Electronic Structure and Optical Properties of Gallium-Doped Hybrid

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Electronic Structure and Optical Properties of Gallium-Doped Hybrid Organic-Inorganic Lead Perovskites from First-Principles Calculations and Spectroscopic Limited Maximum Efficiencies Rishikanta Mayengbam, Ashutosh Srivastava, Susanta K. Tripathy, and Gopinath Palai J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b03835 • Publication Date (Web): 03 Sep 2019 Downloaded from pubs.acs.org on September 3, 2019

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The Journal of Physical Chemistry

Electronic Structure and Optical Properties of Gallium-Doped Hybrid Organic-Inorganic Lead Perovskites from First-Principles Calculations and Spectroscopic Limited Maximum Efficiencies Rishikanta Mayengbama, Ashutosh Srivastavaa, S. K. Tripathya* and G. Palaib aDepartment

of Electronics and Communication Engineering, National Institute of Technology, Silchar 788010, India

bDepartment

of Electronics and Communication Engineering, Gandhi Institute for Technological Advancement (GITA), Bhubaneswar 752054, India

ACS Paragon Plus Environment

The Journal of Physical Chemistry 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

ABSTRACT Low cost and ultra-high power conversion efficiencies of the hybrid organic-inorganic lead perovskites have brought a revolution among the solar cell researchers never seen before. However, stability and toxicity are the major concerns hindering it from getting commercialized. Compositional engineering by employing mixed metal cations and halides has become one of the efficient way to tackle these problems. Taking this route, the structural, electronic and optical properties of Ga-doped tetragonal MAPbI3 perovskites have been investigated with generalized gradient approximation using density functional theory. Structural analysis such as doping effects on the lattice volume, bond length, tilting angles and enthalpies of formation have been calculated and detailed analysis are reported. Band-structure calculations have been performed with and without spin-orbit coupling (SOC) in which impurity bands were observed in the case of the doped structures. Other electronic properties such as effective masses and projected density of states have also been calculated and discussed in depth. For light harvesting, necessary optical properties viz. dielectric function, refractive index, extinction coefficient, absorption coefficient and reflectivity were also computed. From the optical properties, blue-shift behaviour was observed which is found to be consistent with the calculated electronic properties. Lastly, using SLME method, it was found that MAPbI3 with 6.25% Ga dopant concentration has the highest efficiency among all the investigated perovskite materials. All the parameters were calculated and compared with available experimental and reported values and found in fairly good agreement.


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1. INTRODUCTION Since the past decade, perovskite solar cells (PSCs) have become the centre of attraction among the researchers in the photovoltaic community due to its overwhelming rapid upsurge in the power conversion efficiency (PCE) from 3.8% in 20091 to 23.7% in 20182. This is mainly attributed to the unique and outstanding properties of the perovskite material used as an absorber layer in the PSCs. Hybrid organic-inorganic lead perovskite materials have the general chemical formula ABX3, where A is the monovalent cation (CH3NH3+), B is the divalent metal cation (Pb2+), and X is a halide anion (X=I, Br, Cl). The unrivalled properties such as strong absorption, suitable band gap, low effective masses and high mobility of charge carriers, longer carrier lifetimes and diffusion lengths, less defect and low temperature solution process for fabrication have shaped MAPbX3 (MA=CH3NH3+) (X=I, Br, Cl) and its analogues to become the most efficient solar absorber materials among the third-generation solar cells.3-8 Under different range of temperatures, MAPbI3 is observed to exhibit three distinct phases.9 At temperatures below 161.4 K, MAPbI3 has an orthorhombic structure with space group Pnma, from 161.4 K to 330.4 K it remains in tetragonal phase with space group I4/mcm and after 330.4 K, it transforms to cubic phase with space group Pm-3m. Among these various phases, tetragonal phase perovskite materials are mostly used as an absorber layer in PSCs. However, presence of lead (Pb) in perovskite solar cells poses two major roadblocks towards commercialization. They are: (i) stability problem due to oxidation of Pb2+ to Pb4+ in presence of air and moisture that causes deterioration of photovoltaic efficiency within a few days,10 and (ii) toxicity of lead (Pb) which causes harm in both fabrication and environment. To address these issues, rational doping of MAPbI3 with other metal cations has become one of the most effective approaches to stabilize the structure and enhance the PCE.11-13 Due to similar iso-electronic configuration with lead, initially researchers attempted to replace lead (Pb) with other group-14 elements. Stoumpos et al. synthesized MAPbxSn(1-x)I3 (x=0.25, 0.50, 0.75, 1.0) and achieved corresponding tunable band gaps in the range, 1.20 to 1.54 eV, which is suitable for solar cell applications.14 With MASnI3 as the light harvester, Hao et al.15 and Noel et al.16 have also fabricated solar cell devices and obtained PCEs of 5.23% and 6.4%, respectively. Further, Hao et al.17 and Ogomi et al.18 fabricated mixed MAPbxSn(1-x)I3 based solar cells by substituting Pb by Sn and achieved highest efficiencies with Pb content of 50% and 75%, respectively. Later on, Li et al. obtained an incredible efficiency of 13.6% with MAPb0.5Sn0.5I3 by optimizing the electron transport layer.19 However, among the mixed Sn-Pb based perovskite solar cells, pure



MASnI3 was observed to exhibit high electron and hole mobilities, but due to undesirable oxidation of Sn2+ to Sn4+, certain amount of Pb was required to improve the stability and PCE of the structure. Similarly, pure Ge-based PSCs were also reported to be unstable and have very low efficiencies.2022

Furthermore, to study the effects of the replacement of lead by group-13 elements, Al3+ was

doped into MAPbI3 and observed to increase the film quality by minimizing microstrain and reducing defect density.23 Likewise, Wang et al. studied doping of indium into MAPbI3 improves the crystal quality of the film and hence, improves overall photovoltaic performance.24 Recently, Zhou et al. also investigated the effect of doping indium into methyl ammonium lead iodide via both experiments and theoretical calculations, and found that Pb-In halide perovskites show excellent electronic properties due to the impurity bands induced by indium atoms.25 Density functional theory (DFT) calculations have also been carried out extensively on MAPbxSn(1-x)I3 for exploring the structural, electronic and optical properties, where it was reported that partial substitution of lead with other metal cations yield better photo-physical properties.26-29 Recently, Mayengbam et al. have also studied the opto-electronic properties of mixed Pb-Ge perovskites for photovoltaic applications using DFT calculations.30 Gallium is a group-13 element with the electronic configuration [Ar] 3d104s24p1 and is wellknown for its excellent optoelectronic properties as it is employed in the first generation single junction GaAs31, multi-junction InGaAs, InGaP solar cells32 and also in the second-generation cadmium indium gallium selenide (CIGS) solar cell33. Moreover, it has been incorporated as a dopant in the electron transport layer in the third-generation perovskite solar cell.34, 35 Furthermore, a recent study reported that the metal ions with outer ns2 electrons configuration and low ionization energy are preferred for better optical absorption and carrier diffusion in ABX3 structures.36 To the best of our knowledge, there has been no experimental and theoretical work carried out to study the effects of Ga doping into MAPbI3 till date. Therefore, with these keen motivations, we have investigated thoroughly the essential properties of Ga-doped tetragonal MAPbI3 primarily required for an absorber layer in perovskite solar cells. Theoretically, for hybrid organic-inorganic lead perovskites, GGA-PBE 25,37-39 have been used most profoundly to investigate the electronic and optical properties for photovoltaic applications. Moreover, PBE functional provides electronic band structure similar to that of hybrid functional and quasiparticle GW methods.40 Apart from this, it was recently reported that hybrid functional


