Octahedral Dominance and Band Gap Tuning via Pb²⁺-Driven Structural Evolution in α-β-γ CsZnI₃

Abstract

In the quest for stable, lead-reduced perovskites, this study unravels the structural and electronic evolution of CsZnI₃ across its α, β, and γ phases. DFT calculations spotlight the tetrahedral γ phase—with elongated Zn–I bonds (3.17 Å)—as the most stable, sidestepping the octahedral distortions of its metallic α and β counterparts. Pb²⁺ doping (>50%) drives a transformation to mixed octahedral–tetrahedral coordination, slashing the wide 3.15 eV bandgap to a solar-optimal 2.20 eV via lattice shrinkage. Above 50% doping, an optimum emerges—balancing structural integrity with efficient light absorption. These findings elevate Zn-doped or Zn-Pb-based compounds as promising and tunable perovskites for next-gen photovoltaics.

1. Introduction

Metal halide perovskites have emerged as a research hotspot in photovoltaics due to their unique properties. Currently, single-junction solar cells employing organic–inorganic hybrid perovskite materials as the light-absorbing layer have achieved a power conversion efficiency (PCE) of up to 27% [1]. However, the thermal instability of organic–inorganic hybrid perovskites, caused by volatile organic A-site cations, remains a critical limitation [2]. Replacing organic cations with inorganic Cs⁺ ions presents an effective strategy to address this issue [3]. Cesium lead iodide (CsPbI₃) [4], a fully inorganic halide perovskite, offers superior thermal stability over hybrid perovskites. Indeed, although all-inorganic lead halide perovskites (ILHPs) exhibit excellent thermal stability, their low structural stability under ambient conditions still hinders practical applications, motivating consideration of material- and device-engineering strategies to enhance CsPbI₃ solar-cell performance and stability [5]. CsPbI₃ exists in multiple crystal phases, with its black phases (α, β, and γ) exhibiting excellent optoelectronic properties but being metastable at room temperature. Chemical doping has also emerged as an effective means to control perovskite phase behavior and optoelectronic properties. B-site doping strategy exhibits unique advantages in terms of structural control to address the aforementioned challenges, as exemplified by tin- and germanium-based perovskites [6,7,8,9,10,11].

Among the various doping approaches, B-site substitution with smaller cations like Zn²⁺ (0.74 Å) or Mn²⁺ (0.97 Å) stands out. Such dopants effectively stabilize the cubic structure by inducing lattice contraction, increasing the Goldschmidt tolerance factor, and enhancing Pb–I bond strength. These strategies not only suppress defect formation but also improve phase transition tolerance during purification processes, achieving solar cell efficiencies up to 13.5% for Zn-doped CsPbI₃ [12]. In particular, Zn²⁺ has emerged as a highly promising dopant due to its favorable ionic characteristics [13]. The introduction of Zn²⁺, with an ionic radius of 0.74 Å compared to 1.19 Å for Pb²⁺, leads to an increase in the Goldschmidt tolerance factor from 0.81 to 0.93, mitigating octahedral distortions and stabilizing the black-phase perovskite structure [14,15], which is essential for maintaining high photovoltaic efficiency. The incorporation of Zn²⁺ also passivates defects and reduces halide vacancies [15], thereby minimizing nonradiative recombination and improving charge carrier dynamics. Experimentally, Zn²⁺ doping has been demonstrated to enhance photoluminescence quantum yield [16,17], suppress phase degradation, and optimize electronic properties, leading to improved external quantum efficiency in light-emitting and photovoltaic devices. Additionally, Zn²⁺ doping facilitates the formation of pinhole-free, high-crystallinity films with reduced trap states [18,19], ultimately contributing to greater stability and longevity of perovskite-based optoelectronic applications. While the complete elimination of lead remains challenging, strategic doping with non-toxic elements such as Zn offers a viable approach to significantly reducing lead content and mitigate associated environmental risks.

