Theoretical Insights into Perovskite Compounds MAPb1−αXαI3−βYβ

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Cite This: J. Phys. Chem. C 2018, 122, 27205−27213

Theoretical Insights into Perovskite Compounds MAPb1−αXαI3−βYβ (X = Ge, Sn; Y = Cl, Br): An Exploration for Superior Optical Performance Junli Chang,† Hongkuan Yuan,† Qingyang Zhang,† Biao Wang,† Xiaorui Chen,† and Hong Chen*,†,‡ †

School of Physical Science and Technology, Southwest University, Chongqing 400715, People’s Republic of China Key Laboratory of Luminescent and Real-Time Analytical Chemistry, Ministry of Education, College of Chemistry and Chemical Engineering, Southwest University, Chongqing 400715, People’s Republic of China

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‡

ABSTRACT: The power conversion efficiency of the perovskite-based solar cells has been rapidly exceeding 23% in the past few years. In the paper, the electronic and optical properties of the doped series MAPb1−αXαI3−βYβ (X = Ge, Sn; Y = Cl, Br) are explored for ascendant absorption capability. Hybrid density functional has been conducted to obtain exact electronic property. The defect formation energy, with the maximal value of −2.221 eV, indicates that all the doped series can be readily synthesized. Moreover, the charge density distributions suggest that photogenerated holes are easily transferred to the adjacent hole transport layer in Cl/Br-mono than in the others. Furthermore, it is clearly revealed that absorption coefficients of perovskitebased compounds, including the Ge-mono, Sn-mono, Ge−Cl, and Ge−Br, are significantly enhanced in the whole visible-light range and even near infrared. Our simulations pave a new way to deepen the understanding of the intrinsic characteristics of perovskite materials, and deliver basic theoretical insights into designing new-type perovskite-based photovoltaic devices.

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of 6.54%.15 However, its stability was quite poor because of intensive corrosion of the redox electrolyte. Subsequently, the hole conductor of spiro-MeOTAD was introduced to the thinfilm mesoscopic solar cell, then the device stability was remarkably enhanced and its PCE reached up to 9.7%.16 In addition to that, a pure inorganic semiconductor CsSnI3 can also be used for hole conductor instead of a liquid electrolyte and sustainably gain the efficiency of 10.2%.17 It was worth emphasizing that the stability of the perovskite-based devices was preliminarily addressed by means of the achievement of all-solid-state architecture. In other words, the fabrication of all-solid-state devices could be thought as a fundamental breakthrough for extensive promotion of perovskite-based solar cells. In the same year, it was confirmed experimentally that OIHPs were also used as hole or electron transport in addition to light harvest.18,19 From then on, enormous efforts have been devoted into enhancing the efficiency or improving

INTRODUCTION Organic inorganic hybrid perovskites (OIHPs), such as methylammonium lead iodide (MAPbI 3 with MA = CH3NH3+) and formamidinium lead iodide (FAPbI3 with FA = NH2CHNH2+), have received enormous interest because of their predominant properties primarily including low-cost solution processability,1−4 low exciton binding energy,5−7 large carrier diffusion length,8,9 and a tunable band gap with salutary optical absorption. By virtue of these properties, OIHPs have now been widely explored in the field of opt-electronics such as solar cells, photodetectors, light-emitting diodes and lasers.10−13 Particularly, the solar cells based on OIHPs have been standing out from numerous photovoltaic materials. In 2009, OIHPs were first used as visible-light sensitizers with a power conversion efficiency (PCE) of 3.8%.14 Meanwhile, it was experimentally confirmed that the OIHPs are especially promising candidates in terms of realizing a photovoltage of 1.0 V. The research interest on the OIHPs was triggered at that time, and the record of PCE was constantly refreshed in the next few years. In 2011, perovskite-based quantum dot-sensitized solar cells were fabricated with a PCE © 2018 American Chemical Society

Received: September 1, 2018 Revised: October 23, 2018 Published: November 7, 2018 27205

DOI: 10.1021/acs.jpcc.8b08543 J. Phys. Chem. C 2018, 122, 27205−27213

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The Journal of Physical Chemistry C

the halide monodoped compounds are easily transferred to the neighbor hole conductor. Furthermore, the absorption spectra imply that there are obvious red shifts in the Sn- and Gemonodoping and Ge−Br and Ge−Cl codoping series. For the present work, it is revealed that the compound of MAPb1−xGexI3−xBrx is superior than the other doped series in terms of light harvesting. In other words, our study provides a new insight into the mixed doped perovskites, which is helpful for designing high-performance solar cells based on perovskite materials.

