Optical Band-to-Band Transitions

Abstract

The optical constants and the dielectric function of semiconductors are over a wide range of photon energies determined by electronic transitions between various bands of the band structure. We will describe here the theoretical approach to treat these transitions arriving finally at an expression for the absorption coefficient. We will introduce the joint density of states and its critical points leading to prominent structures (van Hove-singularities) in the dielectric function. In the experimental section we will illustrate methods to determine optical functions (ellipsometry and modulation spectroscopy).

Problems

16.1

Calculate the effective density of states, i.e., the onset of degeneracy, for electrons and holes at 10 K and at room temperature in bulk GaAs and ZnSe.

16.2

Calculate the effective density of states for the case of electrons and holes in Si and Ge at room temperature. Pay attention to the presence of equivalent conduction-band minima and find a suitable scheme to average over transverse and longitudinal masses.

16.3

Verify the type of the different critical points in Fig. 16.3a and try to construct qualitatively the imaginary part of the dielectric function for Ge as shown in (b). Try the same for GaAs by comparison of Fig. Ell.2 with Fig. 15.8.