First Principle Insights of Electronic and Optical properties of Cubic

Subscriber access provided by Kaohsiung Medical University

C: Plasmonics; Optical, Magnetic, and Hybrid Materials

First Principle Insights of Electronic and Optical properties of Cubic OrganicInorganic MAGexPb(1-x)I3 Perovskites for Photovoltaic Applications Rishikanta Mayengbam, Susanta Tripathy, and Gopinath Palai J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08436 • Publication Date (Web): 15 Nov 2018 Downloaded from http://pubs.acs.org on November 15, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 38 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

The Journal of Physical Chemistry

First Principle Insights of Electronic and Optical properties of Cubic Organic-Inorganic MAGexPb(1-x)I3 Perovskites for Photovoltaic Applications Rishikanta Mayengbama, S. K. Tripathya* and G. Palaib a

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

Gandhi Institute for Technological Advancement (GITA), Bhubaneswar, India

ACS Paragon Plus Environment

1

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 Owing to power conversion efficiencies as high as 22.1%, hybrid organic-inorganic lead halide perovskites have become the fastest growing solar technology, competing with the conventional thin-film technology. Though unique and exceptional, long-term stability issue and toxic behavior caused by the lead content in the perovskites hampers large-scale commercial production. With this motivation towards achieving a stable and reduced toxic perovskite, we have investigated the structural, electronic and optical properties of mixed MAGexPb(1-x)I3 perovskites with GGA-PBE exchange-correlation within the framework of density functional theory (DFT). Under structural properties, we have calculated the lattice constants, bond lengths, tolerance factors, enthalpies of formation, bulk moduli and their derivatives for x = 0.0, 0.125, 0.375, 0.625 and 0.875. We found that mixed MAGexPb(1-x)I3 perovskites are stable except at x = 0. The electronic properties such as band gaps, energy band level and effective masses have been predicted for all combinations of x. We have also analysed the projected and total density of states in detail. Optical properties like imaginary and real parts of dielectric function, refractive index and extinction coefficient have been discussed. Further, to understand the light trapping capacity, we have examined the absorption coefficients for x = 0.0, 0.125, 0.375, 0.625 and 0.875 and interband transitions are well estimated. The calculated values of all parameters were compared with the available experimental and theoretical values. A fairly good agreement has been obtained between them.


2

Page 2 of 38

Page 3 of 38 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


1. INTRODUCTION In the past few years, among the third generation solar cells, perovskite solar cells (PSCs) have gained the greatest attention among the researchers because of their excellent photoconversion efficiency.1 Hybrid organic-inorganic halide perovskites (IOHPs) have the chemical formula ABX3 where A is the organic cation, B is the metal cation and X is the halide anion. Among these perovskite materials, CH3NH3PbX3 (X = Cl, Br, I) have already attracted much attention as solar cell absorbers. The first experimental work reported by Kojima et.al.2 in 2009 using CH3NH3PbI3 and CH3NH3PbBr3 as solar cell absorbers within a dye-sensitized solar cell (DSSC) architecture achieved a power conversion efficiency (PCE) of 3.8% and 3.13%, respectively. Following it, in 2012, Lee et al.3 and Kim et al.4 have obtained solar cell efficiencies of 10.9% for CH3NH3PbI2Cl and 9.7% for CH3NH3PbI3, respectively. Continuous efforts and progress towards maximizing solar cell efficiency and the reduction of production costs have set off PSCs as an attractive solution for low-cost photovoltaics.5-7 Recently, a maximum PCE of 22.1% has been reported for methylammonium lead iodide (CH3NH3PbI3) and this matches with that of other available commercialized thin-film solar cells.8 The reason behind the high photovoltaic performance is the unique and superior properties of IOHPs characterized by appropriate bandgap,9 high absorption coefficient,3 excellent ambipolar carrier transport nature,10 high defect tolerance,11 long carrier lifetime, better diffusion length,

12

and low-temperature solution process 13. X-ray diffraction of

single crystal CH3NH3PbI3 results revealed that the structure and the symmetry are primarily determined by the temperature.14 At low temperature, it is found in orthorhombic phase (space group: Pnma), which transforms to a tetragonal phase (space group: I4/m) above 161.4 K. The cubic phase (space group: Pm-3m) is observed at temperatures higher than 330.4 K. However, a recent experiment successfully demonstrated controllable growth of stable cubic CH3NH3PbI3 at


3


room temperature.15 Further, the cubic phase of methylammonium lead iodide possess smaller carrier effective masses and suitable bandgap because of higher symmetry. In addition, the dynamic orientation of methylammonium (MA) organic cations is responsible for screening the excitons and increasing the quantum efficiency.16 Thus, this encourages us to investigate the mixed metal cations perovskites taking the cubic model as the reference symmetry. Although CH3NH3PbI3 exhibit a promising high PCE, two main challenges hinder large-scale commercial production. The first concern being the toxicity of lead present in the material, which may cause environmental and health hazards. The other one is the intrinsic unstable nature of lead when exposed to moisture and air that eventually causes Pb2+ to oxidize to Pb4+ leading to degradation of photovoltaic performance.17,18 In order to reduce the bad effects caused by the toxic nature of Pb, researchers started to completely replace Pb2+ with other less toxic divalent metal of the same group in the search of an alternative candidate for photovoltaic applications. In this perspective, Stoumpos et al. prepared tin (Sn)-based perovskites in cubic phase that exhibit large carrier mobility, high conductivity and suitable bandgaps.19 Hao et al. have also fabricated solar cells with CH3NH3SnI3 as light harvester and obtained a PCE of 5.73% under simulated full sunlight.20 However, the same group has also synthesized IOHPs with mixed metal cubic-based iodides and found anomaly in the band gaps after replacement of certain percentage of Pb with Sn.21 On the same note, Ogomi et al. also have acquired an efficiency of 4.18% using CH3NH3Sn0.5Pb0.5I3 as absorber material.22 Further, a whopping efficiency of 13.6% was realized for the first time with 50% Sn-based perovskite solar cell.23 There have been literatures that investigate the structural, electronic and optical properties of cubic phase of pure Sn-based methylammonium iodides via density functional theory (DFT).24,25 Recently, partial substitution of Pb2+ by Sn2+ has already been demonstrated experimentally and obtained much better


