Ag Intercalation in Layered Cs3Bi2Br9 Perovskite for Enhanced Light Emission with Bound Interlayer Excitons

Cesium bismuth bromide (CBB) has garnered considerable attention as a vacancy-ordered layered perovskite with notable optoelectronic applications. However, its use as a light source has been limited due to its weak photoluminescence (PL). Here, we demonstrate metal intercalation as a novel approach to engineer the room-temperature PL of CBB using experimental and computational methods. Ag, when introduced into CBB, occupies vacant sites in the spacer region, forming octahedral coordination with surrounding Br anions. First-principles density functional theory calculations reveal that intercalated Ag represents the most energetically stable Ag species compared to other potential forms, such as Ag substituting Bi. The intercalated Ag forms a strong polaronic trap state close to the conduction band minimum and quickly captures photoexcited electrons with holes remaining in CBB layers, leading to the formation of a bound interlayer exciton, or BIE. The radiative recombination of this BIE exhibits bright room-temperature PL at 600 nm and a decay time of 38.6 ns, 35 times greater than that of free excitons, originating from the spatial separation of photocarriers by half a unit cell separation distance. The BIE as a new form of interlayer exciton is expected to inspire new research directions for vacancy-ordered perovskites.

Table S2.Concentrations of silver species in disordered CBB.

Exciton binding energy.
We used the following Arrhenius function to calculate the exciton binding energy of the Ag-CBB sample:  () = (0)/(1 +  exp (  / B ) ) I(T) and I(0) are the integrated photoluminescence intensity at a given temperature, T, and 0 K, respectively, Eb is the exciton binding energy, and kB is the Boltzmann constant.

Defect formation energies.
Defect formation energies  form are calculated using the equation 1 : Here,   represents a defect in charge state .(  ) is the total energy of a supercell containing   , and  bulk is the total energy of the pristine (defect-free) supercell.|  | is the number of atoms of species  removed (  > 0) or added (  < 0) from the supercell to create the defect, and   are the corresponding chemical potentials.  form is exponentially related to the defect concentration  as follows: sites is the site-concentration of defects in the unit cell,  B is Boltzmann's constant, and  is the temperature.It follows that lower formation energies lead to exponentially higher concentrations, so the chemistry of the system will largely be unaffected by high-energy defects.
When calculating defect formation energies initially, we treat   as a free variable, meaning that formation energies are plotted as lines with slope  on the axes   -vs- form .However, the actual   will be determined by the requirement that the overall system must be charge neutral.To a good approximation,   will thus be located at the intersection point of the lowest-energy positively and negatively charged defects.For Ag-CBB, under most relevant chemical potential conditions, the positive charge of each Ag  + is balanced by the negative charge of  Cs − , thereby positioning   approximately 1.25 eV above the VBM at the intersection of the red and blue curves in Fig. 3.This implies that the probable chemical formulation of Ag-CBB would be AgxCs3-xBi2Br9, where x denotes the concentration of Ag dopants, assuming that Ag  + is the sole species of Ag present.We refrain from explicitly using this chemical formula, however, to prevent any misunderstanding that Ag directly substitutes onto the Cs sites.
For many defects, the preferred charge state may vary with respect to   , resulting in charge-state transition levels within the band gap.Such defects are often relevant for the absorption and emission of carriers.To analyze these species in more detail, we construct configuration coordinate diagrams, 4 for which we used tools from the Nonrad Python package. 5 relax defects, it is generally necessary to break the crystal symmetry.However, the ordered crystal structure of CBB, which is stable at room temperature, is dynamically unstable at 0 K; thus, introducing defects and breaking the symmetry can result in unphysical lattice distortions even beyond the immediate vicinity of the defect.Because we are primarily concerned with properties of the Ag impurity at finite temperature, we therefore choose to restrict lattice distortions when calculating defects in the ordered structure.For comparison, we have also calculated defects in the ground state, disordered structure of CBB, which is 50 meV per formula unit lower in energy than the ordered structure at 0 K.The formation energies are generally consistent across the two structures, giving us confidence that our defect calculations in the ordered structure are accurate.

Chemical potentials
Chemical potentials are chosen to ensure the stability of CBB relative to various limiting phases.
The chemical potentials are related to deviations Δ  from the energies of elemental ground states (bcc Cs, rhombohedral Bi, fcc Ag, and diatomic Br2) as follows: To prevent these elemental phases from precipitating, we require that each Δ  ≤ 0. In addition, to ensure the thermodynamic stability of CBB, these deviations are related to its enthalpy of formation: Other phases may form in certain chemical potential regimes, most notably the binary compounds CsBr and BiBr3 (we have considered other compounds as well, but their formation will not be less likely).To prevent CsBr from precipitating, we require that: and to prevent the formation of BiBr3, we require that: Δ Bi + 3Δ Br ≤ Δ  (BiBr 3 ).
We can use the thermodynamic stability condition to reduce the overall stability region to two dimensions, which we arbitrarily chose to express in terms of Δ Bi and Δ Br .After solving for Δ Cs in terms of the other two chemical potentials, we rewrite the condition to prevent CsBr precipitation as: (Δ  (Cs 3 Bi 2 Br 9 ) − Δ  (CsBr)).
Our stability diagram is shown in Fig. S4.Various chemical potential regions of interest are labeled, and the precise chemical potentials are listed in Table S1.These can provide insights into defect formation under varieties of synthesis conditions.For the purposes of presentation, we will limit our discussion to intermediate chemical potentials in the main text.S1.

Figure S1 :
Figure S1: Crystal structure.Unit cell of CBB with different orientations.

Figure
Figure S2: X-ray diffraction comparison with precursors.

Figure S4 :
Figure S4: Morphology and composition of CBB

Figure S10 .
Figure S10.Formation energies of native point defects and silver impurities under a range of chemical potentials for disordered CBB.

Figure S1 :
Figure S1: Crystal structure.Unit cell of CBB with different orientations.

Figure S2 :
Figure S2: X-ray diffraction comparison with precursors.Comparison of experimental Ag-CBB

Figure S4 :
Figure S4: Morphology and composition of CBB.SEM image and elemental maps of undoped

Figure S5 :
Figure S5: Morphology of Ag-CBB nanowires (NWs): SEM images of Ag-CBB; scale bar, 25 m (A), 5 m (B) and 1 m (C).The magnified images from A in panel C show the edge of the NWs having hexagonal symmetry with elongation by giving extended reaction time, giving rise to the NW morphology.

Figure S6 :
Figure S6: EDS of Ag-CBB.(A) HAADF images of the nanorod particle including the four

Figure S7 :
Figure S7: Band gap measurements.Tauc plots of CBB and Ag-CBB showing obtained band

Figure S9 .
Figure S9.Thermodynamic stability of CBB.Chemical stability diagram for CBB, based on

Figure S10 .
Figure S10.Formation energies of native point defects and silver impurities under a range of

Table S1 .
Chemical potential conditions for CBB.Chemical potential values corresponding to the labeled points in Fig.S4.Ag chemical potentials correspond to the solubility limit of Agcontaining secondary phases.

Table S2 .
Concentrations of silver species in disordered CBB.Calculated Fermi level (  ) position and corresponding concentrations of silver species (intercalated silver: Ag  + ;substitutional silver on a cesium site: Ag Cs 0 ; and substitutional silver on a bismuth site: Ag Bi  ) at different chemical potential conditions identified in Fig.S4and TableS1.