Tunable Interlayer Delocalization of Excitons in Layered Organic-Inorganic Halide Perovskites

Abstract

Layered organic-inorganic halide perovskites exhibit remarkable structural and chemical diversity and hold great promise for optoelectronic devices. In these materials, excitons are thought to be strongly confined within the inorganic metal halide layers with interlayer coupling generally suppressed by the organic cations. Here, we present an in-depth study of the energy and spatial distribution of the lowest-energy excitons in layered organic-inorganic halide perovskites from first-principles many-body perturbation theory, within the GW approximation and the Bethe-Salpeter equation. We find that the quasiparticle band structures, linear absorption spectra, and exciton binding energies depend strongly on the distance and the alignment of adjacent metal halide perovskite layers. Furthermore, we show that exciton delocalization can be modulated by tuning the interlayer distance and alignment, both parameters determined by the chemical composition and size of the organic cations. Our calculations establish the general intuition needed to engineer excitonic properties in novel halide perovskite nanostructures.

Figure 1

Schematic representation of (a) Dion–Jacobson and (b) Ruddlesden–Popper models viewed along the inorganic layer and (c) an intermediate phase along the direction perpendicular to the inorganic layer. Interlayer distance D and alignment coordinates (X, Y) are represented in panels a–c. Alignment coordinates X and Y are defined in crystal coordinates and correspond to the in-plane projection of the vector connecting two closest Pb atoms from adjacent inorganic layers. (d) DFT/PBE band gaps for model layered perovskites with an interlayer distance of 11 Å, as a function of alignment coordinates X and Y. (e) Quasiparticle band gaps of layered perovskites as a function of interlayer distance and layer alignment for different structure types: RP models (blue triangles), intermediate models (yellow disks), and DJ models (red squares). Green data points with different shapes correspond to experimental structures in DJ alignment, and the orange triangle corresponds to an experimental structure with intermediate (0.21, 0.21) alignment.

Figure 2

(a) Quasiparticle band structures calculated from G₀W₀@PBE+SOC for DJ model perovskites with interlayer distances from 10 to 16 Å and for one intermediate model with alignment (0.2, 0.2) and an interlayer distance of 10 Å. (b) Atomic orbital contribution for the VBT (bottom half) and CBB (top half) of DJ model perovskites with interlayer distances of 10 and 16 Å (left and right, respectively) and one intermediate model with alignment (0.2, 0.2) and an interlayer distance of 10 Å (middle). (c) Squared modulus of the electron wave function corresponding to the VBT at high symmetry point A for DJ layered perovskites with interlayer distances of 10 and 16 Å (left and right, respectively) and an intermediate model with alignment (0.2, 0.2) and an interlayer distance of 10 Å (middle).

Figure 3

(a and b) Calculated imaginary part of the dielectric function for light polarization perpendicular to the inorganic layer and parallel to the inorganic layer, respectively, for layered perovskites with interlayer distances of 10 Å (red), 11 Å (yellow), and 15 Å (blue). Similar plots for different layer alignments and for experimental structures are reported in Figures S6 and S7. (c) Exciton binding energies computed from G₀W₀+BSE as a function of interlayer distance and layer alignment. The legend follows the same convention as in Figure 1e.

Figure 4

(a and b) Isosurfaces representing the out-of-plane and in-plane spatial distribution of the lowest-energy exciton for a model DJ structure with an interlayer distance of 10.5 Å. The hole position is fixed at the center Pb atom of the central layer, marked by the green points. A similar diagram is shown for a model DJ structure with an interlayer distance of 16 Å in Figure S8. In both (a) and (b) the Cs ions are removed for clarity and the lead-halide octahedra are represented by the grey squares. (c) Normalized one-dimensional ECF vs electron–hole relative position across layers, for DJ model structures with interlayer distances from 10 to 16 Å. (d) Average interlayer electron–hole separation as a function of the interlayer distance and layer alignment. The legend follows the same convention as in Figure 1e.