Spectroscopy of band-to-band optical transitions in Si-Ge alloys and superlattices

Abstract

We report the results of an extensive study of band-to-band optical transitions in Si-Ge $(n:m)$ superlattices and alloys where $n\ensuremath{\approx}m.$ Our samples were grown by molecular-beam epitaxy on (001) silicon using symmetrically strained layers and characterized by high-resolution x-ray diffraction and transmission electron microscopy. This growth procedure permits the synthesis of continuous Si-Ge superlattices with a thickness of several thousand \AA{}. Optical absorption was studied by photocurrent spectroscopy at 300, 77, and 4.2 K. These results were analyzed to determine the dependence of the photocurrent on the photon energy. The energy dependence of absorption was also measured by optical transmission spectroscopy. Analysis of these experiments gives approximate agreement with photoconductivity experiments on the value of the energy gap, but also shows that the energy dependence of the absorption coefficient varies linearly with the photon energy, while photoconductivity experiments show that the photocurrent increases with the fourth power of the energy. The absorption coefficient, and its dependence on the photon energy, are calculated directly from the joint density of states which is extracted from the electronic band structure. Our calculations show that the dependence of optical absorption on photon energy is linear for perfect superlattices: $\ensuremath{\alpha}(\ensuremath{\Elzxh}\ensuremath{\omega}{)=A}_{0}(\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{-}{E}_{g}{)}^{x},$ where $x=1,$ with the exponent increasing above 1 in the presence of disorder such as from atomic steps, interface roughness, and similar defects.