4

Page 4 of 38

Page 5 of 38 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


performance in terms of PCE and stability.26,27 Another group-14 element, the divalent germanium cation (Ge2+) with the same oxidation state as Pb2+ cation possess promising optical and transport properties comparable to the lead analogs.28 Therefore, these exceptional features and abundant availability of Ge paved the way to explore partial replacement of Pb by Ge in cubic phase of methylammonium lead iodide as absorber material. Moreover, literature survey shows that no experimental and DFT calculations have been carried out till date to understand the structural, electronic and optical properties of mixed cubic Ge-Pb perovskite semiconducting material. In this work, we have investigated the structural, electronic and optical properties of mixed CH3NH3GexPb (1-x)I3 perovskites with x = 0.0, 0.125, 0.375, 0.625 and 0.875. All the computational work have been performed within the framework of DFT with exchange-correlation GGA-PBE. In the structural properties, we have calculated the lattice constants, bulk moduli and their first derivative, and enthalpies of formation. Under electronic properties, we have carried out a detail investigation of band structure, density of states and variation of effective masses with respect to Ge content. Optical properties such as dielectric constants, absorption coefficients, refractive indices and interband transitions have been calculated and discussed keeping in mind the requisites for photovoltaic applications. Theoretically, GGA-PBE 18,28,29,30 gives accurate band gaps, whereas GGA-PBEsol 31,32 and hybrid functional18 are known to underestimate and overestimate the band gap, respectively. Furthermore, PBE functional33 provides electronic band structure similar to that of hybrid functional with good accuracy and less computational cost34. That is why throughout this work, we have used only GGA-PBE exchange correlation functional to compute all the electronic and optical properties.


5


2. COMPUTATIONAL DETAILS:

All the calculations have been performed on 2 × 2 × 2 supercell of cubic CH3NH3PbxGe(1-x)I3 (x = 0.0, 0.125, 0.375, 0.625, 0.875) structures using generalised gradient approximation (GGA) treated by Perdew, Burke, Ernzerhof (PBE) within density functional theory (DFT) as implemented in Atomistic Toolkit-Virtual Nanolab (ATK-VNL) package,35 based on local combination of atomic orbitals (LCAO) method . The valence electrons Pb 6s, 6p; I 5s, 5p; Ge 4s, 4p; N 2s, 2p; C 2s, 2p; and H-1s are explicitly treated and expanded into numeric atomic centered orbitals with a mesh density cut off of 270 Hartree (Ha). In this first principle calculation, optimized norm-conserving Vanderbilt pseudopotential SG1536,37 has been employed for the description of the core electrons. Self-consistent field (SCF) calculations have been carried out taking a tolerance limit of 10-8 Ha for energy convergence. All the structures were optimized until the forces on individual ions are less than 0.05 eV/Å. Throughout this computational work, k-point sampling of 6 × 6 × 6 has been used for Brillouin zone integration in determining structural and electronic properties, while a denser mesh of 10 × 10 × 10 has been taken for accurate calculations of optical spectra and projected density of states. For computing the optical properties of the mixed perovskite series, 1000 bands each from valence band and conduction band have been included in the calculations.

3. RESULTS AND DISCUSSION 3.1 Structural Properties: The cubic methylammonium lead halide (CH3NH3PbX3: X= Cl, Br, I) perovskites in its pristine form contains 12 atoms (Z=1) with space group of Pm-3m. It has a divalent cation Pb2+ in 6-fold


6

Page 6 of 38

Page 7 of 38 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


coordination surrounded by an octahedron of X- anions, and the monovalent disorder cation (CH3NH3+) or MA cation in 12-fold cubo-octahedral coordination.38 This disordered cation leads to three different orientations of the C-N bond along [111], [100], and [011] directions, among which [011] is energetically the most stable.39 Taking into account the relative stability factor and lattice parameters from experimental data of ref. 39, we have constructed a CH3NH3PbI3 cubic unit cell structure with C-N along [011] direction.

x = 0.0

x = 0.125

x = 0.375

x = 0.625

x= 0.875

Figure 1. Optimized geometries of MAGexPb(1-x)I3 series for x = 0.0, 0.125, 0.375, 0.625 and 0.875 as viewed along Y-Z plane (Balls in dark grey, purple, cyan, blue, light grey and white colors represent Pb, I, Ge, N, C and H atoms).

Using the same cubic model, 2 × 2 × 2 supercell structures of the pristine MAPbI3 and four mixed MAGexPb(1-x)I3 perovskites with x = 0.0, 0.125, 0.375, 0.625 and 0.875 were constructed. Each supercell structure of eight formula units comprising 96 atoms have been structurally optimized. Optimized geometries of the mixed MAGexPb(1-x)I3 perovskites are pictorially depicted in Figure 1. The optimized lattice constant of the pristine CH3NH3PbI3 unit cell listed in Table 1 is in good agreement with the experimental values.39,40 In Table 1, we have also listed optimized lattice constants, lattice volumes, and total energies per unit cell for the optimized MAGexPb(1-x)I3 systems that show a decreasing trend with increase in the Ge content. We also observe that, as the concentration of Ge increases, the values of lattice constants decrease owing to the smaller ionic radii of the Ge atoms. Moreover, the table lists the computed bulk modulus and its derivative for


7


Page 8 of 38

the investigated mixed perovskites obtained through second order Murnaghan equation of state (EOS).35 The calculated values of lattice constants, bulk moduli and their first derivatives show a fair agreement with the reported experimental and theoretical values.39-41 Interestingly, the values of bulk moduli of the mixed perovskite series show no substantial difference indicating that Ge incorporation plays less role in modulating mechanical behavior.

Table 1. Lattice constants a (Å) per unit cell, lattice volumes V (Å3) per unit cell, total energies E (eV) per unit cell, bulk moduli ( B ) (in GPa), and their derivative ( B′) for the mixed MAGexPb(1x)I3

perovskites.

Structure

a= b= c

V

E

B

B′

x=0

6.34,6.3139,6.3340

255.6

-10159.2

24.8, 16.441

3.62

x = 0.125

6.31

251.8

-10207.1

24.9

3.47

x = 0.375

6.30

250.8

-10304.5

24.8

3.73

x = 0.625

6.29

249.9

-10401.2

25.2

3.12

x = 0.875

6.28

248.0

-10498.1

24.5

3.71


8

Page 9 of 38 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


Figure 2. Bond lengths of C-N, H-I, and B-I bonds of optimized mixed MAGexPb(1-x)I3 perovskites.

