Composition dependence of the interband critical points in Si1−xGex alloys: A fractional–dimensional space approach

Abstract

The fractional–dimensional space approach is used to analyze the compositional dependence of direct interband transitions in Si1−xGex. The pertinent critical point (CP) parameters are obtained, and a CP structure, identified as E1′, is found. With regard to the CP energy, general agreement with the results obtained by the standard treatment is achieved. The other CP parameters, such as dimensionality, lifetime broadening, and amplitude, directly show an effect of a residual oxide overlayer. Our research shows that the fractional–dimensional space approach has the advantages of directness, flexibility, and sensitivity which provide a straightforward and rapid analysis of critical points, especially useful for deformed optical spectra.