Electronic structure and optical properties of Cs2AX2′X4 (a=ge,sn,pb; x′,x=cl,br,i)

Electronic structure and optical properties of Cs2AX2′X4 (A=Ge,Sn,Pb; X′,X=Cl,Br,I) Electronic structure and optical properties of (A=Ge,Sn,Pb; X′,X=Cl,Br,I) Guangtao Wang, Dongyang Wang, and Xianbiao[.]

Electronic structure and optical properties of (A=Ge,Sn,Pb;

X ′ ,X=Cl,Br,I)

Guangtao Wang, Dongyang Wang, and Xianbiao Shi

Citation: AIP Advances 5, 127224 (2015); doi: 10.1063/1.4939016

View online: http://dx.doi.org/10.1063/1.4939016

View Table of Contents: http://aip.scitation.org/toc/adv/5/12

Published by the American Institute of Physics

Electronic structure and optical properties of Cs2AX′2X4

Guangtao Wang,aDongyang Wang, and Xianbiao Shi

College of Physics and Information Engineering, Henan Normal University, Xinxiang,

Henan 453007, People’s Republic of China

(Received 25 August 2015; accepted 9 December 2015; published online 21 December 2015)

We studied the crystal structures, electronic structures and optical properties of

Cs2AX′2X4(A=Ge,Sn,Pb; X′, X=Cl, Br, I) compounds using the first-principles calcu-lation Our optimized structures agree well with experimental and theoretical re-sults Band structure calculations, using the modified Becke-Johnson (mBJ) poten-tial method, indicate that these compounds (with the exception of Cs2PbX′2I4) are semiconductors with the direct band gap ranging from 0.36 to 4.09 eV We found the compounds Cs2GeBr2I4, Cs2GeCl2I4, Cs2GeI2Br4, Cs2SnI6, and Cs2SnBr2I4may be good candidates for lead-free solar energy absorber materials C 2015 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.[http://dx.doi.org/10.1063/1.4939016]

I INTRODUCTION

As the global demand for energy grows inexorably, solar energy is attracts an increasing amount

of attention owing to its abundant, clean, and renewable characteristics The pursuit of high efficiency solar cells has not slowed since the first generation reported The first generation crystalline silicon based solar cells reached a high efficiency, but they were limited by a low optical absorption coeffi-cient and high cost of fabrication.13Cu-based selenide and sulfide compounds are considered to be

a promising class of materials for solar cell applications, with the higher power conversion efficiency (PCE) to date, about 23.3%.4 8Recently, the hybrid organic-inorganic perovskites metal halides have emerged as promising light-harvesting materials for the next generation of solar cells, with advan-tageous properties including direct band gaps, large absorption coefficients, and high carrier mobil-ities.9 13Miyasaka et al.10 pioneered the incorporation of the hybrid organic-inorganic perovskite halides into solar cells, and found that CH3NH3PbI3based solar cells had a 3.8% PCE, which was improved to 6.5% by Lee et al.14A breakthrough occurred in 2012 with the realization of the long term stability of all-solid-state solar cells using this materials; these had a PCE of 9.7%.15Chung

et al.16 improved the PCE up to 10.2% in a new type of all-solid-state inorganic solar cell, which consisted of the p-type direct band gap semiconductor CsSnI3and n-type TiO2with dye N719 The work of Liu et al.11indicates that the PCE could reach over 15% using an absorbing layer of the vapor-deposited perovskite CH3NH3PbI(3−x)Clx A solution-processed solar cell using CH3NH3PbI3

as the absorption material could achieve a PCE of 20.1%.8

More recently, Lee et al.17designed a new type of solar cell by replacing CsSnI3with the more stable Cs2SnI6as the absorbing layer and achieved a PCE of about 8% Unlike the tin-based perovskite compound CsSnI3, which has Sn2+and must be handled in an inert atmosphere when fabricating the

solar cells, Cs2SnI6contains Sn4+, making it more stable under exposure to air and moisture This