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produces reasonably good band gap but with a discrepancy with experimental lattice parameters.41 Furthermore, it was also concluded from this study that PBE provides a good compromise between the accurate band gap and cell geometry with less computational demands. Hence, in this work, we have performed the calculation by incorporating van der Waals interaction with GGA-PBE. It was found from the simulation results that inclusion of such interaction leads to high overestimation of electronic band gap (included in Figure S1 of the supporting information (SI)) and underestimation of the lattice constants compared to experimental values. In addition, van der Waals forces dominate the electrostatic interaction between the constituent molecules in pure organic materials, and thus van der Waals correction is necessary in predicting accurate structural and electronic characteristics of such compounds.42 On the contrary, in hybrid organic-inorganic materials, such interactions are mostly ionic in nature, which are well captured and described by the standard GGA-PBE functional.37 Therefore, we have used GGA-PBE exchange-correlation functional throughout this work to investigate the structural, electronic and optical properties of the perovskites. In this paper, we have systematically studied the structural, electronic, and optical properties of MAGaxPb(1-x)I3 perovskites with x = 0.0, 0.0625, 0.125 and 0.25. In the structural properties, we have calculated the optimized lattice constants and enthalpies of formation for the pristine and the doped structures. Under the electronic properties, band structures and effective masses have been calculated with and without spin orbit coupling (SOC). More importantly, contribution of each orbital in the electronic states have been analyzed from density of states in conjunction with the calculated band structure. In optical properties, we have computed the dielectric function, refractive index, extinction coefficient, absorption coefficient and reflectivity, and discussed in detail. Finally, absorber layer efficiency has been estimated through the spectroscopic limited maximum efficiency (SLME) methodology and a comparative analysis have been presented.

2. METHODOLOGY AND COMPUTATIONAL DETAILS The entire calculations were performed with generalized gradient approximation (GGA) as exchange-correlation functional treated by Perdew, Burke, Ernzerhof (PBE) within the framework of density functional theory (DFT). The constructions of structures as well as the computations were executed in Atomistix Toolkit-Virtual Nanolab (ATK-VNL) package43, which uses numerical linear combination of atomic orbitals (LCAO) methodology. Norm-conserving



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pseudopotentials are used to describe electron-ion interactions, and the valence electrons Pb 5d,6s,6p; I 4d,5s,5p; Ga 3d,4s,4p; C 2s,2p; N 2s,2p; and H 1s are explicitly treated by the basis sets. For all the self-consistent field calculations, we have employed a mesh density cut off of 300 Hartree (Ha) and total energy convergence criteria of 10-6 Ha. For geometry optimization, all the ions are relaxed to a force less than 0.05 eV/Å using limited-memory Broyden-Fletcher-GoldfarbShanno (LBFGS) algorithm. The tetragonal MAPbI3 unit cell, which comprises of four formula units containing a total of 48 atoms, was constructed using the reported experimental work.44 The optimized unit cell was used to build 1×1×2 and 2×2×1 super cells, which contains 96 and 192 atoms, respectively. Only one Pb atom was replaced by Ga atom in unit cell, 1×1×2 and 2×2×1 supercells to avoid interaction between the dopants, resulting in Ga doping concentration of 6.25%, 12.5% and 25%, respectively. The structural calculations were performed by employing k-point samplings of 6×6×6, 6×6×3 and 3×3×4 on the unit cell, 1×1×2 and 2×2×1 supercells, respectively. A denser mesh with a total of 1000 unoccupied and occupied bands each in the conduction and valence bands, respectively was included for accurate calculation of optical properties. On account of the strong relativistic effect due to presence of heavy Pb ion, SOC have been employed in the calculation of the band structures and also to obtain correct estimation of effective masses.

3. RESULTS AND DISCUSSION 3.1 Structural properties The initial lattice parameters and the atomic positions of the tetragonal phase MAPbI3 (space group: I4/mcm) were obtained from the experimental work.44 Before doping, it is of foremost importance to check the formability of the doped perovskite structures using the Goldschmidt’s tolerance ( t ) and octahedral ( μ ) factors, which can be determined from the following relations:

t=

rA +rX 2(rB +rX )

μ=

rB rX


(1)

(2)

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A perovskite material with a stable structure must have the tolerance and octahedral values within the range of 0.80  t  1.06 and μ  0.41 .45 The tolerance and octahedral factors for MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25 were calculated using the relationship given elsewhere 46 and listed in Table 1. For this, we have used the reported ionic radius of 2.16 Å for MA cation 45 and Shannon ionic radii 47 of 1.19 Å, 0.62 Å and 2.2 Å for lead, gallium and iodine

x=0.0625

x=0

x=0.125

x=0.25



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Fig. 1 Optimized structural geometries of the MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25. atoms, respectively. It can be observed that all investigated structures satisfy the criteria for the formability of stable perovskites. With this affirmation, the pristine MAPbI3 as well the other Gadoped MAPbI3 perovskites were optimized and their structures are shown in Fig. 1. Also, the optimized lattice parameters, lattice volumes and change in volume are depicted in Table 1. The calculated values of the lattice parameters of pristine MAPbI3 are in good agreement with the experimental and other theoretical values. 14,17,37,38,44 Unfortunately, due to lack of experimental work on Ga-doped lead iodide perovskites, obtained structural properties as well other calculated properties could not be compared. Table 1 clearly shows a decrease in lattice parameters with increasing incorporation of impurity atom owing to small ionic radius of Ga, which ultimately causes a gradual reduction in lattice volume. Table 1 Calculated tolerance ( t ) and octahedral ( μ ) factors, lattice parameters (a, c) (in Å), lattice volumes (V) (in Å3) and change in lattice volume (ΔV in %) for the investigated MAGaxPb(1-x)I3 perovskites. MAGaxPb(1-x)I3

t

μ

a=b

c

V

- ΔV in %

x=0

0.91

0.54

8.88

12.75

1006.83

0

Expt.

