Electronic and optical properties of silicon nanocrystals are calculated and discussed within a semiempirical tight-binding approach, which allows to study systems composed of thousands of atoms. Oscillator strengths, frequency-dependent optical absorption cross sections, and static dielectric constants are investigated for both spherical and ellipsoidal nanocrystals, with the aim of pointing out their size- and shape-dependent features. We show that the anisotropy of the optical functions follows the nanocrystal shape, and a comparison is discussed between very elongated structures and quantum wires
T h e present status of the theory of the electronic states of crystals containing point defects in small concentration is reviewed and its application to the case of semiconductors is discussed. T h e basic properties of scattering and resonant and bound states are related to the band structure of the semiconductor making use of different representations (Bloch, Wannier and Kohn-Luttinger). T h e form of the impurity potentials and the effect of the dielectric screening are also discussed. Applications to the cases of donor, acceptor and isoelectronic impurities are described, making use of the effective mass approximation and taking into account interband mixing and central cell corrections. Deep levels are also discussed. Existing calculations are reviewed and compared with some of the experimentally known levels. Optical processes involving transitions between all types of electronic levels are described and experimental evidence for them is reported both in absorption and in emission (luminescence). Effects of external perturbations like uniaxial pressure, electric and magnetic fields are finally examined and are related to existing experiments.
We study the motion of a particle confined in an ellipsoidal quantum
dot, solving the corresponding Schrödinger equation both
numerically, using the appropriate coordinate system, and
variationally. The results from the two methods are compared,
varying the ellipsoid semi-axes. We find that the confined-state
energies split with respect to those of the spherical quantum dot
and this can be explained as a consequence of both a volume-induced
deformation effect and a geometry-induced one. The role of the dot
geometry is shown to be relevant also for the formation of
topological surface states.
We investigate the effects of constraining the motion of atoms in finite slabs used to simulate the rutile TiO2 (110) surface in first-principles calculations. We show that an appropriate choice of fixing atoms in a slab eliminates spurious effects due to the finite size of the slabs, leading to a considerable improvement in the simulation of the (110) surface. The method thus allows for a systematic improvement in convergence in calculating both geometrical and electronic properties. The advantages of this approach are illustrated by presenting the first theoretical results on the displacement of the surface atoms in agreement with experiment.
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