characteristic is vital for the realization of the low-cost, stable, lead-free, and environmentally friendly next generation of solid-states solar cells In addition to the experimental results as mentioned above, there are many first-principle calculations about various perovskite solar materials.18 – 22While search-ing for lead-free, high efficiency photovoltaic materials, Lang et al.23studied the optical properties of

a Electronic mail: wangtao@henannu.edu.cn

2158-3226/2015/5(12)/127224/7 5, 127224-1 © Author(s) 2015

127224-2 Wang, Wang, and Shi AIP Advances 5, 127224 (2015)

MAB3, where M=Cs, CH3NH3, NH2CHNH2; A=Sn, Pb; B=Cl, Br, I However, some of these MAB3

compounds are unstable in the air and moist environments

In this paper, we report the crystal structures, electronic structures and absorption coefficients

of Cs2AX2′X4(A=Ge,Sn,Pb; X′,X=Cl,Br,I) materials determined through the first-principles calcula-tions We found Cs2GeBr2I4, Cs2GeCl2I4, Cs2GeI2Br4, Cs2SnI6, and Cs2SnBr2I4may be good candi-dates for lead-free solar energy absorber materials These materials will provide more options in the pursuit of high PCE solar cell absorber materials

II METHODOLOGY

The structure optimization calculations are based on the density functional theory (DFT) method, as implemented in the Vienna Ab-initio Simulation Package (VASP).30 The generalized gradient approximation (GGA)31formulated by Perdew-Burke-Ernzerhof (PBE)32is employed for exchange-correlation functional The project-augmented wave (PAW) potential is employed to describe the electron-ion potential The wave functions are expanded in plane waves with a cut

off energy of 500 eV The convergence criterion for the electronic self-consistent iteration and the Hellmann-Feynman forces are set to 10−5eV and < 0.01 eV Å−1, respectively The Brillouin-zone integration is performed with 11 × 11 × 11 and 13 × 13 × 11 Γ-centered Monkhorst-Pack (MP)33 grids for cubic and tetragonal phase, respectively The lattice constants of the analyzed materials are listed in TableI

Taking the optimized structures listed in TableI, we use the WIEN2k34code with the PBE and modified Becke-Johnson (mBJ) potential35 to study the electronic structure and optical properties

of the materials The mBJ method successfully in overcomes the problem of underestimating the band gap, since it considers the core electrons as fully relativistic and the valence electrons are treated semi-relativistically To achieve the energy eigenvalue convergence, the basis function are expanded up to RMT× Kmax= 7, where RMT is the minimum radius of muffin-tin spheres and

Kmax is the magnitude of the largest K vector in the plane wave expansion The valence wave functions inside the spheres are expanded up to lmax= 10, and the charge density is expanded as

a Fourier series up to Gmax= 12 The self-consistent potentials are calculated on 1000 k-points

in the first Brillouin zone, and the convergence criterion is set to 0.0001 Ry Denser (8000) k-points in the irreducible wedge of the first Brillouin zone are used for calculations of the optical properties

TABLE I Optimized lattice constant (in Å) of Cs 2 AX ′

2 X 4 The available experimental results are shown in square brackets The predicted lattice constant from the formula in Ref 24 is shown in parentheses.

A Cs 2 AI 6 Cs 2 ABr 2 I 4 Cs 2 ACl 2 I 4 Cs 2 AI 2 Br 4 Cs 2 ABr 6

Ge a =11.804 a =8.153 a =8.163 a =8.162 a =11.081

(a=11.317) c=11.792 c=11.538 c=10.958 (a=10.633)

Sn a =12.032 a =8.369 a =8.335 a =8.251 a =11.243

[a =11.65] 26 c =11.771 c =11.563 c =11.259 [a =10.770] 27

Pb a =12.066 a =8.210 a =8.146 a =8.378 a =11.327

(a =11.553) c =12.246 c =12.069 c =11.089 (a =10.869)