Unlike conventional studies that focus on Zn²⁺ doping in CsPbI₃ to reduce toxicity or modulate electronic properties, this study proposes an inverse design strategy: incorporating Pb²⁺ into CsZnI₃. Previous theoretical studies have demonstrated that CsZnI₃ possesses intrinsic structural and thermodynamic stability within the cubic perovskite framework, along with favorable semiconducting properties [20], providing a solid foundation for using it as a starting point in reverse-design strategies. This study investigates the structural and electronic properties of the α, β, and γ phases of CsZnI₃, with a particular focus on phase stability and the contrasting coordination geometries—tetrahedral in Zn-centered networks versus octahedral in Pb-centered frameworks. Notably, the γ phase, often considered thermodynamically favorable, may exhibit structural instability when adopting octahedral configurations. This study finds that the tetrahedral geometry, inherent to the Zn-based lattice, could confer enhanced stability. Building upon this foundation, we introduced Pb into tetrahedral γ-CsZnI₃, achieving a structural transformation from tetrahedral to octahedral coordination. Furthermore, Pb incorporation effectively modulates the material’s bandgap to a tunable range of 0.9–2.2 eV, significantly enhancing its suitability for both single-junction and tandem-structured perovskite solar cell fabrication and applications [21,22,23].

All conclusions are drawn from density functional theory (DFT) calculations and have not yet been experimentally validated. Nonetheless, by clarifying the structural and electronic trends emerging from Zn-Pb synergistic coordination, this study offers a new theoretical perspective that could contribute to the broader effort of reducing lead content in perovskite materials. These insights may serve as a basis for future experimental efforts to design more stable, efficient, and environmentally conscious inorganic perovskites with tunable bandgaps (1.78–3.15 eV).

2. Materials and Methods

All first-principles calculations were performed using density functional theory (DFT) as implemented in the Vienna Ab initio Simulation Package (VASP) [24,25,26]. The exchange and correlation interactions were treated within the Generalized Gradient Approximation (GGA) using the Perdew–Burke–Ernzerhof (PBE) [27] functional. The interactions between the core and valence electrons were described by the projector-augmented wave (PAW) [28] method. A plane-wave energy cutoff of 500 eV was used throughout the calculations to ensure the convergence of total energy. The Brillouin zone was sampled using a Γ-centered k-point mesh with grid sizes of (6 × 6 × 6), (4 × 4 × 3), (4 × 4 × 3), and (4 × 4 × 3) for the α, β, γ, and tetrahedral γ phases, respectively. The calculation results of the structure are shown in Figure 1. For structural relaxation, both atomic positions and the lattice parameters of the residual forces on each atom were below 0.001 eV/Å, and the total energy difference between consecutive self-consistent field (SCF) iterations was less than 1.0 × 10⁻⁶ eV. The electronic structure calculations were then performed using the optimized structures.

3. Results and Discussion

3.1. Structural Properties

The stability of CsZnI₃ in different structural configurations was analyzed by total energy calculations, as shown in Figure 2. A clear trend of increasing stability from the α phase (−43.26 eV) to the β phase (−43.32 eV), followed by a more pronounced stabilization in the octahedral γ phase (−43.92 eV) and culminating in the lowest energy configuration in the tetrahedral γ phase (−45.74 eV). This substantial energy reduction in the tetrahedral γ phase suggests that the transition from an octahedral to a tetrahedral coordination optimizes the atomic arrangement, enhancing thermodynamic stability. The tetrahedral γ phase structure is significantly more stable than the other phases, indicating that for γ phase CsZnI₃, tetrahedral coordination is likely to be the preferred structure, with their corresponding total energies listed in Table S1. Studies have shown that elements such as Zn, Cd, and Hg tend to favor covalent tetrahedral coordination, further supporting the stability of this phase. Furthermore, the literature [29] indicates that perovskites often exhibit poor dynamic stability due to octahedral rotations, which introduce structural distortions. In contrast, the incorporation of tetrahedral coordination, akin to the structural arrangement in spinels, may suppress these instabilities, making the tetrahedral γ phase not only thermodynamically favorable but also dynamically stable.

The variation in Zn–I bond lengths further supports the observed stability trend in CsZnI₃. As the material transitions from the α phase to the β phase, the average Zn–I bond length increases from 2.91 Å to 2.93 Å, followed by a more substantial increase to 3.12 Å in the octahedral γ phase, where multiple distinct bond lengths are observed. In the tetrahedral γ phase, the Zn–I bond length extends further to 3.17 Å. However, unlike Pb-based perovskites, where shorter bonds strengthen Coulomb interactions and enhance stability [12,30], the tetrahedral coordination in CsZnI₃ enables a different stabilization mechanism, with their corresponding bond lengths listed in Table S2. The tetrahedral arrangement not only elongates bond lengths but also mitigates the instability caused by octahedral rotations, leading to a more robust lattice structure. These findings indicate that the transition from octahedral to tetrahedral configurations is crucial for stabilizing CsZnI₃, providing insights for designing perovskite materials with improved thermodynamic and dynamic stability.

