Theory of interference distortion of Raman scattering line shapes in semiconductors

A Green's-function theory of Raman-scattering line-shape asymmetries is developed here for a system in which a one-phonon (discrete) excitation is degenerate with intervalence-band (continuum) excitations. The scattering cross section is expressed in terms of a generalized dynamic form factor, $\tilde{S}(\overrightarrow{\mathrm{q}}, \omega )$, appropriate for the second Born approximation. The $\tilde{S}(\overrightarrow{\mathrm{q}}, \omega )$ is defined in terms of a composite Green's function which describes the quantum interference between the discrete and continuum states. Introducing a model electron-phonon interaction, the techniques of many-body theory are used to solve for $\tilde{S}(\overrightarrow{\mathrm{q}}, \omega )$ in the random-phase approximation. This automatically leads to an expression which yields the desired line shapes, i.e., gives antiresonances. Measurements of scattering line shapes for degenerate $p$-type silicon over a wide spectral range are described. This allows a fit of the theoretical and experimental line shapes. Examination of the analytic structure of $\tilde{S}(\overrightarrow{\mathrm{q}}, \omega )$ leads to the conclusion that there is a new collective excitation of the crystal. This is the result of the quantum interference between the discrete and continuum states. We associate the creation of this excitation with the onset of line-shape asymmetry in the Raman spectrum of the semiconductor.