et al.. Bright-exciton splittings in inorganic cesium lead halide perovskite nanocrystals. AbstractSince their …rst synthesis in 2015, the all-inorganic lead halide perovskite nanocrystals CsPbX 3 (X = Cl, Br, I) have attracted a great attention due to their outstanding electronic and optical properties as well as their performances which outclass the ones of II-VI conterparts in many application …elds. In addition to these properties, the understanding of the emission features in these systems at the single object scale is crucial e.g. for nanophotonics and quantum optics devices. The details of the band-edge excitonic emission are here theoretically explored. The contribution of the long-range exchange interaction to the bright-exciton splittings is computed in strong and weak con…nement regimes by using the group theory and k.p arguments. We show that the shape anisotropy of a nanocrystal can also be at play with the crystalline (cubic, tetragonal or orthorhombic) structures to explain the emission properties. In the weak con…nement regime, splittings are inversely proportional to the cube of the exciton Bohr radius and we observe an increase of the splittings from iodide, to bromide, then chloride perovskite compounds. However, in the strong con…nement regime, splittings increase inversely proportional to the nanocrystal volume and, for a given nanocrystal size, the splitting values are comparable for the three halide perovskite materials. The present theoretical developments lead to quantitative contributions in good agreement with available experimental data mainly in the weak con…nement regime.

We investigate the theoretical band structure of organic− inorganic perovskites APbX 3 with tetragonal crystal structure. Using D 4h point group symmetry properties, we derive a general 16-band Hamiltonian describing the electronic band diagram in the vicinity of the wave-vector point corresponding to the direct band gap. For bulk crystals, a very good agreement between our predictions and experimental physical parameters, as band gap energies and effective carrier masses, is obtained. Extending this description to three-dimensional confined hybrid halide perovskite, we calculate the size dependence of the excitonic radiative lifetime and fine structure. We describe the exciton fine structure of cube-shaped nanocrystals by an interplay of crystal-field and electron−hole exchange interaction (short-and long-range parts) enhanced by confinement. Using very recent experimental results on FAPbBr 3 nanocrystals, we extract the bulk short-range exchange interaction in this material and predict its value in other hybrid compounds. Finally, we also predict the bright−bright and bright−dark splittings as a function of nanocrystal size.

A 40-band k⋅p model is used to compute the standard k⋅p band parameters at Γ, X, and L valleys in direct-band-gap bulk materials for Td group semiconductors. The values of the effective masses for electrons, heavy holes, and light holes in the Γ, X, and L valleys are in good agreement with those reported in other publications. Satisfactory agreement with available experimental data is also obtained by the present model. Finally, our results show that the effective Landé factor g∗, the κ valence band parameter, and the Dresselhauss spin-orbit coupling constant δ conicide well with available experimental data. The k⋅p Hamiltonian parameters, in particular, are adjusted to get g∗(GaAs)=−0.42, which turn out to be in agreement with the experimental value of −0.44.

We present a generalized theoretical description of the 24×24 k.p approach for determining the band structure of the direct-band-gap semiconductors (GaAs, InAs) as well as the indirect-band-gap semiconductor (Ge), including far-level contribution (essentially the d levels). We extend the sp3s* basis functions by the inclusion of sV* orbitals. We find that the sp3“d”(s*)2 k.p model is fairly sufficient to describe the electronic structure of these systems over a wide energy range, obviating the use of any d orbitals. Finally, the comparison with available experimental and theoretical results shows that the present model reproduces known results for bulk GaAs, InAs, and Ge, that is, their band structure, including s and p valence bands and the lowest two conduction bands.

The band structure of indirect-band gap semiconductors ͑AlAs, GaP͒ as well as indirect-band gap alloys semiconductors ͑GeSi͒ is described theoretically by using a 30ϫ 30 k ϫ p model including the d far-level contribution. For all materials investigated, the resulting electronic band structure parameters are in good agreement with experimental values. The method also provides a good description of the second conduction band which is useful for transport modeling. Finally, our results show that Luttinger parameters, the valence band parameter, and the effective masses in the X and L valleys are in good agreement with available experimental data.

We present a generalized theoretical description of the 30 × 30 k • p approach for determining the band structure of the direct-band-gap semiconductors (InAs, InP, InSb), including the d far-levels contribution. For all materials investigated, the resulting electronic band structure parameters are in good agreement with experimental values. This model gives access to the second conduction band which is useful for transport modelling. We finally show that this method also gives explicit expressions for the Luttinger parameters, the κ valence band parameter and the effective masses in the valley.

The band structure of direct-band-gap semiconductor (InAs) and indirect-band-gap semiconductor (Ge) is described theoretically using a 20×20 k.p model and including far-level contribution (essentially the d levels). By using this model, we obtained a quantitatively correct description of the top of the valence band and the lowest two conduction bands both in terms of energetic positions and band curvatures. In particular, the k.p Hamiltonian parameters are adjusted such that the transverse mass of the germanium conduction band is equal to the experimental value of 0.081.

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