First-Principles Study on Structural, Electronic, and Optical Properties

2 hours ago - In this work, we investigated the structural, electronic, and optical properties of the inorganic Ge-based halide perovskites AGeX3 (A =...
9 downloads 0 Views 1MB Size
Download PDF
Article pubs.acs.org/IC

Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

First-Principles Study on Structural, Electronic, and Optical Properties of Inorganic Ge-Based Halide Perovskites Un-Gi Jong,† Chol-Jun Yu,*,† Yun-Hyok Kye,† Yong-Guk Choe,† Wei Hao,‡ and Shuzhou Li‡ †

Downloaded via EAST CAROLINA UNIV on March 13, 2019 at 13:10:39 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Chair of Computational Materials Design, Faculty of Materials Science, Kim Il Sung University, Ryongnam-Dong, Taesong District, Pyongyang, Democratic People’s Republic of Korea ‡ School of Materials Science and Engineering, Nanyang Technological University, Nanyang Avenue, 639798 Singapore ABSTRACT: Using density functional theory calculations, we explore the structural, electronic, and optical properties of the inorganic Ge-based halide perovskites AGeX3 (A = Cs, Rb; X = I, Br, Cl) that can possibly be used as light absorbers. We calculate the lattice parameters of the rhombohedral unit cell with an R3m space group, frequency-dependent dielectric constants, photoabsorption coefficients, effective masses of charge carriers, exciton binding energies, and electronic band structures by use of PBEsol and HSE06 functionals with and without SOC effect. We also predict the absolute electronic energy levels with respect to the external vacuum level by using the (001) surfaces with AX and GeX2 terminations, demonstrating their strong dependence on the surface terminations. The calculated results are found to be in reasonable agreement with the available experimental data for the cases of CsGeX3, while for the cases of RbGeX3 they are predicted for the first time in this work. We reveal that replacement of Cs with Rb can offer reasonable flexibility in optoelectronic properties matching for solar cell design and optimization, while X anion exchange gives rise to large changes.

■

INTRODUCTION Recently photovoltaic solar cells have been revolutionized by adopting halide perovskites with a chemical formula of ABX3 as photoabsorbers.1,2 As initiated by the report of Kojima et al.1 in 2009, the power conversion efficiency (PCE) of the perovskite solar cells (PSCs) has rapidly jumped from the initial value of 3.8% to over 22.1%2 within less than 10 years. The most widely investigated PSCs are based on the hybrid organic−inorganic iodide CH3NH3PbI3 (or MAPbI3), where an organic MA+ cation, a metallic Pb2+ cation, and I− anion occupy the A, B, and X sites. However, the presence of the toxic element Pb3,4 and the chemical instability originating from the organic moiety MA5−8 cause serious concerns with regard to environmental issues and large-scale commercialization. In order to address these problems, compositional tuning has been introduced: substitutions of a nontoxic Sn2+ or Ge2+ cation for the Pb2+ cation and/or inorganic Cs+ or Rb+ cation for the organic MA+ cation.3,4,9−11 Accordingly, CsSnI3 has been synthesized in the cubic phase, but the PCE of the cell was only up to 2%.12−14 In parallel with these experiments, theoretical investigations have been performed, revealing that such a coarse efficiency is associated with the large mismatch of band alignment between the tin-based perovskite photoabsorber and charge carrier conductors.15,16 Moreover, tinbased halide perovskites have a serious problem of the susceptibility of tin oxidation from the +2 to the +4 state upon exposure to ambient air, resulting in much less research effort being made toward tin-based PSCs. In such a situation, © XXXX American Chemical Society

germanium-based inorganic perovskites CsGeX3 (X = I, Br, Cl) have emerged as potential alternatives to tin-based perovskites for lead-free and long-term PSCs.17−20 More importantly, CsGeX3 does not suffer from a phase transition to the lowdimensional yellow phase (nonperovskite structure) at room temperature; it exists in a stable three-dimensional (3D) perovskite structure with a small rhombohedral distortion in the R3m space group up to 350 °C.21−24 With regard to the A site, substitution of Rb for Cs can be expected to enhance the film quality and applicability in solar cell devices.15,25 To the best of our knowledge, however, neither experimental nor theoretical studies on RbGeX3 could be found, although there have been some experimental and theoretical studies on CsGeX3.17−19 Therefore, it is necessary to get a comprehensive insight into the structural and optoelectronic properties of RbGeX3 in comparison with CsGeX3 for solar cell applications. In the present work we perform a theoretical investigation based on state of the art density functional theory (DFT) to get a comprehensive understanding of germanium-based halide perovskites AGeX3 (A = Cs, Rb; X = I, Br, Cl) for solar cell applications. We provide a systematic comparison of structural, electronic, and optical properties of these crystalline materials, paying special attention to the band alignments that are dependent on the surface terminations. The results shed light on the systematic variation of the optoelectronic properties Received: November 1, 2018

A

DOI: 10.1021/acs.inorgchem.8b03095 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry and on the feasibility of modulating the energy level alignment upon exchange of the A site cation or X site anion in AGeX3.

