An integrated DFT + U and device simulation design of doped CsGeCl₃ for high efficiency flexible solar absorbers

Abstract

The urgent need for non-toxic, high-performance perovskites is a critical bottleneck in the advancement of sustainable solar energy. This work introduces a self-consistent pathway that directly links first-principles quantum mechanics with device-level performance simulation. Using this integrated approach, we investigate Cesium Germanium Chloride (CsGeCl₃) and its enhancement via Manganese (Mn) and Iron (Fe) doping. Our Density Functional Theory with Hubard-U correction (DFT + U) calculations, which supply all critical parameters for the Solar Cell Capacitance Simulator (SCAPS-1D), show that while pristine CsGeCl₃ has a wide bandgap of 3.44 eV and a low simulated efficiency of 5%, strategic doping offers a transformative enhancement. Fe-doping, in particular, engineers an optimal bandgap of 1.21 eV by creating a functional intermediate band, which significantly boosts sub-bandgap photon absorption. Consequently, SCAPS-1D simulations predict a remarkable power conversion efficiency (PCE) of 31.6% for the Fe-doped structure (CsGe_0.875Fe_0.125Cl₃). Furthermore, our analysis confirms that doping improves the mechanical ductility and stability, indicating high suitability for flexible solar applications.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-46832-z.

Introduction

The global demand for renewable energy is growing rapidly as the search for sustainable and eco-friendly alternatives to fossil fuels intensifies. Solar energy is a leading contender, and photovoltaic technologies continue to advance in efficiency and scalability. Among emerging photovoltaics, metal-halide perovskite solar cells (PSCs) have drawn intense interest for their remarkable power conversion efficiencies (PCE) and low-cost fabrication potential^1–3. In just over a decade, PSCs have improved from initial efficiencies of 3.8% to over 25% under optimized conditions^1,4. This swift progress is attributed to the exceptional optoelectronic properties of lead halide perovskites (e.g. CH₃NH₃PbI₃ and related compositions), including strong light absorption, tunable bandgaps and long carrier diffusion lengths^5,6. However, the involvement of water-soluble lead in these absorbers raises serious environmental and health concerns​^4,7. The highest-performing perovskite absorbers contain toxic Pb²⁺ ions, which pose risks of leaching and bioaccumulation if modules are damaged​^4,8,9. Consequently, there is a growing push to develop lead-free perovskite materials that retain the desirable photovoltaic characteristics while eliminating lead^8,9. Researchers have explored a variety of alternative B-site cations in the ABX₃ perovskite structure such as tin (Sn), germanium (Ge), bismuth (Bi), and other metals to replace Pb​^1,10–14. Some of these lead-free perovskites (for instance, tin-based halides) have demonstrated photovoltaic action, but generally their performance and/or stability still lag behind the lead-basedanalogues​. This gap motivates ongoing research into new compositions and engineering strategies to achieve sustainable, non-toxic perovskite solar absorbers. One promising class of lead-free perovskites is the inorganic halide perovskites incorporating germanium. Cesium Germanium Halides (CsGeX₃, X = Cl, Br, I) are Pb-free and consist of abundant elements, making them attractive from an environmental standpoint^13,15–18. In particular, CsGeCl₃ has been identified as a potentially stable perovskite compound with a cubic crystal structure analogous to the lead halides. Its fully inorganic composition could offer better thermal stability and moisture resistance compared to organic–inorganic hybrid perovskites. Despite these advantages, CsGeCl₃ exhibits inherent limitations that hinder its application as a solar absorber. Notably, it has a large bandgap of 3.44 eV, which confines its light absorption to the ultraviolet range^16–19. Such a wide bandgap is far from the optimal ~ 1.3–1.5 eV needed to efficiently harvest the solar spectrum¹¹, resulting in poor photocurrent generation. Also, CsGeCl₃ tends to have unfavorable charge-carrier dynamics¹⁹. Its dielectric constant is relatively low, leading to a high exciton binding energy (~ 70 meV) in the crystal. This means photo-generated electron–hole pairs are strongly Coulomb-bound, which can suppress the free carrier generation at room temperature and shorten carrier diffusion lengths²⁰. Prior studies also indicate that charge carriers in CsGeCl₃ have heavier effective masses and lower mobility compared to lead perovskites, especially as the halide moves from I to Cl​^13,19,21. These factors like a wide bandgap and inefficient charge separation/transport make pristine CsGeCl₃ a poor light absorber for solar cells. Overcoming these challenges is essential to realize its potential in photovoltaics. The drawbacks of CsGeCl₃ outlined above necessitate material engineering approaches to improve its photovoltaic suitability. A key issue is the excessively high bandgap, which must be reduced or tuned closer to the visible range to enhance light absorption. Another issue is the suboptimal charge-carrier behavior (stemming from strong excitonic effects and possible carrier trapping), which impedes efficient photogenerated current extraction. Addressing both of these problems is crucial for making CsGeCl₃ viable as an absorber layer in solar devices. One promising strategy to tackle these issues is bandgap engineering through targeted doping of the perovskite. For halide perovskites, partial substitution at the B-site (the metal cation site) has been shown to tune various properties^11,22,23. Such doping interventions may allow one to narrow the bandgap or enhance charge transport without completely changing the perovskite host matrix²⁴. Transition-metal dopants like Mn and Fe are known to introduce intermediate states or modify the band structure in lead-halide perovskites, which can affect photophysical behaviors^{11,23,25–27}. In this context, manganese (Mn) and iron (Fe) dopants are particularly interesting to investigate. Both Mn and Fe are transition metals that could replace Ge in the lattice. These dopants bring d-electron states that could interact with the host’s band structure^11,28 for example, Mn²⁺ often has a high-spin d⁵ configuration which can introduce levels within the bandgap or at the band edges, potentially narrowing the optical gap or creating doping states for charge transport. Fe dopants might similarly alter the electronic band structure and could improve p-type or n-type character depending on their oxidation states^11,22,28. Recent research on bandgap engineering suggests that careful choice of dopant and concentration is required to achieve the desired tuning without compromising material integrity^{11,16,22,23,26,27,29}. Although Density functional theory (DFT) provides a cost-effective and widely available approach for predicting material properties. It is well known that standard DFT functionals often underestimate bandgaps^11,30,31, potentially biasing subsequent device-level simulations. To more accurately capture the effects of Mn and Fe doping on CsGeCl₃, we employ a DFT + U framework to model the electronic bandgap close to the experimental results^11,31–34. Initially devised to handle strongly correlated d and f electrons, this method has since been extended to mitigate self-interaction errors in s and p orbitals of elements as well^11,31,32,35. Within this study, DFT + U facilitates the precise determination of essential electronic parameters such as band structures, effective carrier masses, band densities, thermal velocities, and work function for both pristine and doped CsGeCl₃. We also incorporated a slab model calculations to evaluate electron affinity from the work function, thereby accounting for surface interactions. Conduction/valence band effective densities of states are determined from DFT + U band curvature analysis. Carrier thermal velocities and mobilities are derived from carrier effective masses. By directly linking these parameters to SCAPS-1D calculations, our device simulations eliminate discrepancies between standardized theoretical and experimental inputs, enabling reliable predictions of photovoltaic performance. Several theoretical studies have been conducted on doping CsGeCl₃ perovskite, but none of these, as far as we know, have utilized DFT + U, leading to underestimated optoelectronic values^{13,15–19,36,37}. At the same time, there are no detailed studies within our knowledge that used DFT + U-derived data exclusively for modeling device-level implementations while using one dimensional Solar Cell Capacitance Simulator (SCAPS-1D)^2,38–41. Thus, our study is formulated to investigate if Mn or Fe doping can decrease the high-bandgap and poor carrier dynamics of CsGeCl₃ in a novel way, and if so, how do these dopants alter its electronic and structural properties modeled inside a solar cell device architecture. Investigating these points will fill a knowledge gap in lead-free perovskite research and guide the development of more efficient, non-toxic perovskite solar cells.

