Comparison of the phonon spectra ofGe70and natural Ge crystals: Effects of isotopic disorder

The difference in phonon energies and broadenings between an isotopically enriched crystal of ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$ (95.9%) and a germanium crystal of natural isotopic composition was measured with high accuracy in first- and second-order Raman spectra (with laser excitation energies of ${\mathit{E}}_{\mathit{L}}$=2.41 eV and ${\mathit{E}}_{\mathit{L}}$=2.183 eV, respectively) and compared to coherent-potential-approximation and lowest-order perturbation-theory calculations. The energy of the first-order O(Γ) phonon shifts up by 4.9±0.1 ${\mathrm{cm}}^{\mathrm{-}1}$ in the isotopically pure crystal, in good agreement with the calculated value of 4.3±0.4 ${\mathrm{cm}}^{\mathrm{-}1}$. No broadening due to isotopic disorder was observed for optical phonons at the Γ point [full width at half maximum (FWHM) of 0.99±0.03 ${\mathrm{cm}}^{\mathrm{-}1}$ at 80 K for both crystals]. However, additional broadening at the W and L point was found in the second-order Raman spectra (FWHM broadening of 6.5±0.5 ${\mathrm{cm}}^{\mathrm{-}1}$ at the L point). This broadening and the shifts of the acoustic- and optical-phonon peaks in the second-order spectra agree well with calculations of the phonon overtone density of states.