Further, we have calculated the bond lengths of B-I (B = Pb/Ge), C-N and H-I (for hydrogen with nitrogen) with different ratios of Pb and Ge cations and shown in Figure 2. Notably, the bond lengths of B-I and C-N bonds decrease whereas the bond length of H-I bond increases with increase in Ge concentration. However, the average H-I bond length of the pristine CH3NH3PbI3 is 2.81 Å that increases with Ge content except at x = 0.875, where the value falls down to 2.79 Å. This unusual trend in H-I bond may be due to the weak electronic coupling between the organic cation and the inorganic framework indicating a structural transformation due to high Ge content. Moreover, the average bond lengths lie in the range of 3.11–3.18 Å and 1.49–1.51 Å for B-I and C-N bonds, respectively. The decrease in bond lengths may also be due the difference in electronegativity values of Pb and Ge.29 Consequently, decrease in B-I bond length indicates increasing bond strength resulting in more stable structures.


9


Page 10 of 38

Figure 3. Estimated tolerance and octahedral factors, and enthalpy of formation per formula unit of the mixed MAGexPb(1-x)I3 systems.

After calculating the lattice constants and bond lengths successfully, it is important to calculate the tolerance factor ( t ) given by Goldschmidt for stable perovskite structure given by the following expression:

t=

rA + rX 2(rB + rX )

(1)

where rA , rB , and rX are the ionic radii of the cation A, cation B, and anion X, respectively in the general formula ABX3 of the perovskite structure. Another criterion taken into consideration for a stable perovskite structure is the octahedral factor ‘ µ ’ given by the relationship:

µ=

rB rX

(2)

For a perovskite structure, generally value of t should lie in the range 0.80 ≤ t ≤ 1.06 and µ should be greater than 0.41.42 For tolerance factor t very close to unity, the formation of an ideal cubic stable structure is expected. Surprisingly, it has been reported that MAGeI3, FAGeI3 (FA = H2N–CH=NH2) and ACGeI3 (AC = CH3C(NH2)2+) form thermodynamically stable perovskites


10

Page 11 of 38 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


with µ below 0.41. This unusual stability of the Ge2+compounds is due to the ability of Ge2+ to adopt highly distorted coordination due to a stereo active lone pair.43 For the mixed MAGexPb(1x)I3 perovskites,

the tolerance factors and octahedral factors are calculated and depicted in Figure

3. We have considered the Shannon ionic radii mentioned in ref. 42 for Pb2+, Ge2+, I- and MA+ cations as 1.19 Å, 0.73 Å, 2.2 Å and 2.17 Å, respectively for calculating tolerance factors and octahedral factors. As observed in the plot, all the structures of the mixed cubic MAGexPb(1-x)I3 systems satisfy the structural stability criteria. However, tolerance and octahedral factors are essential for predicting the formation of stable perovskites ABX3, these criteria do not suffice their thermodynamic stability. Enthalpy of formation is an important parameter that determines the chemical and thermodynamic stability of a material. Heat, moisture, and oxygen are the external agents, which can unstabilize a material. Generally, MAPbI3 decomposes into MAI+PbI2 44 and in the present study, we have calculated the enthalpy of formation ( ∆H ) by considering the following decomposition reaction: = ∆H E (MAGe x Pb (1− x ) I3 ) − E (MAI) − (1 − x) E (PbI 2 ) − xE (I 2 ) − xE (Ge)

(3)

where x denotes the percentage concentration of the Ge atom. A negative and positive ∆H means exothermic and endothermic reaction. Hence, exothermic reaction indicates more stable in nature. For the present study, we have calculated the total energies of the compounds involved during decomposition reaction and the enthalpy of formation per formula unit of MAGexPb(1-x)I3 systems. From Table 2, we notice that enthalpy of formation is positive for MAPbI3, which indicates its unstable nature also observed in the tetragonal phase as reported elsewhere,45 whereas for all the other systems, the enthalpies are negative increasing with Ge content, confirm the formation of stable perovskite structures.


11


Page 12 of 38

Table 2. Calculated total energies, E (in eV) per formula unit for the constituent compounds and the enthalpies of formation, (∆H ) (in eV) of mixed MAGexPb(1-x)I3 perovskites. Compound

E

MAGexPb(1-x)I3

∆H

MAI

-3222.65

MAPbI3

0.03

PbI2

-6936.60

MAGe0.125Pb0.875I3

-0.12

Ge

-1932.70

MAGe0.375Pb0.625I3

-0.43

I2

-5390.00

MAGe0.625Pb0.375I3

-0.72

MAGe0.875Pb0.125I3

-1.01

The enthalpy of formation is associated with structural configuration and can be examined through two main factors: (i) geometrical factor or the tolerance factor, and (ii) B-I bond strength. To understand the formation of a stable perovskite structure, we have plotted the enthalpy of formation values with respect to the tolerance factor in Figure 3. From this figure, it is observed that the enthalpy of formation of the mixed MAGexPb(1-x)I3 systems display linearly falling values with increasing tolerance factor. In conclusion, the degree of deviation from the ideal cubic symmetry determines the value of negative enthalpy of formation also observed in the reported work.31 Second factor, the bond strength is determined by the bond length and the electronegativity difference between the metal cations and halides. Smaller the bond length and higher the electronegativity difference, stronger is the bond. As we can conclude from Figure 2 that the average B-I bond length decreases and the overall electronegativity difference of B-I bond increases with Ge content. Thus, the calculated values of enthalpy of formation and B-I bond strength obey the conditions for a stable cubic structure.


12

Page 13 of 38 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


3.2 Electronic properties The magnitude of the electronic band gap is very crucial for solar cell absorbers since a suitable band gap is required to absorb the photons highly concentrated in the infrared region of the solar spectrum. More importantly, the nature of the band gap helps to estimate the amount of light absorbed in the maximizing the efficiency of the solar cell with minimum optical losses. Therefore, it is of prior interest among all the researchers working in this fascinating field of solar cells to thoroughly investigate the electronic properties of solar absorbers. In this current study, band gaps of the optimized structures of MAGexPb(1-x)I3 system are calculated and plotted in Figure 4. The calculated electronic band gap of the optimized MAPbI3 is found to be 1.60 eV, which is in excellent agreement with the experimental values 1.61 eV 46 and 1.60 eV 47. As illustrated in the Figure 4, with increase in Ge concentration, there is a gradual decrease in the band gaps and found to be 1.49 eV, 1.47 eV, 1.46 eV and 1.35 eV, for x = 0.125, 0.375, 0.625 and 0.875, respectively. However, this declining trend is not linear; it is obvious that the change is due to the substitutional doping of Pb by Ge. As the B-I bond length decreases with increasing Ge proportion, there is an increase in electronic interaction between the Ge cations and I anions causing more orbital overlap. This leads to more band dispersions, and wide bandwidth, which ultimately lowers the band gap. Indeed, we also observe that band gaps calculated within DFT decrease as the symmetry of the cell increases as noticeable from the tolerance factors of the MAGexPb(1-x)I3 series shown in Figure 3. Moreover, this falling trend of band gaps in relation with increasing tolerance factors has also


