Anharmonic decay time, isotopic scattering time, and inhomogeneous line broadening of optical phonons inGe70,Ge76, and natural Ge crystals

High-accuracy (0.02-${\mathrm{cm}}^{\mathrm{-}1}$) first-order Raman spectra of two different isotopically enriched Ge crystals (95.9% ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$ and 86.0% ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$) and a Ge crystal of natural isotopic composition as well as time-resolved picosecond Raman spectra of the isotopically enriched ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$ and natural Ge were measured and compared with theoretical calculations using the self-consistent Born approximation and the coherent-potential approximation. The broadening of the Raman line in the frequency domain was found to be predominantly caused by the anharmonic decay of optical phonons into lower-energy acoustic phonons, resulting in a line broadening that is inversely proportional to the average isotopic mass m¯. Isotopic disorder contributes only a little to the line broadening and depends on the isotopic composition of the material. From the phonon linewidths the anharmonic decay time of optical phonons in Ge at 80 K was determined to be m¯(8.4±0.1)×${10}^{\mathrm{-}2}$ ps (m¯ is the average isotopic mass in atomic-mass units). The isotopic (elastic) scattering time of optical phonons depends strongly on the isotopic composition and is two orders of magnitude longer than the decay time in all samples. The asymmetry observed in the Raman lines is explained in terms of the opacity of the material and the asymmetric phonon self-energies (due to isotopic disorder). The decay time of the time-resolved incoherent anti-Stokes Raman signal is 8±1 ps for both the isotopically enriched and the natural Ge. It is suggested that the discrepancy between the phonon decay time (determined from the frequency-domain measurements) and the nonequilibrium phonon population decay time (determined from the time-domain measurements) is due to effects related to the phonon-generation process in the transient experiment.