8.84a, 8.92b, 8.83c

12.64a,12.68b, 12.69c

Theoretical

8.86d, 8.85e

12.66d,12.65e

x=0.0625

0.92

0.52

8.87

12.74

1003.07

0.37

x = 0.125

0.93

0.50

8.86

12.72

999.33

0.74

x = 0.25

0.95

0.47

8.83

12.69

991.87

1.49

aRef.[14], bRef.[17], cRef.[44], dRef.[37], eRef.[38]


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Further, to understand the bond strength and amount of orbital overlapping which significantly affect the stability and the band gap of the perovskite structure, it is important to calculate the intrinsic structural parameters such as the bond length of B-I and tilting angle B-I-B where B is metal cation.38 Generally, smaller ionic radius of metal cation, higher degree of hybridization and large electronegativity difference leads to shortening the bond length. Respectively, Table S1 and Table S2 in SI lists the average bond lengths of metal B and iodine I, and B-I-B tilting angles of the investigated MAGaxPb(1-x)I3 perovskites along the equatorial (along x-y plane) and apical (along z) directions. As Ga is introduced in the MAPbI3, it can be observed that strength of Ga-I bond is more than the Pb-I bond because of smaller bond length and results in decrease in average overall bond length. It is obvious that the shortening of bonds is due to the smaller Ga ion as well as due to higher electronegativity difference between Ga and I, than between Pb and I. Moreover, it can be perceived that equatorial Ga-I bond is stronger than the apical Ga-I bond in all doped perovskite structures whereas it is opposite in case of the Pb-I bonds in Ga-doped perovskite structures. More importantly, the steric effects caused by the ionic radius of the metal ion introduces metal-iodide tilting. It can be noted from Table S2, apical tilting angle of Pb-I-Pb increases with increase in Ga concentration. This increase in tilting angles is due to the substitution of large Pb atom by smaller Ga atom, which is consistent with the diminishing values of octahedral factor in Table 1. We can observe that the average overall bond length of metal Pb/Ga-I decreases and average B-I-B tilting angle increases with the increasing incorporation of Ga atoms but at x=0.25, the reverse is noticeable which is due to strong coupling between the inorganic metalhalide framework and the organic methylammonium cations resulting from huge reduction in lattice volume. It has been found that MAPbI3 decomposes into MAI+PbI2.48 Therefore, to investigate thermodynamic stability of a material, enthalpy of formation is an essential factor. More negative value of enthalpy of formation means more stable structure. The enthalpies of formation  H  for all of the investigated MAGaxPb(1-x)I3 perovskites have been calculated considering the following equation: H  E (MAGa x Pb(1 x ) I3 )  E (MAI)  (1  x) E (PbI 2 )  xE (I 2 )  xE (Ga)


(3)


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where E and x denote the total energy and percentage concentration of the Ga atom, respectively. The optimized geometries of MAI, PbI2, I2 and Ga structures are shown in Figure S2 of the SI. In addition, the calculated values of total energy per formula unit for optimized MAI, PbI2, I2 and Ga structures are listed in Table S3 of the SI. Further, the total energies and enthalpies of formation have been calculated using relation (3) and listed in Table 2. The estimated value of enthalpy of formation of pristine MAPbI3 is in fair agreement with other theoretical results.49–51 This negative value increases with increase in Ga doping and it indicates high probability for the formation of stable perovskites structure. This is in accord with the monotonously increasing values of tolerance factor in Table 1, which signifies increase in stability. Moreover, this stability factor can be explained in terms of the structural bond strength of Pb-I and Ga-I bonds which as follows. In pristine MAPbI3, the Pb-I bonds are covalent but with the introduction of Ga atoms, the bonds become polar covalent due to higher difference in the electronegativity values of Ga and I atoms. It is also noteworthy to mention that the ionic energy of a polar covalent bond is always greater than the part of covalent energy it replaces.52 Furthermore, the ionic character in the polar covalent bonds of the doped perovskites increases bond strength and the compounds so formed are exothermic in nature. Moreover, the bond dissociation energy of Ga-I bond is reported to be 339 kJ/mol whereas for Pb-I, it is 197 kJ/mol.53 Therefore, with increase in Ga content, this increasing bond energy of Ga-I bond leads to increase in bond strength in doped perovskite structures resulting an increase in the enthalpies of formation. Table 2. Calculated total energies, E (in eV) per formula unit and the corresponding enthalpies of formation ( H ) (in eV) of MAGaxPb(1-x)I3 perovskites. MAGaxPb(1-x)I3

E

H

x=0

-10159.299

-0.038, -0.01a, -0.02b, -0.07c

x=0.0625

-10176.720

-0.114

x = 0.125

-10194.143

-0.194

x = 0.25

-10228.942

-0.305

aRef.[49], bRef.[50], cRef.[51]

3.2 Electronic properties


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For photovoltaic applications, selection of materials for absorber layer with suitable electronic properties play a vital role in improving the device performance. In this respect, the nature and magnitude of band gap is extremely important to estimate the number of absorbed photon and rate of photogenerated charge carriers with minimal optical losses. For efficient generation and transport of free charge carriers, low exciton binding energy as well as low effective masses of holes and electrons are also required. For this purpose, we have calculated the band structures of the optimized MAGaxPb(1-x)I3 perovskite structures with GGA-PBE for x = 0.0, 0.0625, 0.125 and 0.25 along the high symmetry points of the brillouin zone as shown in Fig. 2. Here the fermi level is set to zero. It is clearly observed from the figure that both the valence band maximum (VBM) and conduction band minimum (CBM) for all the computed band structures lie along the Γ-point of the brillouin zone which represent direct nature of the band gaps, and thus, can be called as good optical absorber materials. The calculated band gap of MAPbI3 is 1.69 eV which is in fairly agreement with the experimental results and other theoretical calculations as given in Table 3.37– 39,54,55

With increasing doping concentration of Ga at x = 0.0625, 0.125 and 0.25, MAGaxPb(1-x)I3

perovskites have a higher band gaps of 1.76 eV, 1.83 eV and 2.00 eV, respectively. The increase in band gap due to dopant in metal site B of hybrid organic-inorganic ABX3 perovskite can be rationalised in terms of electronegativity, work function of metal B or the chemical nature of B-I bond.38 Also, it is clear from the figure that impurity band is introduced between the band gap by Ga dopant in all the investigated doped systems which is also noticed in the reported work of Indoping of MAPbI3.25 For x = 0.0625, 0.125 and 0.25, the impurity bands occur at 0.50 eV, 0.74 and 0.93 eV above VBM, respectively which could absorb the photons below band gap energy and increase the photogenerated carriers through trap-assisted transitions. Moreover, we have calculated the spin-dependent band structures for all the explored perovskites and shown in Figure S3 of the SI. From this figure, we can notice that the bands of energies for spin-up and spin-down for all the investigated perovskites overlap with each other, thus revealing that these perovskites are non-magnetic in nature. Table 3 Estimated band gap ( Eg ) (in eV) of MAGaxPb(1-x)I3 perovskites with GGA-PBE (without SOC) and GGA-PBE (with SOC) along with experimental and other theoretical calculations. MAGaxPb(1-x)I3

Band gap ( Eg )



This work

E

PBE g

E

PBE  SOC g

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Expt.

Other theoretical

x=0

1.69

0.62

1.61a, 1.60b

1.66c,d, 1.68e

x=0.0625

1.76

0.76

-

-

x=0.125

1.83

0.81

-

-

x=0.25 2.00 1.00 aRef.[54], bRef.[55], cRef.[37], dRef.[38], eRef.[39]