13


Figure 4. Calculated band gaps of the MAGexPb(1-x)I3 system.

been predicted in other mixed perovskite systems.31 Similar to the work reported48, to analyse the nature of conductivity, we have depicted the position of valence band (VB) and conduction band (CB) edges in Figure 5 for mixed MAGexPb(1-x)I3 perovskites. We have calculated the fermi level using the electron density obtained from the first principles calculation, and employing the relationship for the total number of electrons, density of states and the Fermi-Dirac distribution. The fermi level is shown as dashed lines. The increase in percentage of Ge in MAPbI3 resulted in monotonic downshift of CB edges. On the other hand, the VB edges, show a non-monotonic variation. The energy gap between the fermi level and VB edge in compared with that of the CB edge for MAGexPb(1-x)I3 series predict p-type behavior. Precisely, our estimated values of band gap found a significant change when x move from 0 to 0.125 and 0.625 to 0.875, however, band gap remains remain almost equal for intermediate values of x similar to the reported work 21.


14

Page 14 of 38

Page 15 of 38 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


Figure 5. Energy band levels for MAGexPb(1-x)I3 perovskites.

The calculated band structures for all combinations of the MAGexPb(1-x)I3 system along four high symmetry k-points, Γ(0, 0, 0) , X(1 2,0,0) , R(1 2,1 2,1 2) , and M(1 2,1 2,0) are shown in Figure 6. Here, the fermi level is set to zero. With the treated supercell size, both valence band maximum (VBM) and conduction band minimum (CBM) fold to the Γ-point and band gaps along the Γ-point are found to be direct in nature. The dispersion of conduction bands increases with growing Ge ratio but there is no significant changes in the valence band, which resulted in balanced hole effective masses for the mixed perovskite series.


15


Figure 6. Calculated band structures of MAGexPb(1-x)I3 along with the projected density of states (PDOS).


16

Page 16 of 38

Page 17 of 38 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


To have in depth understanding of electronic behavior, we have shown the atomic character of each orbitals in the right hand column of Figure 6. Since MA+ cation states are far below the energy gap region and remain well localized in space, the molecules do not interfere with the active region of the perovskite structure. Its main role is to function as an electrostatic charge compensator and stabilize the ionic perovskite framework. Thus, for the sake of clarity around the band gap, only the contributions of valence orbitals of Pb, I and Ge atoms for each system are represented and analyzed. For the pristine MAPbI3 structure, it can be noticed from the PDOS plot that the uppermost region of valence band is predominantly contributed by the Pb-6s and I-5p orbitals. Below this, the bands extending to the energy level of -3.5 eV are mainly dominated by I-5p orbital with minor contributions from Pb-6s orbital and I-5s orbital. Ge has the same isoelectronic structure as Pb and so, it shows a very similar contribution in the uppermost valence band region. The contribution of I atoms in valence band remains more or less the same in all the systems under consideration. However, with increase in Ge content, the contribution of Ge-4s orbital in valence band region tends to increase. As observed, the contributions from the orbitals of Pb in valence band region are steadily substituted by the corresponding orbitals of Ge in the mixed systems. In case of the conduction band, for the pristine MAPbI3, Pb-6p orbital plays the major contribution in lowermost region of the conduction band. In higher energy levels of the conduction band, small contributions of I-5s/5p orbitals are observed. The conduction bands of the mixed systems indicates a rising contribution of Ge-4p orbital with an increase in Ge ratio. Hybridized states of I-5p, Pb-6p, and Ge-4s orbitals all together contribute to the higher energy levels in the conduction band. Briefly, we observed that VBM is characterized by hybridized states of Pb-6s and I-5p orbitals in pristine MAPbI3, whereas, in mixed systems, hybridized states of Ge-4s, Pb-6s and I5p control the VBM. Thus, the energy-conversion properties, which was mainly governed by the


17


Pb2+ states in the pristine MAPbI3 are now controlled by the new hybrid states of Ge2+ and Pb2+ in the mixed systems.

Figure 7. Calculated total density of states (TDOS) of the MAGexPb(1-x)I3 system.

The total density of states (TDOS) plot of MAGexPb(1-x)I3 system are calculated and shown in Figure 7. This figure indicates a much-pronounced rise of the valence band edge in comparison to conduction band edge. Nevertheless, the calculated TDOS of all the systems show a similar shape, the number of states calculated from the area under each curve in the energy region from -5 eV to 6 eV represents a different non-linear figure with increasing evolution of Ge. MAGe0.375Pb0.625I3 and MAGe0.625Pb0.375I3 both show a curve similar to the pristine MAPbI3 with a marginally lesser number of states (96.94% and 96.93% respectively) with reference to the pristine MAPbI3 (grey shaded portion). On the other hand, MAGe0.125Pb0.875I3 and MAGe0.875Pb0.125I3 show an exceptionally large number of states with nearly twice the number of states (196.8% and 192.1%


18

Page 18 of 38

Page 19 of 38 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


respectively) of the pristine MAPbI3. Likewise, the number of states in the valence and conduction bands have been calculated separately for the investigated MAGexPb(1-x)I3 perovskite series and we found same number of states in the similar fashion. So, smaller (x = 0.125) and larger (x = 0.875) concentration of Ge in the mixed perovskite systems exhibit a large number of states than that of the intermediate proportion of Ge. Therefore, the probability for large number of carrier concentration increases at x = 0.125 and x = 0.875, which can enhance both transport and device properties. Charge transport property is another key factor for a material in an efficient solar cell absorber. The effective masses of the photo-generated charge carriers contribute significantly to the mobility of electrons and holes inside a solar cell device. The effective masses are solely reflected by the orbital contributions and their blend in the VBM and CBM. The carrier effective masses are estimated by the parabolic fitting of the dispersion relation around the bottom of the conduction band or top of the valence band ( Γ point of the Brillouin zone). meff

 ∂ 2 E (k )  =   2  ∂k 

−1

2

(4)

where E (k ) are the electronic band energies and k is the wave vector. To comprehend the insights of this essential property, Table 3 summarizes the effective masses of holes (mh ) and electrons

(me ) of the investigated MAGexPb(1-x)I3 series along the directions Γ(0,0,0) − R(1 2,1 2,1 2) ,

