Theoretical Insights into Perovskite Compounds MAPb1âÎ±

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Theoretical Insights into Perovskite Compounds MAPb X I Y (X=Ge, Sn; Y=Cl, Br): An Exploration of Superior Optical Performance Junli Chang, Hong-Kuan Yuan, Qingyang Zhang, Biao Wang, Xiaorui Chen, and Hong Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08543 • Publication Date (Web): 07 Nov 2018 Downloaded from http://pubs.acs.org on November 7, 2018

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The Journal of Physical Chemistry

Theoretical Insights into Perovskite Compounds MAPb1−α Xα I3−β Yβ (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 E-mail: [email protected]

Abstract The power conversion efficiency (PCE) of the perovskite-based solar cells (PSCs) has been rapidly exceeding 23% in the past few years. In the paper the electronic and optical properties of the doped series MAPb1−α Xα I3−β Yβ (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 photo-generated holes are easier transferred to the adjacent hole transport layer in the Cl/Br-mono than in the others. Furthermore, it is clearly revealed that absorption coefficients ∗ To

whom correspondence should be addressed of Physical Science and Technology, Southwest University, Chongqing 400715, People’s Republic of

† School

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 of Republic of China

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of perovksite-based compounds, including the Ge-mono, the Sn-mono, the Ge-Cl, and the GeBr, are significantly enhanced in the whole visible-light range and even near infrared. Our simulations pave a new way to deepen understanding the intrinsic characteristics of perovksite materials, and deliver a basic theoretical insights into designing new-type perovskite-based photovoltaic devices.

Introduction Organic inorganic hybrid perovskites (OIHPs), such as methylammonium lead iodide (MAPbI3 + with MA=CH3 NH+ 3 ) and formamidinium lead iodide (FAPbI3 with FA=NH2 CHNH2 ), have re-

ceived 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, photo-detectors, light emitting diodes (LED) and lasers. 10–13 Particularly, the solar cells based on OIHPs have been standing out from numerous of photovoltaic materials. In 2009, OIHPs were firstly used as visible-light sensitizers with power conversion efficiency (PCE) of 3.8%. 14 Meanwhile, it was experimentally confirmed that the OIHPs are especially promising candidates in terms of realizing photo-voltage of 1.0 V. The research interest on the OIHPs was trigged at that time, the record of PCE were constantly refreshed in the next few years. In 2011, perovskite-based quantum-dot-sensitized solar cells were fabricated with the PCE of 6.54%. 15 However, its stability was quite poor because of intensive corrosion of the redox electrolyte. Subsequently, the hole-conductor of the spiro-MeOTAD was introduced to the thin film mesoscopic solar cell, then the device stability was remarkably enhanced and its PCE reached up to 9.7%. 16 In addition to that, 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 all2


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solid-state devices could be thought as a fundamental breakthrough for extensively promotion of perovksite-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 the stability of PSCs. Recently, the perovskite-based solar cell with the efficiency of 23.2% is successfully fabricated by virtue of a fluorine-terminated hole-transport materials instead of common spiro-MeOTAD. 20 Simultaneously, the stability of the resultant device is dramatically enhanced since that its initial performance is still retained 95% after 500 h. So far, there are two major strategies of improving the performance of the PSCs, one is forming hetero-structure 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. Firstly, 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 organic cation of FA in the MAx FA1−x PbI3 , 23 while that based on Csx MA1−x PbI3 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 that 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 perovksite materials. Secondly, for the divalent metal ion doping, it has been confirmed theoretical and experimentally that the remarkable red shift comes out via the Sn/Ge ion doping instead of Pb in situ. 25–33 With respect to 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-bandgap of 1.25 eV, open-circuit voltages of 0.85 V, a short-circuit current density in excess of 29 mAcm−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 semi-transparent top cell of FA0.3 MA0.7 PbI3 . In this respect, the high efficiency of the tandem

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solar cells is achieved with the benefits of organic cation doping and divalent metal ion doping. Thirdly, for the halide ion doping, 9,36–39 the MAPbI3−x Clx in particular has been experimentally identified the carrier diffusion length in excess of 1 micrometer, in contrast to this, that in the pure MAPbI3 is only about 100 nanometers. The comparison implies that the high performance of planar solar cells based on perovskite is closely related to the halide ion doping, which delivers a new way to future development of perovskite-based devices. In addition to that, 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−α Xα I3−β Yβ , (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 remain 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 the Sn-, the Ge, the Br-, the Cl- mono-doped and the Sn-Br, the Sn-Cl, the Ge-Br, the Ge-Cl co-doped 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 VBM for the halide mono-doped compounds are easier transferred to the neighbor hole conductor. Furthermore, the absorption spectra imply that there are obvious red-shifts in the Sn-, Ge- mono-doping and the Ge-Br, the Ge-Cl co-doping series. For the present work, it is revealed that the compound of MAPb1−x Gex I3−x Brx 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.

