Metal halide perovskites have shown the most promising results as the light-harvesting section of photovoltaics and opto-electronic devices. Among the non-toxic halide perovskites, CsGeBr3 was found to be the best candidate for opto-electronic applications; however, it is understood that the efficiency of CsGeBr3 can be further increased with the insertion of transition metals as dopants. In this article, the first-principles density functional theory calculations are used to predict the mechanical, structural, electronic, and optical properties of pristine, Ni-doped, Mn-doped, and Fe-doped CsGeBr3 with 12.5% of doping concentration. All the doped materials are found to be ferromagnetic and mechanically stable. They have finite magnetization values. The optical absorption edge in all the doped materials shows that they have additional peaks within the large emission range of solar radiation, which makes them more suitable than the pristine material for photovoltaics and opto-electronic applications. Among the doped materials, Mn-doped and Fe-doped CsGeBr3 have comparably higher absorption peaks and are almost identical in shape. The electronic bandgap is smaller than the pristine structure in the case of Fe-doped CsGeBr3 and larger for Ni and Mn-doped CsGeBr3. These combinational analyses lead to the decision that, among the non-toxic, inorganic perovskite materials, Fe-doped CsGeBr3 is better suited for the use in opto-electronic applications.

Perovskites are a group of materials, constructed by combining different elements, compounds, and radicals—both organic and inorganic. They can specially be tuned to exhibit relevant functionalities in opto-electronic devices, such as photovoltaic cells, topological insulators, and LEDs. Since 2009, perovskite materials have garnered much popularity as the light-harvesting portion of solar-cells.1–3 This is made possible by their tunable bandgaps, high optical absorption in the relevant photon energy region, broad absorption range, small effective carrier mass, and, consequently, high charge carrier mobility. This class of materials is highly abundant in nature, which makes them cost-effective and easier to fabricate than Si-based photovoltaics. This wide availability made them the prime candidate for use in solar-cells.4,5

Perovskite materials are generally of the form ABX3. Here, A is a cation and B is a metal ion. X is an anion, often halogen, which bonds with both A and B. However, organic–inorganic hybrid in the A-site and oxide in place of halogens are also used.6–8 Starting from a modest (3.8%) power conversion efficiency (PCE) in 2009, within a decade, Pb-based halide perovskites reached 25.2% PCE, which is close to the Si-based photovoltaics’ numbers.9 Although lead halide perovskites are found to exhibit the highest PCE among this family of materials, they have major drawbacks. In ambient conditions, because of their instability, lead compounds decompose into toxic substances,10,11 which can lead to severe environmental effects. They are also detrimental to human health in the long term.12 For these reasons, Pb-based perovskites are deemed to be unsuitable for mass use. Roknuzzaman et al. performed a comprehensive study on possible alternatives to Pb in the metal ion site that can also retain or improve the efficiency of the Pb-halides.13,14 Replacing Pb in the B-site by Ge and Sn had been the most successful in attaining higher opto-electronic efficiency. This can be attributed to the fact that Sn+ and Ge+ have similar electronic (s2p2) configurations to Pb+. CsGeBr3 and CsGeCl3 were found to be the most promising alternatives because of their high optical absorption, high photoconductivity, and structural stability. However, CsGeCl3 has a wide bandgap outside of the visible light (VL) energy range, which renders it unsuitable for photovoltaic use.15 Rahaman and Akther Hossain conducted a study to tune the bandgap of CsGeCl3 by partial doping of Ni, Mn in place of Ge.16 Similarly, separate studies on the effects of doping were conducted on CsGeBr3.17,18 In all cases, the bandgap of the doped materials was found to be lower than its pristine form. However, Mn-doped CsGeBr3 turned out to be brittle.18 

However, there is no study of CsGeBr3 with Fe-doping. There has also not been any study with spin-polarized calculation that can give better insight into their electronic and magnetic properties. In our calculations, we examine the structural, mechanical, electronic, and optical properties of pristine, 12.5% Fe-, Mn-, and Ni-doped CsGeBr3 with spin-polarized calculation from first-principles. The properties most relevant to opto-electronic usage are compared between the pristine and doped materials and are discussed in detail.

The calculations in this study is based on spin-polarized Density Functional Theory (DFT)19 as implemented in Vienna Ab Initio Simulation Package (VASP) with the projector augmented wave (PAW) method.20–26 In each stage of calculations, only the valence electrons were considered and the rest were treated with frozen core approximation.27 

For relaxation, optimization, and calculation of mechanical and electronic properties of the crystals, Monkhorst–Pack scheme was utilized. However, for optical calculations, the gamma-centered method was used for better convergence.28,29 For geometric optimization total energy, internal forces and external stresses were minimized by varying the positions of the atoms as well as the shape and the volume of the cell. 18 × 18 × 18 k-mesh grids were used for the pristine structure, and for the doped cases, 3 × 3 × 3 k-mesh grids were used for better convergence. The convergence requirement was set so that the calculation is carried out until Hellmann–Feynman forces meet the limit 0.03eV/Å and the difference of self-consistent energy between consecutive iterations is at most 10−8 eV.30 The cut-off energy for the plane wave expansion was set to 400 eV for all calculations, except for mechanical calculations. For the mechanical property calculations, cut-off energy was 500 eV to ensure better convergence.31 Partial occupancy for each orbital is demonstrated by the Fermi smearing method. The width of the smearing, σ, was set to 0.05 eV in integrating the Brillouin zone (BZ).32 