Γ(0,0,0) − X(1 2,0,0) , Γ(0,0,0) − M(1 2,1 2,0) and their average values. Further, the (me mh ) (me + mh ) are also estimated in each direction. The corresponding reduced masses µ =• average effective masses of pristine MAPbI3 obtained from our calculation are 0.17 and 0.13, respectively, for holes and electrons. These values are compared with that of previously reported


19


Page 20 of 38

theoretical values obtained using plane wave-based GGA-PBE49 and quasiparticle GW approximation32 respectively as listed in Table 3. As a consequence of the small effective masses, MAPbI3 exhibit high mobility and long diffusion lengths. Our calculated reduced mass is found to be 0.07 m0 , which also matches more closely to the experimental value of 0.10 m0 50, compared to other theoretical results mentioned above32,49. For the investigated mixed MAGexPb(1-x)I3 series, effective masses of electrons and holes increase with an increase in Ge, though we have observed a slight anomalous behavior in the hole effective mass of MAGe0.125Pb0.875I3. Notably, only for MAPbI3 and MAGe0.125Pb0.875I3, we found that that the effective mass of holes is greater than that of electrons indicating a good electron transporter. However, other systems show better hole transport behavior. Altogether, we notice good and balanced transport characteristics of the MAGexPb(1-x)I3 series with reduced masses for the investigated series in the range 0.07–0.16. Table 3. Calculated effective masses of hole (mh ) and electron (me ) along the directions

Γ(0,0,0) − R(1 2,1 2,1 2) ; Γ(0,0,0) − X(1 2,0,0) ; Γ(0,0,0) − M(1 2,1 2,0) , their average masses (AVG) , and the corresponding reduced masses ( µ ) for MAGexPb(1-x)I3 systems.

MAGexPb(1-x)I3

MAPbI3

MAGe0.125Pb0.875I3

MAGe0.375Pb0.625I3

Directions

Effective masses

Γ−R

Γ−X

Γ−M

AVG

mh

0.17

0.13

0.20

0.17, 0.1532, 0.3649

me µ

0.18

0.07

0.13

0.13, 0.1232, 0.3249

0.09

0.05

0.08

0.07, 0.0632, 0.1749, 0.1050

mh

0.17

0.13

0.19

0.16

me µ

0.21

0.07

0.14

0.14

0.09

0.05

0.08

0.08

mh

0.22

0.16

0.21

0.19

me µ

0.43

0.09

0.22

0.25

0.15

0.06

0.11

0.11


20

Page 21 of 38 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


MAGe0.625Pb0.375I3

MAGe0.875Pb0.125I3

mh

0.24

0.17

0.24

0.22

me µ

0.58

0.09

0.28

0.32

0.17

0.06

0.13

0.13

mh

0.25

0.24

0.27

0.25

me µ

0.30

0.64

0.46

0.47

0.14

0.17

0.17

0.16

3.3 Optical properties Optical properties especially strong optical absorption and large dielectric constant are very crucial for high performance of solar cells. The macroscopic optical properties described by the

(ω ) ε1 (ω ) + iε 2 (ω ) are calculated using the linear response method. complex dielectric function ε= The imaginary part of the dielectric function ε 2 (ω ) is obtained by calculating the momentum matrix elements between the occupied and unoccupied wave functions. To analyze the optical properties of the mixed MAGexPb(1-x)I3 perovskites, we have calculated the dielectric function

ε (ω ) of the corresponding perovskites in the photon energy range from zero to 5 eV.

Figure 8. Calculated imaginary parts of the dielectric function ε 2 (ω ) of MAGexPb(1-x)I3 perovskites.


21


The imaginary part of the dielectric function ε 2 (ω ) in Figure 8 exhibits a red shifting behavior associated with the gradual reduction of bandgap due to the increasing incorporation of Ge atoms. For MAPbI3, we observed the strongest peak at 3.0 eV, which is close to the reported value of 3.3 eV 51. A close look on the curve exposed a slightly slanted region around 2.58 eV (visible region) in the pristine MAPbI3 that turns into a pronounced shoulder peak in MAGe0.125Pb0.875I3 and MAGe0.375Pb0.625I3 around 2.4 eV, introduced by the gradual decrease of B-I bond. The decrease in lattice constants increase the orbital overlap of B-I bond and produce such a phenomenon. However, for the other two combinations, viz. MAGe0.625Pb0.375I3 and MAGe0.875Pb0.125I3, the shoulder peak is pushed close to the ultraviolet (UV) region, which can be attributed to the greater alternation in H-I bonds compared to B-I bonds. The trend observed in all the parameters discussed above is associated with bandgap reduction originated from the structural modifications due to the inclusion of Ge in the pristine MAPbI3.

Figure 9. Calculated real parts of the dielectric function ε1 (ω ) of MAGexPb(1-x)I3 perovskites.


22

Page 22 of 38

Page 23 of 38 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


Using the calculated values of ε 2 (ω ) , the real part of the dielectric function ε1 (ω ) is obtained from the Kramer-Kronig relationship. The real part of the dielectric function, ε1 (ω ) for the mixed MAGexPb(1-x)I3 series are shown in Figure 9. The static dielectric constant, ε1 (0) of MAPbI3 has been found to be 4.29 and compared with available reported value estimated to be 5.2 using DFT 51

. Further, our calculation predicted the peak of the ε1 (ω ) curve for MAPbI3 at 2.2 eV, which is

in decent agreement with the experimental value of 2.4 eV reported in ref. 51. From Figure 9, it is evident that the curves are redshifted towards the visible region with an increase of Ge content, causing a rise in values of ε1 (0) and shifting of peaks towards low energies. For an efficient photovoltaic absorber, a large static dielectric constant is vital for a high degree of charge screening which can promote a low level of charge defects and prohibit radiative electron-hole recombination. Further, all other properties such as absorption coefficient α (ω ) , refractive index n(ω ) and extinction coefficient k (ω ) are determined from the computed real and imaginary parts of the dielectric function using the following relationships 52:

n(ω ) =

k (ω ) =

ε12 (ω ) + ε12 (ω ) + ε1 2

ε12 (ω ) + ε12 (ω ) − ε1 2

α (ω ) = 2

ω c

k (ω )


23

(5)

(6)

(7)


Figure 10. Calculated absorption coefficients α (ω ) of MAGexPb(1-x)I3 perovskites.