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 (VASP). 42–44 The projected augment-

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ed wave (PAW) 45 method is adopted to deal with the electron-ion interaction while the exchangecorrelation effects of electrons is treated by means of the functional presented by Perdew, Burke and Ernzerhof (PBE) under the generalized gradient approximation (GGA). 46,47 The constituent elements of C (2s2 2p2 ), N (2s2 2p3 ), H (1s1 ), Pb (5d10 6s2 6p2 ), Br (4s2 4p5 ), Cl (3s2 3p5 ) and I (5s2 5p5 ) are considered as the corresponding valence-electron configurations. And 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 are 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 metal. 50,51 Specifically, the Pb-6p orbital at the CBM is split into 2-fold degenerate state by the SOC, which directly decreases the resulting band gap. On the other hand, the calculation based on the DFT usually underestimates the band gap 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 as, 52,53 HSE EXC = η EXSR (µ ) + (1 − η )EXPBE,SR (µ ) + EXPBE,LR (µ ) + ECPBE

(1)

Obviously, the electronic exchange interaction (labeled X) is separated into short range (labeled SR) and long range (labeled as LR) while the electronic correlation is still in the form of PBE functional. One point to emphasize here is that for HSE06 slowly decaying LR item of Fock exchange is replaced by the corresponding part of density functional. The parameters in Eq.( 1)

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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 energy of 400 eV and critical value of 1 × 10−4 for total energy change on each atom. Γ-centered 2 × 2 × 2 k-points are chosen for Brillion sampling in the reciprocal space. In short, electronic properties are simulated in HSE06+SOC, while lattice relaxation is in DFT+D2. As for optical properties, it is only conducted in the level of DFT+D2, with a denser Γ-centered 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 values 54–58 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 co-doping concentration is only 2.08%.

Results and discussion Geometric structure The prototypical perovskite structure has the formula of ABX3 , generally A represents organic cation (methylammonium, MA+ ; Formamidinium, FA+ ), B denotes divalent metal ion (Pb2+ , Sn2+ , Ge2+ ) and X usually indicates halide ion (I− , Br− , Cl− ). The stability of perovskite structure can be deduced through Goldschmidt tolerance factor, defined as 60,61 RA + RX t=√ . 2(RB + RX )

(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 tolerance factor is closer to 1. In other words, the closer the tolerance factor to 1, the higher the symmetry. Additionally, the octahedral

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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, a 2×2×2 cubic perovskite MAPbI3 is examined to explore the electronic properties. The radii of the component elements are respectively, rMA+ =1.8 Å, 63 rPb2+ =1.19 Åand 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 Table 1: The calculated lattice parameters and volume expansion in the level of DFT-D2 series MAPbI3 Ge-mono Sn-mono Cl-mono Br-mono Ge-Cl Ge-Br Sn-Cl Sn-Br

a*b*c 12.48*12.49*12.65 12.20*12.65*12.15 12.46*12.46*12.63 12.06*12.73*12.28 12.11*12.75*12.27 12.13*12.61*12.10 12.19*12.57*12.15 12.19*12.55*12.29 12.11*12.71*12.26

A*B*C 90.10*89.97*89.49 90.51*89.92*90.11 89.85*90.15*89.51 89.98*90.15*90.62 90.22*90.09*90.45 88.87*91.86*89.21 89.81*90.67*89.35 89.28*91.17*87.78 90.26*89.79*90.14

Volume 1971.64 1875.53 1961.68 1885.62 1894.17 1850.11 1861.67 1878.08 1886.29

Expansion 0.00 -4.87 -0.51 -4.36 -3.93 -6.16 -5.58 -4.75 -4.33

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 mono-doping and co-doping. As for the co-doping, we here focus on the case of neighbor site shown as 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 exist in all the doped series. Among those, the volume shrinkage of the Sn-mono is the smallest, while that of the Ge-Cl co-doped 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 7



Figure 1: Side view of the investigated perovskite-based compounds MAPb1−α Xα I3−β Yβ (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, Ge-Cl doped series, respectively.

