cubic 2.172a 1.585b 3.03e 3g 2.168 3.12.498b e 2.829b e e e

2.27e e e e e e

Tetragonal e e e 2.86i 2.121 2.86Orthorhombic e e e e 2.326 2.73

CsPbBr3 Cubic 1.764a 2.30c 2.36g 1.61 2.361.6f e e e e e

Tetragonal e e e e 0.79 2.3Orthorhombic 1.794b 1.316b 2.25i 2.154 2.23

CsPbI3 Cubic 1.359a e e 1.73f 1.478 1.751.49d e e e e e

Tetragonal 1.60d e e e 1.043 1.7Orthorhombic 2.504b, 1.82d 2.426b e 1.6h 2.54 1.68

a Ref. [44].b Ref. [52].c Ref. [54].d Ref. [46].e Ref. [53].f Ref. [8].g Ref. [33].h Ref. [9].i Ref. [55], [49].

M. Ahmad et al. / Journal of Alloys and Compounds 705 (2017) 828e839832

compounds. The third region, known as conduction band, is at theright side of Fermi level. Major contribution in this band is of Pb-6pand Cs-d in cubic phase of CsPbX3 (X ¼ Cl, Br, I) compounds. Fig-ures of tetragonal and orthorhombic phases show that Halogensalso contribute in the conduction band. From the atomic contri-bution plots it is clear that Pb and Halogen atoms have majorcontribution in valence and conduction bands which reduces theband gap energy. The S, P state of Pb and P state of the Halogens

play a major role in the reduction of band gap energy as shown inthe Figs. 3, 5 and 7. Spin-Orbit coupling (SOC) effect for CsPbX3 (X¼Cl, Br, I) is calculated due to the presence of Pb atoms. The splittingof band maxima occurs due to the SOC effect, which causes thereduction in bandgap energies. Therefore due such a larger effecton electronic properties SOC effect could not be ignored for thecalculations of optoelectronics properties of these compounds[56,57].

Fig. 2. Total density of states (DOS) of CsPbCl3 Pervoskite (a) Cubic (b) Tetragonal (c) Orthorhombic.

Fig. 3. Partial density of states (DOS) of CsPbCl3 Pervoskite (a) Cubic (b) Tetragonal (c) Orthorhombic.

M. Ahmad et al. / Journal of Alloys and Compounds 705 (2017) 828e839 833

Fig. 4. Total density of states (DOS) of CsPbBr3 Pervoskite (a) Cubic (b) Tetragonal (c) Orthorhombic.

Fig. 5. Partial density of states (DOS) of CsPbBr3 Pervoskite (a) Cubic (b) Tetragonal (c) Orthorhombic.

M. Ahmad et al. / Journal of Alloys and Compounds 705 (2017) 828e839834

Fig. 6. Total density of states (DOS) of CsPbI3 Pervoskite (a) Cubic (b) Tetragonal (c) Orthorhombic.

Fig. 7. Partial density of states (DOS) of CsPbI3 Pervoskite (a) Cubic (b) Tetragonal (c) Orthorhombic.

M. Ahmad et al. / Journal of Alloys and Compounds 705 (2017) 828e839 835

Fig. 8. (a) Imaginary and (b) real parts of dielectric function, (c) refractive index, (d) energy loss function, and (d) sum rule of CsPbX3 (X ¼ Cl, Br, I) in cubic phase.

M. Ahmad et al. / Journal of Alloys and Compounds 705 (2017) 828e839836

3.3. Optical properties

CsPbX3 (X ¼ Cl, Br, I) compounds are the best light absorbersamongst all family members of photovoltaic materials [3e6].Therefore, all researchers have great interest in these materials forthe construction of more sustainable and efficient solar cells andother solar devices [5e9]. The calculated optical parameters such asabsorption coefficient, energy loss function and refractive index ofCsPbX3 compounds describe the response of these materials to theincident photons [3e9]. Optical properties of these compounds incubic, tetragonal and orthorhombic phases are provided inFigs. 8e10 and explained with the help of their complex real andimaginary dielectric functions, where ε1 (u) and ε2 (u) are the realand imaginary parts of dielectric function respectively. ε1 (u) rep-resents the stored energy of a medium or material that is availableto be given out. ε2(u) explains the absorption ability and behaviorof these materials and shows the energy gain for the photovoltaicmaterials [58].