For approximating the exchange–correlation term in the Kohn–Sham Hamiltonian, Generalized Gradient Approximation (GGA) was implemented within the modified PBEsol functional.33–35 

CsGeBr3 is semiconducting metal halide perovskite that has cubic structures and space group Pm-3̄m (No. 221).13 There are five atoms in the unit cells, and the Cs atoms are situated on the corners at 1a Wyckoff site with fractional coordinates (0, 0, 0); the Ge atoms are located in the body-centered positions at 1b Wyckoff site with fractional coordinates (0.5, 0.5, 0.5); and the Br atoms are located on the face-centered positions at 3c Wyckoff site, which is (0, 0.5, 0.5) in the fractional coordinates.36 The transition metal dopants (Ni, Mn, Fe) are inserted into the 2 × 2 × 2 supercells with 40 atoms, partially substituting one of the eight Ge atoms, corresponding to 12.5% doping concentration. The crystal structures of pristine and doped CsGeBr3 are shown in Fig. 1.

FIG. 1.

Unit cell of (a) pristine CsGeBr3 with bonds. (b) Supercell (2 × 2 × 2) of doped CsGeBr3 with bonds.

FIG. 1.

Unit cell of (a) pristine CsGeBr3 with bonds. (b) Supercell (2 × 2 × 2) of doped CsGeBr3 with bonds.

Close modal

The stability and distortion of the crystal structures can be quantified by the Goldschmidt tolerance factor, t, given by Eq. (1).37 For doping in the B-site, the weighted average of the B cation and B′ dopant cation was used in the modified tolerance factor [Eq. (2)]38 

(1)
(2)

Here,

where rA is the ionic radius of the A cation, rB is the ionic radius of the B cation, rB is the ionic radius of the dopant in the B-site, and rX is the ionic radius of the halide cation. Doping concentration is represented by x.

Shanon–Prewitt effective ionic radii were used to calculate the tolerance factor of the materials.39,40 They are presented in Table I. Ideal cubic structures have t = 1. The calculated results for the perovskite materials show that they have tolerance factors of slightly higher than 1, which point to slight distortions in the structures.41 Bond angles and bond lengths in the neighborhood of the dopant atoms are presented in Table II. The changes in bond angles and bond lengths due to doping are very small, further confirming the stability of the materials.

TABLE I.

Tolerance factor, t, of pristine and doped (Ni, Mn, Fe) CsGeBr3 materials (x = 0.125).

PhaseTolerance factor, t
CsGeBr3 1.091 
CsGe1−xNixBr3 1.093 
CsGe1−xMnxBr3 1.083 
CsGe1−xFexBr3 1.087 
PhaseTolerance factor, t
CsGeBr3 1.091 
CsGe1−xNixBr3 1.093 
CsGe1−xMnxBr3 1.083 
CsGe1−xFexBr3 1.087 
TABLE II.

Bond angles and bond lengths of pristine and doped (Ni, Mn, Fe) CsGeBr3 materials (x = 0.125).

Bond angle (deg)Bond length (Å)
PhaseCs–Ge–CsBr–Ge–BrBr–Ge–CsCs–Br–CsCs–GeBr–GeCs–Br
CsGeBr3 70.53 90 54.74 90 4.853 2.802 3.962 
CsGe1−xNixBr3 70.53 90 54.74 90 4.861 2.806 3.969 
CsGe1−xMnxBr3 70.53 90 54.74 90 4.860 2.791 3.968 
CsGe1−xFexBr3 70.53 90 54.74 90 4.849 2.794 3.959 
Bond angle (deg)Bond length (Å)
PhaseCs–Ge–CsBr–Ge–BrBr–Ge–CsCs–Br–CsCs–GeBr–GeCs–Br
CsGeBr3 70.53 90 54.74 90 4.853 2.802 3.962 
CsGe1−xNixBr3 70.53 90 54.74 90 4.861 2.806 3.969 
CsGe1−xMnxBr3 70.53 90 54.74 90 4.860 2.791 3.968 
CsGe1−xFexBr3 70.53 90 54.74 90 4.849 2.794 3.959 

Volume optimization was done using the third-order Birch–Murnaghan equation of state.42,43 Volume vs energy curves are presented in Fig. 2. Formation energy of the pristine and the doped materials was calculated by Eqs. (3) and (4), respectively,18 

(3)
(4)

where

FIG. 2.

Equation of states of pristine, Fe-doped, Mn-doped, and Ni-doped CsGeBr3.

FIG. 2.

Equation of states of pristine, Fe-doped, Mn-doped, and Ni-doped CsGeBr3.

Close modal

All the structures have negative values of formation energy, ensuring their thermodynamic stability. The values of the formation energy are presented in Table III along with lattice parameters and volume of the unit cells.

TABLE III.

Lattice parameter, cell volume, and formation energy of pristine and doped (Ni, Mn, Fe) CsGeBr3 materials, compared with available theoretical and experimental results (x = 0.125).

