Second-order Raman scattering in germanium in the vicinity of theE1,E1+Δ1edges

Abstract

The resonance of the ${\Gamma }_1$ and ${\Gamma }_{{25}^{\prime }}$ components of the second-order Raman spectrum of germanium has been measured in the vicinity of the $E_1$, $E_1+{\Delta }_1$ edges. Particular emphasis was paid to the features corresponding to creation of $2\mathrm{TA}\mathrm{}\left(X\right)\mathrm{}$ phonons, $2\mathrm{TO}\mathrm{}\left(L\right)\mathrm{}$ phonons, and the anomalous peak due to $2\mathrm{TO}\left(\Gamma \right)$ phonons. This anomalous peak disappears below the resonant gap and is attributed to an iterative process involving the first-order electron-phonon interaction taken to second order. The remaining resonant features are due to the second-order interactions taken to first order and thus are structurally analogous to the first-order processes. However, because of different contributions of two-band (intervalley) and three-band (intravalley) processes, radically different line shapes can result for these resonances. From these measurements, several electron-two-phonon coupling constants are determined.