Figure 10 summarizes the calculated absorption coefficients of the mixed perovskites, in which we can observe significant differences in their curves. First, as expected from the band gaps, the mixed perovskites show redshift towards the infrared region. Second, only a single peak exists in case of pristine MAPbI3 at 3.3 eV, while for other mixed perovskites, multi-peak characteristics are observed with valleys between the peaks. These peaks correspond to the critical point energies related to optical interband transitions to be discussed later. Finally, yet importantly, it can be also visualized from the figure that the increase in Ge concentration leads to broadening of the absorption regions extending to both infrared and ultraviolet regions. Thus, the mixed perovskites can absorb a wide range of photon energies in the solar spectrum than the pristine MAPbI3. When a semiconductor material is exposed to solar radiation, photon energies larger than the optical band gap will be absorbed causing interband transitions from the valence band to the conduction band, which is responsible for the creation of electron-hole pairs. In order to estimate


24

Page 24 of 38

Page 25 of 38 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


the critical points for interband transitions, we have performed the critical point analysis by fitting the second derivative of the imaginary part of the dielectric function ∂ 2ε 2 (ω ) ∂E 2 . The critical point energies for MAGexPb(1-x)I3 perovskites are calculated and recapitulated in Table 4, Moreover, possible band-to-band transitions are presented in Table 4, and also marked in bandstructure plot in Figure 6. The critical points predicted from our calculation are compared with the reported experimental results 30,53 and a fairly good match has been obtained.

Table 4. Calculated critical point energies of the mixed MAGexPb(1-x)I3 perovskites with corresponding dominant interband transitions. The numbering of bands is based on the convention of the ATK-VNL toolkit.

x=0 1.58, 1.5630, 1.5653

x = 0.125

x = 0.375

x = 0.625

x = 0.875

1.45

1.43

1.42

1.30

Γ319 − Γ320

Γ319 − Γ320

Γ319 − Γ320

Γ319 − Γ320

Γ319 − Γ320

2.50, 2.4630, 2.5553

2.35

2.25

2.20

2.20

Dominant transition Critical point E1 (eV)

M 318 − M 321

Γ319 − Γ330

Γ318 − Γ326

X 314 − X 321

Γ315 − Γ322

2.95

2.77

2.40

2.63

2.34

Dominant transition Critical point E2 (eV)

X 306 − X 322

X 310 − X 322

M 319 − M 321

M 316 − M 323

Γ315 − Γ326

3.20, 3.2030, 3.2253

3.10

2.90

2.85

2.79

Γ307 − Γ330

X 309 − X 326

Γ300 − Γ325

Γ307 − Γ327

X 310 − X 324

-

3.45

4.00

3.00

3.15

Γ300 − Γ330

X 318 − X 333

M 300 − M 323

Γ 284 − Γ324

4.50

-

3.30

3.70

MAGexPb(1-x)I3 Absorption onset, O (eV) Dominant transition Critical point E0 (eV)

Dominant transition Critical point E3 (eV) Dominant transition Critical point E4 (eV)

-


25


Dominant transition Critical point E5 (eV) Dominant transition Critical point E6 (eV)

M 306 − M 333 -

-

-

-

-

-

Dominant transition

Page 26 of 38

Γ 295 − Γ330

M 315 − M 325

3.65

4.01

X 319 − X 331

M 314 − M 334

3.95

4.77

X 313 − X 332

X 318 − X 341

In extension, we have performed the integration over the absorption curves for the mixed MAGexPb(1-x)I3 perovskite systems in different energy regions and listed in Table 5. From the calculated integrated intensities of the absorption curves, it is clear that the increase in Ge content results in a gradual increase in overall absorption. We also found that all the integrated intensities increase in the energy regions 0–1.7 eV, 1.7–3.3 eV and 3.3–5 eV with increase in Ge content except in case of 0.875% Ge content in the region 1.7–3.3 eV. In this regard, it is noteworthy to mention that the photon energies in the near-infrared radiation below 1.7 eV accounts for about 55% of the total solar radiation reaching the earth. Among the investigated series, MAGe0.875Pb0.125I3 has the highest absorptive power in the infrared, almost double than that of MAPbI3 in the range 0–1.7 eV. These observations highlight the fact that the investigated mixed perovskites stand out to be one of the most promising solar cell absorbers.


26

Page 27 of 38 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


Figure 11. Calculated refractive indices, n(ω ) and extinction coefficients, k (ω ) of MAGexPb(1-x)I3 perovskites.

Table 5. Estimated integrated intensities of the absorption curves of MAGexPb(1-x)I3 perovskite series. Integrated absorption coefficients (in 103 eV/cm) of MAGexPb(1-x)I3

Energy range (eV)

x=0

x = 0.125

x = 0.375

x = 0.625

x = 0.875

0–1.7

5.27

7.55

8.86

9.72

10.16

1.7–3.3

320.70

346.86

363.29

373.33

359.38

3.3–5

487.29

489.18

503.14

519.32

544.09

Figure 11 illustrates the calculated refractive index, n(ω ) and the extinction coefficient, k (ω ) of the mixed perovskites from our work. The evaluated value of the static refractive index n(0) of the pristine MAPbI3 is 2.07 and observed peak at 2.25 eV show a good consistency with the reported experimental results53 obtained through spectroscopic ellipsometry. For the mixed perovskites, the values of n(0) increase from 2.11 to 2.4 with an increase of Ge content and the


27


red-shifted peaks exist in the energy range of 2.2–1.8 eV. The extinction coefficient, k (ω ) plotted in Figure 11 on the other hand, has a similar profile resembling α (ω ) . The peak is found at 3.25 eV for MAPbI3 where ε1 (ω ) has minimum value and for other combinations, peaks are shifted towards lower energies. 4. CONCLUSION In summary, we have successfully investigated the structural, electronic and optical properties of mixed MAGexPb(1-x)I3 perovskites using first principle method. Our computed structural analysis shows a monotonic decrease of lattice volume with increase in Ge content which results in gradual reduction in B-I bond length. Further, values of enthalpies of formation for the investigated MAGexPb(1-x)I3 series are found to be negative except for pristine MAPbI3 and also the tolerance factor ( t ) for mixed MAGexPb(1-x)I3 perovskite are well within the specified range. Combining these two factors i.e., enthalpy of formation and tolerance factor ( t ), it is clear that pure MAPbI3 is unstable but stability increases with increase in Ge content. Thus, from the structural point of view, cubic Ge–Pb mixed perovskites are more stable than the pristine MAPbI3 and are less toxic. Our electronic properties results show a reduction in the band gaps due to the increasing orbital overlap controlled by B-I bond length. This trend of decrease in bandgaps is also observed in previous reports of mixed Sn-Pb and Ge-Sn perovskites. In-depth analysis of the band structures of the mixed perovskites has led us to gain information of the more dispersive nature of the conduction bands with respect to valence bands causing the bandgaps to lower and increase in effective masses of electrons. Overall, good and balanced effective masses of electrons and holes have been found for the explored mixed perovskites. Our analysis on PDOS shows the ascending contribution of Ge-4p and Ge-4s orbitals in the conduction and valence band region, respectively with increase ratio of Ge. The calculated TDOS for the mixed perovskites depicted a huge number


