Interband, intraband, and excited-state direct photon absorption of silicon and germanium nanocrystals embedded in a wide band-gap lattice

Abstract

Embedded Si and Ge nanocrystals (NCs) in wide band-gap matrices are studied theoretically using an atomistic pseudopotential approach. Small clusters to large NCs containing the order of several thousand atoms are considered. Effective band-gap values as a function of NC diameter reproduce very well the available experimental and theoretical data. It is observed that the highest occupied molecular orbital for both Si and Ge NCs and the lowest unoccupied molecular orbital for Si NCs display oscillations with respect to size among the different irreducible representations of the ${C}_{3v}$ point group to which these spherical NCs belong. Based on this electronic structure, first, the interband absorption is thoroughly studied, which shows the importance of surface polarization effects that significantly reduce the absorption when included. This reduction is found to increase with decreasing NC size or with increasing permittivity mismatch between the NC core and the host matrix. Reasonable agreement is observed with the experimental absorption spectra where available. The deformation of spherical NCs into prolate or oblate ellipsoids is seen to introduce no pronounced effects for the absorption spectra. Next, intraconduction and intravalence band absorption coefficients are obtained in the wavelength range from far-infrared to visible region. These results can be valuable for the infrared photodetection prospects of these NC arrays. Finally, excited-state absorption at three different optical pump wavelengths, 532, 355, and $266\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ are studied for 3 and $4\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ diameter NCs. This reveals strong absorption windows in the case of holes and a broad spectrum in the case of electrons, which can especially be relevant for the discussions on achieving gain in these structures.