Computational and calculations method

In this work, first-principles quantum mechanical calculations were performed using the Cambridge Serial Total Energy Package (CASTEP), a computational framework based on density functional theory (DFT) for modeling material properties^42,43. The exchange-correlation effects were treated using the Perdew-Burke-Ernzerhof (PBE) functional within the framework of the Generalized-Gradient-Approximation (GGA)^44,45, supplemented by a Hubbard U correction (U_eff = 6.9 eV) applied to the s and p orbital of chlorine atoms and the d orbitals of cesium. Structural relaxation of the CsGeCl₃ lattice was achieved using the L-BFGS algorithm, a quasi-Newton optimization method, to minimize atomic forces and stresses⁴⁶. For Brillouin zone integration, to balance computational efficiency and accuracy a Monkhorst-Pack k-point (3 × 3 × 3) grid was selected⁴⁷. Convergence thresholds for structural optimizations in both pristine and doped configurations included a plane-wave cutoff energy of 350 eV, maximum atomic force below 0.01 eV/Å, energy tolerance of 5.0 × 10⁻⁶ eV per individual atom, atomic displacements were 5.0 × 10⁻⁴ Å and stress limits under 0.02 GPa. These parameters ensured stable configurations for subsequent electronic and optical analyses. Mechanical properties were derived using the Voigt–Reuss–Hill (VRH) averaging scheme based on elastic constants (C_ij) obtained from CASTEP simulations, with stricter convergence criteria (force: 0.01 eV/Å; energy: 4.0 × 10⁻⁶ eV per atom and displacement: 4.0 × 10⁻⁴ Å) to enhance numerical precision^48,49. The electronic band structure was generated through CASTEP’s DFT framework, mapping energy dispersion across high-symmetry k-point trajectories in the Brillouin zone. All computational parameters were implemented to ensure reproducibility while minimizing systematic errors associated with basis set limitations and k-point sampling density. Theoretical background for SCAPS-1D has been added on the supplementary section. The band structure’s high-symmetry spots, or the conduction band minimum (CBM) and valence band maximum (VBM), which act as the key regions where charge carriers display their highest and lowest energies, were numerically identified. The effective mass (m*) was determined using a parabolic curve adapted to simulate the energy dispersion close to these extrema for both holes and electrons⁵⁰. The effective mass values were determined by analyzing the curvature of these parabolic bands, following the fundamental relationship:

1

where represents the second derivative of the energy with respect to the wavevector k at the band extrema. The key parameters for SCAPS simulation, the effective density of states, thermal velocity, and donor acceptor density, were calculated from the effective mass extracted. The effective density of states encapsulating the number of states thermally accessible to charge carriers were calculated separately for conduction band and the valence band utilizing the formula stated below. Where, is the effective masses of electron and is the effective masses of hole.

