Pressure-induced phonon freezing in the ${\text{Zn}}_{1-x}{\text{Be}}_x\text{Se}$ alloy: A study via the percolation model

We use the $1\text{-bond}\to 2\text{-phonon}$ percolation doublet of zinc-blende alloys as a “mesoscope” for an unusual insight into their phonon mode behavior under pressure. We focus on (Zn,Be)Se and show by Raman scattering that the application of pressure disables an anharmonic coupling between the nominal Zn-Se zone-center TO mode and disorder-activated two-phonon zone-edge continua. This reveals an unexpectedly clear percolation-type fine structure of the Zn-Se TO mode, the latter fine structure being unaffected by pressure. In contrast, the original Be-Se doublet at ambient pressure, of the stretching-bending type, turns into a pure-bending singlet at the approach of the high-pressure ZnSe-like rocksalt phase, an unnatural one for the Be-Se bonds. The “freezing” of the Be-Se stretching mode is discussed within the scope of the percolation model (mesoscopic scale), supported by ab initio insight into the pressure dependence of vibrational properties of the ultimate percolation-type Be-impurity motif (microscopic scale). Similar ab initio calculations are performed with (Ga,As)P, for reference purpose.

Figure 1

Pressure dependent Raman spectra of ${\text{Zn}}_{0.76}{\text{Be}}_{0.24}\text{Se}$. The frequency versus pressure variations of the main features are shown in the inset. There, the plain and open circles refer to the LO and TO modes, respectively. Remarkable trends $\left(A,B,C\right)$ are marked by circles. The antiresonances (squares) and the strong peak (star) are characteristic of anharmonic coupling.

Figure 2

Schematic explanation of the features $A$ and $B$ (circles) by referring to pure ZnSe [plain (LO) and open (TO) symbols, digitalized from Ref. 9]. In the alloy the weak ${\text{TO}}_{\text{Zn-Se}}^{\text{Be}}$ mode (thick line–in the corresponding vibration pattern the dotted and plain lines indicate perpendicular planes) appears on top of the strong ${\text{TO}}_{\text{Zn-Se}}^{\text{Zn}}$ one (pure-ZnSe-like, dashed line). The natural splitting of $\sim 8{\text{cm}}^{-1}$ is magnified to $\sim 30{\text{cm}}^{-1}$ by an anharmonic coupling that downshifts the weak mode from the thick line to the thin one. The line shapes of the weak mode over its decoupling process are shown in the inset. The star and squares mark features characteristic of anharmonic coupling, as in Fig. 1. At 8 GPa an arrow marks the position of the harmonic mode, for reference purpose.

Figure 3

Ab initio ZC TO-DOS per impurity of the 2-imp. Be (main curves) and P (inset) motifs in ZnSe- and GaAs-like supercells, respectively. The Be-Se vibration patterns are indicated, emphasizing the bond-stretching modes (dashed areas) in reference to feature $C$ (circle).