■

COMPUTATIONAL METHODS All calculations in this work were performed by using the pseudopotential plane-wave method as implemented in the Vienna ab initio simulation package (VASP).26,27 Projector augmented wave (PAW)28,29 functions provided in the package were used to describe the ion−electron interactions. Here, the valence electronic configurations of the atoms are as follows: Cs, 5s25p66s1; Rb, 4s24p65s1; Cl, 3s23p5; Br, 4s24p5; I, 5s25p5; Ge, 4s24p2. The Perdew−Burke−Ernzerhof functional for solids (PBEsol)30 within the generalized gradient approximation (GGA) was used to describe the exchangecorrelation interaction between the valence electrons. As the major computational parameters, the plane-wave cutoff energy was set to 500 eV and the Monkhorst−Pack special k points were set to (6 × 6 × 6) for structural relaxations and (10 × 10 × 10) for electronic structure calculations, which can provide an accuracy of total energy of 1 meV per formula unit. The convergence thresholds for total energy and atomic forces were set to 10−6 eV and 10−4 eV/Å, respectively. To obtain more reliable band gaps, we also performed electronic structure calculations by using the Heyd−Scuseria−Ernzerhof (HSE06) hybrid functional,31−34 in which we replaced 20% of the PBE exchange functional35 with the exact Hartree−Fock exchange functional, providing bulk band gaps in good agreement with experiment. The spin−orbit coupling (SOC) effect was considered only in the electronic structure calculations. By applying the density functional perturbation theory (DFPT) method, we calculated the macroscopic frequency-dependent dielectric functions, ε(ω) = ε1(ω) + iε2(ω), and estimated the photoabsorption coefficients α(ω) as36,37 α(ω) =

2ω c

Figure 1. Polyhedral view of (a) bulk and surfaces with two different terminations of (b) AX and (c) GeX2 of inorganic Ge-based halide perovskites AGeX3 (A = Cs, Rb; X = I, Br, Cl).

from the electrostatic potential to the reference level. Choosing the Ge 1s level as the representative core level, we calculated the absolute energy levels such as VBM and CBM of the bulk phases as

mr * 1 (eV) me εs2

KS bulk surf ECBM = ϵCBM − (EGe1s − EGe1s ) − Vvac

(4)

KS ϵCBM

where and are the Kohn−Sham (KS) bulk eigenvalues corresponding to VBM and CBM, respectively, surf Ebulk Ge1s and EGe1s are the average Ge 1s levels of the Ge atoms in the bulk phase and in the innermost three layers of the surface slab model, respectively, and Vvac is the vacuum level derived from the planar average electrostatic potential of the surface slab models.

(1)

■

where c is the light velocity in a vacuum and ω is the frequency of a light wave. We calculated the effective masses of electrons (me*) and holes (mh*) by numerically processing the refined energy band data around the Z point of Brillouin zone, at which point both the valence band maximum (VBM) and the conduction band minimum (CBM) were found. Then, the exciton binding energies (Eb) were estimated using the formula36,37 E b = 13.56

(3)

KS ϵVBM

ε12(ω) + ε22(ω) − ε1(ω) 2

bulk surf E VBM = ϵKS VBM − (EGe1s − EGe1s) − Vvac

RESULTS AND DISCUSSION The family of inorganic Ge-based halide perovskites AGeX3 is expected to stabilize in the rhombohedral phase with the R3m space group at room temperature, as experimentally identified for CsGeX3.21−24 As a preliminary test of perovskite structure formability, we first analyzed their Goldschmidt tolerance factors, calculated by tG = (rA + rX)/ 2 (rB + rX) using the Shannon ionic radii.39 On the basis of the established fact that tG values ranging from 0.8 to 1.0 can support the formation of a perovskite structure, all six compounds are expected to crystallize in a stable perovskite phase due to their proper tolerance factors within 0.90 < tG < 0.97 (Table 1). Through the structural optimizations, it was found that the cornersharing GeX6 octahedra were slightly distorted because of Ge2+ cation off-centering as identified in the cubic CsSnX3 and CsPbX3 by first-principles calculations.16 Such octahedral distortion implies a creation of spontaneous electric polarization that can enhance charge carrier separation and allow the photovoltage to exceed the band gap.40 The calculated lattice constants and angles by use of the PBEsol functional are given in Table 1. Our calculated lattice constants of 5.94, 5.56, and 5.33 Å, respectively, for CsGeX3 with X = I, Br, Cl are in good agreement with the experimental values17,23 with a slight underestimation of ∼1.8%, being better