the stability of perovskite-based solar cells (PSCs). Recently, the perovskite-based solar cell with the efficiency of 23.2% is successfully fabricated by virtue of fluorine-terminated holetransport materials instead of common spiro-MeOTAD.20 Simultaneously, the stability of the resultant device is dramatically enhanced because its initial performance still retained 95% after 500 h. So far, there are two major strategies of improving the performance of the PSCs, one is forming heterostructure by selecting a suitable coating layer such as SnS/MAPbI3,21,22 which has been confirmed to have superior performance than the pure MAPbI3; the other is through ion doping. First, the band gap can be effectively tuned by means of organic cation doping, although they almost have little contribution to the electronic states at the band-gap edges. Specifically, the device with the PCE of 14.9% was successfully achieved by varying the content of the organic cation of FA in MAxFA1−xPbI3,23 whereas that based on CsxMA1−xPbI3 was fabricated with the efficiency of 7.68%.24 The efficiency of devices based on organic cation doping is not so high as that of the other doping, but it is also very important because of which these experiments suggest that the electronic and optical properties of perovskite materials can be effectively tuned by organic cation doping. In other words, it is experimentally demonstrated that organic cation doping can be used as a versatile tool to achieve the effective control on perovskite materials. Second, for the divalent metal ion doping, it has been confirmed theoretically and experimentally that the remarkable red shift comes out via Sn/Ge ion doping instead of Pb in situ.25−33 With respect to the mixed Sn−Pb perovskite,29,34,35 it is noteworthy that the efficient tandem solar cells are successfully achieved with the best PCE of 17.6%, low band gap of 1.25 eV, open-circuit voltages of 0.85 V, a short-circuit current density in excess of 29 mA cm−2, and a suitable wavelength range,29 and most importantly, its efficiency can be further increased to 21% when the device is stacked with a semitransparent top cell of FA0.3MA0.7PbI3. In this respect, the high efficiency of the tandem solar cells is achieved with the benefits of organic cation doping and divalent metal ion doping. Third, for halide ion doping,9,36−39 MAPbI3−xClx in particular has been experimentally determined to have the carrier diffusion length in excess of 1 μm, in contrast to this, that in the pure MAPbI is only about 100 nm. The comparison implies that the high performance of planar solar cells based on the perovskite is closely related to halide-ion doping, which delivers a new way to the future development of perovskitebased devices. In addition to this, a double-/triple-cation lead mix halide perovskites have been successfully fabricated with superior PCE and thermal stability.40,41 Based on these progresses, we try to explore the electronic and optical properties of MAPb1−αXαI3−βYβ, (X = Ge, Sn; Y = Cl, Br) that combines the merits of metal doping and halide doping. To the best of our knowledge, the corresponding investigation remains uncertain for the time being, so it is the motivation for this work. To reveal the effect of the mixed ion doping on the prototype MAPbI3, the first-principles calculations have been conducted to explore the electronic and optical properties of Sn-, Ge-, Br-, and Cl-monodoped and Sn−Br, Sn−Cl, Ge−Br, and Ge−Cl codoped compounds. The stability of the doped compounds can be distinctly deduced from the calculations of the defect formation energy. The charge density distributions suggest that the hole at the valence band maximum (VBM) for