2

3

The thermal velocity of charge carriers within a semiconductor as a result of thermal energy was calculated numerically:

4

It is evident from the orbital diagram of iron doped CsGeCl₃ that there exists an intermediate energy state between the VBM and CBM. Even though the lowering of effective mass in iron-doped specimens enhances the photovoltaic action, the existence of such intermediate states greatly boosts the carrier generation rate through easily transferring excited photoelectrons to the CBM²⁶. The intermediate band observed form the band structure has the potential to boost photo conversion efficiency. SCAPS-1D simulation software do not have the feature to consider intermediate band in its calculation⁵¹. A new numerical formulation to simulate intermediate band solar cell explicitly can be a topic of another detailed research. As most of the SCAPS simulation data has been taken from the DFT simulation, we have considered all three specimens of CsGeCl₃ with reduced defect density of n_t ≈ 10¹². The impact of defects in such intermediate band solar cells could be a promising field of future theoretical and experimental studies. Perovskite halides are observed as p-type semiconductors, which holds for both pristine and Mn-doped CsGeCl₃. Surprisingly, in the case of Fe-doped specimens both valence band and conduction band were found equally distributed about the fermi energy level similar to intrinsic semiconductor. Thus, separate calculation schemes were considered for acceptor density. In case of p-type acceptor density has been calculated as followed:

5

Here, was taken to be the value of VBM and the donor density is negligible in p-type material and essentially regarded as zero. Conversely, the donor and acceptor density for Fe-doped CsGeCl₃ were calculated using the following formula;

6

A detailed computational workflow for the extraction and applications of parameters for device simulation has been added on the supplementary Figure S3.

Structural properties

CsGeCl₃ perovskite exhibits multiple structural phases, each associated with distinct space groups including orthorhombic and tetragonal phases under different thermodynamic conditions¹³. However, this study focuses exclusively on the cubic perovskite phase (space group Pm3m as presented in Fig. 1), which forms a three-dimensional framework with distinct coordination geometries as shown on Fig. 1^15,16. Table 1 presents the lattice parameters and volumes of the unit cell for both the pure and doped CsGeCl₃ materials. These values have been computed and subsequently compared with the available experimental data for verification. In the cubic structure as presented in Fig. 1a, Cs⁺ ions are coordinated by twelve equivalent Cl⁻ ions, forming [CsCl₁₂] cuboctahedra^13,15,16. These cuboctahedra share corners with twelve neighboring [CsCl₁₂] units and faces with six adjacent counterparts, while also interfacing with eight [GeCl₆] octahedra through face-sharing interactions. The Cs–Cl distances range between 4.143 Å and 4.154 Å, reflecting the geometric constraints of the cubic lattice. Ge²⁺ ions occupy octahedral sites, coordinated by six Cl⁻ ions to form symmetrical GeCl₆ octahedra with uniform Ge–Cl bond lengths of 2.93047 Å. These octahedra connect via corner-sharing and face-sharing with [CsCl₁₂] cuboctahedra, establishing the structural backbone. Each Cl⁻ ion adopts a 1-coordinate geometry, bridging four Cs⁺ and two Ge²⁺ ions. In case of doped material Ge–Cl bond length varied and bondpopulation has impacted by the dopant which has been discussed at detailed on Mullican bond analysis section. In Fig. 1b, the “X” marked Ge site represents the dopant site. The doping concentration used in our study is 12.5%. This value arises from the substitution of one Germanium (Ge) atom with a dopant atom (Mn or Fe) within a 2 × 2 × 2 supercell of the pristine structure, which contains a total of eight Ge atoms (1/8 = 12.5%). Figure 1c presents the relaxed structure of CsGeCl₃, wherein a 30 Å gap exists between the slab surface. This structure has been utilized to calculate the electron affinity.

Fig. 1.

CsGeCl₃ crystal structure: (a) 2 × 2 × 2 pure supercell, (b) with 12.5% doping (a single ‘Ge’ marked by ‘X’) concentrations, (c) slab model for the calculations of electron affinity.

Table 1.

The lattice parameters and volumes of unit cell for both pure and doped CsGeCl₃ were computed and benchmarked against available experimental results.

Compositions	This DFT + U study		Other DFT study		Experimental study
	a (Å)	Bandgap, Eg (eV)	a (Å)	Bandgap, Eg (eV)	a (Å)	Bandgap, Eg (eV)
CsGeCl3	5.866	3.44	5.3313	3.2413, 2.1313, 0.9716	5.4413	3.4013,19
CsGe0.875Mn0.125Cl3	5.305	2.33	5.26916	0.9716	N/A	N/A
CsGe0.875Fe0.125Cl3	5.265	1.214	N/A	N/A	N/A	N/A

Electronic properties

The electronic properties of CsGeCl₃ and its doped variants play a pivotal role in determining their potential for solar cell applications. These properties, including the band structure and density of states, are fundamental as they govern the material’s light absorption, charge transport efficiency, and overall performance^11,23,38. Figures 2 and 3 illustrates the electronic band structure and partial density of states (PDOS) for pure CsGeCl₃, CsGe_0.875Mn_0.125Cl₃, and CsGe_0.875Fe_0.125Cl₃. In semiconductor theory, the behavior of the CBM and VBM near the Fermi level largely dictates the material’s electronic characteristics. Consequently, much of our analysis focuses on the changes in the band structure and PDOS close to the Fermi level.