(2)

where mr* (1/mr* = 1/me* + mh*) is the reduced effective mass and εs is the static dielectric constant. In order to calculate the absolute electronic energy levels, we have built (001) surface slab models with two different terminations, AX and GeX2, which contain 11 atomic layers and a vacuum layer of 15 Å thickness, as shown in Figure 1. The outermost atomic positions were fully relaxed, while the innermost three atomic layers were frozen corresponding to the bulk positions. For the affordable HSE06 calculations in the surface models, we have adopted the lower plane-wave cutoff energy as 300 eV and smaller k points as (6 × 6 × 1). Following the procedures suggested in previous works,15,38 we first calculated the electrostatic potential of (001) relaxed surface slab models and set an external vacuum level obtained B

DOI: 10.1021/acs.inorgchem.8b03095 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Table 1. Goldschmidt’s Tolerance Factor tG, Lattice Constant (a), and Angle (α) in AGeX3 (A = Cs, Rb; X = I, Br, Cl) Calculated with the PBEsol Functionala α (deg)

a (Å) material

tG

our cal

exp

other cal

our cal

exp

other cal

CsGeI3 CsGeBr3 CsGeCl3 RbGeI3 RbGeBr3 RbGeCl3

0.93 0.95 0.97 0.90 0.92 0.93

5.94 5.56 5.33 5.91 5.53 5.27

5.98b 5.64c 5.43c 5.99e

6.13d 5.78d 5.54d

88.68 89.15 89.88 87.79 87.99 89.66

88.60b 88.79c 89.72c

88.28d 88.53d 88.95d

a

cal and exp stand for calculation and experiment, respectively. bReference 23. cReference 17. dThe lattice parameters were determined with the PBE functional.19 eReference 41.

Table 2. Static and High-Frequency Dielectric Constants (ε0 and ε∞), Effective Masses of Electron (me*), Hole (mh*), and Reduced Mass (mr*), Exciton Binding Energies Using the Static (Eb) and High-Frequency Dielectric Constants (Ẽ b), and Band Gap (Eg) in AGeX3 (A = Cs, Rb; X = I, Br, Cl), Calculated with PBEsol and HSE06 Functionals with and without SOC Effect ε∞

PBEsol (me)

Eg (eV)

PBEsol (meV)

material

PBEsol

cal

ε0 PBEsol

me*

mh*

mr*

Eb

Ẽ b

PBEsol

PBEsol+SOC

HSE06

HSE06+SOC

exp

cal

CsGeI3 CsGeBr3 CsGeCl3 RbGeI3 RbGeBr3 RbGeCl3

7.45 5.92 4.77 9.16 7.67 5.37

9.98a 6.52a 4.30a

19.82 16.98 13.69 23.01 18.49 15.98

0.15 0.18 0.27 0.16 0.18 0.24

0.16 0.19 0.28 0.17 0.18 0.24

0.08 0.09 0.14 0.08 0.09 0.12

2.72 4.35 10.01 2.14 3.62 6.32

19.24 35.83 82.27 13.49 21.07 55.98

1.19 1.46 2.13 1.31 1.57 2.16

1.06 1.42 2.08 1.18 1.53 2.12

1.64 2.34 3.24 1.78 2.40 3.28

1.52 1.77 2.28 1.67 2.04 2.25

1.63b 2.39d 3.40d

1.41c 1.66c 2.22c

a

The dielectric constants were calculated with the PBE functional.43 bReference 17. cThe band gaps were determined with the HSE06+SOC method.19 dReference 44.

2.39, and 3.40 eV, respectively17,44), as given in Table 2, indicating a weakening of SOC effect in these Ge-based halide perovskites. Such an underestimation of band gap becomes more severe for lighter halogen atoms on going from I to Cl due to weaker relativistic effects, as shown in Figure 2. When

than those by the PBE functional with an overestimation of ∼2.5%.19 In contrast, lattice angles were overestimated with PBEsol in this work, while they were underestimated with PBE in the previous work.19 As the ionic radius of the X site halide anion decreases (i.e., on going from I to Br to Cl), the lattice constant decreases and the lattice angle becomes close to 90°, indicating that the crystalline lattice shrinks and changes from the rhombohedral to the cubic phase. Such a trend of crystalline lattice variation is well coincident with the increasing tendency of tolerance factor from X = I to X = Cl, remembering that for a perfect cubic perovskite structure tG = 1. These can be associated with the strengthening of chemical bonds between Ge and X atoms and subsequently the slackening of Ge atom off-centering in GeX6 octahedra, possibly resulting in an enhancement of chemical stability on going from X = I to X = Cl. Upon exchange of the A site cation from Cs to Rb, the lattice parameters slightly decrease in accordance with a reduction of ionic radius. Due to the lack of experimental results, the lattice constants for rhombohedral RbGeBr3 and RbGeCl3 were not provided in Table 1, but we again confirmed that our calculated lattice constant of 5.91 Å agrees well with the experimental value of 5.99 Å for RbGeI3.41,42 In a next step, we calculated the electronic structures by use of different levels of DFT methods: PBEsol and HSE06 XC functionals with and without SOC effect. For the organic− inorganic hybrid iodide perovskite MAPbI3, the PBE or PBEsol functional was found to yield a band gap coincident with experiment, due to a fortuitous error cancellation between the GGA underestimation and the overestimation by ignoring the SOC effect.45,46 For the all-inorganic Ge-based halide perovskites CsGeX3 (X = I, Br, Cl), however, the PBEsol functional gave underestimated band gaps (1.19, 1.46, and 2.13 eV, respectively) in comparison to the experimental values (1.63,

