Vibrational-mechanical properties of the highly-mismatched Cd1-xBexTe semiconductor alloy: experiment and ab initio calculations

Abstract

The emerging CdTe-BeTe semiconductor alloy that exhibits a dramatic mismatch in bond covalency and bond stiffness clarifying its vibrational-mechanical properties is used as a benchmark to test the limits of the percolation model (PM) worked out to explain the complex Raman spectra of the related but less contrasted Zn_1-xBe_x-chalcogenides. The test is done by way of experiment ([Formula: see text]), combining Raman scattering with X-ray diffraction at high pressure, and ab initio calculations ([Formula: see text] ~ 0-0.5; [Formula: see text]~1). The (macroscopic) bulk modulus [Formula: see text] drops below the CdTe value on minor Be incorporation, at variance with a linear [Formula: see text] versus [Formula: see text] increase predicted ab initio, thus hinting at large anharmonic effects in the real crystal. Yet, no anomaly occurs at the (microscopic) bond scale as the regular bimodal PM-type Raman signal predicted ab initio for Be-Te in minority ([Formula: see text]~0, 0.5) is barely detected experimentally. At large Be content ([Formula: see text]~1), the same bimodal signal relaxes all the way down to inversion, an unprecedented case. However, specific pressure dependencies of the regular ([Formula: see text]~0, 0.5) and inverted ([Formula: see text]~1) Be-Te Raman doublets are in line with the predictions of the PM. Hence, the PM applies as such to Cd_1-xBe_xTe without further refinement, albeit in a "relaxed" form. This enhances the model's validity as a generic descriptor of phonons in alloys.

Figure 1

Cd_1−xBe_xTe structural, optical and mechanical properties. (a) CPMG Cd_0.93Be_0.07Te ¹²⁵Te NMR signal. The binomial distribution of Te-centered nearest-neighbor (NN) tetrahedon clusters depending on the number of Cd atoms at the vertices in case of a random Cd $\leftrightarrow$ Be substitution is added for comparison (inset). The NMR peaks are labeled accordingly. (b) Composition dependence of the main Cd_1−xBe_xTe electronic transitions measured at room temperature by transmission (filled symbols, Fig. S5a) and ellipsometry (hollow symbols, Fig. S5b). CdTe (Ref.) and BeTe (Ref.) values taken from the literature are added, for reference purpose. Linear (dashed) trends between parent values are guidelines for the eye. Laser lines used to excite the Raman spectra are positioned to appreciate resonance conditions. Antagonist arrows help to appreciate the shift of electronic transitions by lowering temperature from ambient to liquid nitrogen, by referring to the $E_0$ gap of CdTe Ref.. (c) Pressure dependence of the zincblende (zb), rocksalt (rs) and Cmcm (cm) Cd_0.89Be_0.11Te lattice constant(s) measured by high-pressure X-ray diffraction (Fig. S1c). (d) The $B_0$ value derived for Cd_0.89Be_0.11Te in its native zb phase (filled circle) from the corresponding volume vs. pressure dependence (Fig. S1d) is compared with the parent values taken from the literature (filled triangles, Refs.^,) and with current ab initio data obtained with the AIMPRO (hollow diamonds) and SIESTA (hollow squares) codes. Corresponding linear $x$-dependencies are shown (dashed lines), for reference purpose.

Figure 2

Cd_1−xBe_xTe vibrational properties. Panels are arranged anti-clockwise, with an overview at the top-center (a), in the sense of increasing $x$ values from left ($x$~0) to right ($x$~1) for direct vertical comparisons of the side panels, i.e., (b) vs. (c) and (f) vs. (e), with (d) in-between offering a snapshot at intermediary composition. (a) Theoretical overview of the Cd_1−xBe_xTe TO Raman frequencies (curves) and intensities (color of curves) at 0 GPa within a four-mode $\left\{2,\times ,\left(C,d,-,T,e\right),,,2,\times ,(Be-Te)\right\}$ description in absence of mechanical coupling ($\omega \prime$=0). A sensitivity of bond vibrations to first neighbors is assumed, as for Zn_1−xBe_xTe. The current experimental TO and LO Raman frequencies (hollow symbols) are indicated. BeTe data from the literature (filled symbols) are added for reference purpose. The prototypical parent-like supercell (216-atom) containing one isolated impurity-duo used to generate an ab initio insight into the end (x ~ 0,1) Cd_1−xBe_xTe TO Raman frequencies is sketched out. Labels (i) to (iv) refer to in-chain, out-of-chain, near-chain and away-from-chain bond vibrations, as indicated. The Be-Te doublet due to the sole effect of the local strain, i.e., in absence of dispersion, is schematically represented (straight-dashed lines). The dispersion effect affecting the impurity modes ($x$~0,1) is emphasized (vertical arrows). (b) High-pressure/low-temperature Cd_0.89Be_0.11Te Raman spectra in the upstroke. The Be–Te signal, modeled via Lorentzian functions (dotted lines) transiently exhibits a minor feature at ~ 3.5 GPa (asterisk). (c,d,e) ab initio (AIMPRO) pressure dependence of the Be–Te Raman signal (c) due to the Be-duo ($x\sim 0$), (d) at intermediary Be content ($x=0.5$) and (e) in presence of the Cd-duo ($x\sim 1$), giving rise to various local modes (asterisks). (f) Raman cross section of the irregular-inverted (see text) Be–Te TO Raman doublet depending on pressure at minor Cd content ($x\sim$ 0.81). A minor mechanical coupling is considered ($\omega \prime$=50 cm⁻¹). Straight and dotted lines represent the pressure dependencies of the raw-uncoupled Be-Te frequencies. In panels (b,c), a color code is used to distinguish between the raw-uncoupled TO’s stemming from “same” (red) and “alien” (blue) environments. Paired vertical—horizontal arrows in panels (c–f) emphasize pressure-induced changes in Raman intensity—frequency for a given mode, correspondingly.