Optical gap of silicon crystallites embedded in various wide-band amorphous matrices: role of environment

Within the framework of the envelope-function approximation the single-particle and the optical gaps of silicon nanocrystals embedded in amorphous SiO2, Si3N4, Al2O3 and ZrO2 dielectric matrices were calculated. We employ the model of an Si quantum dot surrounded by a spherical thin intermediate layer with a radially varying permittivity, separating the nanocrystal and the host dielectric matrix. The latter was modelled by the finite-height potential barriers. It has been shown that both the single-particle and optical gaps of the nanocrystals essentially depend on the surrounding material due to the variation of the band offsets for different matrices, which leads to essential shifts of the size-quantized levels. At the same time, an influence of the polarization fields on the optical gap was found to be weak compared to the variation of the confining potential, because of the mutual cancellation of single- and two-particle polarization contributions, which is known as a 'compensation effect'. As a result, hydrogen-like screened electron-hole Coulomb interactions, in fact, individually contribute to the excitonic correction. It has been revealed that the excitonic corrections have close values for the nanocrystals embedded in all the considered matrices: the dispersion of their values is even considerably less than that of the polarization correction values.