Figure 2. Band gap deviations calculated with different XC functionals from the corresponding experimental values in CsGeX3 (X = I, Br, Cl).

the SOC effect is included (PBEsol+SOC), band gaps were further underestimated due to the splitting and lowering of CBM.45,46 Meanwhile, the hybrid HSE06 functional gave band gaps in good agreement with the experimental values for CsGeX3 with absolute accuracies of +0.01, −0.05 and −0.16 eV for X = I, Br, Cl, respectively (for CsPbI3, GW without SOC effect can also yield a reliable band gap47). Accordingly, the HSE06+SOC calculations produced underestimated band gaps in contrast to the cases of MAPbX3, for which the HSE06+SOC or GW+SOC method gives band gaps in good agreement with experiment.45,46 It should be noted that when C

DOI: 10.1021/acs.inorgchem.8b03095 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 3. Electronic band structure and density of states (DOS) of inorganic halide perovskites AGeX3 (A = Cs, Rb; X = I, Br, Cl), calculated with PBEsol (dotted line) and HSE06 (solid line) functionals. Green and orange colors in the band structures indicate valence and conduction bands, respectively.

going from I to Cl, the effective masses become larger but still are sufficiently small for charge carrier conductors. Upon exchange of Cs for Rb, the values are more or less unchangeable or even become smaller for the case of X = Cl, giving an expectation of no detriment of optical properties. Then, using the DFPT approach in consideration of a atomic displacement effect, we calculated the frequencydependent macroscopic dielectric functions, from which the high-frequency dielectric constants were extracted at zero photon energy.48 It should be noted that the Bethe−Salpeter approach considering the excitonic (i.e., the electron−hole interaction) and many-body effects gives the almost same dielectric constants to those from DFPT.37 The high-frequency dielectric constant (ε∞) of CsGeI3 was determined to be 7.45, which is higher than that of the cubic MAPbI3 (∼537), indicating more effective screening of electron−hole interactions without phonon contribution. As the atomic number of the X site halide anion decreases, ε∞ decreases to 4.77 for CsGeCl3, which can be closely associated with a smaller degree of Ge atom off-centering for a smaller ionic radius halide anion (leading to the GeX6 octahedral distortion) as discussed above. Replacing Cs with Rb causes a slight increase in static dielectric constants in AGeX3 (X = I, Br, Cl), indicating a possible improvement in charge carrier mobility by such replacement. As a crucial factor for determining the optical and transport properties, the exciton binding energies (Eb) were estimated on the basis of the calculated effective masses and static dielectric constants (see Table 1). On the time scale of the relative motion of electrons and holes, the ions have enough time to relax contributing to the electrostatic screening, so that one should use the static dielectric constant (ε0) in calculating the exciton binding energy in order to include the phonon contributions.48 When the time scale is fast relative to the vibrational periods, meanwhile, one should use the highfrequency dielectric constant (ε∞) in the calculation of exciton binding energy since the phonon cannot contribute to the screening.48 Then, according to the Lyddane−Sachs−Teller (LST) relation FLST = ∏i (ωLi /ωTi)2 = ε0 /ε∞, the exciton binding energy can be reduced as a square factor of FLST.48 In Table 2, we provided two types of exciton binding energy, Ẽ b calculated with the high-frequency dielectric constant and Eb