Phasea (Å)V (Å3)ΔHf (eV)Remarks
CsGeBr3 5.58 173.74  Calc.17  
 5.63 178.45  Expt.47  
 5.61 176.56 −1.202 This study 
CsGe1−xNixBr3 5.54 170.03  Calc.17  
 5.54 170.03 −1.141 This study 
CsGe1−xMnxBr3 5.40 157.11  Calc.18,a 
 5.56 171.88 −1.201 This study 
CsGe1−xFexBr3 5.56 171.88 −1.164 This study 
Phasea (Å)V (Å3)ΔHf (eV)Remarks
CsGeBr3 5.58 173.74  Calc.17  
 5.63 178.45  Expt.47  
 5.61 176.56 −1.202 This study 
CsGe1−xNixBr3 5.54 170.03  Calc.17  
 5.54 170.03 −1.141 This study 
CsGe1−xMnxBr3 5.40 157.11  Calc.18,a 
 5.56 171.88 −1.201 This study 
CsGe1−xFexBr3 5.56 171.88 −1.164 This study 
a

x = 0.25.

For the pristine cell, the lattice parameter value (5.61 Å), calculated by spin-polarized DFT, is in better agreement with the previously calculated experimental value (5.63 Å) than other calculated theoretical results. Available theoretical values for calculations of Mn-doped and Ni-doped materials are also shown in Table III. For the Ni-doped structure, the value of lattice parameter (5.54 Å) is the same as the previously available result, but there is a slight discrepancy in the Mn-doped structure. This is because the previous calculation was for 25% doping concentration. The partial insertion of transition metal dopants reduces the lattice parameter and volume of the unit cells for all of the doped materials. Among the materials studied, the Ni-doped structure has the highest volume, while the Mn-doped structure has the lowest. This can be explained by the relative position of transition metals on the Periodic Table in comparison with Ge. Ge has an atomic radius of 1.25 Å. Ni is the rightmost of the three dopants and has the lowest atomic radius of 1.35 Å.44 Mn and Fe are similar in that they have the same atomic radius and their lattice parameter (5.56, 5.56 Å) and volume values are identical too. So, it is evident that, by replacing one Ge atom with dopants with a bigger atomic radius, the bond strength between nearby atoms increased and the lattice parameter of the doped structures decreased.

Mechanical behavior of the materials can be well understood by analyzing the elastic constants. The 6 × 6 stiffness tensor Cij provides the information about hardness, ductility, and stability of the materials.45 Since the pristine and doped CsGeBr3 materials all have cubic structures, as confirmed by the tolerance factor calculations, C11 = C22 = C33, C12 = C13 = C23, and C44 = C55 = C66.46 So, knowing only the components, C11, C12, and C44 suffice to determine the stability of the materials. Any stable material needs to follow the Born stability criterion46 

(5)

The independent components of stiffness tensor for the pristine and transition metal-doped CsGeBr3 are calculated and given in Table IV with previously available results.17,18 It is clear from Table IV that all the studied materials satisfies the Born stability requirements. To understand the ductile nature of a material, Cauchy pressure,45C12C44, can be calculated, which is included in Table IV. Ductile materials should have a positive value of Cauchy pressure, and brittle materials have negative. From the value of Cauchy pressure presented in Table IV, it is clear that all the studied materials are ductile.

TABLE IV.

Elastic constants, Cij (GPa), and Cauchy pressure of pristine and doped (Ni, Mn, Fe) CsGeBr3 materials, compared with theoretical and experimentally available results (x = 0.125).

PhaseC11C12C44C12C44Remarks
CsGeBr3 47.34 10.46 10.10 0.36 Calc.18  
48.08 10.82 10.07 0.75 Calc.18  
49.15 11.07 10.54 0.53 This study 
CsGe1−xNixBr3 48.28 13.70 9.98 4.22 Calc.17  
35.58 10.95 9.58 1.37 This study 
CsGe1−xMnxBr3 60.66 11.58 15.55 −3.97 Calc.18,a 
41.23 5.41 4.17 1.24 Calc.18,a 
44.73 12.35 10.84 1.51 This study 
CsGe1−xFexBr3 43.65 14.16 10.33 3.83 This study 
PhaseC11C12C44C12C44Remarks
CsGeBr3 47.34 10.46 10.10 0.36 Calc.18  
48.08 10.82 10.07 0.75 Calc.18  
49.15 11.07 10.54 0.53 This study 
CsGe1−xNixBr3 48.28 13.70 9.98 4.22 Calc.17  
35.58 10.95 9.58 1.37 This study 
CsGe1−xMnxBr3 60.66 11.58 15.55 −3.97 Calc.18,a 
41.23 5.41 4.17 1.24 Calc.18,a 
44.73 12.35 10.84 1.51 This study 
CsGe1−xFexBr3 43.65 14.16 10.33 3.83 This study 
a

x = 0.25.

Additionally, the shear modulus (G), bulk modulus (B), and Young’s modulus (E) of the materials are approximated by Voigt–Reuss–Hill (VRH) average48–50 and are presented in Table V. B of each material is small as seen from Table V, which imply that all the studied materials are flexible. The value of B for Ni-doped and Mn-doped crystals are smaller compared to the pristine structure but is slightly higher for the Fe-doped material. G and E provides information about the stiffness of a material. The doped crystals have lower values for both shear modulus and Young’s modulus in comparison with the pristine structure, meaning they can be more readily fabricated into thin films for opto-electronic devices usage.

TABLE V.

Bulk modulus (B), shear modulus (G), Young’s modulus (Y) in GPa unit, and Poisson’s ratio (ν), Pugh’s ratio (B/G) of pristine and doped (Ni, Mn, Fe) CsGeBr3 materials, compared with theoretical and experimentally available results (x = 0.125).

