Dynamic dielectric response to electron-hole and electron-electron interactions

Abstract

The interaction potential between two charged particles in a dielectric medium is shown to have the form $U(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},{\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}_{\mathrm{c}.\mathrm{m}.})=\frac{V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})}{\ensuremath{\epsilon}(q,\ensuremath{\omega}=\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},{\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}_{\mathrm{c}.\mathrm{m}.})}$, where $V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ is the bare Coulomb potential, ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}_{\mathrm{c}.\mathrm{m}.}$ is the center-of-mass velocity, and $\ensuremath{\epsilon}(q,\ensuremath{\omega})$ is the dielectric constant of the medium. An analysis of the dielectric screening is performed, incorporating core electron, lattice ion, and free-carrier contributions. The random-phase-approximation dielectric constant for arbitrary degeneracy is employed in calculating the free-carrier component of $\ensuremath{\epsilon}(q,\ensuremath{\omega})$. It is found that although screening of the bare potential by lattice ions may sometimes be evaluated in the static or high-frequency limits, it is virtually always a poor approximation to treat the free-carrier screening in either of these limits. Dynamic screening processes have been incorporated into a calculation of relaxation times for electron-hole scattering in semiconductors for which ${m}_{h}\ensuremath{\gg}{m}_{e}$. Sample calculations for GaAs at a wide variety of temperatures and photoexcited carrier densities show that dynamic screening has a significant effect on the relaxation time in most regimes. It is equally important to treat the screening of electron-electron interactions dynamically when calculating transport properties which are sensitive to electron-electron scattering.