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COMPUTATIONAL DETAILS Based on the density functional theory (DFT), all the calculations in the present work have been performed by using the Vienna ab initio simulation package.42−44 The projected augmented wave45 method is adopted to deal with the electron−ion interaction while the exchange-correlation effects of electrons are treated by means of the functional presented by Perdew, Burke and Ernzerhof (PBE) under the generalized gradient approximation.46,47 The constituent elements of C (2s 2 2p 2 ), N (2s 2 2p 3 ), H (1s 1 ), Pb (5d106s26p2), Br (4s24p5), Cl (3s23p5), and I (5s25p5) are considered as the corresponding valence−electron configurations. In addition, periodic boundary conditions are taken into account for the investigated systems. A cutoff energy of 500 eV and a Γ-centered 4 × 4 × 4 Monkhorst−Pack grid are selected for the expansion of wave function and the sampling of the first Brillouin zone, respectively.48 As for the convergence criteria of lattice relaxation and self-consistent calculations, the Hellmann−Feynman force is less than 0.02 eV/Å, and the threshold of the total energy change is set to 1 × 105. With regard to geometry optimization, both Gaussian smearing and the conjugate gradient algorithm are adopted for good convergence. As for electronic property, the tetrahedron method with Blöchl corrections is used, and dispersion weak interaction correction is in the form of D2 presented by Grimme.49 Besides, it is imperative of the spin orbit coupling (SOC) interaction to be considered for OIHPs because of evident impact on the electronic orbit of conduction band minimum (CBM) of heavy metals.50,51 Specifically, the Pb 6p orbital at the CBM is split into the twofold degenerate state by SOC, which directly decreases the resulting band gap. On the other hand, the calculation based on the DFT usually underestimates the band gap by about 1 eV. Consequently, HSE06, a screened hybrid functional originally proposed by Hery, Scuseria and Ernzerhof, is adopted for the exact electronic structure, for which the corresponding exchange−correlation energy is defined as52,53 HSE E XC = ηE XSR (μ) + (1 − η)E XPBE,SR (μ) + E XPBE,LR (μ)

+ ECPBE

(1)

Obviously, the electronic exchange interaction (labeled X) is separated into short range (labeled SR) and long range (labeled LR) whereas the electronic correlation is still in the form of PBE functional. One point to emphasize here is that for HSE06 slowly decaying the LR item of Fock exchange is replaced by the corresponding part of density functional. The parameters in eq 1 μ and η indicate the range separation (for screening) of 0.2 Å−1 and mixing coefficient of 0.38, respectively. Considering the limitation of computation resource, the lower convergence criteria are set as, a cut-off 27206

DOI: 10.1021/acs.jpcc.8b08543 J. Phys. Chem. C 2018, 122, 27205−27213

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The Journal of Physical Chemistry C energy of 400 eV and a critical value of 1 × 10−4 for total energy change on each atom. Γ-centered 2 × 2 × 2 k-points are chosen for Brillouin sampling in the reciprocal space. In short, electronic properties are simulated in HSE06 + SOC, whereas lattice relaxation is in DFT + D2. As for optical properties, it is only conducted in the level of DFT + D2, with denser Γcentered 6 × 6 × 6 k-points. For the cubic MAPbI3 primitive cell, the relaxed lattice parameter is a = 6.235 Å and the direct band gap of 1.72 eV is consistent with the previously reported experimental values54−58 and theoretical values,27,59 which suggest that our simulation results are reliable and reasonable. A large 2 × 2 × 2 supercell model with 96 atoms has been adapted to explore electronic properties in our simulations, which means that the codoping concentration is only 2.08%.

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RESULTS AND DISCUSSION Geometric Structure. The prototypical perovskite structure has the formula of ABX3, generally A represents the organic cation (methylammonium, MA+; formamidinium, FA+), B denotes the divalent metal ion (Pb2+, Sn2+, Ge2+), and X usually indicates the halide ion (I−, Br−, Cl−). The stability of perovskite structure can be deduced through the Goldschmidt tolerance factor, defined as60,61 t=

RA + RX 2 (RB + RX)

Figure 1. Side view of the investigated perovskite-based compounds MAPb1−αXαI3−βYβ (X = Ge, Sn; Y = Cl, Br). Specifically, in the upper (a−c) refer to pure, Br-mono, Cl-mono doped series; in the middle (d−f) corresponds to Sn-mono, Sn−Br, Sn−Cl doped series; and similarly in the lower (g−i) represent Ge-mono, Ge−Br and Ge−Cl doped series, respectively.

(2)

