Zero-dimensional excitons

Brus L. (1986), Zero-dimensional excitons in semiconductor clusters , IEEE J. Quantum Electron. 22, 1909-1914. 

Y. Terai, S. Kuroda, K. Takita, T. Okuno, Y. Masumoto, Zero-Dimensional Excitonic Properties of Self- Organized Quantum Dots of CdTe Grown by Molecular Beam Epitaxy, Applied Physics Letters, 73 (1998), Article ID. 3757. doi 10.1063/1.122885. 

On the hybridization of zero-dimensional Frenkel and Wannier Mott excitons... 

In the previous sections we have considered the hybridization of Frenkel and Wannier-Mott excitons in two-dimensional (quantum wells) and one-dimensional (quantum wires) geometries. For the sake of completeness, in this subsection we shall briefly and qualitatively discuss the zero-dimensional (0D) case that corresponds to a quantum dot geometry. We have in mind a configuration where a semiconductor QD is located near a small size organic cluster or is just covered by a thin shell of an organic material. 

Interestingly the formation of excitons in nanoparticles stabilized on thin films -a basic cluster formation process in thin film physics - leads to the creation of quantum dots, i.e. quasi-zero dimensional structures that confine carriers in all the three spatial dimensions, thereby enhancing applicable phenomena such as light emission and gas sensing. 

Matrix-stabilized (glass, NaCl) CuCl nanocrystals is a typical zero-dimensional material, which constitutes a quantum dot system in which excitons are weakly confined [4]. Small angle X-ray scattering study has established that the resultant... 

Zero-dimensional defects or point defects conclude the list of defect types with Fig. 5.87. Interstitial electrons, electron holes, and excitons (hole-electron combinations of increased energy) are involved in the electrical conduction mechanisms of materials, including conducting polymers. Vacancies and interstitial motifs, of major importance for the explanation of diffusivity and chemical reactivity in ionic crystals, can also be found in copolymers and on co-crystallization with small molecules. Of special importance for the crystal of linear macromolecules is, however, the chain disorder listed in Fig. 5.86 (compare also with Fig. 2.98). The ideal chain packing (a) is only rarely continued along the whole molecule (fuUy extended-chain crystals, see the example of Fig. 5.78). A most common defect is the chain fold (b). Often collected into fold surfaces, but also possible as a larger defect in the crystal interior. Twists, jogs, kinks, and ends are other polymer point defects of interest. 

Nanoclusters cannot be considered as infinite arrays of atoms and molecules. They represent a new class of materials with hybrid molecular-solid state properties. There is clear evidence that nanoclusters can exhibit structure and properties quite distinct from those of bulk systems. These clusters might be termed quantum dots (QDs) that is, an electron or exciton can be confined in zero-dimensional space. 

The macroscopical surface excitons obtained when retardation is taken into account, i.e. surface polaritons, cannot spontaneously transform into bulk emitted photons. Therefore, surface polaritons are sometimes said to have zero radiation width (it goes without saying that a plane boundary without defects it implies). At the same time the Coulomb surface excitons and polaritons in two-dimensional crystals possess, as was shown in Ch. 4, the radiation width T To(A/27ra)2, where A is the radiation wavelength, a is the lattice constant, and To the radiative width in an isolated molecule. For example, for A=500 nm and a = 0.5 nm the factor (A/2-7Ta)2 2x 104, which leads to enormous increase of the radiative width. For dipole allowed transitions To 5x10 " em, so that the value of T 10 cm-1 corresponds to picosecond lifetimes r = 2-kK/T x, 10 12s. 

To calculate the effective transition dipole moment we need to know the wave-function of the exciton. In a quantum dot it depends on two interactions (i) the electron and hole confinement potential, which we shall assume to be infinite for r > Ri and zero for r < f i and (ii) the electron and hole Coulomb attraction. For these interactions we have to consider the following characteristic lengths f i - the radius of the quantum dot, and ag - the Bohr radius of an exciton in a macroscopic three-dimensional semiconductor. The problem of solving the two-particle Schrodinger equation for an arbitrary ratio of these lengths is quite difficult but the situation simplifies substantially in two important limiting cases. 

Unusual magnetic and electrical properties might also arise from quasi one-dimensional crystal structures of these compounds. The acceptor stacks /especially TCNQ/ may be either regular, i, e. with equally spaced molecules, or alternating when composed of diads, triads or tetrads. In the latter case some substances exhibit EPR spectrum characteristic of mobile, thermally activated triplet states /triplet excitons/, The spectrum may result from the excitation of two or more coupled TCNQ entities /6, 7/. The triplet character of the paramagnetic excitation is shown by the anisotropic two-lines EPR spectrum which results from a zero field splitting of the triplet levels being described by the spin Hamiltonian /8/j... 

Owing to the crystal structure, the excitons are one-dimensional. The solid line is an image of the dispersion curves of the triplet exciton bands of the two triplet components between which the zero-field ESR transition was induced. After [7]. 

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