-

-

Additionally, we have also calculated electronic band structures using GGA-PBE with spin orbit coupling (SOC) wherein the inclusion of SOC caused a considerable reduction in band gaps as presented in Table 3 and shown in Figure S4 of the SI. This effect is caused by the splitting of conduction band minimum into degenerate states (shown in Figure S4), which is also observed in other theoretical work.39 It is also evident from the Table 3 that trend of the calculated band gaps by incorporating SOC is consistent with the calculated band gaps using GGA-PBE. For exploring the insight of electronic properties, we have calculated the partial density of states for the optimized structures of all the MAGaxPb(1-x)I3 perovskite materials, and plotted in Fig. 2 in projection to the corresponding band structure diagrams. From this plot, it can be perceived that for pristine MAPbI3, the VBM is mainly predominated by the hybridization of Pb-6s and I-5p orbitals, while the bands below it extending till the energy level of -3.25 eV are mainly controlled by I-5p and Pb-6p orbitals which is consistent with other theoretical calculations.25, 39 As far as the doped MAGaxPb(1-x)I3 structures are concerned, the dominant contributions of Pb-6s and I-5p orbitals in the VBM are observed as similar to the pristine structure. However, due to the increasing concentration of Ga incorporation, the contribution of Ga-4p orbital rises in the lower energy levels of the valence band. The most significant of all is the presence of impurity bands owing to Ga incorporation near the VBM, which is in agreement with our calculated band structure. The impurity states so formed are the consequence of the strong interaction between Ga-4s and I-5p orbitals, in which the latter has a greater contribution. With increase in Ga content, both Ga-4s and I-5p orbitals extend their tails away from the VBM and towards higher energy levels. In view of the conduction bands, the pristine MAPbI3 has CBM primarily dominated by Pb-6p orbital with minor contribution of I-5p orbital. With the introduction of Ga into the un-doped structure, the interaction between Ga and I cause the Pb-6p orbital to shift towards higher energy


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which finally lead to increase in band gap. As the concentration of Ga increases, the contribution of Ga-4p orbital rises in the conduction band and it leads to further increase in the band gap.

x=0



x=0.0625


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x=0.125



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x=0.25 Fig. 2. Calculated band structures of optimized MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25 along with the projected density of states. Furthermore, for photogenerated charge carriers, the effective masses play an significant role in the dissociation of excitons into free electrons and holes. In general, the exciton binding energy is calculated using the following relationship:

me*e 4 Eb  2 2h 1 (0) 2

(4)

where, Eb , me* and 1 (0) are the exciton binding energy, the effective mass of electron and the static dielectric constant of the semiconducting material, respectively. To achieve a good photovoltaic action, exciton binding energy have to be lower than the thermal energy at room


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 Table 4 Estimated electron (me ) and hole (mh ) effective masses along R(0.5,0,0.5) , X(0.5, 0,0) and M(0.5, 0.5, 0) , with their average values (AVG) and the corresponding reduced mass calculated from PBE and PBE-SOC.

Effective masses

MAGaxPb(1-x)I3 Directions

me

mh

M

R

X

M

R

X

PBE

1.36

0.13

1.10

0.33

0.22

0.28

PBE-SOC

0.30

0.26

0.15

0.32

0.99

0.19

PBE

1.09

0.12

1.01

0.44

0.28

PBE-SOC

0.19

1.44

0.13

0.45

PBE

1.85

0.44

1.48

PBE-SOC

0.24

0.14

PBE

1.49

PBE-SOC

0.13

AVG AVG me mh



0.86

0.28

0.21

0.24

0.50

0.16

0.35

0.74

0.36

0.24

0.59

0.29

0.59

0.45

0.25

0.32

0.28

0.26

1.26

0.29

0.23

0.12

0.29

0.24

0.22

0.17

0.25

0.10

0.21

1.29

0.39

0.34

0.3

0.99

0.34

0.26

0.15

0.73

0.33

0.33

0.29

0.34

0.32

0.16

x=0

x=0.0625

x=0.125

x=0.25

temperature. In this work, we have calculated the effective mass from the electronic band structure through the second derivative of the energy E (k ) versus the wave vector k around the CBM and VBM as given by the relation:

  2 E (k )  m h   2  k   eff

1

2

(5)

 Table 4 summarizes the computed effective masses of holes (mh ) and electrons (me ) of the

investigated MAGaxPb(1-x)I3 perovskites along the directions R(0.5,0,0.5) , X(0.5, 0,0) and M(0.5, 0.5, 0) , and their average values (AVG). Further, the calculated effective masses are used to



determine the corresponding reduced masses using this equation,   (me  mh ) (me  mh ) for each of the investigated perovskites. It is important to mention that VBM and CBM occurs at different values of k with GGAPBE and GGA-PBE with SOC methods which is also seen in previous theoretical work.56 The calculated electron and hole effective masses of pristine MAPbI3 from PBE-SOC are in fair agreement with other previous theoretical results.38, 57–62 Thus, we have analysed the effective masses for all the investigated combinations of MAGaxPb(1-x)I3 perovskites using the results obtained from PBE-SOC. For x = 0.0625 and 0.25, effective hole mass is smaller than the electron effective mass, and vice versa for x = 0.0 and 0.125. Furthermore, the corresponding reduced mass for MAPbI3 is 0.16 which agree well with the experimental value of 0.10.63 Though the un-doped and the doped perovskites exhibit a balanced ambipolar transport nature, the excellent transport properties are sighted in MAGa0.125Pb0.875I3. 3.3 Optical properties Optical properties viz. absorption edge, strength of absorption at different wavelengths and reflection coefficient are vital and essential in determining the internal and external quantum efficiencies of the solar cell. These optical properties are the outcome of the interactions of light wave with the valence electrons of the material. When electromagnetic radiation such as light wave interacts with a material, the optical response of the material is given by the complex dielectric function,  ( )  1 ( )  i 2 ( ) . The imaginary part of the dielectric function,  2 ( ) is calculated from the momentum matrix elements between the occupied and unoccupied wave functions. Here, we have calculated the imaginary part of the dielectric function for the optimized geometries of the investigated MAGaxPb(1-x)I3 perovskites and plotted in the photon energy range 0–5 eV in Fig. 3. The imaginary part represents the losses in the material and precisely, indicates the ohmic resistance of the material. The curve of pristine MAPbI3 is observed to increase with increase in photon energy and reaches a peak value at 3.14 eV, which is in good agreement with experimental and other theoretical calculations.25,64–66 This peak corresponds to the inter-band electronic transition between I-5p and Pb-6p states. However, for x = 0.0625, 0.125 and 0.25, impurity bands modify the imaginary part spectrum in the doped systems by introducing a curve symbolic of a Gaussian distribution just before the optical band gap which is consistent with the calculated band


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structure and partial density of states. Notably, this Gaussian curve intensifies with the increase in the density of impurity bands with increase in Ga content. The peaks for these doped systems are found at 3.15 eV, 3.20 eV and 3.30 eV, respectively, for 0.0625, 0.125 and 0.25 indicating a blue shift with increase of Ga incorporation. Moreover, the intensities of these peaks get lower with the rise in Ga content.

Fig. 3 Calculated imaginary part of the dielectric function  2 ( ) for MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25. On the other hand, the real part of the dielectric function, 1 ( ) is calculated from the  2 ( ) by using the Kramers-Kronig transformation and plotted in Fig. 4.67 Generally, the real part represents the ability of the material to store the electric energy, or the ability to permit the electric field through it. The calculated value of the static dielectric constant 1 (0) of the pristine MAPbI3 is 4.13, which agrees well with the experimental results.64,66 The real part of the dielectric function increases with photon energy and has the peak value at 2.30 eV, then decreases to a minimum



value at 3.85 eV, and then finally increases with photon energy. It is also worth mentioning that

1 ( ) is correlated to  2 ( ) since the maximum and the minimum values of 1 ( ) occur at those values of photon energy where  2 ( ) has the highest slope, when in rising or falling. Nevertheless, for x = 0.0625, 0.125 and 0.25, 1 (0) has a monotonously increasing values of 4.38, 4.44 and 4.62, respectively, with the rise of Ga concentration, making the dissociation of excitons easier as can concluded from equation (4). Moreover, this make them suitable candidates for dielectric applications. The higher values of 1 (0) in doped systems is attributed to the impurity bands introduced by Ga atoms. With increase in photon energy and below 1.12 eV, 1 ( ) curve for all the doped systems displays similar Gaussian curve as observed in case of  2 ( ) . Then, it increases with photon energy reaching a maximum value at 2.30 eV for all x = 0.0625, 0.125 and 0.25, but a gradual decrease in peak value with increasing dopant content. After that, the curve follows the trend that of the pristine system with the minimum value getting gradually shifted towards lower energies with rise in Ga content.


