Electronic and Optical Properties of Silicon Nanocrystals: a Tight Binding Study

Abstract

From the theoretical point of view, the silicon nanocrystal physics still today is not a completely clear subject. While the quantum confinement effect has been recognized as the major cause of the photoluminescence, many doubts remain on the way in which the phenomenon takes place in real nanocrystals. This thesis is the result of a deep work in the understanding of the optical properties of silicon nanocrystals. A Tight Binding method has been used for studing the energy levels and the dielectric properties of spherical and ellipsoidal silicon nanocrystals. The method is very efficient, allowing the study of structures with more than 10000 atoms, and being able to reproduce with a great accuracy the Bulk Silicon dielectric function. The comparison with the experimental results shows that for Si nanocrystals the method works well, both for the energy gap and the absorption spectra prediction. The optical gap, the imaginary part of the dielectric function, the static dielectric function, and the radiative electron-hole recombination times have been calculated for a set of silicon spheres, on increasing their size. An interesting feature is the existence of an energy gap between the energy of the first transition and the threshold of the absorption cross section. This is an indication that the electronic features of the bulk silicon are always reflected into the silicon nanocrystal physics. A very nice confirmation of this trend is the k-space projection of the nanocrystal states, which gives a fair explanation of this phenomenon. Finally, the shape effects on the optical properties are shown. Several sets of ellipsoidal nanocrystals, with different sizes and shapes, have been analyzed, and the effects of the geometrical anisotropy on the polarization of the dielectric tensor is discussed.