A Cs 2 ACl 2 Br 4 Cs 2 AI 2 Cl 4 Cs 2 ABr 2 Cl 4 Cs 2 ACl 6

c =11.037 c =10.331 c =10.536 [a =10.23] 25

Sn a =7.805 a =8.125 a =7.787 a =10.724

c=11.196 c=11.563 c=10.714 [a=10.355] 28

c =11.376 c =10.422 c =10.709 [a =10.416] 29

FIG 1 Crystal structure of (a) the cubic phase Cs 2 AX 6 and (b) the tetragonal phase Cs 2 AX ′

2 X 4

III RESULTS AND DISCUSSION

Cs2AX6compounds crystallize in a cubic structure with the Fm¯3m (No.225) space group, as shown in Fig.1(a) In the case of Cs2AX2′X4, shown in Fig.1(b), the X ion at the apex of the octahedron along the z-axis is replaced by the other halogen ion X′ The symmetry of this new crystal is lowered

to I4/mmm (No.139) The optimized lattice constants of Cs2AX2′X4for cubic and tetragonal phase are presented in TableI The results are in good agreement with the available experiment data25–29 and the theoretical prediction reported by Brik et al.24The lattice constants and bond length in the octahedron of these crystals are shown in Fig.2(a),2(b),2(c)and Fig.2(d),2(e),2(f) The changes

in lattice parameters and bond length can be ascribed to radius changes among A and the halogen ions When X′and X are fixed, the lattice parameter a of Cs2AX2′X4in the tetragonal phase decreases with the radius of the A ion from Pb, Sn, to Ge, with a corresponding increase of the lattice parameter

c This leads to a distortion of the octahedron and lowers the symmetry of the crystal, as shown in Fig.1 When the A and X ions are fixed, the bond length of A-X′along the z axis decreases from I,

Br, to Cl

FIG 2 The lattice constant (solid-line for a, dashed-line for c, Å), bond length (BL in Å, solid-line for BL in x-y plane, dashed-line for BL along c-axis), band gap (E g in eV), and octahedron ionicity (F o ) of Cs 2 AX′2X 4 are presented as a function

of X ′ atoms type in the (a,b,c), (d,e,f), (g,h,i) and (j,k,l), respectively The color line in black, red, and green for A = Ge, Sn, and Pb, respectively For the tetragonal phase, the lattice constant was defined to be a =√2a 0 , where a 0 is the lattice constant

of a conventional cell and a is the super-cell lattice constant.

127224-4 Wang, Wang, and Shi AIP Advances 5, 127224 (2015)

FIG 3 (a) Band structure with mBJ (blue lines) and PBE (red lines) methods and (b) projected density of state with mBJ method in cubic phase Cs 2 PbBr 6 The zero energy is at the VBM.

We calculate the projected density of states (PDOS) and the band structure of Cs2AX′2X4with mBJ and PBE methods, and summarize their band gaps with mBJ method in Fig 2(g),2(h),2(i) Our results indicate that Cs2PbX′

2I4(X′= Cl,Br,I) show metallic characteristic, and all the other com-pounds behave as semiconductors with a band gap (Eg) ranging from 0.36 to 4.09 eV, as shown in Fig.2(g),2(h),2(i) We consider the example of Cs2PbBr6for further investigation; its band structure and PDOS are shown in Fig.3 The mBJ method significantly improves the band gap and overcomes the underestimation of PBE method In Fig.3(a), we note the direct band gap of 1.26 eV located

at Γ(0, 0, 0) point This Egis smaller than the direct band gap of CH3NH3PbBr3(2.2 eV), located at

R(0.5, 0.5, 0.5).36The conduction band maximum (CBM) only consists of one band derived from the hybridization of Pb-6s and Br-4p states, while the valence band minimum (VBM) is derived from the Br-5p states This is significantly different from the CBM of CsPbBr3, which is threefold degener-ated at the R point and derived from the Pb-6p state.23For CH3NH3PbBr3, the calculated band gap with spin-orbital coupling (SOC) is 1.0 eV smaller than that without SOC, but the SOC effect in the

