Dispersive Phonon Linewidths: The ${\mathrm{E}}_2$ Phonons of ZnO

Phonon linewidths can exhibit a large variation when either pressure or isotopic masses are changed. These effects yield detailed information about the mechanisms responsible for linewidths and lifetimes, e.g., anharmonicity or isotopic disorder. We report Raman measurements of the linewidth of the upper ${\mathrm{E}}_2$ phonons of ZnO crystals with several isotopic compositions and their dependence on pressure. Changes by a factor of 12 are observed at a given temperature. Comparison with calculated densities of one-phonon states, responsible for isotope scattering, and of two-phonon states, responsible for anharmonic decay, yields a consistent picture of these phenomena. Isotopic disorder broadening by $7{\mathrm{c}\mathrm{m}}^{-1}$ is found in samples with mixed ${}^{16}\mathrm{O}–{}^{18}\mathrm{O}$ content, whereas the anharmonic processes involve decay into sums and differences of two phonons.

Figure 1

Raman spectra of the ${\mathrm{E}}_2^{\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}}$ phonons at 7 K for three ZnO samples. Note the broad and asymmetric spectrum of the ${{}^{\mathrm{16}}\mathrm{O}}_{0.5}{{}^{\mathrm{18}}\mathrm{O}}_{0.5}$ sample. The dashed line is a fit with a Lorentzian including spectral resolution, the anharmonic contribution and the disorder effects (see text).

Figure 2

Resolution-corrected FWHM of the ${\mathrm{E}}_2^{\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}}$ phonons obtained from 7 K Raman spectra for several isotopic compositions. The points corresponding to ${}^{\mathrm{64}}\mathrm{Z}\mathrm{n}{}^x\mathrm{O}$ samples are plotted at the measured frequencies, the others have been shifted as explained in the text. The solid line displays the calculated ${\rho }_{+}^{(2)}(\omega )$ scaled by a factor of $57{\mathrm{c}\mathrm{m}}^{-2}$. The large width observed for ${}^{\mathrm{nat}}\mathrm{Z}\mathrm{n}{{}^{\mathrm{16}}\mathrm{O}}_{0.5}{{}^{\mathrm{18}}\mathrm{O}}_{0.5}$ illustrates the effect of isotopic mass fluctuations. Similar values of FWHM were found for other samples containing the same mixture of O isotopes. The inset displays the one-phonon DOS, ${\rho }^{(1)}(\omega )$.

Figure 3

Effect of hydrostatic pressure on the linewidths of three ZnO samples after correcting for spectral resolution. The measurements were performed at 300 K. The lines are guides to the eye.

Figure 4

Experimental points of Fig. 3 replotted vs peak frequency, with the frequency shifts and scaling described in the text. The solid line was obtained by adding to the ${\Gamma }_{+}(\omega )$ of Eq. (2) a constant attributed to ${\Gamma }_{-}(\omega )$ (dashed line).

Figure 5

Linewidths of ZnO with several isotopic compositions at 300 K, after correction for resolution. The solid line represents ${\Gamma }_{+}(\omega )+{\Gamma }_{-}(\omega )$, from Eqs. (2, 3). The points have been shifted as done in Fig. 2. The dot-dashed line indicates the pressure dependence shown in Fig. 4.