The imaginary part has a direct relation with the band gap en-ergy. The cubic, tetragonal and orthorhombic plots for CsPbX3(X ¼ Cl, Br, I) compounds describe that in the range of visible andinfrared light CsPbI3 has the maximum peaks due to its smallerband gap as compare to the other two compounds. All spectra areobtained under the same conditions to avoid any effect of externalfactors. The spectra describe that the critical energy for CsPbX3

(X¼ Cl, Br, I) shifted towards the lower energy as we go from Cl to I.The ε2 (u) plots for CsPbCl3 in cubic, tetragonal and orthorhombicstructures show similar pattern of increase in the ε2 (u) value anddecrease in the critical energy. The plots give critical points at 3 eV,2.8 eV and 2.7 eV, related to their band gaps of 3.08 eV, 2.86 eV and2.75 eV. Similarly for CsPbBr3 the critical points are 2.36 eV, 2.3 eVand 2.25 eV for CsPbI3 1.7 eV, 1.6 eV and 1.6 eV in Cubic, tetragonaland orthorhombic phases respectively. For tetragonal and ortho-rhombic structure, we plot ε2 (u) [100], [001] and [100], [010], [001]plans respectively because their axes are different. The spectrapeaks are high for CsPbI3 in all structures as compare to the othertwo, its peak is very high at orthorhombic structures but the otherpeak after the critical point disappear which were present in cubic,limiting thewideness of absorption band spectra. The CsPbBr3 has awide band and sharp peaks at orthorhombic phase, but its tetrag-onal plot behavior is different from others due to a huge differencein their lattice constants. The different peaks after the critical pointsare described by density of states in which the electron transitiontakes place. The first peak is due to the electrons transition fromHalogen (Cl, Br, I)-p state in valence band to the Pb-p state inconduction band. The second peak occurs due to the transition ofelectron (Cl, Br, I)-p valence state to the Cs-d and Pb-p combinedconduction band. The third and fourth peaks arise due the electrontransition of mixed Pb-s and (Cl, Br, I)-p from valence band to themixed Pb-p, Cs-d,p states of conduction band. In tetragonal and

Fig. 9. Imaginary ε2(u) and real ε1(u) parts of dielectric function, refractive index n(u), energy loss function L(u), and sum rule s(u) of CsPbX3 (X ¼ Cl, Br, I) in tetragonal phase.

M. Ahmad et al. / Journal of Alloys and Compounds 705 (2017) 828e839 837

orthorhombic structure most of the electronic transitions occur dueto mixed states of valence to mixed states of conduction bandscaused by the reduction of energy bandgap.

The real part ε1 (u) of the frequency dependent dielectricfunction for CsPbX3 (X ¼ Cl, Br, I) cubic, tetragonal and ortho-rhombic is given in Figures (4.7), (4.8), and (4.9). In ε1 (u) spectrathe zero frequency limits ε0 (u) is the most important quantitywhich describes the electronic part of the static dielectric constant.The calculated values of ε0 (u) for CsPbCl3 are 4.1, 4.4, and 4.5 incubic, tetragonal and orthorhombic phases respectively. ForCsPbBr3 ε0 (u) the values are 4.6, 3.2, and 5 and for CsPbI3 thosevalues are 5, 6.2, and 12.7 in cubic, tetragonal and orthorhombicstructures respectively. The total plots of ε1 (u) for CsPbX3 (X ¼ Cl,Br, I) compounds describe the inverse relation between the bandgap energy and ε0 (u). The CsPbI3 has larger value of ε0 (u) than theother two compounds. Therefore, ε1 (u) shows themetallicity of thecompounds, as it starts increasing from zero frequency limit, rea-ches to maximum value, followed by a decreases and a at certainenergy it goes below the zero point. The negative ε1 (u) shows themetallic nature of the compounds. The values of ε2 (u) and ε1 (u) inFigs. 8e10 show that CsPbI3 in orthorhombic phase can absorb thehighest amount of energy over a wide photon energy range and atthe same time it can retain that energy the most. Therefore,orthorhombic CsPbI3 is highly suitable and desirable for solar en-ergy storage and solar cell applications. However, the other twomembers of this family; CsPbCl3 and CsPbBr3, cannot be under-estimated in any phase for similar applications.