28

Page 28 of 38

Page 29 of 38 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


of available states in the case of MAGe0.125Pb0.875I3 and MAGe0.875Pb0.125I3 while the other combinations retained the almost the same number of states as pristine MAPbI3. In accordance with the bandstructure and TDOS, we obtained a gradual decrease in the energy level of CB edges in contrast to the non-monotonic variation of the VB edges. However, p-type nature of conductivity was found in all of the investigated perovskite series. The calculated optical properties of mixed perovskites predicted red shifted behavior for real and imaginary parts of the dielectric function. Consequently, static dielectric constants increase with an increase in Ge content and the absorption onset is lowered and redshifted towards near infrared region. Not only this, the increase in the evolution of Ge leads to broader optical absorption extending to both infrared and ultraviolet regions, hence absorbing maximum amount of photons. Among the series, MAGe0.875Pb0.125I3 has the strongest absorption in the infrared region, almost double than that of MAPbI3. Thus, our investigated mixed MAGexPb(1-x)I3 perovskite series could be a better alternative to be a solar cell absorber for photovoltaic applications. As far as possible, we have compared our results with the available experimental and theoretical values and fairly good agreement has been found between them. These assure the reliability and the correctness of our approach and hopefully this will encourage the researchers to carry out experimental work.

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


29


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 Prof. Sivaji Bandyopadhyay, Director, National Institute of Technology, Silchar for his continuous support in conducting this work. REFERENCES 1. Xu, Q.; Yang, D.; Lv, J.; Sun, Y. Y.; Zhang, L. Perovskite Solar Absorbers: Materials by Design. Small Methods 2018, 2, 1700316. 2. Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050–6051. 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. Kim, H. S.; Lee, C. R.; Im, J. H.; Lee, K. B.; Moehl, T.; Marchioro, A.; Moon, S. J.; Humphry-Baker, R.; Yum, J. H.; Moser, J. E.; et al. Lead Iodide Perovskite Sensitized AllSolid-State Submicron Thin Film Mesoscopic Solar Cell with Efficiency Exceeding 9%. Sci. Rep. 2012, 2, 591. 5. Malinkiewicz, O.; Yella, A.; Lee, Y. H.; Espallargas, G. M.; Graetzel, M.; Nazeeruddin, M. K.; Bolink, H. J. Perovskite Solar Cells Employing Organic Charge-Transport Layers. Nat. Photonics 2014, 8,128–132.


30

Page 30 of 38

Page 31 of 38 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


6. Chen, W.; Wu, Y.; Yue, Y.; Liu, J.; Zhang, W.; Yang, X.; Chen, H.; Bi, E.; Ashraful, I.; Grätzel, M.; et al. Efficient and Stable Large-Area Perovskite Solar Cells with Inorganic Charge Extraction Layers. Science 2015, 350, 144. 7. Bi, D.; Tress, W.; Dar, M. I.; Gao, P.; Luo, J.; Renevier, C.; Schenk, K.; Abate, A.; Giordano, F.; Baena, J. P. C.; et al. Efficient Luminescent Solar Cells Based on Tailored Mixed-Cation Perovskites. Sci. Adv. 2016, 2, e1501170. 8. Yang, W. S.; Park, B. W.; Jung, E. H.; Jeon, N. J.; Kim, Y. C.; Lee, D. U.; Shin, S. S.; Seo, J.; Kim, E. K.; Noh, J. H.; et al. Iodide Management in Formamidinium-Lead-Halide– Based Perovskite Layers For Efficient Solar Cells. Science 2017, 356, 1376–1379, 9. Eperon, G. E.; Stranks, S. D.; Menelaou, C.; Johnston, M. B.; Herz, L. M.; Snaith, H. J. Formamidinium Lead Trihalide: A Broadly Tunable Perovskite for Efficient Planar Heterojunction Solar Cells, Environ. Sci. 2014, 7, 982–988, 10. 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. 11. 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. 12. Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J.; Leijtens, T.; Herz, L. M.; Petrozza, A.; Snaith, H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal Trihalide Perovskite Absorber. Science 2013, 342, 341– 344.


31


13. You, J.; Hong, Z.; Yang, Y.; Chen, Q.; Cai, M.; Song, T. B.; Chen, C. C.; Lu, S.; Liu, Y.; Zhou, H.; et al. Low-Temperature Solution-Processed Perovskite Solar Cells with High Efficiency and Flexibility. ACS Nano 2014, 8, 1674–1680. 14. Baikie, T.; Fang, Y.; Kadro, J. M.; Schreyer, M.; Wei, F.; Mhaisalkar, S. G.; Graetzel, M.; White, T. J. Synthesis and Crystal Chemistry of the Hybrid Perovskite (CH3NH3)PbI3 for Solid-State Sensitised Solar Cell Applications. J. Mater. Chem. A 2013, 1, 5628–5641. 15. Luan, M.; Song, J.; Wei, X.; Chen, F.; Liu, J. Controllable Growth of Bulk Cubic-Phase CH3NH3PbI3 Single Crystal with Exciting Room Temperature Stability. CrystEngComm 2016, 18, 5257–5261. 16. Zhu, H.; Miyata, K.; Fu, Y.; Wang, J.; Joshi, P. P.; Niesner, D.; Williams, K. W.; Jin, S.; Zhu, X. Y. Screening in Crystalline Liquids Protects Energetic Carriers in Hybrid Perovskites. Science 2016, 353, 1409–1413. 17. Conings, B.; Drijkoningen, J.; Gauquelin, N.; Babayigit, A.; D'Haen, J.; D'Olieslaeger, L.; Ethirajan, A.; Verbeeck, J.; Manca, J.; Mosconi, E.; et al. Intrinsic Thermal Instability of Methylammonium Lead Trihalide Perovskite. Adv. Energy Mater. 2015, 5, 1500477. 18. Sun, P. P.; Li, Q. S.; Feng, S.; Li, Z. S. Mixed Ge/Pb Perovskite Light Absorbers with an Ascendant Efficiency Explored from Theoretical View. Phys. Chem. Chem. Phys. 2016, 18, 14408–14418. 19. 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. 20. Hao, F.; Stoumpos, C. C.; Cao, D. H; Chang, R. P.; Kanatzidis, M. G. Lead-Free SolidState Organic–Inorganic Halide Perovskite Solar Cells. Nat. Photonics 2014, 8, 489–494.