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Fig. 4 Calculated real part of the dielectric function 1 ( ) for MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25.



Fig. 5 Calculated refractive index n( ) for MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25. All other properties such as refractive index n( ) and extinction coefficient k ( ) are computed employing both values of 1 ( ) and  2 ( ) , while absorption coefficient  ( ) and reflectivity R( ) are calculated using n( ) and k ( ) using the relationships given elsewhere.68 Refractive index is a physicochemical property whose value changes due to the interaction between atoms in a material on illumination of light. The calculated refractive index n( ) of the investigated perovskites is shown as a function of photon energy in Fig. 5. The plots for n( ) of all the systems resemble with real part of dielectric function. From this plot, we can observe that the calculated value of the static refractive index n(0) for the pristine MAPbI3 is 2.03 which agrees


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well with experimental work.66 For x = 0.0625, 0.125 and 0.25, respectively, the calculated n(0) values are 2.09, 2.11 and 2.15 and thus, Ga doping modulates the refractive index.

Fig. 6 Calculated extinction coefficient k ( ) for MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25. Extinction coefficient signifies how strongly a material absorbs light at a given wavelength. Fig. 6 depicts the calculated extinction coefficient k ( ) for MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25 combinations. From this figure, it is evident that k ( ) has a profile similar to imaginary part of dielectric function with prominent absorption

occurring at the peaks located at 3.4 eV for x = 0.0, 0.0625, 0.125 and at 3.5 eV for x = 0.25.



Apart from k ( ) , the absorption coefficient decides how far light with a particular wavelength can infiltrate a material before it is absorbed. The evaluated absorption coefficients  ( ) for MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25 are shown in Fig.7, where we can notice a blue-shift of the absorption edge as the doping concentration of Ga increases. In addition, inclusion of Ga into MAPbI3 increases the absorption before the optical band gap, due to presence of impurity bands in between the forbidden gap. These observations are consistent with the electronic calculations comprising band structure and partial density of states. Furthermore, Ga incorporation causes the peak of pristine MAPbI3 to decrease with increase in dopant concentration and also shift it from 3.5 eV towards higher energies at 3.55 eV, 3.56 and 3.7 eV for x = 0.0625, 0.125 and 0.25, respectively.

Fig. 7 Calculated absorption coefficient  ( ) for MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25.


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Fig. 8 Calculated reflectivity R( ) for MAGaxPb(1-x)I3 perovskites for x = 0.0, 0.0625, 0.125 and 0.25. The reflectivity R( ) provides the information about the amount of reflected light and thus, we have calculated R( ) for MAGaxPb(1-x)I3 perovskites which is shown in Fig. 8. As we can see, MAPbI3 reflects around 11.6% at zero energy which increases to 12.5%, 12.7% and 13.3% for x = 0.0625, 0.125 and 0.25, respectively. With the rising dopant concentration of Ga, reflectivity of the investigated perovskite systems decreases with increase in photon energy. Since reflectivity is predominantly determined by virtue of refractive index, both the plots of R( ) and n( ) resemble each other.



Page 26 of 37

3.4 Absorber layer efficiencies The highest achievable efficiency of a single junction solar cell as a function of absorber layer band gap is given by Shockley-Queisser (SQ) limit and is applicable only for direct band gap semiconductors.69 The maximum efficiency  in SQ method is calculated as follows:



Voc J sc FF Pin

(6)



where, J sc  q  sun ( E )dE

(7)

Eg

Voc 

kT  J sc  ln   1 q  J0 

(8)



J 0  q  bb ( E , T )dE

(9)

Eg

FF 

Vmp  J mp Voc  J sc

(10)

In the above equations, J sc is the short-circuit current density, Voc is the open-circuit voltage, J 0 is the reverse saturation current density and FF is the fill factor. Also, q , Eg , sun ( E ) , k , T ,

bb ( E , T ) , Vmp and J mp denote the elementary charge, the energy band gap, the photon flux of 1.5G solar spectrum, Boltzmann’s constant, the temperature of the solar cell, the blackbody spectrum, the voltage and current density at the maximum power point, respectively. In SQ method, it is assumed that every photon with energy greater than the band gap create one electron-hole pair. Moreover, it is significant to mention that only absorption, black-body radiation and radiative recombination losses are considered in this calculation. Spectroscopic limited maximum efficiency (SLME) improves the SQ method by using ab-initio calculated absorption coefficient and at the same time incorporates non-radiative recombination.70 In SLME, the maximum power density is obtained from the J-V characteristic of the solar cell, which is given as follows:


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P  JV  ( J sc  J 0 (e

q kT

 1))V

(11)

where, J is the total current density and V is the voltage potential across the absorber layer. The short circuit current density J sc and the reverse saturation current density J 0 can be calculated from the given relationships: 

J sc  q  (1  e 2 ( E ) Lsun ( E )dE 0

J0 

q fr





0

(1  e 2 ( E ) Lbb ( E , T )dE

(12) (13)

where  ( E ) , L and f r are the absorption coefficient, thickness of the material and the fraction of the radiative recombination current which is the difference between the lowest possible direct allowed transition and the fundamental band gaps, respectively. The maximum theoretical efficiency of a solar cell is then estimated by the relation:



Pm Pin

(14)

where Pm and Pin are the maximum power density and the incident power density from the solar spectrum. Table 5 presents the calculated absorber efficiencies of the explored Ga-doped MAPbI3 perovskite series using SLME where an absorber thickness L = 500nm is considered throughout the calculation. Both the SLME as well as the SQ limit were calculated at a temperature T = 300K for comparative analysis of results. Our calculations have shown that all the studied perovskite materials have direct band gap at  -point. For photons energies E  Eg , the calculated SLME is less than SQ limit but very close to the SQ limit. This can be explained in two ways: (i) SQ limit considers the thickness of the layer to be infinite making the efficiency more than the SLME, and (ii) by virtue of its high absorptive power, a thin layer of perovskite material is enough to get high efficiency. In addition, the efficiency decreases with higher concentration of doping in both the cases. Below the band gap, there is possibility for significant absorption due to impurity bands. In order to analyze this, we have calculated the efficiency below the energy band gap using SLME. From table 5, it is noticeable that efficiency due absorption of sub band gap photons increases with increase in doping content. Among all the investigated perovskite materials, MAGa0.0625Pb93.75I3



Page 28 of 37

has the overall highest efficiency. Last but not least, the impurity bands might act as trap states for the recombination rate to increase which might affect the performance of the solar cell. Table 5 Calculated absorber layer efficiencies of the investigated MAGaxPb(1-x)I3 perovskite materials using SLME where the ab-initio calculated absorption coefficients are considered for the photon energy range above (  Eg ) and below the band gap (< Eg ) to account the contribution by the impurity bands. The SQ limit corresponding to the particular band gap is also given as reference. MAGaxPb(1-x)I3