Cs2PbBr6has little impact on the Eg(a change of ∼ 0.2 eV) This is because that the CBM in Cs2PbBr6

is derived from the hybridization of Pb-6s and Br-4p states, while the CBM of CsPbBr3is derived from the Pb-6p state and the SOC have a significant impact for this compound

All the tetragonal phase compounds have a similar electronic structure, except for a difference in band gap, as shown in Fig.2(g),2(h),2(i) Therefore, we show results of one representative compound

Cs2PbI2Cl4 The band structure and PDOS are presented in Fig.4 The band structure in Fig.4(a)also shows that the mBJ method can effectively overcome the underestimate of band gap with PBE method

We note that both the CBM and VBM lie at the Γ(0, 0, 0) point, with a direct band gap Eg = 0.96 eV The CBM is derived from the mixture of Pb-6s, I-5p, and Cl-3p states The VBM is mainly derived from the I-5p and Cl-3p states; the band center of I-5p is higher than the Cl-3p states, as shown in Fig.4(b) Since the Pb-6p state has no contribution to the CBM, the SOC effect does not need to be considered This is also provides a evidence for the existence of Pb4+in the tetragonal phase.

The band gaps of all the compounds are plotted in Fig 2(g),2(h),2(i) The trend of Eg can

be understood by considering the Pauling electronegativity ( χA) of the A ion and the octahedron ionicity (Fo) We defined the octahedron ionicity (Fo) as Fo= (2 × FAX ′+ 4 × FAX)/6, where the

FAX = 1 − e− (χ A −χX) 2 /4is the Pauling ionicity, and χAand χXrefer to the electronegativity of A and

X atoms When X′and X are fixed, the band gap Eg increases with the decreasing of χ , from Pb,

FIG 4 (a) Band structure with mBJ (blue lines) and PBE (red lines) methods and (b) projected density of state with mBJ method in tetragonal phase Cs 2 PbI 2 Cl 4 The zero energy is at the VBM.

Ge, to Sn ( χGe= 2.01, χS n= 1.96, χPb= 2.33) The octahedron ionicity Foindicates the electron transfers from X (and/or X′) to A in the octahedron In Fig.2(g),2(h),2(i), it shows that the larger

Fo, the larger band gap The parameter Focan help us to search for new compounds with suitable band gap, before doing first-principle calculations

Semiconductors with Eg between 1.0 eV and 1.5 eV are generally well accepted to have the greatest potential in the application of high efficiency solar cells With this in mind, we predict that Cs2GeBr2I4, Cs2GeCl2I4, Cs2GeI2Br4, Cs2SnI6, Cs2SnBr2I4, Cs2SnCl2I4, Cs2PbBr6, Cs2PbI2Cl4,

Cs2PbCl2Br4, and Cs2PbBr2Cl4will be more promising candidates for the solar cell absorbers Now,

we focus on these materials and compare their optical properties In Fig.5, we present the absorption coefficient of Cs2AX′2X4in the range of 300 to 800 nm It is seen from figure that the optical absorption coefficient of tetragonal phase exhibit strong anisotropy with respect to the relative orientation of the polarization of light and crystal lattice This polarization anisotropy results from anisotropy of the tetragonal phase dielectric tensor ϵ(ω) We denote the two components of the electric field (E) relative

to the optical axis The dielectric component for E⊥c is ϵ⊥= ϵxx= ϵyyand that for E∥c is ϵ∥= ϵzz, So

we label the optical absorption coefficient for the light polarization in the ab plane as α⊥and along

c axis as α∥for the tetragonal phase The absorption coefficient α⊥of Cs2GeCl2I4has a high and sharp peak around 400 nm (Fig.5(a)), indicating a strong absorption of purple light The absorption coefficients α⊥of Cs2GeBr2I4, Cs2GeCl2I4, Cs2SnBr2I4, Cs2SnCl2I4, Cs2PbI2Cl4, and Cs2PbCl2Br4

are larger than those α∥, while the cases are reversed for Cs2GeI2Br4and Cs2PbI2Cl4 The absorption coefficients of the Pb-based compounds are larger than those of the Ge- and Sn-based compounds

