Stability Criteria and Optoelectronic Properties of Mg3ZBr3 (Z = As, Sb, Bi) Perovskites for Evaluating the Performance in PIN Photo Diode

The toxicity and stability issues of lead-based perovskites motivate the search for non-toxic, durable alternatives. This work examines lead-free $\mathrm{Mg_3ZBr_3}$ ($Z=\mathrm{As,Sb,Bi}$) halide perovskites as optoelectronic materials, with emphasis on $\mathrm{Mg_3AsBr_3}$ and $\mathrm{Mg_3SbBr_3}$. First-principles calculations establish cubic $Pm\bar{3}m$ frameworks stabilized by strong Mg–Br linkages, and indirect band gaps of $2.0645,\mathrm{eV}$ for $\mathrm{Mg_3AsBr_3}$ and $1.6533,\mathrm{eV}$ for $\mathrm{Mg_3SbBr_3}$ obtained using hybrid functionals. Optical spectra show a rapid rise in absorption above the gap and an increasing static dielectric response along $\mathrm{As}\rightarrow\mathrm{Sb}\rightarrow\mathrm{Bi}$, indicating strengthened light–matter coupling. Phonon dispersions lack imaginary branches, confirming dynamical stability, and exhibit large mode anharmonicity (Grüneisen signatures) consistent with soft-lattice heat transport. Moving down the pnictogen series expands the lattice and lowers the Goldschmidt tolerance factor, while enhanced pnictogen–Br $p$-orbital hybridization and stereochemically active $n\mathrm{s}^{2}$ lone pairs (Sb, Bi) narrow the band gap and increase the optical dielectric response. Elastic analyses confirm Born stability and moderate stiffness, with Hill-averaged bulk moduli decreasing from approximately $44,\mathrm{GPa}$ ($\mathrm{Mg_3AsBr_3}$) to $35,\mathrm{GPa}$ ($\mathrm{Mg_3BiBr_3}$). Drift–diffusion $p$–$i$–$n$ simulations qualitatively track band-edge-limited spectra, aligning with the computed gaps. Together, these results position these materials as promising lead-free candidates for stable thin-film photodiode and photovoltaic applications.

💡 Research Summary

This paper addresses the pressing need for lead‑free, environmentally benign perovskite materials by systematically investigating the structural, electronic, optical, vibrational, mechanical, and device‑level properties of the Mg₃ZBr₃ (Z = As, Sb, Bi) family using first‑principles density‑functional theory (DFT) and drift‑diffusion simulations. Geometry optimizations performed with the projector‑augmented wave (PAW) method in VASP, first at the PBE level and then refined with the screened hybrid functional HSE06, reveal that all three compounds adopt a simple cubic Pm‑3m (space group 221) structure. The lattice constant expands from 5.48 Å (Mg₃AsBr₃) to 5.72 Å (Mg₃BiBr₃), reflecting the increasing ionic radius of the pnictogen. Correspondingly, the Goldschmidt tolerance factor drops from 0.78 to 0.63, indicating that the Bi‑containing phase is close to the geometric stability limit and may favor octahedral tilting at ambient conditions.

Electronic‑structure calculations with HSE06 predict indirect band gaps of 2.06 eV (Mg₃AsBr₃), 1.65 eV (Mg₃SbBr₃), and 1.52 eV (Mg₃BiBr₃). The conduction‑band minimum (CBM) is primarily Mg‑Br σ* antibonding with contributions from pnictogen‑p orbitals, while the valence‑band maximum (VBM) consists of strong pnictogen‑p/Br‑p hybridization. The presence of stereochemically active ns² lone pairs on Sb³⁺ and Bi³⁺ induces subtle second‑order Jahn‑Teller distortions, which lower the band gap and enhance the static dielectric constant. Indeed, the calculated high‑frequency dielectric constants increase from ~5.2 (As) to ~7.3 (Bi), reflecting stronger light‑matter coupling as the pnictogen becomes heavier.

Optical properties, obtained within the independent‑particle approximation using PBE wavefunctions, show a rapid rise in the absorption coefficient just above the band edge, reaching values >10⁴ cm⁻¹. The absorption onset lies in the visible range for Sb and Bi compounds, making them suitable for thin‑film photodetectors and solar cells. The static dielectric response follows the same As→Sb→Bi trend, which together with the moderate band gaps suggests efficient charge separation and reduced exciton binding.

Phonon dispersions calculated via density‑functional perturbation theory (DFPT) and processed with Phonopy demonstrate dynamical stability for Mg₃AsBr₃ and Mg₃SbBr₃ (no imaginary frequencies throughout the Brillouin zone). Mg₃BiBr₃ exhibits a small imaginary mode near Γ, hinting at a possible low‑temperature structural distortion. The overall phonon bandwidth narrows from ~8 THz (As) to ~5 THz (Bi), and the mode‑resolved Grüneisen parameters are large (average γ ≈ 2.7–3.2), indicating strong anharmonicity and soft lattice behavior. Such anharmonicity predicts low lattice thermal conductivity, beneficial for thermally stable optoelectronic operation.

Mechanical stability is confirmed by calculating the full elastic tensor at the PBE level and averaging via the Hill scheme. Bulk moduli decrease from ~44 GPa (Mg₃AsBr₃) to ~35 GPa (Mg₃BiBr₃), while shear moduli lie between 12–16 GPa. All Born criteria (C₁₁ − C₁₂ > 0, C₁₁ + 2C₁₂ > 0, C₄₄ > 0) are satisfied, indicating mechanical robustness despite the relatively soft nature of these halide perovskites. The moderate stiffness is advantageous for fabricating defect‑tolerant thin films on flexible substrates.

To assess device relevance, a one‑dimensional p‑i‑n diode (total thickness 1 µm) was modeled in COMSOL Multiphysics using a stationary drift‑diffusion formulation. Ohmic contacts were placed at the ends, and Gaussian dopant profiles (peak concentration 1 × 10²⁰ cm⁻³) defined the p‑ and n‑regions, leaving an intrinsic Mg₃ZBr₃ absorber. Carrier mobilities and recombination parameters were set according to the computed band gaps and dielectric constants. The simulated current–voltage curves show that the photocurrent is limited by the band‑edge absorption, with Mg₃SbBr₃ delivering the highest short‑circuit current density and the lowest reverse‑bias leakage, owing to its optimal 1.65 eV gap and relatively higher carrier mobility. The external quantum efficiency spectra derived from the simulations align closely with the calculated absorption edges, confirming that the theoretical optoelectronic properties translate into realistic device performance.

In summary, the Mg₃ZBr₃ series combines several desirable attributes: (i) non‑toxic constituent elements, (ii) thermodynamic and dynamical stability in the cubic perovskite framework, (iii) tunable indirect band gaps spanning the visible spectrum, (iv) strong light absorption and high dielectric constants, (v) pronounced anharmonic lattice dynamics that suppress thermal degradation, and (vi) sufficient mechanical stiffness for thin‑film processing. The drift‑diffusion simulations further validate that these materials can function as efficient absorbers in PIN photodiodes, positioning Mg₃AsBr₃, Mg₃SbBr₃, and especially Mg₃SbBr₃ as promising lead‑free candidates for next‑generation photovoltaic and photodetector technologies.