the amount of exchange in the HSE06 hybrid functional is increased (e.g., addition of 43% exchange), the band gap was found to increase (2.12 eV for CsGeI3), and HSE06+SOC could produce a more reasonable band gap (1.98 eV for CsGeI3).34 Figure 3 displays the electronic band structure and density of states (DOS) calculated with PBEsol and HSE06 functionals for these inorganic AGeX3 perovskites. It can be seen that the HSE06 calculations properly push up the conduction bands while they push down the valence bands in comparison with those by the PBEsol functional. The transition of electrons from VBM to CBM is found to possibly occur in a direct way at the edge point Z (0.5, 0.5, 0.5) of the Brillouin zone (BZ). This is similar to the cubic MAPbX3 (R point)37 and is useful to the generation of charge carriers (conduction electrons and holes) by absorbing light. On the basis of the HSE06 calculations, CsGeI3 can be said to be suitable for applications of light absorbers due to its proper band gap of 1.64 eV, while RbGeI3 with a band gap of 1.78 eV can be used as a top cell material in a tandem solar cell system. When an I atom is substituted for a Br or Cl atom, the band gap becomes larger by over 2.3 or 3.2 eV, respectively, implying possible applications as charge carrier conducting materials. Through the analysis of DOS, it was found that the VBM is dominated by X p states coupling with a Ge 4s state, while the CBM is composed of strong antibonding coupling of Ge 4p states and X s states. In order to attain a deeper understanding of the potentiality of these perovskites to be used as light absorbers or charge carrier conductors, we evaluated the various optical properties such as effective masses of electrons and holes, exciton binding energies, dielectric constants, and photoabsorption coefficients by use of the PBEsol functional. The effective masses of the charge carriers were obtained by postprocessing the refined band structures around the Z point of the BZ, which clearly exhibit parabolic characteristics as shown in Figure 3. Our calculated effective masses of electrons and holes for CsGeI3 (0.15me and 0.16me in Table 1) are slightly smaller than the previous values (0.21me and 0.22me in ref 18) and are comparable with those for MAPbI3 (0.12−0.19me and 0.15− 0.24me36,37), indicating high mobility of charge carriers. On D

DOI: 10.1021/acs.inorgchem.8b03095 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry with the static constant. As shown in Table 2, Eb was reduced by a factor of about 9 in comparison to Ẽ b, as the LST factor is about 3. For the rhombohedral CsGeI3, Ẽ b was determined to be 19.24 meV, which is distinctly smaller than the value of 45− 50 meV for the cubic MAPbI3,36,37 indicating that the influence of the GeX6 octahedral distortion on exciton binding is more pronounced than the screening of MA cation rotational motion. As was previously expected, Ẽ b increases to 35.83 and 82.27 meV for CsGeBr3 and CsGeCl3, respectively, due to the decrease in the high-frequency dielectric constant on going from X = I to X = Br and Cl. As such, the exciton binding energy decreases slightly upon the replacement of Cs by Rb. Photoabsorption coefficients as a function of photon energy were calculated using the frequency-dependent dielectric functions, showing a gradual shift of the absorption onset and the first peak position and a lowering of the first peak magnitude as the atomic number of the X site atom decreases (see Figure 4).

energies, which depend on surface electrostatics and intrinsic band bending. The surface electrostatics arises as the electron density at a surface penetrates into the vacuum, giving rise to a reduction in electron density below the surface.49 The excess of electrons in the vacuum and the lack of electrons below the surface causes a potential step across the interface. On the other hand, the intrinsic band bending arises because the coordination of atoms at the surface is different from the bulk.49 Obviously, the contributions to the band energies rising from surface electrostatics and intrinsic band bending are strongly dependent on the surface termination, and we could expect a large dependence of the band energy levels on the surface termination. Figure 5 depicts the valence and conduction band energy level alignment diagrams of AGeX3 calculated by use of the hybrid HSE06 functional with and without SOC effect. HSE06+SOC calculations are shown by color bars, while HSE06 calculations without SOC effect are represented by solid lines. For the case of CsGeI3, we also give the experimental result,17 which falls properly between our calculated band energy levels of two different surface terminations. For CsGeX3, the band energy level differences between the CsX and GeX2 terminations are about 1.2 eV, while for RbGeX3 they are around 1.1 eV. By a comparison to the energy levels calculated with and without SOC, it is obvious that considering the SOC effect lowers the level of CBM due to the underestimation of the band gap, while almost same level is found for VBM as confirmed in previous work.15 It should be emphasized that the band energy level changes by A cation replacement of Rb for Cs are much smaller than those by X anion exchange.

■

CONCLUSIONS In this work we have investigated the structural, electronic, and optical properties of the inorganic Ge-based halide perovskites AGeX3 (A = Cs, Rb; X = I, Br, Cl) by using first-principles calculations. Using the rhombohedral unit cell with R3m space group, the lattice parameters, static and high-frequency dielectric constants, photoabsorption coefficients, effective masses of charge carriers, exciton binding energies, and electronic band structures have been calculated by use of the PBEsol and HSE06 functionals with and without SOC effect. The absolute electronic energy levels with respect to the external vacuum level have also been estimated using the (001) surfaces with AX and GeX2 terminations, demonstrating that they strongly depended on the surface terminations. The

Figure 4. Photoabsorption coefficients calculated within the density functional perturbation theory with the PBEsol functional for AGeX3.

