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

Abstract

The one-photon absorption cross section of nanocrystals (NCs) of the inorganic perovskite CsPbBr3 is studied theoretically using a multiband k⋅p envelope-function model combined with a treatment of intercarrier correlation by many-body perturbation theory. A confined exciton is described first within the Hartree-Fock (HF) approximation and correlation between the electron and hole is then included in leading order by computing the first-order vertex correction to the electron-photon interaction. The vertex correction is found to give an enhancement of the near-threshold absorption cross section by a factor of up to 4 relative to the HF (mean-field) value of the cross section, for NCs with an edge length L=9–12 nm (regime of intermediate confinement). The vertex-correction enhancement factors are found to decrease with increasing exciton energy; the absorption cross section for photons of energy ω=3.1 eV (about 0.7 eV above threshold) is enhanced by a factor of only 1.4–1.5 relative to the HF value. The k⋅p corrections to the absorption cross section are also significant; they are found to increase the cross section at an energy ω=3.1 eV by about 30% relative to the value found in the effective-mass approximation. The theoretical absorption cross section at ω=3.1 eV, assuming a Kane parameter EP=20 eV, is found to be intermediate among the set of measured values (which vary among themselves by nearly an order of magnitude) and to obey a power-law dependence σ(1)(ω)∝L2.9 on the NC edge length L, in good agreement with experiment. The dominant contribution to the theoretical exponent 2.9 is shown to be the density of final-state excitons. We also calculate the radiative lifetimes of the ground-state 1Se–1Sh exciton of NCs of CsPbBr3 and CsPbI3, finding an overestimate by a factor of up to about two (for EP=20 and 17 eV, respectively) compared to the available experimental data, which vary among themselves by about ±40%. The sources of theoretical uncertainty and the possible reasons for the discrepancies with experiment are discussed. The main theoretical uncertainty in these calculations is in the value of the Kane parameter EP.