Mechanical Stability and Energy Gap Evolution in Cs-Based Ag, Bi Halide Double Perovskites under High Pressure: A Theoretical DFT Approach

Abstract

Due to their intrinsic stability and reduced toxicity, lead-free halide double perovskite semiconductors have become potential alternatives to lead-based perovskites. In the present study, we used density functional theory simulations to investigate the mechanical stability and band gap evolution of double perovskites Cs₂AgBiX₆ (X = Cl and Br) under an applied pressure. To investigate the pressure-dependent properties, the hydrostatic pressure induced was in the range of 0-100 GPa. The mechanical behaviors indicated that the materials under study are both ductile and mechanically stable and that the induced pressure enhances the ductility. As a result of the induced pressure, the covalent bonds transformed into metallic bonds with a reduction in bond lengths. Electronic properties, energy bands, and electronic density of states were obtained with the hybrid HSE06 functional, including spin-orbit coupling (HSE06 + SOC) calculations. The electronic structure study revealed that Cs₂AgBiX₆ samples behave as X-Γ indirect gap semiconductors, and the gap reduces with the applied pressure. The pressure-driven samples ultimately transform from the semiconductor to a metallic phase at the given pressure range. Also, the calculations demonstrated that the applied pressure and spin-orbit coupling of the states pushed VBM and CBM toward the Fermi level which caused the evolution of the band gap. The relationship between the structure and band gap demonstrates the potential for designing lead-free inorganic perovskites for optoelectronic applications, including solar cells as well as X-ray detectors.

Figure 1

(a) Crystal structure of the Cs₂AgBiX₆ (X = Cl and Br) double perovskite unit cells generated using Vesta tool. (b) Energy–volume plot for Cs₂AgBiCl₆ and (c) energy–volume plot for Cs₂AgBiBr₆.

Figure 2

Variation of lattice constants with the induced pressure.

Figure 3

Total energy of Cs₂AgBiCl₆ in Fm3̅m phase as a function of the strain parameter δ. (a) Bulk modulus, (b) pure shear elastic constant, C₄₄, and (c) tetragonal shear constant, C₁₁ – C₁₂.

Figure 4

Display of the total energy of Cs₂AgBiBr₆ in Fm3̅m phase as a function of strain parameter δ. (a) Bulk modulus, (b) pure shear elastic constant, C₄₄, and (c) tetragonal shear constant, C₁₁–C₁₂.

Figure 5

Effect of induced pressure on the elastic moduli of (a) Cs₂AgBiCl₆ and (b) Cs₂AgBiBr₆.

Figure 6

Band structure of Cs₂AgBiBr₆ at (a) 0 GPa, (b) 10 GPa, (c) 20 GPa, and (d) 30 GPa pressure. Spin–orbit coupling (SOC) was taken into account when calculating the band structure and density of states of the perovskites. The evolution of the small direct bands compared to indirect ones was observed as a result of the applied pressure. However, the fundamental band gap is still indirect.

Figure 7

Band structure of the Cs₂AgBiCl₆ halide double perovskite calculated at (a) 0 GPa, (b) 20 GPa, (c) 40 GPa, and (d) 60 GPa pressure. The low-energy direct band transitions and narrowing of the energy gap with the applied induced pressure can be visualized clearly from the plots.

Figure 8

Band structure displaying the metallic character of the perovskites (a) Cs₂AgBiBr₆ and (b) Cs₂AgBiCl₆ at 50 and 100 GPa, respectively.

Figure 9

Graph showing the total density of states simulated with SOC along with the contribution from the most dominant orbitals in the band formation of the Cs₂AgBiBr₆ halide double perovskite at the given applied pressures.

Figure 10

Graph showing the total density of states simulated with SOC along with the contribution from the most dominant orbitals in the band formation of the Cs₂AgBiCl₆ halide double perovskite at the given applied pressures.

Figure 11

pDOS of Cs₂AgBiBr₆ perovskite in the Fm3̅m phase at 0 GPa. (a) Cs-atom, (b) Ag-atom, (d) Bi-atom, and (d) Br-atom.

Figure 12

pDOS) of Cs₂AgBiCl₆ perovskite in the Fm3̅m phase at 0 GPa. (a) Cs-atom, (b) Ag-atom, (c) Bi-atom, and (d) Cl-atom.

Figure 13

Molecular orbital diagrams of the two investigated perovskites. Thick black lines indicate the atomic single-electron energies, while blue and green rectangles, respectively, illustrate the Bi-halide and Ag-halide hybrid bands. The orange color rectangles display the bands produced in Cs₂BiAgCl₆ and Cs₂BiAgBr₆ perovskites. Rectangles that are filled or left unfilled show the valence and conduction bands, respectively. All the bands were aligned with the Bi-5d_1/2 energy level.

Figure 14

Band gap evolution in Cs₂AgBiBr₆ and Cs₂AgBiCl₆ perovskite structures with pressure.