32

Page 32 of 38

Page 33 of 38 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


21. 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. 22. Ogomi, Y.; Morita, A.; Tsukamoto, S.; Saitho, T.; Fujikawa, N.; Shen, Q.; Toyoda, T.; Yoshino, K.; Pandey, S. S.; Ma, T.; et al. CH3NH3SnxPb(1–x) I3 Perovskite Solar Cells Covering up to 1060 nm. J. Phys. Chem. Lett. 2014, 5, 51004–1011. 23. Li, Y.; Sun, W.; Yan, W.; Ye, S.; Rao, H.; Peng, H.; Zhao, Z.; Bian, Z.; Liu, Z.; Zhou H.; et al. 50% Sn‐Based Planar Perovskite Solar Cell with Power Conversion Efficiency up to 13.6%. Adv. Energy Mat. 2016, 6, 1601353. 24. 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. 25. 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. 26. Liu, X.; Yang, Z.; Chueh, C. C.; Rajagopal, A.; Williams, S. T.; Sun, Y.; Jen, A. K. Y. Improved Efficiency and Stability of Pb–Sn Binary Perovskite Solar Cells by Cs Substitution. J. Mater. Chem. A 2016, 4, 17939–17945. 27. Leijtens, T.; Prasanna, R.; Gold-Parker, A.; Toney, M. F.; McGehee, M. D. Mechanism of Tin Oxidation and Stabilization by Lead Substitution in Tin Halide Perovskites. ACS Energy Lett. 2017, 2, 2159–2165. 28. Qian, J.; Xu, B.; Tian, W. A Comprehensive Theoretical Study of Halide Perovskites ABX3. Org. Electron. 2016, 37, 61–73.


33


29. Pazoki, M.; Jacobsson, T. J.; Hagfeldt, A.; Boschloo G.; Edvinsson, T. Effect of Metal Cation Replacement on the Electronic Structure of Metal Organic Halide Perovskites: Replacement of Lead with Alkaline-Earth Metals. Phys. Rev. B 2016, 93, 144105. 30. Shirayama, M.; Kadowaki, H.; Miyadera, T.; Sugita, T.; Tamakoshi, M.; Kato, M.; Fujiseki, T.; Murata, D.; Hara, S.; Murakami, T. N.; et al. Optical Transitions in Hybrid Perovskite Solar Cells: Ellipsometry, Density Functional Theory, and Quantum Efficiency Analyses for CH3NH3PbI3. Phys. Rev. Appl. 2016, 5, 014012. 31. Nagane, S.; Ghosh, D.; Hoye, R. L.; Zhao, B.; Ahmad, S.; Walker, A. B.; Islam, M. S.; Ogale, S.; Sadhanala, A. Lead-Free Perovskite Semiconductors Based on Germanium–Tin Solid Solutions: Structural and Optoelectronic Properties. J. Phys. Chem. C 2018, 122, 5940–5947. 32. Brivio, F.; Butler, K. T.; Walsh, A.; Van Schilfgaarde, M. Relativistic Quasiparticle SelfConsistent Electronic Structure of Hybrid Halide Perovskite Photovoltaic Absorbers. Phys. Rev. B 2014, 89, 155204. 33. 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. 34. 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 exchangecorrelation functional benchmark study. Chem. Phys. 2019, 516, 225-231. 35. 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.


34

Page 34 of 38

Page 35 of 38 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


36. Hamann, D. R. Optimized Norm-conserving Vanderbilt Pseudopotentials. Phys. Rev. B 2013, 88, 085117. 37. Schlipf, M.; Gygi, F. Optimization Algorithm for the Generation of ONCV Pseudopotentials. Comput. Phys. Commun. 2015, 196, 36–44. 38. Gao, P.; Grätzel, M.; Nazeeruddin, M. K. Organohalide Lead Perovskites for Photovoltaic Applications. Energy Environ. Sci. 2014, 7, 2448–2463. 39. Ren, Y.; Oswald, I. W.; Wang, X.; McCandless, G. T.; Chan, J. Y. Orientation of Organic Cations in Hybrid Inorganic–organic Perovskite CH3NH3PbI3 from Subatomic Resolution Single Crystal Neutron Diffraction Structural Studies. Cryst. Growth Des. 2016, 16, 2945– 2951. 40. Poglitsch, A.; Weber, D. Dynamic Disorder in Methylammoniumtrihalogenoplumbates (II) Observed by Millimeter‐wave Spectroscopy. J. Chem. Phys. 1987, 87, 6373–6378. 41. Faghihnasiri, M.; Izadifard, M.; Ghazi, M. E. DFT Study of Mechanical Properties and Stability of Cubic Methylammonium Lead Halide Perovskites (CH3NH3PbX3, X= I, Br, Cl). J. Phys. Chem. C 2017, 121, 27059–27070. 42. 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. 43. Stoumpos, C. C.; Frazer, L.; Clark, D. J.; Kim, Y. S.; Rhim, S. H.; Freeman, A. J.; Ketterson, J. B.; Jang J. I.; Kanatzidis, M. G. Hybrid Germanium Iodide Perovskite Semiconductors: Active Lone Pairs, Structural Distortions, Direct and Indirect Energy Gaps, and Strong Nonlinear Optical Properties. J. Am. Chem. Soc. 2015, 137, 6804–6819.


35


Page 36 of 38

44. 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. 45. Tenuta,

E.;

Zheng,

C.;

Rubel,

O.

Thermodynamic

Origin

of

Instability

in Hybrid Halide Perovskites. Sci. Rep. 2016, 6, 37654. 46. 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. 47. 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. 48. 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, 92089215. 49. Giorgi, G.; Fujisawa, J.I.; Segawa, H; Yamashita, K. Small photocarrier effective masses featuring ambipolar transport in methylammonium lead iodide perovskite: a density functional analysis. J. Phys. Chem. Lett. 2013, 4, 4213-4216. 50. 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.; et al. 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. 51. 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.


36

Page 37 of 38 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


52. Tripathy, S. K.; Kumar, V. Electronic, Elastic and Optical Properties of ZnGeP2 Semiconductor under Hydrostatic Pressures. Mater. Sci. Eng. B 2014, 182, 52–58. 53. 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.


37


TOC Graphic


38

Page 38 of 38

First Principle Insights of Electronic and Optical properties of Cubic

Recommend Documents