PhaseBGYB/GνRemarks
CsGeBr3 23.15 12.30 44.64 1.88 0.27 Calc.17  
23.24 12.92 32.07 1.88 0.27 Calc.17  
23.76 13.39 33.81 1.78 0.26 This study 
CsGe1−xNixBr3 25.23 12.60 42.23 2.00 0.28 Calc.17  
19.16 10.59 26.83 1.81 0.27 This study 
CsGe1−xMnxBr3 28.68 17.96 56.76 1.59 0.24 Calc.18,a 
23.14 12.74 32.28 1.82 0.27 This study 
CsGe1−xFexBr3 23.99 11.92 30.67 2.01 0.29 This study 
PhaseBGYB/GνRemarks
CsGeBr3 23.15 12.30 44.64 1.88 0.27 Calc.17  
23.24 12.92 32.07 1.88 0.27 Calc.17  
23.76 13.39 33.81 1.78 0.26 This study 
CsGe1−xNixBr3 25.23 12.60 42.23 2.00 0.28 Calc.17  
19.16 10.59 26.83 1.81 0.27 This study 
CsGe1−xMnxBr3 28.68 17.96 56.76 1.59 0.24 Calc.18,a 
23.14 12.74 32.28 1.82 0.27 This study 
CsGe1−xFexBr3 23.99 11.92 30.67 2.01 0.29 This study 
a

x = 0.25.

Two other identifier of ductility for any material is the Pugh’s ratio (B/G) and Poisson’s ratio (ν). The critical value for B/G is 1.75, and 0.26 for ν, above which a material is ductile, and brittle below.51,52ν and B/G, for the materials examined, are enlisted in Table V. The value of both the ratio for the pristine and doped CsGeBr3 is larger than the critical values that confirm that all the studied materials are ductile. This is consistent with the findings from the calculated elastic constants.

Electronic behavior of the materials can be understood by calculating the band structure (BS) and density of states (DOS). Here, the basic electronic properties for both pristine and metal-doped (Ni, Mn, Fe) CsGeBr3 are calculated using Generalized Gradient Approximation (GGA) of the modified Perdew–Burke–Ernzerhof functional for solids (PBESol).33,53,54 Although hybrid functional Heyd–Scuseria–Ernzerhof (HSE) gives more accurate values for bandgap,35,55 the importance in this study is given to the relative changes in bandgap due to doping introduction rather than the actual values.

The band structure of each material was calculated along the high symmetry points of the Brillouin Zone (BZ) and is presented in Fig. 3. The Fermi level is represented by a dotted horizontal line and is set to 0 eV. From the band structure, the value of bandgap can be calculated, which is an important property for materials used in opto-electronic devices. The bandgap for both spin-up and spin-down states of the studied materials are presented in Table VI with previously reported results. Pristine CsGeBr3 has spin-symmetry, and so the spin-up and spin-down states are identical. Thus, in Fig. 3(a), only the spin-down states are visible as they overlap the spin-up states underneath. The pristine material was calculated to have a bandgap of 0.704 eV, which is in agreement with previously calculated results.13 From Fig. 3, it can be seen that both the maximum of the valence band and the minimum of the conduction band are in the R point of the Brillouin zone, which indicate that the material is a direct bandgap semiconductor. Doping the material with transition metals breaks the spin-symmetry. As a result, the band gaps for doped CsGeBr3 materials have different values for spin-up and spin-down states. The bandgap drops for Fe-doped spin-down state in comparison with the pristine crystal, while the band gaps increase for the cases of Mn-doped and Ni-doped structures. Following the bandgap values, Ni-doped and Mn-doped CsGeBr3 materials can be identified as conventional semiconductors. However, Fe-doped CsGeBr3 is a narrow-band gap semiconductor and, thus, promises to be a remarkable candidate for photovoltaic application.

FIG. 3.

Band structure of (a) pristine, (b) Fe-doped, (c) Mn-doped, and (d) Ni-doped CsGeBr3.

FIG. 3.

Band structure of (a) pristine, (b) Fe-doped, (c) Mn-doped, and (d) Ni-doped CsGeBr3.

Close modal
TABLE VI.

Bandgap (Eg) of pristine and doped (Ni, Mn, Fe) CsGeBr3 materials, compared with the available theoretical results (x = 0.125).

PhaseEg (eV)Remarks
CsGeBr3 0.704 Calc.17  
0.706 Calc.18  
0.704 (up) This study 
0.704 (down) 
CsGe1−xNixBr3 0.351 Calc.17  
0.491 (up) This study 
1.628 (down) 
CsGe1−xMnxBr3 1.798 Calc.18,a 
1.085 (up) This study 
1.036 (down) 
CsGe1−xFexBr3 0.443 (up) This study 
1.051 (down) 
PhaseEg (eV)Remarks
CsGeBr3 0.704 Calc.17  
0.706 Calc.18  
0.704 (up) This study 
0.704 (down) 
CsGe1−xNixBr3 0.351 Calc.17  
0.491 (up) This study 
1.628 (down) 
CsGe1−xMnxBr3 1.798 Calc.18,a 
1.085 (up) This study 
1.036 (down) 
CsGe1−xFexBr3 0.443 (up) This study 
1.051 (down) 
a

x = 0.25.

