Quantum-size effect in model nanocrystalline/amorphous mixed-phase silicon structures

The quantum-size effect is investigated theoretically in model nanocrystalline/amorphous mixed-phase Si structures. We show that the peak energies of the imaginary part of the dielectric function of the model structures shift as a function of the size of nanocrystalline Si and the thickness of amorphous Si which surrounds the nanocrystalline Si. This effect cannot be explained by the conventional quantum confinement model because of the lack of an apparent potential which confines electrons within the nanocrystalline Si embedded in amorphous Si. Atomic positions of the amorphous Si are modeled by a Monte Carlo calculation with the Stillinger-Weber potential for the interaction between Si atoms. The electronic calculation is based on an empirical pseudopotential method with basis states represented in a real-space grid. Dielectric functions of modeled structures containing up to 13 824 Si atoms are calculated, which has been made possible by calculating a time-dependent representation of the linear-response function.