For optical materials, the knowledge of refractive index n(u) is

essential for its use as photonic and optical devices. The n(u) plotsupto 50 eV photon energy for CsPbX3 (X ¼ Cl, Br, I) compounds aregiven in Figs. 8e10. These graphs show a variation of the refractiveindex with energy of incident photon. The value of n(0) increasesfrom Cl to I and also increases when we go from cubic to ortho-rhombic phase. CsPbI3 has the highest value of n (u) in ortho-rhombic phase followed by CsPbBr3 in orthorhombic phase. Themaximum value of n(u) in orthorhombic phase is 3.7. This value ismuch higher than the refractive index of diamond; the naturalmaterial with the highest refractive index. Thus, orthorhombicCsPbBr3 can be used as an alternative and artificial gem stone.

The figures show that refractive index for CsPbX3 (X ¼ Cl, Br, I)compounds in various phase structures decreases after theachievement of their maximum value at certain energy until atcertain photon energy of 13 eV or higher, it reaches below unity.This is exactly according to the Paul Drude's Model [59e62]. For allthree family members of CsPbX3 (X ¼ Cl, Br, I) family and for allphases, the energy of photon that corresponds to refractive indexbelow 1, falls in the g-rays, x-rays and a portion of ultraviolet (UV)photons region. Therefore, it is concluded that the materialsbecome superluminal or superluminescent for g-rays, x-rays and aportion of UV photons. In the phenomenon of superluminescence,the group velocity of the incident photon inside the material ormedium exceeds the speed of light in vacuum ‘c’.

The electron energy loss function L(u) is another useful tool toinvestigate the behavior of a material with the light. This propertyof a medium or a material measures the propagation loss of energyinside the medium or material. The peaks in the plots of electron

Fig. 10. Imaginary ε2(u) and real ε1(u) parts of dielectric function, refractive index n(u), energy loss function L(u), and sum rule s(u) of CsPbX3 (X ¼ Cl, Br, I) in orthorhombic phase.

M. Ahmad et al. / Journal of Alloys and Compounds 705 (2017) 828e839838

energy loss function for CsPbX3 (X ¼ Cl, Br, I) compounds describethat loss of energy occurs when the energy of incident photon ishigher than the bandgap of the material. The L(u) peaks appearbetween 18 eV and 22 eV for CsPbX3 (X ¼ Cl, Br, I) in the cubicstructure and between 18 eV and 20 eV in the tetragonal phaserespectively. Orthorhombic CsPbX3 (X ¼ Cl, Br, I) also have thepeaks between 19 eV and 20 eV. The peaks of L(u) show the plasmaresonance and their corresponding frequencies are called plasmafrequencies. The plots show that no scattering appears at energylower than the band gap.

Sum rule s(u) is a precious tool for the measurement of thestrength or numbers of electrons involved in the optical transition.The sum rule (oscillator strength) describes transition strengthfromvalence band to the conduction band. The oscillator strength isplotted for each unit cell of CsPbX3 (X ¼ Cl, Br, I) compounds andtheir different structures as shown in the Figs. 8e10. It is clear fromthe figures that the oscillator's sum rule increases when the bandgap energy decreases, as we go from Cl to I. A slight increase alsooccur in the sum rule when shifting from cubic to tetragonal andfinally to orthorhombic structure. At the energy lower than theband gap there is no electron in the unoccupied bands and hencethe sum rule drops rapidly. The numbers of electrons arise rapidlynear the band gap energy and this raped rising is continuous up to20 eV causing an increase in the sum rule and the oscillatorsstrength which saturates at 40 eV.

From the comparison of all optical properties discussed, it isclear that CsPbBr3 orthorhombic and CsPbI3 cubic is the bestamongst the three materials for light absorption and hence for the

solar cell applications. But at the same time the other two are alsogood to be used for similar applications.

4. Conclusion

Structural analysis and electronic and optical properties ofOrganic-Inorganic perovskites CsPbX3 (X ¼ Cl, Br, I) are very suit-able to make solar cells and energy storage devices. The investi-gation of CsPbX3 (X ¼ Cl, Br, I) is performed in cubic, tetragonal andorthorhombic phases. The small bandgaps of these materials showthat they behave like semiconductors which can strongly absorbincoming photon if its energy is in the range of the bandgap of eachmaterial. Their superluminescence ability at photon energy of13 MeV or higher makes them very diverse for practical use.

Acknowledgment

We acknowledge the financial support from the Higher Educa-tion Commission, Pakistan (HEC), Project no. 20-3959/NRPU/R&D/HEC2014/234

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