The total density of states (TDOS) and partial density of states (PDOS) for pristine and doped CsGeBr3 are shown in Figs. 4 and 5, respectively, with spin-polarized DFT calculations. The Fermi-level is represented by a vertical lines at zero energy level. The TDOS profile of the pristine CsGeBr3 preserves spin-symmetry. This confirms that CsGeBr3 is a non-magnetic material. With the introduction of doping, the DOS profiles change significantly. The spin-symmetries are broken, and intermediate states are seen to appear near the Fermi-level of Ni-doped CsGeBr3 and Fe-doped CsGeBr3 materials.

FIG. 4.

Total density of states for (a) pristine, (b) Fe-doped, (c) Mn-doped, and (d) Ni-doped CsGeBr3.

FIG. 4.

Total density of states for (a) pristine, (b) Fe-doped, (c) Mn-doped, and (d) Ni-doped CsGeBr3.

Close modal
FIG. 5.

Partial density of states for (a) pristine, (b) Fe-doped, (c) Mn-doped, and (d) Ni-doped CsGeBr3.

FIG. 5.

Partial density of states for (a) pristine, (b) Fe-doped, (c) Mn-doped, and (d) Ni-doped CsGeBr3.

Close modal

From the PDOS profiles in Fig. 5, it is evident that the total density of states of the materials is mainly composed of Br-4p orbitals. Additionally, Cs-6s, Cs-5p and Ge-4s, Ge-4p orbitals provide small contributions to the density of states. However, in the doped structures, the contribution of spin-down states is higher than the spin-up states near the Fermi-level. This is mainly due to the spin-down d-orbital states of the transition metal dopants that incorporate magnetism in the system.

The non-magnetic perovskite material CsGeBr3 acquires finite magnetism after transition metal doping. The values of cell magnetization are calculated to be 1.747 μB, 4.605 μB and 3.745 μB for Ni-doped, Mn-doped and Fe-doped CsGeBr3, respectively. All the doped materials show strong asymmetry near the Fermi-level in the spin-down states of the d-orbitals of the transition metals, which causes ferromagnetic behavior.56 

With the insertion of dopants, the Fermi-levels move closer to the valence bands, which in turn reduce the bandgap of the materials. In the cases of Fe-doped and Ni-doped structures, the intermediate states observed in the band structures can be explained by the PDOS profiles in Fig. 5. Fe-doped CsGeBr3 has DOS contributions from the d-orbitals of the Fe atom near the Fermi-level. Mn-doped CsGeBr3 is very similar to Fe-doped CsGeBr3 but has higher contributions from the spin-down states. For Ni-doped CsGeBr3 material, Ge, Br, and Mn all contribute to the intermediate states of PDOS.

Optical parameters of the perovskite materials are crucial for their use in solar-cells and other opto-electronic devices. Electronic structure of the materials can be understood more deeply by the optical profiles too. Here, the dielectric function, reflectivity, and absorption coefficient of pristine and transition metal doped CsGeBr3 are calculated. A comparative analysis of the above-mentioned optical properties of the materials is presented in Fig. 6.

FIG. 6.

(a) Real part of dielectric function. (b) Imaginary part of dielectric function. (c) Absorption coefficient in the relevant range (inset: absorption coefficient for high photon energy), and (d) reflectivity of the pristine and doped CsGeBr3.

FIG. 6.

(a) Real part of dielectric function. (b) Imaginary part of dielectric function. (c) Absorption coefficient in the relevant range (inset: absorption coefficient for high photon energy), and (d) reflectivity of the pristine and doped CsGeBr3.

Close modal

Dielectric function, ϵ, is the characteristic of a material that determines its behavior under incident light energy.57 Both the real part, ϵ1, and imaginary part, ϵ2, of the dielectric functions of the different materials are compared in Figs. 5(a) and 5(b). The doped materials have additional higher peaks at low energy region as compared to the pristine perovskite. Ni-doped CsGeBr3 has very high peaks between 0 and 1 eV of photon energy. However, in the Infrared (IR) and Visible Light (VL) regions, Fe- and Mn-doped CsGeBr3 have higher and almost identical peaks. This range of incident photon energy is very important for opto-electronic device applications.

The value of real part of the dielectric function, ϵ1, at 0 eV is called the dielectric constant, ϵ0. The dielectric constant regulates the charge recombination rate and energy harvesting efficiency of opto-electronic devices. Higher values of ϵ0 correspond to lower rate of charge recombination.58ϵ0 is found to be slightly higher for Mn (8.28) and Fe (8.33) than the pristine structure (7.42). For Ni-doped CsGeBr3, it increases almost threefold (19.87).

The imaginary part of the dielectric function, ϵ2, can give insights into the optical conductivity of materials. With the insertion of doped materials, ϵ2, at low energy region, increases significantly. This is the reason to have high absorption at this region of incident photon energy.

Absorption coefficient is the measurement of light penetration into the materials at photons of different energies.57 This quantity is crucial to determine the overall efficiency of energy conversion in the opto-electronic devices. For solar spectra absorption, the optimum range is between Infrared (IR) and Visible Light (VL) regions, which is lower than 5 eV. It is evident from Fig. 5(c) that doped CsGeBr3 has additional peaks at this desired energy region. The formation of additional peaks at the low energy region due to doping agrees with the previously available optical properties calculations of Ni-doped and Mn-doped crystals.17,18 Higher peaks at the lower energy region for Fe-doped and Mn-doped CsGeBr3 are noticeable. In the inset image, the absorption coefficients up to 30 eV are shown. At higher photon energies, the curves become almost identical.