The parameter Ri corresponds to the radius of the constituent elements. As for OIHPs, the tolerance factor should be between 0.813 and 1.107,62 otherwise it is difficult to form a classic perovskite structure. Common symmetries include orthorhombic, tetragonal, and cubic. The symmetry is enhanced with the ambient temperature arising, meanwhile the tolerance factor is closer to 1. In other words, the closer the tolerance factor to 1, the higher the symmetry. Additionally, the octahedral factor is also a paramount parameter to determine the stability of perovskite structure,62 with the form of μ = RB/RX. To assure the formation of perovskite structure, the value of octahedral factor should be limited in the range of 0.442 ≤ μ < 0.895. Otherwise, it is still uncertain of that even though its tolerance factor is reasonable. For the present work, 2 × 2 × 2 cubic perovskite MAPbI3 is examined to explore the electronic properties. The radii of the component elements are, rMA+ = 1.8 Å,63 rPb2+ = 1.19 Å, and rI− = 2.2 Å. Note that the organic polar molecule MA+ is herein treated as a packed sphere, similarly with an ordinary atom.64 In addition, its tolerance factor is 0.834 and octahedral factor is 0.540, both of which satisfy the aforementioned corresponding limitation.62 The investigated prototypical perovskite MAPbI3 is consisted of 96 atoms involving C, N, H, Pb, and I. To obtain superior optical absorption, the congener elements of Sn/Ge and Br/Cl are as the substituents instead of lead or iodine in situ. Naturally, there are two cases, the monodoping and codoping. As for codoping, we here focus on the case of neighbor site as shown in Figure 1. The calculated lattice parameters are listed in Table 1, where the parameter of expansion refers to the volume change compared with the volume of prototypical MAPbI3. As expected, volume contraction clearly exists in all the doped series. Among these, the volume shrinkage of Sn-mono is the smallest, whereas that of the Ge−Cl codoped is the largest. To probe the inherent mechanism, we next analyze the bond length change arising out of ion doping.

As shown in Figure 1, a typical structure, purely inorganic framework, is herein adopted to discuss the geometry variation of the investigated lattices. For simplicity, for pure MAPbI3 we define the horizontal bond (h) and the vertical one (v) to distinguish two cases, as Pb−I (h) and Pb−I (v), analogously in the other compounds. The bond length change of Sn-mono is smallest among all the doped compounds, and only both of Sn−I bond lengths (labeled in Figure 1) maintain the same value, just like the primitive MAPbI3. The bond length change of the Ge-doping series is significantly larger than the other doped ones. To distinctly illustrate the difference, we here adapt the bond length change as compared with the corresponding Pb−I in arche-type MAPbI3, specifically for Ge-mono, Ge−I (h) with −10.1%, Ge−I (v) with 4.53%; for the Ge−Br (h) with 1.2%, Ge−I (v) with 8.5%; for Ge−Cl (h) with 4.1%, and Ge−I (v) with 6.3%. Based on the analyses, the volume variation of the Ge-doped series should be in the order of Ge−Cl > Ge−Br > Ge−I, which is consistent with the volume expansion order as shown in Table 1. Hence, we can deduce that the smallest volume change is in good agreement with the characteristics of bond length variation. Defect Formation Energy. To determine the stability of all the doped series MAPb1−αXαI3−βYβ(X = Ge, Sn; Y = Cl, Br), the defect formation energy is introduced with the following form65 Ef (def) = ΔH(doped) − ΔH(MAPbI3)

(3)

where ΔH(doped) and ΔH(MAPbI3) indicate the formation enthalpy of the prototype and the corresponding doped. Specifically, the definition of the formation enthalpy can be expressed as65,66 ΔH(doped) = E(doped) − niμi (bulk) 27207

(4)

DOI: 10.1021/acs.jpcc.8b08543 J. Phys. Chem. C 2018, 122, 27205−27213

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The Journal of Physical Chemistry C Table 1. Calculated Lattice Parameters and Volume Expansion in the Level of DFT-D2 a×b×c

series MAPbI3 Ge-mono Sn-mono Cl-mono Br-mono Ge−Cl Ge−Br Sn−Cl Sn−Br

12.48 12.20 12.46 12.06 12.11 12.13 12.19 12.19 12.11

× × × × × × × × ×

12.49 12.65 12.46 12.73 12.75 12.61 12.57 12.55 12.71

A×B×C

× × × × × × × × ×

12.65 12.15 12.63 12.28 12.27 12.10 12.15 12.29 12.26

90.10 90.51 89.85 89.98 90.22 88.87 89.81 89.28 90.26

× × × × × × × × ×

89.97 89.92 90.15 90.15 90.09 91.86 90.67 91.17 89.79

× × × × × × × × ×

89.49 90.11 89.51 90.62 90.45 89.21 89.35 87.78 90.14

volume

expansion

1971.64 1875.53 1961.68 1885.62 1894.17 1850.11 1861.67 1878.08 1886.29

0.00 −4.87 −0.51 −4.36 −3.93 −6.16 −5.58 −4.75 −4.33

with the parameters of the total energy E(doped), the chemical potential (μi), and the number of each constituent atom ni. Then combining eqs 3 and 4, the defect formation energy can be described as Ef (doped) = E(doped) − E(pure) −

