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 ${\mathrm{CsPbBr}}_{3}$ and ${\mathrm{CsPbI}}_{3}$. The calculations use an envelope-function $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ 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 ${\mathrm{CsPbBr}}_{3}$ and ${\mathrm{CsPbI}}_{3}$ 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 ${\mathrm{CsPbBr}}_{3}$ 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 ${\mathrm{CsPbBr}}_{3}$, which vary from large redshifts of order 100 meV to blueshifts of several meV.