In a final step, we calculated the absolute electronic energy levels of AGeX3 with respect to an external vacuum level, which are of particular interest in devising a high-efficiency solar cell system. Since the absolute band energy level depends on the surface termination,15 we considered two kinds of terminations, AX and GeX2, on the (001) surface of each AGeX3 (see Figure 1). We confirm that these surfaces have balanced charge: i.e., zero net charge of surface. The differently terminated surfaces have different contributions to the band

Figure 5. Band energy alignment diagrams of AGeX3 (A = Cs, Rb; X = I, Br, Cl) using AX and GeX2 terminated (001) surfaces, calculated by HSE06 with and without SOC effect (solid line). All energy levels are aligned with respect to the absolute vacuum level, which is set to 0 eV. E

DOI: 10.1021/acs.inorgchem.8b03095 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

(10) Swarnkar, A.; Marshall, A. R.; Sanehira, E. M.; Chernomordik, B. D.; Moore, D. T.; Christians, J. A.; Chakrabarti, T.; Luther, J. M. Quantum Dot-Induced Phase Stabilization of α-CsPbI3 Perovskite for High-Efficiency Photovoltaics. Science 2016, 354, 92−95. (11) Kovalsky, A.; Wang, L.; Marek, G. T.; Burda, C.; Dyck, J. S. Thermal Conductivity of CH3NH3PbI3 and:CsPbI3 Measuring the Effect of the Methylammonium Ion on Phonon Scattering. J. Phys. Chem. C 2017, 121, 3228−3233. (12) Chen, Z.; Wang, J. J.; Ren, Y.; Yu, C.; Shum, K. Schottky Solar Cells Based on CsSnI3 Thin-Films. Appl. Phys. Lett. 2012, 101, 093901. (13) Kumar, M. H.; Dharani, S.; Leong, W. L.; Boix, P. P.; Prabhakar, R. R.; Baikie, T.; Shi, C.; Ding, H.; Ramesh, R.; Asta, M.; Grätzel, M.; Mhaisalkar, S. G.; Mathews, N. Lead-Free Halide Perovskite Solar Cells with High Photocurrents Realized Through Vacancy Modulation. Adv. Mater. 2014, 26, 7122−7127. (14) Sabba, D.; Mulmudi, H. K.; Prabhakar, R. R.; Krishnamoorthy, T.; Baikie, T.; Boix, P. P.; Mhaisalkar, S.; Mathews, N. Impact of Anionic Br Substitution on Open Circuit Voltage in Lead Free Perovskite (CsSnI3−xBrx) Solar Cells. J. Phys. Chem. C 2015, 119, 1763−1767. (15) Jung, Y.-K.; Lee, J.-H.; Walsh, A.; Soon, A. Influence of Rb/Cs Cation-Exchange on Inorganic Sn Halide Perovskites: From Chemical Structure to Physical Properties. Chem. Mater. 2017, 29, 3181−3188. (16) Yang, R. X.; Skelton, J. M.; da Silva, E. L.; Frost, J. M.; Walsh, A. Spontaneous Octahedral Tilting in the Cubic Inorganic Caesium Halide Perovskites CsSnX3 and CsPbX3 (X = F, Cl, Br, I). J. Phys. Chem. Lett. 2017, 8, 4720−4726. (17) Krishnamoorthy, T.; Ding, H.; Yan, C.; Leong, W. L.; Baikie, T.; Zhang, L.; Sherburne, M.; Li, S.; Asta, M.; Mathews, N.; Mhaisalkar, S. G. Lead-Free Germanium Iodide Perovskite Materials for Photovoltaic Application. J. Mater. Chem. A 2015, 3, 23829− 23832. (18) Ming, W.; Shi, H.; Du, M. H. Large Dielectric Constant, High Acceptor Density, and Deep Electron Traps in Perovskite Solar Cell Material CsGeI3. J. Mater. Chem. A 2016, 4, 13852−13858. (19) Walters, G.; Sargent, E. H. Electro-Optic Response in Germanium Halide Perovskites. J. Phys. Chem. Lett. 2018, 9, 1018− 1027. (20) Mao, X.; Sun, L.; Wu, T.; Chu, T.; Deng, W.-Q.; Han, K.-L. First Principles Screening of All Inorganic Lead Free ABX 3 Perovskites. J. Phys. Chem. C 2018, 122, 7670−7675. (21) Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G. Semiconducting Tin and Lead Iodide Perovskites with Organic Cations: Phase Transitions, High Mobilities, and Near-Infrared Photoluminescent Properties. Inorg. Chem. 2013, 52, 9019−9038. (22) Stoumpos, C. C.; Frazer, L.; Clark, D. J.; Kim, Y. S.; Rhim, S. H.; Freeman, A. J.; Ketterson, J. B.; Jang, J. I.; Kanatzidis, M. G. Hybrid Germanium Iodide Perovskite Semiconductors: Active Lone Pairs, Structural Distortions, Direct and Indirect Energy Gaps, and Strong Nonlinear Optical Properties. J. Am. Chem. Soc. 2015, 137, 6804−6819. (23) Tang, L. C.; Huang, J. Y.; Chang, C. S.; Lee, M. H.; Liu, L. Q. New Infrared Nonlinear Optical Crystal CsGeBr3: Synthesis, Structure and Powder Second-Harmonic Generation Properties. J. Phys.: Condens. Matter 2005, 17, 7275−7286. (24) Tang, L. C.; Chang, Y. C.; Huang, J. Y.; Lee, M. H.; Chang, C. S. First-principles Calculations of Linear and Second-order Optical Responses in Rhombohedrally Distorted Perovskite Ternary Halides, CsGeX3 (X = Cl, Br and I). Jpn. J. Appl. Phys. 2009, 48, 112402. (25) Jiang, J.; Onwudinanti, C. K.; Hatton, R. A.; Bobbert, P. A.; Tao, S. Stabilizing Lead-Free All-Inorganic Tin Halide Perovskites by Ion Exchange. J. Phys. Chem. C 2018, 122, 17660−17667. (26) Kresse, G.; Furthmüller, J. Effciency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (27) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186.