In Fig.6, we define the Ideal Power Absorption Coefficient IPAC = I0(E) ∗ a(E), where the I0(E)

is the standard AM 1.5G solar spectrum39and a(E) is the photon absorptivity The absorptivity is given

by a(E) = 1 − e−2α (E)×L, which depends on the absorption coefficient α(E) and absorber thickness

L.40 , 41Here we used typical absorber thickness of L= 500 nm, because that such absorber thickness

is often used in the experiments.13 , 17 , 42For α(E), it is derived from weighted average of absorption coefficient as α(E) = (α⊥+ 2α∥)/3 The area enclosed by the IPAC curves and the abscissa axis is equal to the absorption power of the materials We integrate the IPAC curves from 300 to 800 nm and present the resulting absorption power values in Fig 6 In Fig.6(a), the absorption power of

Cs2GeBr2I4(718.21 W/m2) is larger than the other Ge-based compounds In Fig.6(b), the absorption power of Cs2SnCl2I4(719.78 W/m2) is higher than the other Sn-based compounds Both of them are compatible to the largest value of 748.79 W/m2derived from CsPbICl The Pb-based compounds

127224-6 Wang, Wang, and Shi AIP Advances 5, 127224 (2015)

FIG 5 Absorption coe fficient of Cs 2 AX ′

2 X 4 , where A ion is (a) Ge, (b) Sn, and (c) Pb, respectively The optical absorption coe fficient 37 , 38 for the light polarization in the a-b plane (solid line) note as α ⊥ and along c axis (dashed line) note as α∥for the tetragonal phase, respectively.

Cs2PbBr6and Cs2PbI2Cl4have larger absorption powers than the Ge-based and Sn-based compounds, but they are not environmentally friendly The environmentally friendly compounds Cs2GeBr2I4,

Cs2GeCl2I4, Cs2GeI2Br4, Cs2SnI6, and Cs2SnBr2I4may be good candidates for solar energy absorber materials

FIG 6 Ideal Power Absorption Coefficient (IPAC) of Cs 2 AX′2X 4 under the standard AM 1.5G solar spectrum,39as a function

of the wavelength Panels (a), (b), and (c) correspond to A=Ge, Sn and Pb, respectively IPAC = I 0 [1 − e(2L×(2α⊥ +α∥)/3 ], where the I 0 is the standard AM 1.5G solar spectrum, α ⊥ and α ∥ are the absorption coefficient and the L is the absorber thickness.40,41An arrow points from each curve to a number that represents the result of the integration of that curve; this corresponds to the absorption power (in W/m 2 ).

IV SUMMARY

In this work, we have studied the electronic structure and optical properties of Cs2AX2′X4(A=Ge,

Sn, Pb; X′, X=Cl, Br, I) compounds using first-principles calculations The optimized crystal struc-tures we determined are in good agreement with the experimental data We found that the trends of band gaps are consistent with the octahedron ionicity The Pb-based compounds have larger absorp-tion powers than the Ge-based and Sn-based compounds, but they are not environmentally friendly

We found that Cs2GeBr2I4, Cs2GeCl2I4, Cs2GeI2Br4, Cs2SnI6, and Cs2SnBr2I4might be environmen-tally friendly solar energy absorber materials

ACKNOWLEDGMENTS

The authors acknowledge support from the NSF of China (No.11274095, No.10947001) and the Program for Science and Technology Innovation Talents in the Universities of Henan Province (No.2012HASTIT009, No.104200510014, and No.114100510021) This work is supported by The High Performance Computing Center of Henan Normal University

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