Fig. 2.

The band structure of (a) pure CsGeCl₃, (b) CsGe_0.875Mn_0.125Cl₃, and (c) CsGe_0.875Fe_0.125Cl₃.

Fig. 3.

The total and partial density of states (a) pure CsGeCl₃, (b) CsGe_0.875Mn_0.125Cl₃, and (c) CsGe_0.875Fe_0.125Cl₃.

In pristine CsGeCl₃, we find a 3.44 eV bandgap as shown in Fig. 2a, which is consistent with experimental data. The PDOS in Fig. 3a indicates that the VBM is primarily composed of Cl-3p orbitals, while the CBM is mainly derived from Ge-4p orbitals. This bandgap of 3.44 eV is too large for efficient solar absorption. It is a direct bandgap, as the VBM and CBM align at the same k-point¹¹. For doped concentrations, the VBM and CBM shift to different k-points, suggesting an indirect bandgap. From Fig. 2b, the bandgap in CsGe_0.875Mn_0.125Cl₃ narrows to 2.33 eV. The PDOS in Fig. 3b shows that Ge-3p orbitals move closer to the Fermi level (E_F), while Mn-3d orbitals introduce additional states near E_F.

In CsGe_0.875Fe_0.125Cl₃, substituting Ge with Fe introduces Fe-3d orbitals that significantly modify the electronic structure, resulting in an intermediate electronic state at the midpoint of the original bandgap as noticed at Figs. 2c and 3c. The figure showed that the VBM to CBM gap is 1.214 eV, with the Fe-induced Intermediate Band (IB) splitting it into sub-gaps of 0.608 eV (VBM→IB) and 0.607 eV (IB→CBM). From the PDOS analysis it gets clear that this mid-gap state emerges from the Fe-3d, effectively reducing the bandgap by bringing Ge-4p orbitals closer to the Fermi level and enabling Fe-3d orbitals to contribute prominently to the CBM. Such behavior aligns with the Intermediate Band Solar Cell (IBSC) concept, where an intermediate band (IB) within the bandgap enables sub-bandgap photon absorption^52–54. Unlike impurity photovoltaics (IPV), which typically feature discrete energy levels, IBSCs rely on a continuous IB that remains isolated from the conduction and valence bands^52,53. In principle, this configuration permits absorption of two sub-bandgap photons to generate a single electron–hole pair at the bandgap energy. Delocalization of carriers in the IB can also extend the lifetime of this intermediate state, providing more time for the second photon absorption and allowing transitions that do not necessarily involve the same electron^52,53. In the Fe-doped system, these intermediate states just below the Fermi level, functions as absorbers for sub-bandgap photons, facilitating a two-step excitation process: (i) from the valence band to the IB, and (ii) from the IB to the conduction band. This mechanism enhances visible-light absorption efficiency. The proximity of the Fermi level to these states suggests partial occupancy, creating a pathway for efficient charge transfer. By integrating IB functionality through Fe doping, this approach boosts light absorption and charge transport, offering a promising strategy to implement IBSC principles in lead-free perovskites for high-performance photovoltaic devices.

Electron density maps in Fig. 4. reveal enhanced electron density around the dopant sites (Mn, Fe). In the perovskite structure, Cs remains ionic, while Ge and Mn/Fe engage in covalent bonding with Cl. Upon doping, the hybridization pattern is not confined solely to the dopant site; rather, the electron density slice at Fig. 4 shows that these covalent interactions extend throughout the crystal lattice. This redistribution of electronic charge strengthens the overall bonding network and improves charge transport, thereby enhancing photovoltaic performance.

Fig. 4.

The charge density map of (a) pure CsGeCl₃, (b) CsGe_0.875Mn_0.125Cl₃, and (c) CsGe_0.875Fe_0.125Cl₃.

Orbital and Mulliken atomic population analysis

In pristine CsGeCl₃, the [GeCl₆] octahedra exhibits uniform Ge-Cl bond lengths of 2.93 Å with a bond population of 0.20 across all eight units in the supercell. The Highest Occupied Crystal Orbital (HOCO) originates from the hybridization of Cl-3p orbitals with a mixture of Ge-4s and a minor contribution from Ge-4p orbitals, as confirmed by PDOS analysis and orbital shapes in the HOCO figures at supplementary Figure S1. The Lowest Unoccupied Crystal Orbital (LUCO) primarily comprises Ge-4p and Cl-3p orbitals, with a delocalized charge distribution consistent with the structure’s bandgap of ~ 3.4 eV. The [MnCl₆] octahedron in the Mn-doped structure has an average Mn-Cl bond length of 2.57 Å with a bond population of 0.27. The structural distortions are less pronounced compared to Fe doping, with neighboring [GeCl₆] units showing Ge–Cl bond lengths of 2.73 Å (population 0.07) in one unit, 2.64 Å (population 0.11) in three units, and 2.66 Å (population 0.10) in three units. In general, the HOCO arises from hybridization of Cl-3p with Ge-4s orbitals. After Mn doping clear contributions from Mn-3d orbitals arises, as evidenced by t_2g splitting in the HOCO . In the octahedral [MnCl₆]⁴⁻ environment, Mn²⁺ (d⁵) undergoes ligand field splitting into t_2g and e_g states, with the t_2g orbitals lower in energy and contributing to the HOCO. For the LUCO, Ge-4p and Cl-3p orbitals dominate, along with Mn-3d orbitals in the e_g states. Mn doping reduces the bandgap to 2.33 eV, improving the light-harvesting capability compared to the pristine material.

