Since the exciton is located just below the conduction-band energy, the Gaussian tail of the exciton transition determines the shape of the absorption edge. This is further broadened in the samples studied in Fig. 5.14, since there is a dependence of the exciton energy on particle size and the samples measured have a size distribution of about 30% of the average size quoted in the figure. In a real crystal, the line is broadened by structural defects and acquires an inhomogeneous (Gaussian) line shape with a much larger width (100–200 meV). Note the gradual loss of distinction of the exciton peaks as the quantum dots shrink to the size of the exciton Bohr diameter (8 nm). The different curves correspond to crystals of different sizes, as marked. These transitions change the nature of the absorption edge and give it a Gaussian shape. The peaks near the absorption edge are due to exciton transitions. Absorption data at 10 K for CdS xSe 1– x quantum dots. However, in strongly ionic crystals, such as alkali halides, a self-trapping of holes at exciton formation takes place which leads to an essential deviation from the hydrogen-like model.įigure 5.14.
#Bose freespace free#
In the case of weak electron–phonon interaction, both the electron and the hole can be considered as free particles which results in the hydrogen-like spectrum of exciton energies with a large number of excited states. In this model, the exciton is considered as an electron–hole pair bound by a Coulomb interaction. For semiconductor crystals with covalent or slightly ionic bonding, a better description of excitons is given by another model proposed by G Wannier and N Mott. The Frenkel model is a good approximation for molecular crystals with van der Waals bonding, where the exciton is well localized within one molecule. There is a variety of intermediate cases, when the exciton motion can be described either as a hopping process or by a strong scattering regime. In the opposite case, the exciton strongly polarizes the crystal lattice, and self-trapping of the exciton occurs. In the limits of a weak interaction, the exciton can be considered as a free particle with a well-defined wave vector and kinetic energy. The character of exciton motion depends on the strength of the exciton interaction with phonons. So, the excitons play a significant role in most of the photoconductivity and light emission processes. Due to the translation symmetry of the crystal, the exciton can move along the lattice sites transferring the energy to the electrically active or luminescence centers.
In the Frenkel model, the exciton is considered as an electronic excitation of one crystal site with the energy close to, but a bit smaller than that necessary for the excitation of a free electron.
Originally, the concept of excitons was introduced by Ya I Frenkel in 1931 to explain the light absorption in crystals which does not lead to photoconductivity. A characteristic feature of excitons is that their formation (e.g., at optical excitation) does not lead to the separation of carriers, so that the excitons are electrically neutral excitations. Permogorov, in Encyclopedia of Condensed Matter Physics, 2005 IntroductionĮxcitons represent a wide class of intrinsic electronic excitations in crystals of semiconductors and dielectrics.
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