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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 the Sn-mono is smallest among all the doped compounds, and only both of Sn-I bond lengths (labelled in Figure 1) keep 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 archetype MAPbI3 , specifically for the 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%, Ge-I(v) with 6.3%. Based on the analyses, the volume variation of the Ge-doped series should be in the order of the Ge-Cl>the Ge-Br>the Ge-I, which is in consistent with the volume-expansion order shown in Table 1. Hence we can deduce that the smallest volume change is in good agreement with the characteristics of bondlength variation.

Defect formation energy To determine the stability of all the doped series MAPb1−α Xα I3−β Yβ (X=Ge,Sn;Y=Cl,Br), the defect formation energy is introduced, with the following form, 65 E f (de f ) = ∆H(doped) − ∆H(MAPbI3 ),

(3)

where ∆H(doped) and ∆ H(MAPbI3 ) indicate the formation enthalpy of the prototype and the corresponding doped. Specifically, the definition of the formation enthalpy can be expressed as, 65,66 ∆H(doped) = E(doped) − ni µi (bulk),

(4)

with the parameters of the total energy E(doped), the chemical potential (µi ) and the number of each constituent atom ni . Then combining Eq.( 3) and Eq.( 4), the defect formation energy can be

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described as, E f (doped) = E(doped) − E(pure) − ∑ mi µi (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 satisfied, 66 ∆µMA + ∆µPb + 3∆µI = ∆H(MAPbI3 ).

(6)

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

(7a)

∆µPb = µPb − µPb(bulk) ,

(7b)

1 ∆µI = µI − µI2 (gas) . 2

(7c)

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: The formation enthalpy, the minimum defect formation energy, the corresponding chemical potential change of host atoms for the doped perovskite series. All the units are in eV. Series MAPbI3 Ge-mono Sn-mono Cl-mono Br-mono Ge-Cl Ge-Br Sn-Cl Sn-Br

∆H -55.12 -58.604 -57.341 -58.813 -58.695 -58.874 -58.853 -59.547 -59.658

Emin f – -3.484 -2.221 -3.693 -3.575 -3.754 -3.733 -4.427 -4.538

∆µPb – -2.348 -2.348 0 0 -2.348 -2.348 -2.348 -2.348

∆ µI – 0 0 -1.174 -1.174 0 0 0 0

Table 2 lists the minimum defect formation energy, which corresponds to the host Pb/I-poor 10


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growth condition. Figure 2 intuitively shows that the defect formation energy for all the doped compounds are negative, which suggests that the doped perovskite series can be achieved in experiment. Specially, for the Sn-mono, its value of -2.221 eV is maximal, which is mainly attributed to poor stability of the Sn2+ in perovskite. Sn2+ , unlike Pb2+ , is easily oxidized to the stable Sn4+ due to the presence of oxygen in the ambient environment. As for the Cl-mono, its defect formation energy is minimum among mono-doping series, which means that it is more favorable to synthesize the Cl-mono than the others. Moreover, the electron-hole diffusion length in the mixed halide (MAPbI3−x Clx ) has been demonstrated over 1 micrometer, 9 which suggest that the alternative doping of chlorine ion significantly enhance carrier transfer ability as compared with that for pure iodine ion. With respect to co-doped series, as listed in Table 1, the Sn-Br shows the minimum volume variation, which agrees well with the minimum defect formation energy in Figure 2.

Br-mono

Cl-mono

21 .2 -2

-2

54 .7 -3

-4

Sn-mono

Sn-Br

Sn-Cl

Ge-mono

Ge-Br

Ge-Cl

0

Defect formation energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


33 .7 -3

84 .4 -3

93 .6 -3

27 .4 -4

Figure 2: The defect formation energy MAPb1−α Xα I3−β Yβ (X=Ge,Sn;Y=Cl,Br).

75 .5 -3

38 .5 -4

for

the

doped

perovskite

series

Additionally, the thermal stable range of ∆MA, ∆Pb and ∆I should comply with the limits of ∆µH(MAPbI3 ) ≤ ∆µMA ≤ 0, 11


(8a)


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∆µH(MAPbI3 ) ≤ ∆µPb ≤ 0,

(8b)

∆µH(MAPbI3 ) ≤ ∆µI ≤ 0.

(8c)

Simultaneously, to avoid the formation of impurity phase of MAI and PbI2 , it is necessary for the chemical potential of the constituent elements must be subjected to the following constraints, ∆µMA + ∆µI < ∆µMAI ,

(9a)

∆µPb + 2∆µI < ∆µPbI2 .

