Many-Body Effects in the Optical Properties of Semiconductors

The high-frequency optical absorption of semiconductors of the diamond structure type has been investigated theoretically for the almost-free-electron energy-band model isotropically extended to three dimensions. Model-independent arguments show that ignoring interactions between particles so that all excitations are infinitely long-lived leads to calculated values of the absorptive part of the dielectric constant, ${\epsilon }_2(q\to 0,\omega )$, well below the experimental results for Ge and Si. Within our model, we have investigated self-energy and vertex corrections to ${\epsilon }_2\left(\omega \right)$ due to many-body effects resulting from the Coulomb interactions between particles. Both these corrections significantly raise the theoretical value of ${\epsilon }_2\left(\omega \right)$, bringing them substantially closer to experimental ones.