∑ miμi (bulk)

(5)

i

where the parameter mi represents the number of atom transferred into (mi > 0) or out from (mi < 0) the chemical reservoir. Meanwhile, to assure the formation of prototypical MAPbI3, the eq 6 below must be satisfied66 ΔμMA + ΔμPb + 3ΔμI = ΔH(MAPbI3)

(6)

The parameter of Δμ represents the chemical potential difference between the individual atom in the composite and in the elemental bulk phase, and can be described as ΔμMA = μMA − μMA(gas)

(7a)

ΔμPb = μPb − μPb(bulk)

(7b)

Figure 2. Defect formation energy for the doped perovskite series MAPb1−αXαI3−βYβ (X = Ge, Sn; Y = Cl, Br).

unlike Pb2+, is easily oxidized to the stable Sn4+ because of the presence of oxygen in the ambient environment. As for Clmono, its defect formation energy is minimum among monodoping series, which means that it is more favorable to synthesize Cl-mono than others. Moreover, the electron−hole diffusion length in the mixed halide (MAPbI3−xClx) has been demonstrated over 1 μm,9 which suggests that the alternative doping of chlorine ion significantly enhances carrier transfer ability as compared with that for the pure iodine ion. With respect to codoped series, as listed in Table 1, Sn−Br shows the minimum volume variation, which agrees well with the minimum defect formation energy in Figure 2. Additionally, the thermal stable range of ΔMA, ΔPb, and ΔI should comply with the limits of

1 μ (7c) 2 I2(gas) The parameters of μi denote the chemical potentials of the component atom i, with the maximum values of gas MA, bulk Pb, and gas I2. Table 2 lists the minimum defect formation energy, which corresponds to the host Pb/I-poor growth condition. Figure 2 ΔμI = μI −

Table 2. Formation Enthalpy, Minimum Defect Formation Energy, and Corresponding Chemical Potential Change of Host Atoms for the Doped Perovskite Seriesa series

ΔH

Emin f

ΔμPb

ΔμI

MAPbI3 Ge-mono Sn-mono Cl-mono Br-mono Ge−Cl Ge−Br Sn−Cl Sn−Br

−55.12 −58.604 −57.341 −58.813 −58.695 −58.874 −58.853 −59.547 −59.658

−3.484 −2.221 −3.693 −3.575 −3.754 −3.733 −4.427 −4.538

−2.348 −2.348 0 0 −2.348 −2.348 −2.348 −2.348

0 0 −1.174 −1.174 0 0 0 0

ΔμH(MAPbI ) ≤ ΔμMA ≤ 0

(8a)

ΔμH(MAPbI ) ≤ ΔμPb ≤ 0

(8b)

ΔμH(MAPbI ) ≤ ΔμI ≤ 0

(8c)

3

3

3

Simultaneously, to avoid the formation of impurity phase of MAI and PbI2, it is necessary that the chemical potential of the constituent elements must be subjected to the following constraints

a

All the units are in eV.

intuitively shows that the defect formation energy for all the doped compounds is negative, which suggests that the doped perovskite series can be achieved in experiment. Specially, for Sn-mono, its value of −2.221 eV is maximal, which is mainly attributed to poor stability of Sn2+ in the perovskite. Sn2+,

ΔμMA + ΔμI < ΔμMAI

(9a)

ΔμPb + 2ΔμI < ΔμPbI

(9b)

2

The physically accessible area for pure MAPbI3 and the doped compounds can be hence deduced in terms of the coordinate plane defined by Δμ and Δμ as shown in Figure 3. The related dissociation energy from MAPbI3 to MAI and 27208

DOI: 10.1021/acs.jpcc.8b08543 J. Phys. Chem. C 2018, 122, 27205−27213

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Figure 3. Physical accessible regions for the investigated systems in the plane defined by ΔμMA and ΔμI. The specific corresponding relation keeps in the same with the Figure 1.