SLME (%)

SQ limit (%)

(  Eg )

(< Eg )

Total

x=0

27.88

1.68

29.56

29.15

x=0.0625

27.13

2.55

29.68

27.94

x=0.125

25.91

3.17

29.08

26.54

x=0.25

22.37

3.91

26.28

22.84

4. CONCLUSION In summary, a systematic study of the structural, electronic, optical properties of Ga-doped MAPbI3 perovskites with respect to solar cell applications have been reported successfully. From structural viewpoint, Ga doping was found to decrease the lattice volume due to small ionic cations. Moreover, the bond length decreases improving the stability of the perovskite structure which is in agreement with the calculated enthalpies of formation and tolerance factors. The apical tilting angle Pb-I-Pb increases with Ga concentration for all the studied MAGaxPb(1-x)I3 perovskites. Similarly, the average overall titling angle is found to increase except for x=0.25, where strong coupling between inorganic framework (Ga/Pb)I6 and organic MA cation causes an anomalous behaviour. In electronic properties, it has been revealed from the band structure that band gaps increase with dopant concentration. The trend of band gaps from our calculation using GGA-PBE has uniformity with the results calculated from PBE-SOC. Besides this, the most striking feature is the presence of impurity bands induced by the incorporation of gallium atoms. The impurity bands mainly due to the overlap of Ga-4s and I-5p orbitals and a detailed analysis on projected density of states have been presented. Additionally, the increment of band gaps is


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observed due to shifting of Pb-6p orbital towards higher energies following the interaction of Ga and I atoms. Our analysis on effective masses show that PBE-SOC gives better results, which agrees well with the experimental results. Although the calculated reduced masses do not follow a particular trend but good and balanced transport properties are exhibited by the gallium-doped MAPbI3 structures, the best among them is MAGa0.125Pb0.875I3. In our analysis of the calculated optical properties, blue shift has been noticed in the absorption edges and the peaks. Impurity bands due to gallium atoms introduce a sub-band gap absorption before the electronic band gap which might increase the efficiency of the solar absorber. Finally, using the ab-initio calculated properties of the investigated perovskite materials, proper estimation of the absorber layer efficiencies using SLME method have been performed. From this calculation, it was found that 6.25% Ga-doped MAPbI3 has the highest overall efficiency among all the studied perovskite materials. Overall, such low-toxic semiconductors have enormous potential in improving stability of the solar cell device for long-term use and at the same time, proper doping increases the solar cell efficiency. Another possible application of these semiconductors with impurity bands is intermediate band photovoltaics, which is considered to increase power conversion efficiency of solar cell many-fold. Supporting Information Band structure of pristine MAPbI3 using GGA-PBE with vdW corrections. Bond lengths and tilting angles for the investigated MAGaxPb(1-x)I3 perovskites. Optimized geometries and total Energies, E (in eV) per formula unit of the MAI, PbI2, I2 and Ga structures. Spin-up and spindown band structures, and band structures of optimized MAGaxPb(1-x)I3 perovskites with SOC.

AUTHOR INFORMATION Corresponding author *E-mail: [email protected] , Mobile no.09465407913 Notes The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work is funded by Early Career Research scheme (File no. ECR/2016/001404) under SERB, New Delhi, Government of India. The authors are also thankful to CSIR, New Delhi for providing financial support to carry out this work. The authors are thankful to Prof. Sivaji Bandyopadhyay, Director, National Institute of Technology, Silchar for his continuous support in conducting this work.

REFERENCES 1. Kojima, A.; Teshima, K.; Shirai Y.; Miyasaka, T. Organometal halide perovskites as visiblelight sensitizers for photovoltaic cells. J. Am. Chem. Soc. 2009, 131, 6050–6051. 2. National Renewable Energy Laboratory (NREL) https://www.nrel.gov/pv/assets/pdfs/bestreserch-cell-efficiencies.20190327.pdf (accessed on 09-04-2019). 3. Lee, M. M.; Teuscher, J.; Miyasaka, T.; Murakami, T. N.; Snaith, H. J. Efficient hybrid solar cells based on meso-superstructured organometal halide perovskites. Science 2012, 338, 643– 647. 4. Eperon, G. E.; Stranks, S. D.; Menelaou, C.; Johnston, M. B.; Herza L. M.; Snaith, H. J. Formamidinium lead trihalide: a broadly tunable perovskite for efficient planar heterojunction solar cells. Environ. Sci. 2014, 7, 982–988. 5. Giorgi, G.; Fujisawa, J. I.; Segawa H.; Yamashita, K. Cation role in structural and electronic properties of 3D organic–inorganic halide perovskites: a DFT analysis. J. Phys. Chem. C 2014, 118, 12176–12183. 6. Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J.; Leijtens, T.; Herz, L.; Petrozza, M. A.; Snaith. H. J. Electron-hole diffusion lengths exceeding 1 micrometer in an organometal trihalide perovskite absorber. Science 2013, 342, 341–344. 7. Yin, W. J.; Shi, T.; Yan, Y. Unique properties of halide perovskites as possible origins of the superior solar cell performance. Adv. Mater. 2014, 26, 4653–4658.


Page 30 of 37

Page 31 of 37 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


8. You, J.; Hong, Z.; Yang, Y.; Chen, Q.; Cai, M.; Song, T. B.; Chen, C. C.; Lu, S.; Liu, Y.; Zhou, H.; Yang, Y. Low-temperature solution-processed perovskite solar cells with high efficiency and flexibility. ACS Nano 2014, 8, 1674–1680. 9. Baikie, T.; Fang, Y.; Kadro, J. M.; Schreyer, M.; Wei, F. S.; Mhaisalkar, G.; Graetzel, M.; White, T. J. Synthesis and crystal chemistry of the hybrid perovskite (CH3NH3)PbI3 for solidstate sensitised solar cell applications. J. Mater. Chem. A 2013, 1, 5628–5641. 10. Conings, B.; Drijkoningen, J.; Gauquelin, N.; Babayigit, A.; D'Haen, J.; D'Olieslaeger, L.; Ethirajan, A.; Verbeeck, J.; Manca, J.; Mosconi, E.; Angelis, F. D. Intrinsic thermal instability of methylammonium lead trihalide perovskite. Adv. Energy Mater. 2015, 5, 1500477. 11. Zhou, Y.; Chen, J.; Bakr, O. M.; Sun, H.T. Metal-doped lead halide perovskites: synthesis, properties, and optoelectronic applications. Chem. Mater. 2018, 30, 6589–6613. 12. 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. 13. Zhang, X.; Li, L.; Sun, Z.; Luo, J. Rational chemical doping of metal halide perovskites. Chem. Soc. Rev. 2019, 48, 517–539. 14. 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. 15. Hao, F.; Stoumpos, C. C.; Cao, D. H.; Chang, R. P.; Kanatzidis, M. G. Lead-free solid-state organic–inorganic halide perovskite solar cells. Nat. Photonics 2014, 8, 489. 16. Noel, N. K.; Stranks, S. D.; Abate, A.; Wehrenfennig, C.; Guarnera, S.; Haghighirad, A. A.; Sadhanala, A.; Eperon, G. E.; Pathak, S. K.; Johnston, M. B.; Petrozza, A. Lead-free organic– inorganic tin halide perovskites for photovoltaic applications. Energy Environ. Sci. 2014, 7, 3061–3068. 17. Hao, F.; Stoumpos, C. C.; Chang, R. P.; Kanatzidis, M. G. Anomalous band gap behavior in mixed Sn and Pb perovskites enables broadening of absorption spectrum in solar cells. J. Am. Chem. Soc. 2014, 136, 8094–8099.



