Effects of the indirect transitions on optical dispersion relations

We report generalized expressions for the indirect-band-gap contribution to the real (${\epsilon }_1$) and imaginary parts (${\epsilon }_2$) of the dielectric function of semiconductors. The ${\epsilon }_2$ spectrum is assumed to yield a continuous absorption obeying the well-known power law of (ħω-$E_g^{\mathrm{id}{)}^2}$ and have a steep high-energy end at the high-energy cutoff $E_c$. The corresponding ${\epsilon }_1$ spectrum shows no clear structure at the $E_g^{\mathrm{id}}$ edge, but a strong negative peak at the $E_c$. Analyses are presented on the optical dispersion relations of InP at 30 K, and results are in satisfactory agreement with the experimental data over the entire range of photon energies (0–6.0 eV). With use of this model it is possible to analyze the optical dispersion relations in a large number of semiconductors, such as Si, GaP, AlSb, and CdSe.