Giant exciton-light coupling in large size semiconductor quantum dots
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Giant exciton-light coupling in large size semiconductor quantum dots Bernard Gil, Alexey V. Kavokin 1, Université de Montpellier II-Groupe d’Etude des Semiconducteurs – case courrier 074 – 34 095 Montpellier CEDEX 5 France 1-. LASMEA, UMR 6602, Université Blaise Pascal Clermont-Ferrand II, 24, Avenue des Landais, 63177 Aubière, France ABSTRACT: We investigate the strength of the coupling of the electronic states with the electromagnetic field in semiconductor nanospheres, taking into account the retardation effect. We show that the coupling strength is particularly strong: the bulk properties are so enhanced that the radiative decay time can reach some 30 picoseconds for quantum dots sizes of some 30 nm.
There is currently a renewed interest towards the investigation of semiconductor nanospheres for single photon emission. Many researchers have focused their attention in direction of the increase of carrier confinement with dot size. This gave the huge documentation that can be found dedicated to this topics in the scientific literature. In contrast with this, very few works deal with such objets larger than the exciton Bohr radius, and even less are dedicated to dots of size comparable with the wavelength of light in the semiconductor. When symmetry allows the coupling of the excited electronic states of a direct bandgap semiconductors with the radiation field, shining the crystal produces a more or less pronounced modification of its dielectric constant in the spectral region where a quantum of the radiation field can be absorbed by an exciton. In a bulk crystal, the efficiency of the light-matter interaction, characterized by the longitudinal-transverse splitting h ωLT is connected to the exciton oscillator strength f by the direct
2π he2 f proportionality relation: hωLT = , where ε b is the dielectric constant, V is εb m0 ω0 V the volume of the semiconductor, ω 0 is the exciton resonance frequency. Table 1 summarizes some of these quantities for some typical direct bandgap semiconductors1. For the sake of the completeness we also give the values of the exciton binding energies, of the Bohr radii aB, of the dielectric constant ε ∞, and the in vacuum values of the bandgap at 2K (expressed in nanometers). Coming now to the light-matter interaction issue in nanospheres, three different cases have to be distinguished. 1. In case of a nanosphere smaller than the Bohr diameter of the exciton 2aB, (due to the small value aB, one may deal with very small objects in the case of wide bandgap semiconductors), the oscillator strength is renormalized according to Ref. [2] as : 1 K = hωLTk 03 aB3 . (1) 6 2π Where k0 = is the wave vector of light at the exciton resonance frequency. K is a λ0 characteristic of the long-range exchange splitting of the exciton in a QD [3] and is
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also its radiative recombination rate. We note that the modification of the oscillator strength is proportional to the ratio between the volume of the exciton to the “volume” of the photon. 2. In the second case where the nanospher
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