18. Ogomi, Y.; Morita, A.; Tsukamoto, S.; Saitho, T.; Fujikawa, N.; Shen, Q.; Toyoda, T.; Yoshino, K.; Pandey, S. S.; Ma, T.; Hayase, S. CH3NH3SnxPb(1–x) I3 perovskite solar cells covering up to 1060 nm. J. Phys. Chem. Lett. 2014, 5, 1004–1011. 19. Li, Y.; Sun, W.; Yan, W.; Ye, S.; Rao, H.; Peng, H.; Zhao, Z.; Bian, Z.; Liu, Z.; Zhou, H.; Huang, C. 50% Sn‐based planar perovskite solar cell with power conversion efficiency up to 13.6%. Adv. Energy Mater. 2016, 6, 1601353. 20. Stoumpos, C. C.; Frazer, L.; Clark, D. J.; Y. S. Kim, S.H. Rhim, A.J. Freeman, J.B. Ketterson, J.I. Jang and M.G. Kanatzidis, 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. 21. Kopacic, I.; Friesenbichler, B.; Hoefler, S. F.; Kunert, B.; Plank, H.; Rath, T.; Trimmel, G. Enhanced performance of germanium halide perovskite solar cells through compositional engineering. ACS Appl. Energy Mater. 2018, 1, 343–347. 22. Krishnamoorthy, T.; Ding, H.; Yan, C.; Leong, W. L.; Baikie, T.; Zhang, Z.; Sherburne, M.; Li, S.; Asta, M.; Mathews, N.; Mhaisalkar, S. G. Lead-free germanium iodide perovskite materials for photovoltaic applications. J. Mater. Chem. A 2015, 3, 23829–23832. 23. Wang, J. T. W.; Wang, Z.; Pathak, S.; Zhang, W.; Wisnivesky-Rocca-Rivarola, F.; Huang, J.; Nayak, P. K.; Patel, J. B.; Yusof, H. A. M.; Vaynzof, Y.; Zhu, R. Efficient perovskite solar cells by metal ion doping. Energy Environ. Sci. 2016, 9, 2892–2901. 24. Wang, Z. K.; Li, M.; Yang, Y. G.; Hu, Y.; Ma, H.; Gao, X. Y.; Liao, L. S. High efficiency Pb–In binary metal perovskite solar cells. Adv. Mater. 2016, 28, 6695–6703. 25. Zhou, L.; Su, J.; Lin, Z.; Chen, D.; Zhu, W.; Zhang, C.; Zhang, J.; Chang, J.; Hao, Y. Theoretical and experimental investigation of mixed Pb–In halide perovskites. J. Phys. Chem. C 2018, 122, 15945–15953. 26. Lang, L.; Yang, J. H.; Liu, H. R.; Xiang, H. J.; Gong, X. G. First-principles study on the electronic and optical properties of cubic ABX3 halide perovskites. Phys. Lett. A 2014, 378, 290–293.


Page 32 of 37

Page 33 of 37 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


27. Bernal, C.; Yang, K. First-principles hybrid functional study of the organic–inorganic perovskites CH3NH3SnBr3 and CH3NH3SnI3. J. Phys. Chem. C 2014, 118, 24383–24388. 28. 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. 29. Mosconi, E.; Umari, P.; De Angelis, F. Electronic and optical properties of mixed Sn–Pb organohalide perovskites: a first principles investigation. J. Mater. Chem. A 2015, 3, 9208– 9215. 30. Mayengbam, R.; Tripathy, S. K.; Palai, G. First-principle insights of electronic and optical properties of cubic organic–inorganic MAGexPb(1–x)I3 perovskites for photovoltaic applications. J. Phys. Chem. C 2018, 122, 28245–28255. 31. Moon, S.; Kim, K.; Kim, Y.; Heo, J.; Lee, J. Highly efficient single-junction GaAs thin-film solar cell on flexible substrate. Sci. Rep. 2016, 6, 30107. 32. Philipps, S. P.; Dimroth, F.; Bett, A. W. In McEvoy's Handbook of Photovoltaics; Kalogirou, S, Ed.; Academic Press, 2018, Chapter 1-4-B, 439–472. 33. Ramanujam, J.; Singh, U. P. Copper indium gallium selenide based solar cells–a review. Energy Environ. Sci. 2017, 10, 1306–1319. 34. Roose, B.; Johansen, C. M.; Dupraz, K.; Jaouen, T.; Aebi, P.; Steiner, U.; Abate, A. A Gadoped SnO2 mesoporous contact for UV stable highly efficient perovskite solar cells. J. Mater. Chem. A 2018, 6, 1850–1857. 35. Liu, H.; Zhang, Z.; Zhang, X.; Cai, Y.; Zhou, Y.; Qin, Q.; Lu, X.; Gao, X.; Shui, L.; Wu, S.; Liu, J. M. Enhanced performance of planar perovskite solar cells using low-temperature processed Ga-doped TiO2 compact film as efficient electron-transport layer. Electrochim. Acta 2018, 272, 68–76. 36. Wang, K.; Liang, Z.; Wang, X.; Cui, X. Lead replacement in CH3NH3PbI3 perovskites. Adv. Electron. Mater. 2015, 1, 1500089.



37. Mosconi, E.; Amat, A.; Nazeeruddin, M. K.; Grätzel, M.; De Angelis, F. First-principles modeling of mixed halide organometal perovskites for photovoltaic applications. J. Phys. Chem. C 2013, 117, 13902–13913. 38. Pazoki, M.; Jacobsson, T. J.; Hagfeldt, A.; Boschloo, G.; Edvinsson, T. Effect of metal cation replacement on the electronic structure of metalorganic halide perovskites: replacement of lead with alkaline-earth metals. Phys. Rev. B 2016, 93, 144105. 39. Gao, W.; Gao, X.; Abtew, T. A.; Sun, Y. Y.; Zhang, S.; Zhang, P. Quasiparticle band gap of organic-inorganic hybrid perovskites: Crystal structure, spin-orbit coupling, and self-energy effects. Phys. Rev. B 2016, 93, 085202. 40. Yin, W. J.; Yang, J. H.; Kang, J.; Yan, Y; Wei, S. H. Halide perovskite materials for solar cells: a theoretical review. J. Mater. Chem. A 2015, 3, 8926–8942. 41. Hernández-Haro, N.; Ortega-Castro, J.; Martynov, Y. B.; Nazmitdinov, R. G; Frontera, A. DFT prediction of band gap in organic-inorganic metal halide perovskites: An exchange-correlation functional benchmark study. Chem. Phys. 2019, 516, 225-231. 42. Nabok, D.; Puschnig, P.; Ambrosch-Draxl, C. Cohesive and surface energies of π-conjugated organic molecular crystals: A first-principles study. Phys. Rev. B 2008, 77, 245316. 43. Mayengbam, R.; Tripathy, S. K.; Palai, G.; Dhar, S. S. First-principles study of phase transition, electronic, elastic and optical properties of defect chalcopyrite ZnGa2Te4 semiconductor under different pressures. J. Phys. Chem. Solids 2018, 119, 193–201. 44. Yamada, Y.; Yamada, T.; Phuong, L. Q.; Maruyama, N.; Nishimura, H.; Wakamiya, A.; Murata, Y.; Kanemitsu, Y. Dynamic optical properties of CH3NH3PbI3 single crystals as revealed by one-and two-photon excited photoluminescence measurements. J. Am. Chem. Soc. 2015, 137, 10456–10459. 45. Travis, W.; Glover, E. N. K.; Bronstein, H.; Scanlon, D. O.; Palgrave, R. G. On the application of the tolerance factor to inorganic and hybrid halide perovskites: a revised system. Chem. Sci. 2016, 7, 4548–4556.


