Origin of anomalous band-gap bowing in two-dimensional tin-lead mixed perovskite alloys

The origin of the pronounced and composition-dependent band-gap bowing in Sn/Pb mixed perovskite alloys has been under debate for a long time. Previous studies reported conflicting results on whether the chemical or structural effect is the dominant mechanism. In this paper, the band-gap bowing effect and its possible origins in recently synthesized two-dimensional (2D) ${\mathrm{Cs}}_2{\mathrm{Pb}}_x{\mathrm{Sn}}_{1\text{−}x}{\mathrm{I}}_2{\mathrm{Cl}}_2$ alloys are investigated from first-principles calculations. In agreement with experiments, a large and composition-dependent bowing coefficient is observed. By analyzing the contribution from volume deformation, charge exchange, structural relaxation, and short-range order, it is found that the dominant mechanism causing the anomalous gap bowing is the structural relaxation-induced wave-function localization, forming isovalent-defect-like states, despite the negligible octahedral distortion and small lattice mismatch between the two end compounds. This is understood by the s-p repulsion-induced strong antibonding character of the valence-band maximum which leads to a large deformation potential, thus even a small atomic displacement can result in a large shift of the energy level. These results thus highlight the critical role of strong deformation potential and structural relaxation effect in unusual band evolution of 2D Sn/Pb perovskite alloys, and can be helpful to the modulation of their band gap for optoelectronic applications.

Figure 1

Structures for side (a) and top (b) view, band structures (c), band alignment relative to the vacuum level of monolayer ${\mathrm{Cs}}_2\mathrm{Pb}\left(\mathrm{Sn}\right){\mathrm{I}}_2{\mathrm{Cl}}_2$ (d), and the charge densities of CBM and VBM (wave function norm square) (e). Cyan, green, purple, blue, and red balls representing Cs, Cl, I, Pb, and Sn atoms, respectively.

Figure 2

Band gap and bowing parameters (a) and band edge energy (b) of 2D ${\mathrm{Cs}}_2{\mathrm{Pb}}_x{\mathrm{Sn}}_{1\text{−}x}{\mathrm{I}}_2{\mathrm{Cl}}_2$ alloys as functions of Pb concentration. Band edge energy is aligned relative to the vacuum level.

Figure 3

The charge densities of CBM (a) and VBM (b) of 2D ${\mathrm{Cs}}_2{\mathrm{Pb}}_x{\mathrm{Sn}}_{1\text{−}x}{\mathrm{I}}_2{\mathrm{Cl}}_2$ alloys for different Pb concentrations ($x$); Cs and I atoms are omitted to show the distribution of Sn and Pb atoms more clearly.

Figure 4

Band gap bowing parameters (a) and bond length (b) of 2D ${\mathrm{Cs}}_2{\mathrm{Pb}}_x{\mathrm{Sn}}_{1\text{−}x}{\mathrm{I}}_2{\mathrm{Cl}}_2$ alloys as functions of Pb concentration. (c), (d) The charge densities of VBM of 2D ${\mathrm{Cs}}_2{\mathrm{Pb}}_x{\mathrm{Sn}}_{1\text{−}x}{\mathrm{I}}_2{\mathrm{Cl}}_2$ alloys for unrelaxed and relaxed structure at Pb concentration $=0.984$.

Figure 5

(a) Normalized formation energy (NFE) of 2D ${\mathrm{Cs}}_2{\mathrm{Pb}}_x{\mathrm{Sn}}_{1\text{−}x}{\mathrm{I}}_2{\mathrm{Cl}}_2$ alloys for different Pb concentrations. (b) Fitted ECIs for pairs from the nearest to the sixth neighbors.