(9b)

The physically accessible area for pure MAPbI3 and the doped compounds can be hence deduced in terms of the coordinates plane defined by ∆µ and ∆µ as shown in Figure 3. The related dissociation energy from MAPbI3 to MAI and PbI2 , defined as EMAI + EPbI2 − EMAPbI3 , is in correspondence with the covered region in Figure 3(a), 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 the Cl-mono and Br-mono is close to each other under the I-poor condition in Figure 3(b) and (c). By contrast, a significant difference is presented for the Sn-mono and Ge-mono under the condition of Pb-poor in Figure 3(d) and (g), which is attributed to the readily oxidation of Sn2+ to Sn4+ . Moreover, for mono-doping 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 3(b–d) and (g), but for co-doped series in Figure 3(e),(f),(h) and (i), it is obvious that the Pb-poor 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 The Figure 4 indicates that the band gap can be apparently tuned via ion doping, but the electronic states distributions of band gap edges almost remain the same with those of pure MAPbI3 . 12


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0.0

-2.4

(a)

(b)

-2.5

(c)

-2.5

-2.7

-2.7

-2.8

-2.8

-3.0

-3.0

-3.1

-3.1

-3.3

-3.3

-3.4

-3.4

-3.5

-3.6

-3.7

-0.5

-1.0

0.0

0.1

(d)

-3.1

(e)

-0.2

-3.0

(f)

-3.3

-3.2

-0.5

-3.5

-3.4

-0.8

-3.7

-3.5

-1.1

-3.8

-3.7

-1.3

-4.0

-3.9

-1.6

-4.2

-4.1

-1.9

-4.4

-4.3

-2.2

-4.5

-0.5

-1.0

0.0

-1.1

(g)

-4.4

-2.3

(h)

-1.4

-2.3

(i)

-2.5

-2.5

-1.7

-2.7

-2.7

-2.0

-2.8

-2.9

-2.3

-3.0

-3.0

-2.6

-3.2

-3.2

-2.9

-3.4

-3.4

-3.2

-3.6

-0.5

-1.0

-3.5

-2

-1 Pb

0

-3.6

-3.7

-2

-1

0

Pb

-3.8

-2

-1

0

Pb

Figure 3: The physical accessible regions for the investigated systems in the plane defined by ∆µMA and ∆µI . The specific corresponding relation keeps in the same with the Figure 1 Analogously with previous investigation, 27,59,67–69 the valence band maximum (VBM) is mainly occupied by the σ -anti-bonding states of I-5p and Pb-6s orbitals, the conduction band minimum (CBM) is primarily consisted of Pb-6p orbitals. The contributions of doped ions on the density of state are not significantly for the time being, and a special discussion will be delivered in the section of charge distribution. As for 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 first-principles calculations, have been demonstrated to exist in the perovskite materials, which makes OIHPs having better light harvesting than those merely having ordinary p-s transition. To get more insight into 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 photo-generated holes 13


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Total

Total

Total

Pb-6s

Pb-6s

Pb-6s

Pb-6p

Pb-6p

Pb-6p

I-5s

I-5s

I-5s

I-5p

I-5p

I-5p

Organic cations

Br-4s

Cl-3s

Br-4p

Cl-3p

Organic cations

Organic cations

(b)

DOS (arb. units)

(a)

(c)

Total

Total

Pb-6s

Pb-6s

Pb-6p

Pb-6p

I-5s

I-5s

I-5p

I-5p

Sn-5s

Sn-5s

Sn-5p

Sn-5p

Organic cations

Br-4s

Total Pb-6s Pb-6p I-5s I-5p Sn-5s Sn-5p Cl-3s Cl-3p

Br-4p

Organic cations

Organic cations

(d)

(e)

DOS (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

DOS (arb. units)


Total

Total

Total

Pb-6s

Pb-6s

Pb-6s

Pb-6p

Pb-6p

Pb-6p

I-5s

I-5s

I-5s

I-5p

I-5p

I-5p

Ge-4s

Ge-4s

Ge-4s

Ge-4p

Ge-4p

Ge-4p

Organic cations

Br-4s

Cl-3s

Br-4p

Cl-3p

Organic cations

Organic cations

(g)

-3

(f)

(h)

-2

-1

0

Energy (eV)

1

2

3

-3

(i)

-2

-1

0

1

2

3

Energy (eV)

-3

-2

-1

0

1

2

3

energy (eV)

Figure 4: The simulated density of states (DOS) for pure MAPbI3 and the doped compounds MAPb1−α Xα I3−β Yβ (X=Ge,Sn;Y=Cl,Br), specifically pure (a), Br-mono (b), Cl-mono (c),Snmono (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.

