Microscopic Theory of the Dielectric Function

In this chapter, we derive the dielectric function for direct gap transitions in the electronic band structure using Fermi’s Golden Rule. We discuss the relationship between the electronic band structure and locations in the Brillouin zone when there is a high density of transitions with the same energy resulting in a critical point. We show the analysis of the dielectric function at critical points to determine the transition energy and peak broadening. A number of examples of the dielectric functions of semiconductors over the visible wavelength range are presented. We also discuss the effect of doping on the dielectric function.