Self-energy effects of the optical phonons of heavily dopedp−GaAsandp−Ge

We have studied, using first-order Raman scattering, the self-energy of the long-wavelength transverse-optical phonons of $p-\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ as well as the optical phonons of $p-\mathrm{G}\mathrm{e}$. The phonon Raman lines of $p-\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ are shifted to lower energies and become broadened compared with those of the pure material. They also show an asymmetrical line shape characteristic of a Fano-type discrete-continuum interference. The electronic continuum interacting with the transverse-optical phonons of $p-\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ has been characterized as indirect intraband transitions with initial and final states in the heavy-hole valence band. The phonon Raman lines of $p-\mathrm{G}\mathrm{e}$ display effects similar to those of $p-\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$. However, the frequency shifts and broadening depend on the wavelength of the laser light used to excite the spectra. Intra- and inter-valence-band transitions provide the continuum responsible for the Fano asymmetry. The dependence of the self-energy of the phonons on the incident photon energy is attributed to the dispersive nature of the intraband electron-phonon coupling with the heavy-hole band. By fitting the frequency shifts of the phonon Raman lines measured for different laser wavelengths to the theory a value of 32 ± 6 eV is obtained for the deformation-potential constant $d_0$ of Ge.