Signature of Tetrahedral Ge in the Raman Spectrum of Amorphous Phase-Change Materials

We computed the Raman spectrum of amorphous GeTe by ab initio simulations and empirical bond polarizability models. The calculated spectrum is in very good agreement with experimental data and contains the signatures of all the peculiar local structures of the amorphous phase revealed by recent ab initio simulations, namely, tetrahedral Ge and defective octahedral sites for a fraction of Ge (mostly 4-coordinated) and for all Te (mostly 3-coordinated) atoms. In particular, the spectrum above $190{\mathrm{cm}}^{-1}$ is dominated by tetrahedral structures, while the most prominent peaks around 120 and $165{\mathrm{cm}}^{-1}$ are mainly due to vibrations of atoms in defective octahedral sites. Finally, the peak around $75{\mathrm{cm}}^{-1}$, which dominates the spectrum in $HV$ scattering geometry, is mostly due to vibrational modes involving threefold coordinated Te atoms.

Figure 1

(a) Projection of the phonon DOS of $a$-GeTe on different species [Te, Ge in tetrahedral (tetra) and defective octahedral (octa) sites]. The contribution to the DOS of the $j$th mode with eigenvector $\mathbf{e}(j,\kappa )$ is multiplied by $\sum _{\kappa }\frac{|\mathbf{e}(j,\kappa ){|}^2}{M_{\kappa }}$, where the sum over $\kappa$ is restricted to atoms of a given species with mass $M_{\kappa }$. Inset: a sketch of the geometry of defective octahedral sites of 4-coordinated Ge and 3-coordinated Te. (b) Inverse Participation Ratio (IPR) (see text).

Figure 2

(a) Reduced Raman spectrum of the 216-atoms $a$-GeTe model computed within the BPM for unpolarized light in backscattering geometry (see text) compared with the analogous experimental spectrum from Ref. 11. The reduced spectrum is obtained by multiplying by ${\omega }_s^{-4}\omega (n_B+1{)}^{-1}$ the Raman scattering (Stokes) cross section given by Eq. (2) in EPAPS 21. (b) Theoretical and experimental (adapted from Ref. 11) polarized Raman spectra in $HV$ and $VV$ geometries. The theoretical spectra are obtained by substituting the $\delta$ functions in Eq. (2) in EPAPS 21 with Lorentzian functions $5{\mathrm{cm}}^{-1}$ wide. We averaged over all possible incident directions of the light [28]. Inset: distribution of ${\mathrm{GeTe}}_{4-n}{\mathrm{Ge}}_n$ polyhedra for fourfold coordinated Ge in the $a$-GeTe model.

Figure 3

Projection of the reduced Raman spectrum in Fig. 2 on (a) all atoms belonging to ${\mathrm{GeTe}}_{4-n}{\mathrm{Ge}}_n$ tetrahedra and (b) tetrahedral Ge, octahedral Ge and Te atoms.