Page 34 of 37

Page 35 of 37 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


46. Bartesaghi, D.; Ray, A.; Jiang, J.; Bouwer, R. K.; Tao, S; Savenije, T. J. Partially replacing Pb2+ by Mn2+ in hybrid metal halide perovskites: Structural and electronic properties. APL Mater. 2018, 6, 121106. 47. Shannon, R. D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. A 1976, 32, 751–767. 48. Buin, A.; Pietsch, P.; Xu, J.; Voznyy, O.; Ip, A. H.; Comin, R.; Sargent, E. H.; Materials processing routes to trap-free halide perovskites. Nano Lett. 2014, 14, 6281–6286. 49. Ali, R.; Hou, G. J.; Zhu, Z. G.; Yan, Q. B.; Zheng, Q. R.; Su, G. Stable mixed group II (Ca, Sr) and XIV (Ge, Sn) lead-free perovskite solar cells. J. Mater. Chem. A 2018, 6, 9220–9227. 50. Yang, D.; Lv, J.; Zhao, X.; Xu, Q.; Fu, Y.; Zhan, Y.; Zunger, A.; Zhang, L. Functionalitydirected screening of Pb-free hybrid organic–inorganic perovskites with desired intrinsic photovoltaic functionalities. Chem. Mater. 2017, 29, 524–538. 51. Jiang, L.; Wu, T.; Sun, L.; Li, Y. J.; Li, A. L.; Lu, R. F.; Zou, K.; Deng, W. Q. First-principles screening of lead-free methylammonium metal iodine perovskites for photovoltaic application. J. Phys. Chem. C 2017, 121, 24359–24364. 52. Sanderson, R. Chemical Bonds and Bonds Energy; Elsevier, 2012. 53. Dean, J. A. Lange's Handbook of Chemistry; McGraw-Hill, Inc.: New York; London, 1999. 54. Yamada, Y.; Nakamura, T.; Endo, M.; Wakamiya, A.; Kanemitsu, Y. Near-band-edge optical responses of solution-processed organic–inorganic hybrid perovskite CH3NH3PbI3 on mesoporous TiO2 electrodes. Appl. Phys. Express 2014, 7, 032302. 55. Chen, L. C.; Weng, C. Y. Optoelectronic properties of MAPbI3 perovskite/titanium dioxide heterostructures on porous silicon substrates for cyan sensor applications. Nanoscale Res. Lett. 2015, 10, 404. 56. Zheng, F.; Tan, L. Z.; Liu, S.; Rappe, A. M. Rashba spin–orbit coupling enhanced carrier lifetime in CH3NH3PbI3. Nano Lett. 2015, 15, 7794–7800.



57. Mosconi, E; Umari, P.; De Angelis, F. Electronic and optical properties of MAPbX3 perovskites (X= I, Br, Cl): a unified DFT and GW theoretical analysis. Phys. Chem. Chem. Phys., 2016, 18, 27158–27164. 58. Umari, P.; Mosconi, E; De Angelis, F. Relativistic GW calculations on CH3NH3PbI3 and CH3NH3SnI3 perovskites for solar cell applications. Sci. Rep., 2014, 4, 4467. 59. Giorgi, G.; Yamashita, K. Alternative, lead-free, hybrid organic–inorganic perovskites for solar applications: a DFT analysis. Chem. Lett., 2015, 44, 826–828. 60. Feng, J.; Xiao, B. Crystal structures, optical properties, and effective mass tensors of CH3NH3PbX3 (X= I and Br) phases predicted from HSE06. J. Phys. Chem. Lett., 2014, 5, 1278– 1282. 61. Giorgi, G.; Yamashita, K. Organic–inorganic halide perovskites: an ambipolar class of materials with enhanced photovoltaic performances. J. Mater. Chem. A, 2015, 3, 8981–8991. 62. Quarti, C.; Mosconi, E.; De Angelis, F. Interplay of orientational order and electronic structure in methylammonium lead iodide: implications for solar cell operation. Chem. Mater., 2014, 26, 6557–6569. 63. Galkowski, K.; Mitioglu, A.; Miyata, A.; Plochocka, P.; Portugall, O.; Eperon, G. E.; Wang, J. T. W.; Stergiopoulos, T.; Stranks, S. D.; Snaith, H. J.; Nicholas, R. J. Determination of the exciton binding energy and effective masses for methylammonium and formamidinium lead tri-halide perovskite semiconductors. Energy Environ. Sci. 2016, 9, 962–970. 64. Shirayama, M.; Kadowaki, H.; Miyadera, T.; Sugita, T.; Tamakoshi, M.; Kato, M.; Fujiseki, T.; Murata, D.; Hara, S.; Murakami, T. N.; Fujimoto, S. Optical transitions in hybrid perovskite solar cells: ellipsometry, density functional theory, and quantum efficiency analyses for CH3NH3PbI3. Phys. Rev. Appl. 2016, 5, 014012. 65. Demchenko, D. O.; Izyumskaya, N.; Feneberg, M.; Avrutin, V.; Özgür, Ü.; Goldhahn, R.; Morkoç, H. Optical properties of the organic-inorganic hybrid perovskite CH3NH3PbI3: Theory and experiment. Phys. Rev. B 2016, 94, 075206. 66. Ndione, P. F.; Li, Z.; Zhu, K. Effects of alloying on the optical properties of organic–inorganic lead halide perovskite thin films. J. Mater. Chem. C 2016, 4, 7775-7782.


Page 36 of 37

Page 37 of 37 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


67. Kumar, V.; Tripathy, S. K. First-principle calculations of the electronic, optical and elastic properties of ZnSiP2 semiconductor. J. Alloy. Compd. 2014, 582, 101-107. 68. Tripathy, S. K.; Kumar, V. Electronic, elastic and optical properties of ZnGeP2 semiconductor under hydrostatic pressures. Mat. Sci. Eng. B 2014, 182, 52-58. 69. Shockley, W; Queisser, H. J. Detailed balance limit of efficiency of p‐n junction solar cells. J. Appl. Phys. 1961, 32, 510-519. 70. Yu, L.; Zunger, A. Identification of potential photovoltaic absorbers based on first-principles spectroscopic screening of materials. Phys. Rev. Lett. 2012, 108, 068701.

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Electronic Structure and Optical Properties of Gallium-Doped Hybrid

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