In the CsGe_0.875Fe_0.125Cl₃, the [FeCl₆] octahedron exhibits reduced Fe–Cl bond lengths of 2.39 Å with an increased bond population of 0.32. This bond shortening induces distortions in neighboring [GeCl₆] octahedra, with six Ge–Cl bond lengths varying as follows: 2.86 Å (population 0.02) in most distant one corner unit, 2.60 Å (population 0.11) in two units, 2.61 Å (population 0.12) in two units, and 2.66 Å (population 0.08) in the remaining units. The HOCO comprises Cl-3p orbitals hybridized with Ge-4s, along with Fe-3d contributions. In octahedral [ FeCl₆]⁴⁻, Fe²⁺ (d⁶) undergoes crystal field splitting into t_2g and e_g, with the t_2g orbitals predominantly occupied (as visible in HOCO images). For the LUCO, Ge-4p and Cl-3p orbitals again dominate, aided by Fe-3d (e_g) states.

Optical properties

The pristine, Mn-doped, and Fe-doped CsGeCl₃ samples’ absorption coefficient, dielectric function, and reflectivity were studied to understand their radiation response across a wide photon energy range. Figure 5. presents the optical absorption spectra for pure CsGeCl₃ and its doped counterparts. The absorption characteristics reveal significant differences in light absorption capabilities across the visible and ultraviolet regions. Pristine CsGeCl₃ demonstrates limited absorption within the visible spectrum, aligning with its wide bandgap of 3.44 eV. However, doping with Mn and Fe introduces new electronic states near the Fermi level, as revealed by the partial density of states (PDOS) analysis, leading to enhanced absorption in the visible region. As illustrated in Fig. 5, Mn- and Fe-doped CsGeCl₃ exhibit significantly improved optical absorption compared to the undoped material, indicating their greater potential for solar cell applications by enabling more efficient capture and conversion of visible light into electrical energy. On Fig. 5, the absorption onset for pristine begins around 3 eV, consistent with its wide bandgap. For Mn-doped, the onset shifts significantly to lower energies (~ 2.3 eV), and for Fe-doped, it shifts even further to ~ 1.2 eV. This demonstrates a clear red-shift into the visible spectrum. Furthermore, the Fe-doped material achieves a considerably higher absorption coefficient in the visible range compared to the pristine and Mn-doped variants.

Fig. 5.

Computed optical absorption spectra for all the studied compounds.

Figure 6a and b present the real and imaginary components of the dielectric constant, respectively. The real part, shown in Fig. 6a, represents the material’s response to an external electric field, influencing optical properties such as refractive index, light transmission, and reflection. A reduction in the real dielectric constant is observed in the doped samples compared to the pristine phase, indicating a modification in the material’s polarization behavior due to doping. Figure 6b illustrates the imaginary part of the dielectric constant, which corresponds to the material’s ability to absorb electromagnetic energy. Both Mn and Fe doping result in elevated values for the real and imaginary parts at lower photon energies, suggesting improved light absorption in the visible range. Also, the observed shift in the dielectric peaks toward higher photon energies aligns with the trends in the absorption spectra, further supporting the enhanced optical absorption of the doped compounds.

Fig. 6.

Real (a) and imaginary (b) components of the dielectric function have been computed for each of the studied compounds.

The photovoltaic potential of the absorber material is further clarified by considering the exciton binding energy (EBE), a critical factor governing charge carrier generation. An efficient conversion of photons to free carriers necessitates a low EBE, enabling excitons to dissociate using thermal energy⁵⁵. Our results indicate that the superior performance of the Fe-doped is not only due to its modified band structure but also linked to its intrinsic dielectric properties. The calculated enhancement in the static dielectric constant, coupled with the low carrier effective masses (at Table 4), provides compelling evidence for a significantly reduced EBE in the Fe-doped system. This suppressed exciton binding facilitates more efficient charge separation, offering a fundamental explanation for the marked improvement in quantum efficiency and the substantially higher short-circuit current density (at Table 5) predicted by our device simulations.

Table 4.

SCAPS-1D Parameters of pure and metal-doped CsGeCl₃ were calculated.