PbI2, defined as EMAI + EPbI2 − EMAPbI3, is in correspondence with the covered region in Figure 3a, which implies that the growth conditions must be severely controlled to ensure the formation of the stoichiometric perovskite of MAPbI3. The minimal formation energy for Cl-mono and Br-mono is close to each other under the I-poor condition in Figure 3b,c. By contrast, a significant difference is presented for the Sn-mono and Ge-mono under the condition of Pb-poor in Figure 3d,g, which is attributed to the readily oxidation of Sn2+ to Sn4+. Moreover, for monodoping series, it is clearly manifested that the defect formation energy decreases with the decrease of the chemical potential of host atoms Pb or I in Figure 3b−d,g, but for codoped series in Figure 3e,f,h,i, it is obvious that the Pbpoor growth condition is more favorable to synthesize them. Actually, the vacancy is an indispensable factor to achieve alternative doping, and easier to form under the host-atom poor growth condition. Electronic Properties. Figure 4 indicates that the band gap can be apparently tuned via ion doping, but the electronic state distributions of band gap edges almost remain the same with those of pure MAPbI3. Analogously with previous investigation,27,59,67−69 the VBM is mainly occupied by the σ-antibonding states of I 5p and Pb 6s orbitals, the CBM is primarily consisted of Pb 6p orbitals. The contributions of doped ions on the density of state are not significant for the time being, and a special discussion will be delivered in the section of charge distribution. As for the organic cation, methyl-ammonium, it still have few contributions to electronic distributions in the edges of band gap.59,67−69 It is noteworthy that uncommon p−p band-gap transitions, by the firstprinciples calculations, have been demonstrated to exist in

the perovskite materials, which makes OIHPs have better light harvesting than those merely having ordinary p−s transition. To gain more insight into the electronic structure change arising from ion doping, we further examine the partial charge density distribution at VBM. Both hole transfer on VBM and electron transfer on CBM are crucial for photoelectric conversion. Specially, the charge density distribution on VBM, localized on the surface, indicates that it is advantageous for photogenerated holes being transferred to the adjacent hole transport layer (HTL), which is directly related to the resulting photovoltaic performance. From the perspective, photogenerated holes and electrons are more thoroughly separated, which implies that the electron−hole recombination ratio is remarkably reduced. As shown in Figure 5, charge density distribution is relatively uniform, in line with the bond length in Figure 1. The charge density distribution at the VBM is localized primarily at Pb2+ and I− ions, which agrees well with the DOS in Figure 4. By comparing (a) and (d) in Figure 5, it is revealed that the charge density distribution at in situ is apparently changed because of the replacement of Pb2+ with Sn2+, and that in the adjacent I-ion is remarkably enhanced. In other words, the charge at the VBM in Sn-mono is more photoexcited to the adjacent HTL, which means that Sn-mono has better optical absorption. In this respect, the Sn−Cl and the Ge−Br doped compounds exhibit remarkable advantages than the others. Additionally, the charge density distributions in the anion-doped compounds and Cl-mono in particular in Figure 5b,c, unveil that the hole is more readily transferred to the adjacent HTL, which is in consistent with the previous experimental report that the carrier diffusion length in MAPbI3−xClx can be over 1 μm.9 27209

DOI: 10.1021/acs.jpcc.8b08543 J. Phys. Chem. C 2018, 122, 27205−27213

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Figure 4. Simulated density of states (DOS) for pure MAPbI3 and the doped compounds MAPb1−αXαI3−βYβ (X = Ge, Sn; Y = Cl, Br), specifically pure (a), Br-mono (b), Cl-mono (c), Sn-mono (d), Sn−Br co-doped (e), Sn−Cl co-doped (f), Ge-mono (g), Ge−Br co-doped (h), Ge−Cl codoped (i). Fermi level is referenced to the valence band maximum and set to zero.

Optical Properties. To evaluate the light-harvesting capability of the perovskite-based doped compounds MAPbI3, the frequency-dependent complex dielectric function ε is herein adopted, and the imaginary part of which can be described by70 ε2(ℏω) =

2e 2π ∑ |⟨ψ c|u·̂ r|ψkv⟩|2 δ(Ekc − Ekv − ℏω) Ωε0 c,v, k k (10)

where Ω is the volume of the arche-type cell, ω indicates the incident-light frequency, ũ represents the external field vector, and r refers to the momentum operator. Ψkv and Ψkc , respectively, denote the wave functions in the occupied and unoccupied state at the k point in the reciprocal space. Moreover, the real part of dielectric function can be readily derived from the famous Kramer−Kronig relationship71 ε1(ω) = 1 + Figure 5. Partial charge density distribution at the VBM. Figure (a−i) corresponds to the prototype, Pb−Br, Pb−Cl, Sn−I, Sn−Br, Sn−Cl, Ge−I, Ge−Br, and Ge−Cl with the iso-value of 0.0008 e Å−3, respectively.