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being transferred to the adjacent hole transport layer (HTL), which is directly related to the resulting photovoltaic performance. From the perspective, photo-generated holes and electrons is more thoroughly separated, which implies that 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− ion, 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 due to the replacement of Pb2+ with the Sn2+ , and that in the adjacent I- ion is remarkably enhanced. In other words, the charge at the VBM in the Sn-mono is more photo-excited to the adjacent HTL, which means that the 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 the Cl-mono in particular in Figure 5(b)–(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−x Clx can be over 1micrometer. 9

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 by, 70

ε2 (¯hω ) =

2e2 π ∑ | ⟨ψkc|uˆ · r|ψkv⟩ |2δ (Ekc − Ekv − h¯ ω ), Ωε0 c,v,k

(10)

where Ω is the volume of the archetype cell, ω indicates the incident-light frequency, uˆ represents the external field vector, and r refers to the momentum operator. The Ψvk and Ψck , 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

15



Figure 5: Partial charge density distribution at the VBM. Figure (a)-(i) correspond to the prototype, the Pb-Br, the Pb-Cl, the Sn-I, the Sn-Br, the Sn-Cl, the Ge-I, the Ge-Br and the Ge-Cl with the iso-value of 0.0008 eÅ−3 , respectively.

16


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Kramer-Kronig relationship, 71 2 ε1 (ω ) = 1 + P π

∫ ∞ ′ ω ε2 (ω ′ ) 0

ω ′2 − ω 2

dω ′,

(11)

where P refers to the principle value of the intergral. Then the absorption coefficient of the doped perovskite-based series can be determined by virtue of the following expression, 72 √ A (ω ) = 2ω

√ −ε1 (ω ) +

√

ε12 (ω ) + ε22 (ω ).

(12)

Absorption spectra in Figure 6 suggests that perovskite compounds of the Cl-mono and the Brmono is not favorable for the improvement of optical capability, although large diffusion length has been demonstrated to exceed 1 um for the Cl-mono compounds. 9 For the cases of the Sn-Cl and the 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 perovksite-based series including the Cl-mono, the Br-mono, the Sn-Cl and the Sn-Br is no evidently improved, and especially for the Cl-mno and the Br-mono, 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 the defect formation energy in Figure 2, the Sn-mono should be excluded due to the poor stability, which is attributed to the fact that the Sn2+ is easily oxidized into Sn4+ in the iodide-based perovksite. 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.

Conclusion A first-principles investigation based on density function theory on the electronic and optical properties of perovskite-based series MAPb1−α Xα I3−β Yβ (X=Ge,Sn;Y=Cl,Br) is presented. Our 17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Absorption coefficient (arb. units)


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Pure Br-mono Cl-mono Sn-mono Ge-mono Sn-Br Sn-Cl Ge-Br Ge-Cl

300

400

500

600

700

800

900

1000

Wavelength (nm)

Figure 6: The absorption spectra for pure MAPbI3 , Ge-mono, Sn-mono, Cl-mono, Br-mono doped compounds and Ge-Cl, Ge-Br, Sn-Cl, Sn-Br co-doped series. The black corresponds to pure MAPbI3 , and the others represent doped perovskite series as shown in the legend.

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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 the Sn-mono is the maximal values of -2.221 eV, which indicates that the Sn-mono compound is also be experimentally achieved, although the Sn2+ is readily oxidized into the Sn4+ . Charge density distributions show that it is more advantageous for carrier being transferred to adjacent hole transport layer in the anion-doped compounds. Furthermore, it is found that the absorption coefficient of the Ge-Br co-doped 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 co-doped compound may alleviate to a certain extent the amount of the heavy metal lead, i.e., it is more environmental friendly of the Ge-Br as compared to the prototypical MAPbI3 . Therefore, our simulations suggest that MAPb1−α GeI3−β Brβ is a better choice to realize perovskite-based thim-film solar cells with high efficiency and low toxicity.

Acknowledgement 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. CSTC2011BA6004 and CSTC-2017jcyjBX0035, and Fundamental Research Funds for the Central Universities under Grant Nos. XDJK2018C080.

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Theoretical Insights into Perovskite Compounds MAPb1âÎ±

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