Reflectivity refers to the reflection of light by the material in comparison to the incident light.57 With higher reflectivity, materials will be less efficient in opto-electronics applications since the absorption will be lower. From Fig. 5(d), it can be seen that, although reflectivity of the doped materials increases, it is still very low at a lower photon energy. This coincides with the graph of absorption coefficient, meaning that there will be less energy loss in this region for these materials. Overall, the optical properties show that doping enhances the optical efficiency of the pristine material greatly.

In this study, we have calculated the mechanical, structural, electronic, and optical properties of perovskite materials used for solar-cells and other opto-electronic devices. The structural and optical calculations are in agreement with the previously available theoretical and experimental results. While the pristine structure is non-magnetic, all the doped structures acquire finite magnetism and showed ferromagnetic behavior due to the transition metal dopants. As compared with pristine, Ni-doped, and Mn-doped CsGeBr3 perovskite, the Fe-doped CsGeBr3 material has a lower bandgap, higher absorption peaks at low photon energy, and higher ductility. Fe is also more readily available than other transition metal elements and, thus, is more suitable for the use in mass production of devices. Thus, Fe-doped CsGeBr3 proves to be a better candidate for opto-electronic and photovoltaic applications than the pristine and other doped structures.

The authors acknowledge the Centennial Research Grant (CRG) of the University of Dhaka for financial support of the project.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
W.
Zhang
,
G. E.
Eperon
, and
H. J.
Snaith
, “Metal halide perovskites for energy applications,”
Nat. Energy
1
(
6
),
16048
(
2016
).
2.
W.-J.
Yin
,
T.
Shi
, and
Y.
Yan
, “Unique properties of halide perovskites as possible origins of the superior solar cell performance,”
Adv. Mater.
26
(
27
),
4653
4658
(
2014
).
3.
Q.
Jeangros
,
M.
Duchamp
,
J.
Werner
,
M.
Kruth
,
R. E.
Dunin-Borkowski
,
B.
Niesen
,
C.
Ballif
, and
A.
Hessler-Wyser
, “In situ TEM analysis of organic–inorganic metal-halide perovskite solar cells under electrical bias,”
Nano Lett.
16
(
11
),
7013
7018
(
2016
).
4.
Y.-C.
Hsiao
,
T.
Wu
,
M.
Li
,
Q.
Liu
,
W.
Qin
, and
B.
Hu
, “Fundamental physics behind high-efficiency organo-metal halide perovskite solar cells,”
J. Mater. Chem. A
3
(
30
),
15372
15385
(
2015
).
5.
T.
Leijtens
,
G. E.
Eperon
,
N. K.
Noel
,
S. N.
Habisreutinger
,
A.
Petrozza
, and
H. J.
Snaith
, “Stability of metal halide perovskite solar cells,”
Adv. Energy Mater.
5
(
20
),
1500963
(
2015
).
6.
T. M.
Koh
,
K.
Fu
,
Y.
Fang
,
S.
Chen
,
T. C.
Sum
,
N.
Mathews
,
S. G.
Mhaisalkar
,
P. P.
Boix
, and
T.
Baikie
, “Formamidinium-containing metal-halide: An alternative material for near-IR absorption perovskite solar cells,”
J. Phys. Chem. C
118
(
30
),
16458
16462
(
2014
).
7.
G. E.
Eperon
,
G. M.
Paternò
,
R. J.
Sutton
,
A.
Zampetti
,
A. A.
Haghighirad
,
F.
Cacialli
, and
H. J.
Snaith
, “Inorganic caesium lead iodide perovskite solar cells,”
J. Mater. Chem. A
3
(
39
),
19688
19695
(
2015
).
8.
P.
Ramasamy
,
D.-H.
Lim
,
B.
Kim
,
S.-H.
Lee
,
M.-S.
Lee
, and
J.-S.
Lee
, “All-inorganic cesium lead halide perovskite nanocrystals for photodetector applications,”
Chem. Commun.
52
(
10
),
2067
2070
(
2016
).
9.
N. G.
Park
, “Research direction toward scalable, stable, and high efficiency perovskite solar cells,”
Adv. Energy Mater.
10
(
13
),
1903106
(
2020
).
10.
A.
Babayigit
,
D. D.
Thanh
,
A.
Ethirajan
,
J.
Manca
,
M.
Muller
,
H. G.
Boyen
, and
B.
Conings
, “Assessing the toxicity of Pb- and Sn-based perovskite solar cells in model organism Danio rerio,”
Sci. Rep.
6
(
1
),
18721
(
2016
).
11.
A.
Babayigit
,
A.
Ethirajan
,
M.
Muller
, and
B.
Conings
, “Toxicity of organometal halide perovskite solar cells,”
Nat. Mater.
15
(
3
),
247
251
(
2016
).
12.
M.
Jaishankar
,
T.
Tseten
,
N.
Anbalagan
,
B. B.
Mathew
, and
