One-Phonon Collision Corrections to the High-Frequency Dielectric Function of Semiconductors

Expressions for the one-phonon collision corrections to the high-frequency long-wavelength (k → 0) dielectric function $\epsilon \left(\omega \right)$ of a semiconductor have been computed in the low-temperature cold-electron-plasma limit. Only interactions with a single optical-phonon branch are considered, but expressions for both polar and deformation-potential coupling have been included. Our results differ from previously published work on one-phonon collision corrections in that we have taken dynamic screening into account, a feature which is important when the electron-plasma frequency is comparable to or greater than optical-phonon frequencies. The principal effect of dynamic screening is to replace the noninteracting phonon and electron excitation frequencies in the collision terms with the collective-oscillation frequencies of the interacting electron-phonon system.