Calculation of the biexciton shift in nanocrystals of inorganic perovskites

Abstract

We calculate the shift in emission frequency of the trion and biexciton (relative to that of the single exciton) for nanocrystals (NCs) of inorganic perovskites CsPbBr3 and CsPbI3. The calculations use an envelope-function k · p model combined with self-consistent Hartree-Fock and a treatment of the intercarrier correlation energy in the lowest (second) order of many-body perturbation theory. The carriers in the trion and biexciton are assumed to have relaxed nonradiatively to the ground state at the band edge before emission occurs. The theoretical trion shifts for both CsPbBr3 and CsPbI3 are found to be in fair agreement with available experimental data, which include low-temperature single-dot measurements, though are perhaps systematically small by a factor of order 1.5, which can plausibly be explained by a combination of a slightly overestimated dielectric constant and omitted third-and higher-order terms in the correlation energy. Taking this level of agreement into account, we estimate that the ground-state biexciton shift for CsPbBr3 is a redshift of order 10-20 meV for NCs with an edge-length of 12 nm. This value is intermediate among the numerous high-temperature measurements on NCs of CsPbBr3, which vary from large redshifts of order 100 meV to blueshifts of several meV.

One-photon absorption by inorganic perovskite nanocrystals: A theoretical study

“…In fact, as discussed in Ref. [27], the energies of noninteracting excited nS and nP states in the sphere of radius R also agree closely, to within a few percent, with the energies of the analogous "S-like" and "P-like" states [28] in the cube of edge length L.…”

“…The above choice of R ensures that the ground-state eigenvalue for noninteracting electrons in the cube and the sphere is the same [12,27]. In fact, as discussed in Ref.…”

“…In Ref. [27], it is shown that the first-order Coulomb energy for the ground-state exciton differs between the sphere and the cube by only about 1.5%. Moreover, the interband matrix element for the radiative decay of a single exciton depends on a simple overlap of the electron and hole envelope functions [20,29] (see also Appendix A).…”

“…The first step in the many-body procedure is to solve the self-consistent HF equations including exact exchange [25,33] for the spherical 4 × 4 k • p model [27]. The single-particle basis states of the many-body procedure (Sec.…”

“…The HF potential here is defined as in Ref. [27] via a configuration average. With this definition, the HF potential for the excited electron states is due entirely to the 1S h state, while that for the excited hole states is due entirely to the 1S e state.…”