K. N.
Beeregowda
, “Toxicity, mechanism and health effects of some heavy metals,”
Interdiscip. Toxicol.
7
(
2
),
60
(
2014
).
13.
M.
Roknuzzaman
,
K. K.
Ostrikov
,
H.
Wang
,
A.
Du
, and
T.
Tesfamichael
, “Towards lead-free perovskite photovoltaics and optoelectronics by ab-initio simulations,”
Sci. Rep.
7
(
1
),
14025
(
2017
).
14.
T.
Krishnamoorthy
,
H.
Ding
,
C.
Yan
,
W. L.
Leong
,
T.
Baikie
,
Z.
Zhang
,
M.
Sherburne
,
S.
Li
,
M.
Asta
,
N.
Mathews
, and
S. G.
Mhaisalkar
, “Lead-free germanium iodide perovskite materials for photovoltaic applications,”
J. Mater. Chem. A
3
(
47
),
23829
23832
(
2015
).
15.
R. J.
Sutton
,
G. E.
Eperon
,
L.
Miranda
,
E. S.
Parrott
,
B. A.
Kamino
,
J. B.
Patel
,
M. T.
Hörantner
,
M. B.
Johnston
,
A. A.
Haghighirad
,
D. T.
Moore
, and
H. J.
Snaith
, “Bandgap-tunable cesium lead halide perovskites with high thermal stability for efficient solar cells,”
Adv. Energy Mater.
6
(
8
),
1502458
(
2016
).
16.
M. Z.
Rahaman
and
A. K. M.
Akther Hossain
, “Effect of metal doping on the visible light absorption, electronic structure and mechanical properties of non-toxic metal halide CsGeCl3,”
RSC Adv.
8
(
58
),
33010
33018
(
2018
).
17.
M. N.
Islam
,
M. A.
Hadi
, and
J.
Podder
, “Influence of Ni doping in a lead-halide and a lead-free halide perovskites for optoelectronic applications,”
AIP Adv.
9
(
12
),
125321
(
2019
).
18.
K. M.
Hossain
,
M. Z.
Hasan
, and
M. L.
Ali
, “Narrowing bandgap and enhanced mechanical and optoelectronic properties of perovskite halides: Effects of metal doping,”
AIP Adv.
11
(
1
),
015052
(
2021
).
19.
R. G.
Parr
, “Density functional theory of atoms and molecules,” in
Horizons of Quantum Chemistry
(
Springer
,
Dordrecht
,
1980
), pp.
5
15
.
20.
P. E.
Blöchl
, “Projector augmented-wave method,”
Phys. Rev. B
50
(
24
),
17953
(
1994
).
21.
G.
Kresse
and
D.
Joubert
, “From ultrasoft pseudopotentials to the projector augmented-wave method,”
Phys. Rev. B
59
(
3
),
1758
(
1999
).
22.
G.
Kresse
and
J.
Hafner
, “Ab initio molecular dynamics for liquid metals,”
Phys. Rev. B
47
(
1
),
558
(
1993
).
23.
G.
Kresse
and
J.
Hafner
, “Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium,”
Phys. Rev. B
49
(
20
),
14251
(
1994
).
24.
G.
Kresse
and
J.
Furthmüller
, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,”
Comput. Mater. Sci.
6
(
1
),
15
50
(
1996
).
25.
G.
Kresse
and
J.
Furthmüller
, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,”
Phys. Rev. B
54
(
16
),
11169
(
1996
).
26.
J.
Hafner
, “Ab-initio simulations of materials using VASP: Density-functional theory and beyond,”
J. Comput. Chem.
29
(
13
),
2044
2078
(
2008
).
27.
U.
Von Barth
and
C. D.
Gelatt
, “Validity of the frozen-core approximation and pseudopotential theory for cohesive energy calculations,”
Phys. Rev. B
21
(
6
),
2222
(
1980
).
28.
H. J.
Monkhorst
and
J. D.
Pack
, “Special points for Brillouin-zone integrations,”
Phys. Rev. B
13
(
12
),
5188
(
1976
).
29.
R. A.
Evarestov
and
V. P.
Smirnov
, “Modification of the Monkhorst-Pack special points meshes in the Brillouin zone for density functional theory and Hartree-Fock calculations,”
Phys. Rev. B
70
(
23
),
233101
(
2004
).
30.
M.
Di Ventra
and
S. T.
Pantelides
, “Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems,”
Phys. Rev. B
61
(
23
),
16207
(
2000
).
31.
K.
Choudhary
and
F.
Tavazza
, “Convergence and machine learning predictions of Monkhorst-Pack k-points and plane-wave cut-off in high-throughput DFT calculations,”
Comput. Mater. Sci.
161
,
300
308
(
2019
).
32.
J. J.
Jorgensen
and
G. L. W.
Hart
, “Effectiveness of smearing and tetrahedron methods: Best practices in DFT codes,”
Modell. Simul. Mater. Sci. Eng.
29
(
6
),
065014
(
2021
).
33.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
, “Generalized gradient approximation made simple,”
Phys. Rev. Lett.
77
(
18
),
3865
(
1996
).
34.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
, “Erratum: Generalized gradient approximation made simple,”
Phys. Rev. Lett.
78
,
1396
(
1997
).
35.
A.
Seidl
,
A.
Görling
,
P.
Vogl
,
J. A.
Majewski
, and
M.
Levy