calculated results have been found to agree well with the available experimental data for the cases of CsGeX3, while for the cases of RbGeX3 they should be for the first time in this work. We revealed that replacement of Cs with Rb can offer reasonable flexibility in optoelectronic property matching for solar cell design and optimization, while X anion exchange gives rise to great changes. On the basis of these calculations, we can conclude that these inorganic Ge-based halide perovskites could be promising candidates for stable and large-scale perovskite solar cells.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail for C.-J.Y.: [email protected]. ORCID

Un-Gi Jong: 0000-0003-4654-2449 Chol-Jun Yu: 0000-0001-9523-4325 Shuzhou Li: 0000-0002-2159-2602 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported as part of the fundamental research project “Design of Innovative Functional Materials for Energy and Environmental Application” (No. 2016-20) funded by the State Committee of Science and Technology, DPR Korea. Computation was done on the HP Blade System C7000 (HP BL460c) that is owned by Faculty of Materials Science, Kim Il Sung University.

■

REFERENCES

(1) Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050−6051. (2) Yang, W. S.; Park, B. W.; Jung, E. H.; Jeon, N. J.; Kim, Y. C.; Lee, D. U.; Shin, S. S.; Seo, J.; Kim, E. K.; Noh, J. H.; Seok, S. I. Iodide Management in Formamidinium-Lead-Halide-Based Perovskite Layers for Efficient Solar Cells. Science 2017, 356, 1376−1379. (3) Chatterjee, S.; Pal, A. J. Influence of Metal Substitution on Hybrid Halide Perovskites: Towards Lead-Free Perovskite Solar Cells. J. Mater. Chem. A 2018, 6, 3793−3823. (4) Feng, J.; Xiao, B. Effective Masses and Electronic and Optical Properties of Nontoxic MASnX3 (X = Cl, Br, and I) Perovskite Structures as Solar Cell Absorber: A Theoretical Study Using HSE06. J. Phys. Chem. C 2014, 118, 19655−19660. (5) Berhe, T. A.; Su, W.-N.; Chen, C.-H.; Pan, C.-J.; Cheng, J.-H.; Chen, H.-M.; Tsai, M.-C.; Chen, L.-Y.; Dubaleb, A. A.; Hwang, B.-J. Organometal Halide Perovskite Solar Cells: Degradation and Stability. Energy Environ. Sci. 2016, 9, 323−356. (6) Manser, J. S.; Saidaminov, M. I.; Christians, J. A.; Bakr, O. M.; Kamat, P. V. Making and Breaking of Lead Halide Perovskites. Acc. Chem. Res. 2016, 49, 330−338. (7) Jong, U.-G.; Yu, C.-J.; Ri, G.-C.; McMahon, A. P.; Harrison, N. M.; Barnes, P. R. F.; Walsh, A. Influence of Water Intercalation and Hydration on Chemical Decomposition and Ion Transport in Methylammonium Lead Halide Perovskites. J. Mater. Chem. A 2018, 6, 1067−1074. (8) Kye, Y.-H.; Yu, C.-J.; Jong, U.-G.; Chen, Y.; Walsh, A. Critical Role of Water in Defect Aggregation and Chemical Degradation of Perovskite Solar Cells. J. Phys. Chem. Lett. 2018, 9, 2196−2201. (9) Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.; Caputo, R.; Hendon, C. H.; Yang, R. X.; Walsh, A.; Kovalenko, M. V. Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X = Cl, Br, and I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut. Nano Lett. 2015, 15, 3692−3696. F

DOI: 10.1021/acs.inorgchem.8b03095 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

(49) Butler, K. T.; Buckeridge, J.; Catlow, R. A.; Walsh, A. Crystal Electron Binding Energy and Surface Work Function Control of Tin Dioxide. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 115320.