Parameters	FTO	ETL (WS2)	ETL (PCBM)	CsGeCl3	CsGe0.875Mn0.125Cl3	CsGe0.875Fe0.125Cl3	HTL (P3HT)
Thickness (µm)	0.05	0.100	0.100	0.200	0.200	0.300	0.150
Bandgap (eV)	3.500	1.800	2.000	3.447	2.331	1.212	1.700
Electron affinity (eV)	4.000	3.950	3.900	3.970	3.970	3.970	3.500
Dielectric permittivity	9.000	13.600	3.900	2.7	3.160	3.230	3.000
CB effective density of states (1/cm3)	2.2 × 1018	2.8 × 1018	2.5 × 1021	1.32 × 1021	8.9 × 1019	3.21 × 1018	2 × 1021
VB effective density of states (1/cm3)	1.8 × 1019	1.9 × 1019	2.5 × 1021	9.28 × 1018	1.41 × 1021	4.84 × 1018	2 × 1021
Electron thermal velocity (cm/s)	1 × 107	1 × 107	1 × 107	2.87 × 106	7.05 × 106	2.14 × 107	1 × 107
Hole thermal velocity (cm/s)	1 × 107	1 × 107	1 × 107	1.5 × 107	1.36 × 107	1.86 × 107	1 × 107
Electron mobility (cm2/Vs)	20	100	2 × 10−1	20	20	20	1.8 × 10−3
Hole mobility (cm2/Vs)	10	100	2 × 10−1	20	20	20	1.8 × 10−2
Donor density ND (1/cm3)	1 × 1019	1 × 1018	2.93 × 1017	0	0	2.6 × 108	0
Acceptor density NA (1/cm3)	0	0	0	8 × 1015	5 × 1015	2.6 × 108	1 × 1018

Table 5.

The comparative analysis of pure and metal-doped CsGeCl₃ on highest PCE on optimized thickness.

ETL	Absorber material	PCE (%)	Thickness (μm)	VOC (V)	JSC (mA/cm2)	Fill factor (%)
PCBM	CsGeCl3	5.09	0.20	1.54	4.71	70.16
	CsGe0.875Mn0.125Cl3	5.16	0.31	1.52	6.32	53.4
	CsGe0.875Fe0.125Cl3	31.2	0.42	1.1	34.61	81.48
WS2	CsGeCl3	4.39	0.22	1.53	4.05	70.36
	CsGe0.875Mn0.125Cl3	5.54	0.31	1.52	5.59	64.89
	CsGe0.875Fe0.125Cl3	31.62	0.42	1.1	34.97	81.66

Mechanical properties

Understanding the mechanical characteristics of materials including elasticity, ductility, and structural stability is crucial for determining their suitability in practical applications, particularly in optoelectronic devices. To evaluate these properties, the elastic constants C₁₁, C₁₂, and C₄₄ were calculated for both pristine CsGeCl₃ and its Mn- and Fe-doped variants, providing insight into their mechanical responses under stress^11,23,48. The elastic constants offer critical information about a material’s resistance to deformation and its structural integrity under applied stress. The mechanical stability of the cubic crystal structure was verified by confirming that the computed elastic constants fulfill the Born stability criteria. The results indicate that both the Mn- and Fe-doped phases of CsGeCl₃ meet the stability criteria, with no violations observed, as indicated by positive values for the elastic constants (Table 2). Cauchy pressure, calculated as the difference between C₁₂ and C₄₄, is a useful parameter for assessing a material’s ductile or brittle nature. A positive Cauchy pressure suggests ductile behavior, and both Mn- and Fe-doped CsGeCl₃ exhibited positive Cauchy pressure values, confirming that these materials are ductile. This property is especially advantageous for flexible thin-film applications.

Table 2.

The computed elastic constants for both undoped and metal-doped CsGeCl₃ are presented.

Phase	C11	C12	C44	C12–C44	C11–C12	C11+2C12
CsGeCl3	51.383	13.66	11.984	1.676	37.723	78.703
CsGe0.875Mn0.125Cl3	41.627	13.813	11.726	2.087	27.814	69.253
CsGe0.875Fe0.125Cl3	26.192	14.326	7.782	6.544	11.866	54.844

In addition to the elastic constants, essential mechanical parameters including bulk modulus (B), shear modulus (G), Young’s modulus (E), Poisson’s ratio (ν), and Vickers hardness (H_v) were calculated and presented at Table 3. using the Voigt–Reuss–Hill (VRH) averaging scheme.

Table 3.

The mechanical properties of pure and metal-doped CsGeCl₃ were calculated.

Phase	Bulk Modulus, B (GPa)	Shear Modulus, G (GPa)	Young’s modulus, E (GPa)	Pugh’s ratio, (B/G)	Poisson’s ratio, (v)	Hardness, (Hv)
CsGeCl3	26.22	14.383	36.479	1.822	0.268	2.224
CsGe0.875Mn0.125Cl3	23.52	12.767	32.439	1.842	0.27	1.958
CsGe0.875Fe0.125Cl3	12.07	4.751	12.58	2.54	0.328	0.543

Data from Table 3. show that both Mn- and Fe-doped CsGeCl₃ exhibit enhanced mechanical properties compared to the pure CsGeCl₃. As shown in Table 3, the introduction of Mn and Fe dopants significantly alters the mechanical properties of CsGeCl₃. Both dopants lead to a decrease in the elastic moduli (B, G, and E) and hardness (H_v), with the Fe-doped phase showing a much more pronounced reduction in overall stiffness and hardness. This softening of the material is accompanied by a substantial increase in ductility. The enhancement in ductile behavior is evident from the rise in both Pugh’s ratio (B/G) and Poisson’s ratio (v), particularly for CsGe_1−0.125Fe_0.125Cl₃, which exhibits a B/G value of 2.54. As shown in Table 3. the Fe-doped material has the lowest Young’s modulus by a significant margin, making it the most flexible and least stiff. It also has the highest Pugh’s ratio (2.54) and the highest Poisson’s ratio (0.328), indicating it is substantially more ductile than the other two materials. This combination of high ductility and low stiffness makes Fe-doped CsGeCl₃ the best candidate for creating thin films that are less prone to cracking or delamination.

