Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states

Abstract

We present a theoretical analysis of the band-edge exciton structure in nanometer-size crystallites of direct semiconductors with a cubic lattice structure or a hexagonal lattice structure which can be described within the framework of a quasicubic model. The lowest energy exciton, eightfold degenerate in spherically symmetric dots, is split into five levels by the crystal shape asymmetry, the intrinsic crystal field ͑in hexagonal lattice structures͒, and the electron-hole exchange interaction. Transition oscillator strengths and the size dependence of the splittings have been calculated. Two of the five states, including the ground state, are optically passive ͑dark excitons͒. The oscillator strengths of the other three levels ͑bright excitons͒ depend strongly on crystal size, shape, and energy band parameters. The relative ordering of the energy levels is also heavily influenced by these parameters. The distance between the first optically active state and the optically forbidden ground exciton state increases with decreasing size, leading to an increase of the Stokes shift in the luminescence. Our results are in good agreement with the size dependence of Stokes shifts obtained in fluorescence line narrowing and photoluminescence experiments in CdSe nanocrystals. Mixing of the dark and bright excitons in an external magnetic field allows the direct optical recombination of the dark exciton ground state. The observed shortening of the luminescence decay time in CdSe nanoncrystals in a magnetic field is also in excellent agreement with the theory, giving further support to the validity of our model. ͓S0163-1829͑96͒05831-6͔

Electron–Phonon Coupling in CdSe/CdS Core/Shell Quantum Dots

“…60 In contrast, the resonance Raman-determined EPCs are nearly independent of these properties. 34,39 Accordingly, this seems unlikely to be a dominant source of EPC in CdSe QDs.…”

Photoluminescence Enhancement through Symmetry Breaking Induced by Defects in Nanocrystals

“…11 In wurtzite CdSe NCs, both the hexagonal crystal field and the NC shape asymmetry contribute to splitting the hole levels. 9,12 The reduction of the NC symmetry associated with these effects leads to an exciton fine structure consisting of five sublevels, and also activates the lowest ±1 exciton level. 9 Even so, the presence of the dark exciton dominates the PL.…”

“…9,12 The reduction of the NC symmetry associated with these effects leads to an exciton fine structure consisting of five sublevels, and also activates the lowest ±1 exciton level. 9 Even so, the presence of the dark exciton dominates the PL. The reduction of the spherical symmetry splits the four fold degenerate ground 1S 3/2 hole levels in spherical NCs into two spin sublevels separated by energy ∆: The lower, ±3/2, and the upper ±1/2, hole sublevels.…”

“…12 In elongated CdSe NCs, ∆ sh is negative and in small size NCs can lead to ∆ ax = 0 even if the NCs do not have a spherical shape. 9 These "quasi-spherical" NCs possess the optical properties of pure spherical NCs, and can have very long radiative decay time for the smallest NCs even at room temperatures.…”

Förster Coupling in Nanoparticle Excitonic Circuits

“…For a multi-band, inhomogeneous systems, care must be taken to conserve the current of the full (Bloch plus envelope) wave function at the material interfaces [18]. For strong confinement, one can sometimes ignore the electron-hole Coulomb interaction altogether (or treat it as a perturbation) [16,19]. Additionally, atomistic calculations at varying degrees of precision, have been carried out.…”