Lattice dynamics of the model percolation-type (Zn,Be)Se alloy: Inelastic neutron scattering, ab initio study, and shell-model calculations

The random Zn${}_{1\text{−}x}$Be${}_x$Se zincblende alloy is known to exhibit a peculiar three-mode [$1\times$(Zn-Se),$2\times$(Be-Se)] vibration pattern near the Brillouin zone (BZ) center, of the so-called percolation type, apparent in its Raman spectra. This is due to an unusually large contrast between the physical properties (length, ionicity) of the constituting bonds. In the present work, the inelastic neutron scattering is applied to study the dispersion of modes away from the BZ center, with special attention to the $\vec{q}$ dependence of the BeSe-like transverse optic doublet. The discussion is supported by calculations of lattice dynamics done both ab initio (using the siesta code) and within the shell model. The BeSe-like doublet is found to survive nearly unchanged throughout the BZ up to the zone edge, indicating that its origin is at the ultimate bond scale. The microscopic mechanism of splitting is clarified by ab initio calculations. Namely, the local lattice relaxation needed to accommodate the contrast in physical properties of the Zn-Se and Be-Se bonds splits the stretching and bending modes of connected, i.e., percolativelike, (Be-Se) bonds.

Figure 1

BeSe phonon dispersion calculated at 300 K within the shell model (solid lines). The corresponding ab initio curves at 0 K taken from Ref. [24] (dashed lines) and the Raman frequencies measured at 300 K (near $\Gamma$, thick dots) taken from Ref. [23] are added for comparison.

Figure 2

Room-temperature Raman spectra taken (a) with the Zn${}_{0.67}$Be${}_{0.33}$Se single crystal studied by INS by using the 633.0-nm He-Ne laser line in the pure-TO geometry corresponding to backscattering along the [110]-growth axis (refer to the double arrow) with crossed incident ($\overrightarrow{e_i}$) and scattered ($\overrightarrow{e_s}$) polarizations (geometry 1) and (b) with the Zn${}_{0.69}$Be${}_{0.31}$Se epitaxial layer by using the 514.5-nm Ar+ laser line in pure-LO and pure-TO geometries, corresponding to backscattering along the [001]-growth (geometry 2) and [110]-edge (geometry 1′) crystal axis (refer to the double arrow), respectively. Corresponding theoretical percolation-type TO- and LO-coupled (solid lines) and LO-uncoupled (dashed lines) Raman spectra calculated based on a random Zn ↔ Be substitution are superimposed for comparison. The stars mark a Fano interference between the theoretically forbidden DALA band and the ${\mathrm{TO}}_{\mathrm{Zn}\text{−}\mathrm{Se}}$ mode (a) and a parasitical laser line (b).

Figure 3

Ab initio Γ-projected T–Ph-DOS per Be atom of the –Be–Se–Be– motif inserted in a ZnSe-like (64-atom) supercell, as obtained at 0 K with (red line, on the right) and without (green line, on the left) relaxation. The individual vibration patterns, schematically shown, are labeled in standard notation (as for the –CH${}_2$– methylene group). Corresponding vibration frequencies obtained for the same –Be–Se–Be– motif within the shell model are indicated in the middle panel. The experimental BeSe-like TO Raman frequencies (taken from Fig. 2) are shown in the top panel).

Figure 4

Transversal (dark blue lines) and longitudinal (yellow lines) components in the density of modes calculated using the ab initio SIESTA code over two different special quasirandom 192-atom supercells (upper and lower panels), describing the Zn${}_{0.67}$Be${}_{0.33}$Se solid solution. Densities of modes are further resolved in the values of the wavevector, chosen to scan the dispersion from $\Gamma$ to $X$.

Figure 5

Ph-DOS measured by INS at 13 K with the Zn${}_{0.67}$Be${}_{0.33}$Se powder (circles). The theoretical Ph-DOS calculated via the shell model at 13 K is superimposed (solid curve) for comparison.

Figure 6

Selection of TO and LO INS spectra taken at 13 K at well-spanned $q_x$ values along $\Gamma \to X$ [100] in the Zn-Se (top left panel) and Be-Se (other panels) spectral ranges. At $q_x$ = 0.8, the LO doublet is only resolved via a contour modeling of the INS profile (thick curve) using two Gaussian functions.

Figure 7

Acoustic (squares) and optic (circles) phonon frequencies of the Zn${}_{0.67}$Be${}_{0.33}$Se single crystal measured by INS (circles and squares) at 13 K at different $\vec{q}$ wavevectors along the usual high-symmetry directions in reciprocal space in both the transverse (black symbols) and longitudinal (yellow-clear symbols) symmetries. The TO Raman frequencies (at Γ, black diamonds) observed at 300 K are added for the sake of completeness. The theoretical phonon dispersion curves, as inferred from direct calculation of the neutron scattering cross section of Zn${}_{0.67}$Be${}_{0.33}$Se via the shell model, are also shown using an explicit grayscale (refer to the right) for comparison.