Effects of Halogen Substitution on the Optoelectronic Properties of Two-Dimensional All-Inorganic Double Perovskite ${\mathrm{Cs}}_4\mathrm{Ag}\mathrm{Bi}{X}_8$ ($X=\mathrm{Cl},\mathrm{Br},\mathrm{I}$) with Ruddlesden-Popper Structure

Due to the influence of dimension, two-dimensional (2D) all-inorganic double perovskites may be superior to their three-dimensional (3D) counterparts as environmentally friendly and efficient optoelectronic materials. Nevertheless, how the halogens affect the optoelectronic performance of 2D all-inorganic double perovskite is still unknown. Here, the photoelectric properties, including band structures, optical absorption spectra, carrier mobilities, and exciton binding energies, of 2D all-inorganic double perovskites ${\mathrm{Cs}}_4\mathrm{Ag}\mathrm{Bi}{X}_8$ ($X$ = $\mathrm{Cl}$, $\mathrm{Br}$, $\mathrm{I}$) with the Ruddlesden-Popper structure are studied via density-functional theory along with the spin-orbit coupling effect. Considering the influence of the exciton effect in low-dimensional materials, we also calculate light absorption by using the GW Bethe-Salpeter equation method. The obtained results show that the substitution of $\mathrm{Cl}$ with $\mathrm{Br}$ or $\mathrm{I}$ atoms decreases the band gap (from 2.706 eV to 2.221 and 1.715 eV) for ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Cl}}_8$, enhances the light-absorption performance, increases the mobility of carriers, and reduces the exciton binding energy (from 1529.90 meV to 1268.70 and 941.71 meV). Moreover, the outcomes demonstrate that 2D all-inorganic double perovskites ${\mathrm{Cs}}_4\mathrm{Ag}\mathrm{Bi}{X}_8$ ($X$ = $\mathrm{Cl}$, $\mathrm{Br}$, $\mathrm{I}$) might be better candidates for luminescent devices than photovoltaic materials, and the excellent performance of ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{I}}_8$ makes it the optimal among the three. Our study will expand theoretical explorations for research into 2D all-inorganic double perovskite materials for potential luminescent or photovoltaic applications.

Figure 1

(a) Atomic model of 2D all-inorganic double perovskite ${\mathrm{Cs}}_4\mathrm{Ag}\mathrm{Bi}{X}_8$ ($X$ = $\mathrm{Cl}$, $\mathrm{Br}$, $\mathrm{I}$). Layers are connected by van der Waals forces. (b) Top view of 2D all-inorganic double perovskite ${\mathrm{Cs}}_4\mathrm{Ag}\mathrm{Bi}{X}_8$ ($X$ = $\mathrm{Cl}$, $\mathrm{Br}$, $\mathrm{I}$).

Figure 2

Band structures of 2D all-inorganic double perovskite (a),(d),(g) ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Cl}}_8$; (b),(e),(h) ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Br}}_8;$ and (c),(f),(i) ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{I}}_8$ using PBE, PBE +SOC, and HSE + SOC methods. Inset in (a) shows the first Brillouin zone of the 2D all-inorganic double perovskite, ${\mathrm{Cs}}_4\mathrm{Ag}\mathrm{Bi}{X}_8$ ($X$ = $\mathrm{Cl}$, $\mathrm{Br}$, $\mathrm{I}$), and the k path for band-structure calculations.

Figure 3

Comparison of band gaps of 2D all-inorganic double perovskite ${\mathrm{Cs}}_4\mathrm{Ag}\mathrm{Bi}{X}_8$ ($X$ = $\mathrm{Cl}$, $\mathrm{Br}$, $\mathrm{I}$) obtained through PBE, HSE06, PBE + SOC, and HSE + SOC methods.

Figure 4

PDOS calculated via the PBE + SOC method for 2D all-inorganic double perovskites (a) ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Cl}}_8$, (b) ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Br}}_8,$ and (c) ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{I}}_8$. Inset in (c) is the locally magnified detail of the curve around the Fermi level.

Figure 5

(a) TDOS calculated by the PBE + SOC method for ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Cl}}_8$, ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Br}}_8,$ and ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{I}}_8$. Inset shows the locally magnified detail of the curve around the Fermi level. $\mathrm{Cl}$, $\mathrm{Br},$ and $\mathrm{I}$ contributions calculated at the PBE + SOC level for ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Cl}}_8$, ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Br}}_8,$ and ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{I}}_8$ (b) valence and (c) conduction bands.

Figure 6

Optical absorption spectrum calculated with the PBE + SOC method for 2D all-inorganic double perovskites ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Cl}}_8$, ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Br}}_8,$ and ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{I}}_8$.

Figure 7

Band-edge positions of conduction band and valence band with respect to lattice deformation along (a)–(c) a direction and (d) –(f) b direction for ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Cl}}_8$, ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Br}}_8,$ and ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{I}}_8$ at the PBE + SOC level. (g)–(i) Total energy related to lattice deformation along a and b directions for ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Cl}}_8$, ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Br}}_8,$ and ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{I}}_8$ at the PBE + SOC level.

Figure 8

Comparison of calculated (a) effective masses, m*; (b) DP constants; (c) carrier mobilities; and (d) elastic modulus, C_2D, along the a and b directions for 2D all-inorganic double perovskites ${\mathrm{Cs}}_4\mathrm{Ag}\mathrm{Bi}{X}_8$ ($X$ = $\mathrm{Cl}$, $\mathrm{Br}$, $\mathrm{I}$).

Figure 9

Comparison of exciton binding energy, E_b, of 2D all-inorganic double perovskites ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Cl}}_8$, ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{Br}}_8,$ and ${\mathrm{Cs}}_4{\mathrm{Ag}\mathrm{Bi}\mathrm{I}}_8$ with and without SOC.