Exciton Fine Structure in Perovskite Nanocrystals

Abstract

The bright emission observed in cesium lead halide perovskite nanocrystals (NCs) has recently been explained in terms of a bright exciton ground state [Becker et al. Nature 2018, 553, 189−193], a claim that would make these materials the first known examples in which the exciton ground state is not an optically forbidden dark exciton. This unprecedented claim has been the subject of intense experimental investigation that has so far failed to detect the dark ground-state exciton. Here, we review the effective-mass/electron−hole exchange theory for the exciton fine structure in cubic and tetragonal CsPbBr 3 NCs. In our calculations, the crystal field and the short-range electron−hole exchange constant were calculated using density functional theory together with hybrid functionals and spin−orbit coupling. Corrections associated with long-range exchange and surface image charges were calculated using measured bulk effective mass and dielectric parameters. As expected, within the context of the exchange model, we find an optically inactive ground exciton level. However, in this model, the level order for the optically active excitons in tetragonal CsPbBr 3 NCs is opposite to what has been observed experimentally. An alternate explanation for the observed bright exciton level order in CsPbBr 3 NCs is offered in terms of the Rashba effect, which supports the existence of a bright ground-state exciton in these NCs. The size dependence of the exciton fine structure calculated for perovskite NCs shows that the bright−dark level inversion caused by the Rashba effect is suppressed by the enhanced electron−hole exchange interaction in small NCs.

Size-Dependent Lattice Structure and Confinement Properties in CsPbI3 Perovskite Nanocrystals: Negative Surface Energy for Stabilization

“…The energy relative to the bandgap of the ground state in a cube-shaped NC in the weak confinement regime is then described as Eq. S19, 26 where the total exciton effective mass is Mx = me + mh:…”

“…This procedure is done numerically and is described in the literature. 26,27 Exciton energy versus size for parabolic bands…”

Quasicubic model for metal halide perovskite nanocrystals

“…In cubic phase metal halide perovskites (MHPs), the conduction and valence band edges are located at the R-point of the first Brilluoin zone [1], for which the point symmetry group is O h [2,11]. We first develop a model for the confined conduction and valence band levels of a MHP nanocrystal in terms of the multiband k·P theory developed for spherical nanocrystals [4,5].…”

Calculation of the biexciton shift in nanocrystals of inorganic perovskites

“…from which it follows that E X1 −Ē X = ∆ 10 /4, where ∆ 10 = E X1 − E X0 is the bright-dark FS splitting. (We are assuming that any FS in the bright state, which is due to nonspherical or noncubic symmetry-breaking interactions [30,[56][57][58], has been experimentally averaged.) For the biexciton, the configuration-averaged en-ergyĒ XX = E XX0 , since there is only one state.…”