Solar cell device applications

The performance of the SCAPS devices designed with both PCBM and WS₂ as electron transport layers (ETL) and P3HT as the hole transport layer (HTL) was evaluated by analyzing key photovoltaic parameters, such as open-circuit voltage (V_OC), current density (J_SC), quantum efficiency (QE) and power conversion efficiency (PCE). The devices incorporated doped and pristine CsGeCl₃ as the absorber material, intending to optimize light absorption and enhance charge transport for improved solar cell efficiency. SCAPS-1D input parameters for pure and metal-doped CsGeCl₃ were calculated and presented at Table 4. For FTO, HTL and ETLs input parameters has been incorporated from previous published studies^18,56–59.

The photovoltaic measurements in Fig. 7 demonstrate the transformative effect of iron doping on CsGeCl₃ solar cells. The Fe-doped device achieves a massive short-circuit current density J_SC of roughly 32 mA/cm², a value explained by its remarkable quantum efficiency (QE) that approaches nearly 100% across the most useful part of the solar spectrum (400–700 nm). This performance eclipses that of the pure and Mn-doped cells, which struggle with low currents of only 4–6 mA/cm² due to their poor quantum efficiencies (below 35%). Interestingly, the huge gain in current for the Fe-doped cell comes at the cost of a lower open-circuit voltage (~ 1.1 V compared to ~ 1.5 V), but this trade-off is favorable for overall power output. Across these measurements, the choice of ETL (whether PCBM or WS₂ ) proves to be a minor factor compared to the fundamental improvements brought about by the iron doping.

Fig. 7.

IV graph and QE vs. Wavelength graph of (a), (b) PCBM as ETL and (c), (d) WS₂ as ETL.

Figure 8 presents the calculated photovoltaic parameters power conversion efficiency (PCE), open-circuit voltage (V_OC​), short-circuit current density (J_SC​), and fill factor (FF) as a function of absorber layer thickness for pure and doped CsGeCl₃. The analysis compares devices using two different electron transport layers (ETLs): PCBM and WS₂. Both the pure and Mn-doped CsGeCl₃ absorbers show limited change in performance as they get thicker (Fig. 8a–d). For the pure material, increasing thickness consistently lowers the PCE, dropping from 5.1% to 4.7% with a PCBM ETL due to a sharp fall in the fill factor. While Mn-doping boosts the initial current density, this advantage is negated by declining voltage and fill factor values at greater thicknesses. In both cases, it appears that any benefit from increased light absorption is quickly offset by rising recombination losses which will be discussed later. Experimental research has successfully demonstrated the fabrication of CsGeCl₃ quantum rods using solvothermal process, achieving a PCE of 2.57% under standard illumination conditions⁶⁰. The behavior of the Fe-doped compound stands in sharp contrast (Fig. 8e and f). Here, a thicker absorber layer is clearly beneficial. As the thickness increases from 0.25 μm to 0.45 μm, the current density (J_SC​) climbs dramatically from approximately 31 mA/cm² to 35 mA/cm². This surge in current drives the PCE upwards from ~ 29% to a peak of 31.5% with PCBM, and a highest efficiency of 32% with a WS₂ ETL. Although the open-circuit voltage and fill factor dip slightly, these minor losses are insignificant compared to the substantial current gains, demonstrating that Fe-doping successfully creates a material that maximizes current generation without succumbing to severe recombination issues.

Fig. 8.

The calculated photovoltaic parameters PCE, V_OC, J_SC, and FF are presented. For configurations (a), (c), and (e), PCBM is used as the ETL, while WS₂ serves as the ETL in configurations (b), (d), and (f).

A comparative analysis of pure and metal-doped CsGeCl₃, demonstrating the highest PCE achieved at an optimized thickness, is presented in Table 5. From the provided table, it is evident that CsGe_0.875Fe_0.125Cl₃ achieves the highest PCE, irrespective of the transport layers utilized.

Analysis of different recombination rates

One of the primary challenges in solar cell simulation is accurately modeling the recombination rates of photogenerated electron–hole pairs⁶¹. In direct band gap semiconductors, radiative recombination is typically the dominant process and is characterized by the coefficient ⁶¹. For halide perovskites, reported values of range from 10⁻⁹ to 10⁻¹⁵ cm³/s. However, in materials with an indirect band gap, such as CsGeCl₃, radiative recombination is significantly suppressed due to the phonon-assisted nature of the transition.

