Infrared absorption and scattering by electron-hole droplets in Ge

Abstract

The scattering and absorption of fat-infrared radiation by electron-hole liquid droplets in Ge is calculated using Mie theory. These processes show a strong resonance at ${\ensuremath{\omega}}_{0}\ensuremath{\approx}\frac{{\ensuremath{\omega}}_{p}}{\ensuremath{\surd}3}$ [here ${\ensuremath{\omega}}_{p}$ is the plasmon frequency of the electron-hole liquid (EHL)]. The line shape of the resonance is determined primarily by three factors: (i) interband transitions from the heavy- to light-hole bands; (ii) the finite quasiparticle lifetime; and (iii) the size of the droplets. Assuming droplets with radii $R$, of approximately 1 \ensuremath{\mu}m, and taking the first two effects into account by means of the dielectric constant, we obtain good fits to the currently available experimental data. From the data we conclude that density of the EHL is 2.2 \ifmmode\times\else\texttimes\fi{} ${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ at 1.5\ifmmode^\circ\else\textdegree\fi{}K, and that the EHL has an effective quasiparticle lifetime $\ensuremath{\tau}\ensuremath{\approx}0.33$ me${\mathrm{V}}^{\ensuremath{-}1}$. Finally, we discuss the line shapes of large droplets ($R>2$ \ensuremath{\mu}m). Comparison of our calculations with the experimental data of Timusk and Silin leads to the conclusion that large radius droplets, $R=8$ \ensuremath{\mu}m, occur in Sb-doped Ge.