3.2. Electronic Properties

3.2.1. Band Structure

The calculated band structures of CsZnI₃ shown in Figure 3 using the PBE method reveal a striking evolution in electronic properties as the crystal structure transitions from the α phase to the tetrahedral γ phase. For the α phase, the band structure was calculated along the high symmetry k-point path Γ–X–M–R–Γ. The β phase utilized the Γ–X–M–A–R–Z–Γ route, while the octahedral and tetrahedral γ phases were evaluated along the identical Γ–X–S–Y–Γ–Z–U–R–T–Z|X path. Notably, all the semiconducting phases exhibit a direct bandgap with the valence band maximum (VBM) and conduction band minimum (CBM), both located at the Γ point.

The metallic behavior observed in the α phase arises from extensive orbital overlap, consistent with previous reports [20] that have attributed similar orbital interactions to the absence of a clear separation between valence and conduction bands. The transition to the β phase, however, introduces a direct band gap of 0.17 eV at the Γ point, signifying the onset of semiconducting behavior. Comparable trends have been observed in other perovskite structures, where the lowering of crystal symmetry induces notable rearrangements in the electronic structure, underscoring the high sensitivity of these materials to subtle changes in atomic coordination [5].

The structural transformation into the octahedral and tetrahedral γ phases leads to pronounced changes in the electronic band structure. In the octahedral γ phase, the conduction band minimum shifts upward, increasing the band gap to 1.60 eV, likely due to the change in orbital hybridization caused by the local coordination modification. The dramatic increase to a 3.15 eV band gap in the tetrahedral γ phase, despite using the same k-path, underscores the critical role of coordination geometry in determining orbital overlap. In the tetrahedral configuration, the reduction in orbital overlap at the conduction band minimum minimizes antibonding interactions, leading to a wider band gap. These findings are consistent with previous studies showing that changes in atomic coordination [31], particularly the shift from octahedral to tetrahedral environments, play a crucial role in tuning the electronic structure. Although the PBE method underestimates absolute band gap values indicated by Table S3, the observed trends corroborate the established notion that structural transformations in perovskite materials directly influence their electronic and optical properties, thus offering a viable pathway for engineering material properties for specific optoelectronic applications.

3.2.2. Density of States

Building on the band structure analysis, we examine the density of states (DOS) to further elucidate the distribution and availability of electronic states across different energy levels. The PDOS analysis of various CsZnI₃ phases in Figure 4 reveals a notable shift in electronic states near the Fermi level, aligning with trends reported in the literature. In the α phase, the system exhibits metallic characteristics, whereas the β, octahedral γ, and tetrahedral γ phases display semiconducting behavior. Specifically, the valence band maximum (VBM) is largely dominated by I-5p orbitals, while the conduction band minimum (CBM) is primarily derived from I-5p and Zn-4s states, with minimal contribution from Cs orbitals. This supports previous findings that Cs mainly acts as a structural stabilizer, not directly affecting the band edge states [30]. As the structure transitions from the α phase to the β phase and subsequently to the γ phase, there is a progressive increase in the Zn-3d contribution at the VBM, indicating enhanced hybridization and increased localization of Zn states, which can significantly influence the hole effective mass [20]. As CsZnI₃ transforms from the β phase to the octahedral γ phase and then to the tetrahedral γ phase, the Zn–I bond length continuously extends. Meanwhile, the PDOS near the CBM shows I-5p and Zn-4s peaks nearly coinciding in energy, and their peak intensities increase synchronously. This indicates that in a more open structure, these two orbitals maintain significant spatial overlap and enhance hybridization. Within the octahedral γ phase, orbitals such as Zn-3d, Zn-3p, I-5s, and I-5d contribute weakly and approximately equally to the PDOS near the CBM, forming a balanced multi-orbital antibonding network. However, upon transitioning to the tetrahedral γ phase, the constraints of the octahedral field are further weakened, with the contributions from I-5s (particularly pronounced) and I-5d orbitals to the CBM being selectively amplified.

These findings underscore the intricate relationship between structural phase transitions and electronic state modifications in CsZnI₃, highlighting the role of orbital interactions in shaping its electronic and optical properties.