, “Generalized Kohn-Sham schemes and the band-gap problem,”
Phys. Rev. B
53
(
7
),
3764
(
1996
).
36.
L. L.
Boyle
and
J. E.
Lawrenson
, “The origin dependence of Wyckoff site description of a crystal structure,”
Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr.
29
(
4
),
353
357
(
1973
).
37.
C. J.
Bartel
,
C.
Sutton
,
B. R.
Goldsmith
,
R.
Ouyang
,
C. B.
Musgrave
,
L. M.
Ghiringhelli
, and
M.
Scheffler
, “New tolerance factor to predict the stability of perovskite oxides and halides,”
Sci. Adv.
5
(
2
),
eaav0693
(
2019
).
38.
M. A.
Ahmed
,
E.
Dhahri
,
S. I.
El-Dek
, and
M. S.
Ayoub
, “Size confinement and magnetization improvement by La3+ doping in BiFeO3 quantum dots,”
Solid State Sci.
20
,
23
28
(
2013
).
39.
R. D.
Shannon
and
C. T.
Prewitt
, “Revised values of effective ionic radii,”
Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem.
26
(
7
),
1046
1048
(
1970
).
40.
R. D.
Shannon
, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,”
Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr.
32
(
5
),
751
767
(
1976
).
41.
S.
Švarcová
,
K.
Wiik
,
J.
Tolchard
,
H. J.
Bouwmeester
, and
T.
Grande
, “Structural instability of cubic perovskite BaxSr1−xCo1−yFeyO3−δ,”
Solid State Ionics
178
(
35–36
),
1787
1791
(
2008
).
42.
F.
Birch
, “Finite elastic strain of cubic crystals,”
Phys. Rev.
71
(
11
),
809
(
1947
).
43.
F. D.
Murnaghan
, “The compressibility of media under extreme pressures,”
Proc. Natl. Acad. Sci. U. S. A.
30
(
9
),
244
247
(
1944
).
44.
F.
Torrens
and
G.
Castellano
, “Periodic table,” in
New Frontiers in Nanochemistry
(
Apple Academic Press
,
2020
), pp.
403
425
.
45.
D. G.
Pettifor
, “Theoretical predictions of structure and related properties of intermetallics,”
Mater. Sci. Technol.
8
(
4
),
345
349
(
1992
).
46.
M.
Born
, “On the stability of crystal lattices. I,” in
Mathematical Proceedings of the Cambridge Philosophical Society
(
Cambridge University Press
,
1940
), Vol. 36, No. 2, pp.
160
172
.
47.
L. C.
Tang
,
J. Y.
Huang
,
C. S.
Chang
,
M. H.
Lee
, and
L. Q.
Liu
, “New infrared nonlinear optical crystal CsGeBr3: Synthesis, structure and powder second-harmonic generation properties,”
J. Phys.: Condens. Matter
17
(
46
),
7275
(
2005
).
48.
R.
Hill
, “The elastic behaviour of a crystalline aggregate,”
Proc. Phys. Soc., London, Sect. A
65
(
5
),
349
(
1952
).
49.
L.
Zuo
,
M.
Humbert
, and
C.
Esling
, “Elastic properties of polycrystals in the Voigt-Reuss-Hill approximation,”
J. Appl. Crystallogr.
25
(
6
),
751
755
(
1992
).
50.
D. H.
Chung
and
W. R.
Buessem
, “The Voigt-Reuss-Hill approximation and elastic moduli of polycrystalline MgO, CaF2, β-ZnS, ZnSe, and CdTe,”
J. Appl. Phys.
38
(
6
),
2535
2540
(
1967
).
51.
S. F.
Pugh
, “XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals,”
Philos. Mag.
45
(
367
),
823
843
(
1954
).
52.
B. G.
Pfrommer
,
M.
Côté
,
S. G.
Louie
, and
M. L.
Cohen
, “Relaxation of crystals with the quasi-Newton method,”
J. Comput. Phys.
131
(
1
),
233
240
(
1997
).
53.
M.
Ropo
,
K.
Kokko
, and
L.
Vitos
, “Assessing the Perdew-Burke-Ernzerhof exchange-correlation density functional revised for metallic bulk and surface systems,”
Phys. Rev. B
77
(
19
),
195445
(
2008
).
54.
G. I.
Csonka
,
J. P.
Perdew
,
A.
Ruzsinszky
,
P. H. T.
Philipsen
,
S.
Lebègue
,
J.
Paier
,
O. A.
Vydrov
, and
J. G.
Ángyán
, “Assessing the performance of recent density functionals for bulk solids,”
Phys. Rev. B
79
(
15
),
155107
(
2009
).
55.
J.
Heyd
,
G. E.
Scuseria
, and
M.
Ernzerhof
, “Hybrid functionals based on a screened Coulomb potential,”
J. Chem. Phys.
118
(
18
),
8207
8215
(
2003
).
56.
J.
Drga
,
J.
Chovanec
, and
S.
Šimkovič
, “Density of states and magnetic properties of Al2O3, Cr2O3,”
Conference: Preparation of Ceramic Materials
1
(
2015
).
57.
M.
Fox
,
Optical Properties of Solids
(
Oxford University Press
,
2002
).
58.
M. P.
Hughes
,
K. D.
Rosenthal
,
R. R.
Dasari
,
B. R.
Luginbuhl
,
B.
Yurash
,
S. R.
Marder
, and
T. Q.
Nguyen
, “Charge recombination dynamics in organic photovoltaic systems with enhanced dielectric constant,”
Adv. Funct. Mater.
29
(
29
),
1901269
(
2019
).