While Auger recombination generally plays a minor role under standard illumination conditions, it becomes more significant in indirect band gap materials where radiative recombination is intrinsically weak. Reported values of the Auger recombination coefficient for CsPbI₃ and CsPbBr₃ fall in the range of 10⁻²⁷ to 10⁻²⁹ cm⁶/s, with bulk CsPbBr₃ exhibiting values between approximately 3 × 10⁻²⁷ and 4 × 10⁻²⁸ cm⁶/s⁶². In comparison, similar lead-free tin-based perovskites such as MASnI₃ have been experimentally shown to exhibit significantly lower Auger coefficients, on the order of 10⁻³⁰ cm⁶/s at room temperature, as determined by time-resolved photoluminescence (TRPL) measurements⁶³. Based on extrapolated trends, CsSnCl₃ exhibits Auger coefficients ​ and ​ in the range 10⁻³¹  to 10⁻³² cm⁶/s at 300 K for carrier concentrations around 10¹⁷ cm⁻³, indicating that Auger recombination is negligible under solar illumination⁶⁴. Similarly, for CsGeI₃, values of ​ ​and ​ ​ are estimated to be around 10⁻²⁹ cm⁶/s under comparable conditions⁶⁵.

Given the lack of experimentally established recombination parameters for CsGeCl₃, and its indirect band gap nature, we have chosen to perform a parametric study of PCE over a wide range of recombination coefficients. In our simulation, the horizontal axis of the figure represents the radiative recombination coefficient , varied from 10⁻⁹ to 10⁻¹⁵ cm³/s, while the vertical axis corresponds to the Auger recombination coefficient , ranging from 10⁻²⁷ to 10⁻³² cm⁶/s. Both axes are presented in logarithmic scale to enhance visualization and highlight the sensitivity of PCE to these parameters.

For both the pure and Mn-doped CsGeCl₃ specimens, variations in the both recombination coefficients have negligible impact on the PCE (See Supplementary Figure S2). In contrast, the Fe-doped specimen exhibits sensitivity to both radiative and Auger recombination processes. In this case as shown in Fig. 9, the PCE decreases from a maximum of 31.20% to 24.56% when both recombination coefficients are set to their highest considered values, using PCBM as the ETL. Similarly, for the WS₂-based ETL, the PCE varies from 30.00% to 23.42% under the same recombination conditions. The study reveals that doping CsGeCl₃ with Fe improves the overall photovoltaic performance by significantly enhancing the current density and quantum efficiency, especially in the visible and near-ultraviolet regions. The ETL material whether PCBM or WS₂ also plays a key role in optimizing device performance, with both materials showing complementary effects on the photovoltaic parameters. Increasing the absorber thickness generally leads to higher current density but may have diminishing returns on V_OC and PCE due to recombination effects. These findings underline the potential of Fe-doped CsGeCl₃ in combination with optimized ETL materials for high-performance thin-film solar cells.

Fig. 9.

PCE for across range of varied Auger Recombination ) and Radiative Recombination Coefficient for CsGe_0.875Fe_0.125Cl₃ with different ETL.

Summary and conclusions

This study investigates how Mn and Fe doping in CsGeCl₃ perovskites can enhance their optical absorption, mechanical stability, and photovoltaic performance, addressing challenges faced by lead-free perovskites in solar cell applications. We employed DFT + U to model the electronic properties and used SCAPS-1D simulations to predict the performance of doped CsGeCl₃ in solar cell configurations, incorporating PCBM and WS₂ as ETLs and P3HT as the HTL. Our results demonstrate that Fe-doping significantly improves optical absorption, achieving a quantum efficiency of nearly 98% within the 1.5 to 3.25 eV incident photon energy range, surpassing both pure CsGeCl₃ (~ 20% QE) and Mn-doped CsGeCl₃ (~ 40% QE) for both ETLs. The results of SCAPS-1D simulations confirmed that Fe-doped CsGeCl₃ achieved a PCE of 31.6%, a remarkable improvement over the 5% efficiency of the pristine and Mn-doped materials. Due to the introduction of d-electron states by Mn and Fe dopants, which modify the band structure and create intermediate energy levels, thereby enhancing optical absorption, charge transport, and overall device performance. Mechanical evaluations show that doping increases the material’s hardness, shear modulus, and overall stability, enhancing its suitability for thin-film solar cell applications. Besides, the doped materials exhibit improved ductility, which is advantageous for device fabrication and long-term stability. In photovoltaic simulations, Fe-doped CsGeCl₃ exhibited the highest current density and PCE, with performance improvements observed as the absorber layer thickness increased. The study also demonstrated that optimizing the thickness of the absorber material and selecting appropriate electron transport layers (ETLs), such as PCBM and WS₂, are critical in maximizing device performance. These findings highlight the potential of Fe-doped CsGeCl₃ as a leading material for high-efficiency, lead-free solar cells. Future work should focus on experimentally validating these predictions, optimizing device structures, and evaluating long-term stability under real-world conditions. Further research into scaling up the material for commercial use is essential for advancing its practical application in renewable energy technologies.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

D.K.P. conceptualized the study. The methodology was designed by D.K.P. . The investigation was conducted by D.K.P. and F.H.H. D.K.P. and S.Z oversaw the software . Data was curated by D.K.P., S.Z., S., M.L.R., A.K.M.A.H., and A.F.M.Y.H. Formal analysis was performed by all authors. The original manuscript draft was written by D.K.P. and S.Z. F.H.H. provided supervision for the project. The final manuscript was reviewed and edited by D.K.P. and F.H.H. All authors read and approved the final manuscript.

Funding

BRAC University Research Seed Grant Initiative 2024 (RSGI-2024) and Department of Mathematics and Physical Sciences, BRAC University, Bangladesh.

Data availability

The theoretical data supporting the findings of this investigation are available upon request from the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.