3.3. Doping Analysis and Structural Evolution

Next, we doped the tetrahedral gamma phase CsZnI₃, replacing Zn in CsZnI₃ with Pb, and gradually increased the number of replaced atoms from 0 to 4. We selected the most stable replacement structure in the calculation results as the result, as shown in Figure 5. Figures S1 and S2 in the Supporting Information present the structural characterization and DOS analysis. The calculation results show that Pb²⁺ doping in the tetrahedral γ phase CsZnI₃ induces systematic modifications in both the structural and electronic properties of the material. To more accurately characterize structural stability at varying Pb²⁺ doping levels, we calculated the total energy (Table S4) and the binding energy for each configuration. Although the binding energy at a 0.25 doping ratio is slightly higher than that of the undoped structure, the difference is minimal; overall, the binding energy decreases steadily with increasing doping concentration, indicating enhanced structural stability. However, structural stability does not necessarily imply dynamic (or vibrational) stability; thus, a synergistic optimization of both aspects is required. Concurrently, a distinct evolution of the coordination environment is observed, as evidenced by the structures at different doping levels, as shown in Figure 5a: at low doping concentrations (25%), the structure retains a fully tetrahedral geometry, whereas beyond 50% doping, octahedral [PbI₆]⁴⁻ units begin to emerge.

Structurally driven transition toward mixed octahedral–tetrahedral coordination occurs when Pb²⁺ doping concentrations exceed 50%, induced by the synergistic effects of lattice contraction, atomic positional displacements, and bond length alterations. The transition from tetrahedral to octahedral coordination is a significant structural change. This evolution in local geometry mirrors observations in related perovskite and spinel systems, where the substitution of smaller B-site cations with larger ones (e.g., Pb²⁺ replacing Zn²⁺) can induce lattice shrinkage and promote octahedral connectivity. Such behavior has been attributed to changes in the Goldschmidt tolerance factor and modifications in bond lengths, which in turn affect both lattice dynamics and phase stability.

Electronically, our computational results demonstrate a progressive bandgap reduction from 3.15 eV with increasing Pb²⁺ concentration. This trend aligns with established correlations between dopant-driven absorption edge redshifts and electronic structure modifications [21]. Significantly, we identify that exceeding 50% Pb²⁺ doping establishes a critical optimization window—this optimum simultaneously achieves a photovoltaic–optimal bandgap (0.9–2.2 eV) [21,22,23], preserves structural integrity, and enhances light absorption efficiency. Such balanced performance parameters, particularly the concurrent maintenance of stability and optoelectronic tunability, position Zn-doped and Zn–Pb hybrid perovskites as promising eco-conscious candidates for next-generation photovoltaic systems. The demonstrated dopant-driven bandgap engineering capability provides crucial design guidelines for developing high-efficiency, durable perovskite solar cells. The end-member y = 1 (pure CsPbI₃) is plotted only to anchor our energy scale and to show the continuous evolution of stability and bandgap. Unfortunately, we are currently unable to conclusively determine whether the tetrahedral γ-CsPbI₃ is unconditionally stable at room temperature. Our focus is on the intermediate compositions (0.5 < y < 0.75), where DFT reveals a true sweet-spot of mixed octahedral–tetrahedral coordination, enhanced thermodynamic favorability, and a solar-optimal band gap (~1.78–2.20 eV).

4. Conclusions

This work establishes CsZnI₃ and alloying Cs(Zn-Pb)I₃ as a structurally robust, lead-reduced perovskite candidate for photovoltaics by performing first-principle calculations. Density functional theory (DFT) calculations reveal that the tetrahedral γ-CsZnI₃ exhibits superior thermodynamic stability compared to the octahedral structures of its α and β phase structures. Electronic-structure analysis further reveals that while CsZnI₃ transitions from metallic (α) to semiconducting (γ) behavior, with the pure γ phase exhibiting a wide direct bandgap of 3.15 eV, Pb²⁺ incorporation effectively narrows this gap to 1.78 eV through lattice contraction. When the Pb doping concentration exceeds 50%, it effectively balances the crystal structure stability and bandgap width. These findings position Zn-doped and Zn-Pb alloyed CsZnI₃ derivatives as highly tunable halide perovskites with reduced lead content, offering a compromise between performance and environmental impact for next-generation photovoltaic applications.