Silicon nanocrystals (NCs) represent one of the most promising material systems for light emission applications in microphotonics. In recent years, several groups have reported on the observation of optical gain or stimulated emission in silicon NCs or in porous silicon (PSi). These results suggest that silicon-NC-based waveguide amplifiers or silicon lasers are achievable. However, in order to obtain clear and reproducible evidence of stimulated emission, it is necessary to understand the physical mechanisms at work in the light emission process. In this paper, we report on the detailed theoretical aspects of the energy levels and recombination rates in doped and undoped Si NCs, and we discuss the effects of energy transfer mechanisms. The theoretical calculations are extended toward computational simulations of ensembles of interacting nanocrystals. We will show that inhomogeneous broadening and energy transfer remain significant problems that must be overcome in order to improve the gain profile and to minimize nonradiative effects. Finally, we suggest means by which these objectives may be achieved.

Graphene-based superlattice (SL) formed by a periodic gap modulation is studied theoretically using a Dirac-type Hamiltonian. Analyzing the dispersion relation we have found that new Dirac points arise in the electronic spectrum under certain conditions. As a result, the gap between conduction and valence minibands disappears. The expressions for the positions of these Dirac points in k-space and threshold value of the potential for their emergence were obtained. Also, the dispersion law and renormalized group velocities around the new Dirac points were calculated. At some parameters of the system, we have revealed interface states which form the top of the valence miniband.

The valley-orbit splitting in silicon quantum dots with shallow donors has been theoretically studied. In particular, the chemical-shift calculation was carried out within the frames of k · p approximation for singleand many-donor cases. For both cases, the great value of the chemical shift has been obtained compared to its bulk value. Such increase of the chemical shift becomes possible due to the quantum confinement effect in a dot. It is shown for the single-donor case that the level splitting and chemical shift strongly depend on the dot radius and donor position inside the nanocrystal. In the many-donor case, the chemical shift is almost proportional to the number of donors.

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