2 P π

∫0

∞

ω′ε2(ω′) dω′ ω′ 2 − ω 2

(11)

where P refers to the principle value of the integral. Then, the absorption coefficient of the doped perovskite-based series can be determined by virtue of the following expression72 A(ω) = 27210

2 ω −ε1(ω) +

ε12(ω) + ε2 2(ω)

(12)

DOI: 10.1021/acs.jpcc.8b08543 J. Phys. Chem. C 2018, 122, 27205−27213

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HTL in the anion-doped compounds. Furthermore, it is found that the absorption coefficient of the Ge−Br codoped compound is significantly enhanced as compared with the others, in the range of the whole visible light and even near the infrared. In addition, the injection of Ge ion in the Ge−Br codoped compound may alleviate the amount of the heavy metal lead to a certain extent, that is, it is more environmental friendly of Ge−Br as compared to the prototypical MAPbI3. Therefore, our simulations suggest that MAPb1−αGeI3−βBrβ is a better choice to realize perovskite-based thin-film solar cells with high efficiency and low toxicity.

Absorption spectra in Figure 6 suggests that the perovskite compounds of Cl-mono and Br-mono are not favorable for the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Junli Chang: 0000-0001-5285-433X Hongkuan Yuan: 0000-0002-2075-9327 Hong Chen: 0000-0003-4283-6095 Figure 6. Absorption spectra for pure MAPbI3, Ge-mono, Sn-mono, Cl-mono, and Br-mono doped compounds and Ge−Cl, Ge−Br, Sn− Cl, and Sn−Br codoped series. The black corresponds to pure MAPbI3 and the others represent doped perovskite series as shown in the legend.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China under grant nos. 11875226 and 11874306, the Natural Science Foundation of Chongqing under grant nos. CSTC-2011BA6004 and CSTC2017jcyjBX0035, and Fundamental Research Funds for the Central Universities under grant no. XDJK2018C080.

improvement of optical capability, although large diffusion length has been demonstrated to exceed 1 μm for the Cl-mono compounds.9 For the cases of Sn−Cl and Sn−Br, the optical absorption coefficient is only enhanced in a relatively narrow range of 300−468 nm. In other words, with respect to that of the primitive MAPbI3, the light harvesting of the perovskitebased series including Cl-mono, Br-mono, Sn−Cl and Sn−Br is not evidently improved, and especially for Cl-mono and Brmono, the optical absorption ability is evidently decreased. By contrast, the other Ge-mono, Sn-mono, Ge−Cl, and Ge−Br present the outstanding improvement, almost existing in the whole visible-light range and even in the near-infrared range. Combining the aforementioned defect formation energy in Figure 2, the Sn-mono should be excluded because of the poor stability, which is attributed to the fact that Sn2+ is easily oxidized into Sn4+ in the iodide-based perovskite.51 In addition, the charge density distributions in Figure 5 indicate that the Ge−Br compound is superior than the others in terms of enhancing the light harvesting because of more favorable carrier transfer.

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CONCLUSIONS A first-principles investigation based on density function theory on the electronic and optical properties of perovskite-based series MAPb1−αXαI3−βYβ (X = Ge, Sn; Y = Cl, Br) is presented. Our calculations have shown that valence band maximum and the conduction band minimum are mainly composed of I 5p and Pb 6p orbitals, respectively. Unusual p−p transition is hence confirmed to also exist in the doped series, which directly relates to the outstanding photovoltaic performance. The calculations of the defect formation energy suggest that it is favorable to synthesize the dope perovskite-based compounds, and that for Sn-mono is the maximal values of −2.221 eV, which indicates that the Sn-mono compound is also be experimentally achieved, although Sn2+ is readily oxidized into Sn4+. Charge density distributions show that it is more advantageous for the carrier being transferred to the adjacent 27211

DOI: 10.1021/acs.jpcc.8b08543 J. Phys. Chem. C 2018, 122, 27205−27213

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