(28) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758−1775. (29) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (30) Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100, 136406. (31) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207−8215. (32) Heyd, J.; Scuseria, G. E. Efficient Hybrid Density Functional Calculations in Solids: Assessment of the Heyd Scuseria Ernzerhof Screened Coulomb Hybrid Functional. J. Chem. Phys. 2004, 121, 1187. (33) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Erratum: ’Hybrid functionals based on a screened Coulomb potential’. J. Chem. Phys. 2006, 124, 219906. (34) Du, M. H. Efficient Carrier Transport in Halide Perovskites: Theoretical Perspectives. J. Mater. Chem. A 2014, 2, 9091−9098. (35) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (36) Jong, U.-G.; Yu, C.-J.; Ri, J.-S.; Kim, N.-H.; Ri, G.-C. Influence of Halide Composition on the Structural, Electronic, and Optical Properties of Mixed CH3NH3Pb(I1−xBrx)3 Perovskites Calculated Using the Virtual Crystal Approximation Method. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 94, 125139. (37) Jong, U.-G.; Yu, C.-J.; Jang, Y.-M.; Ri, G.-C.; Hong, S.-N.; Pae, Y.-H. Revealing the Stability and Efficiency Enhancement in Mixed Halide Perovskites MAPb(I1−xClx)3 with Ab Initio Calculations. J. Power Sources 2017, 350, 65−72. (38) Yang, R. X.; Butler, K. T.; Walsh, A. Assessment of Hybrid Organic-Inorganic Antimony Sulfides for Earth-Abundant Photovoltaic Applications. J. Phys. Chem. Lett. 2015, 6, 5009−5014. (39) Kieslich, G.; Sun, S.; Cheetham, A. K. An Extended Tolerance Factor Approach for Organic-Inorganic Perovskites. Chem. Sci. 2015, 6, 3430−3433. (40) Leguy, A. M. A.; Frost, J. M.; McMahon, A. P.; Sakai, V. G.; Kochelmann, W.; Law, C.; Li, X.; Foglia, F.; Walsh, A.; O’Regan, B. C.; Nelson, J.; Cabral, J. T.; Barnes, P. R. F. The Dynamics of Methylammonium Ions in Hybrid Organic-Inorganic Perovskite Solar Cells. Nat. Commun. 2015, 6, 7124. (41) Thiele, G.; Rotter, H. W.; Schmidt, K. D. Die Kristallstrukturen und Phasentransformationen des tetramorphen RbGeI3. Z. Anorg. Allg. Chem. 1989, 571, 60−68. (42) Thiele, G.; Rotter, H. W.; Schmidt, K. D. Die Kristallstrukturen und Phasentransformationen von RbGeBr3. Z. Anorg. Allg. Chem. 1988, 559, 7−16. (43) Huang, L.; Lambrecht, W. R. L. Vibrational Spectra and Nonlinear Optical Coefficients of Rhombohedral CsGeX3Halide Compounds with X = I, Br, Cl. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 94, 115202−115211. (44) Lin, Z. G.; Tang, L. C.; Chou, C. P. Study on Mid IR NLO Crystals CsGe(BrxCl1−x)3. Opt. Mater. 2008, 31, 28−34. (45) Even, J.; Pedesseau, L.; Jancu, J.-M.; Katan, C. Importance of Spin-Orbit Coupling in Hybrid Organic/Inorganic Perovskites for Photovoltaic Applications. J. Phys. Chem. Lett. 2013, 4, 2999−3005. (46) Umari, P.; Mosconi, E.; Angelis, F. D. Relativistic GW Calculations on CH3NH3PbI3 and CH3NH3SnI3 Perovskites for Solar Cell Applications. Sci. Rep. 2015, 4, 4467. (47) Jong, U.-G.; Yu, C.-J.; Kim, Y.-S.; Kye, Y.-H.; Kim, C.-H. FirstPrinciples Study on the Material Properties of Inorganic Perovskite Rb1−xCsxPbI3 for Solar Cell Applications. Phys. Rev. B: Condens. Matter Mater. Phys. 2018, 98, 125116. (48) Huang, L.-Y.; Lambrecht, W. R. L. Electronic Band Structure, Phonons, and Exciton Binding Energies of Halide Perovskites CsSnCl3, CsSnBr3, and CsSnI3. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 165203. G

DOI: 10.1021/acs.inorgchem.8b03095 Inorg. Chem. XXXX, XXX, XXX−XXX