The temperature dependance of the interband critical points in silicon within a fractional-dimensional space approach

The fractional-dimensional space approach (FDSA) is used to analyse the temperature dependence of direct interband transitions in Si. The critical point (CP) parameters are obtained. The results obtained by the FDSA show general or even better agreement with the theoretical calculation than the standard treatment. In the temperature range of 20-450 degreesC, the results obtained by FDSA indicate that the excitonic effects can be ignored, and the CP E-1 - E-0' can be treated as a band character. Our research shows that the FDSA provides a good way to derive basic information on relevant physical quantities from the observed optical spectra, and it has the advantages of directness, flexibility, and sensitivity, which enable us to obtain the CP parameters efficiently without ambiguity. This method is especially useful in the cases where the limitations of the standard treatment are serious.