Confinement of Acoustical Vibrations in a Semiconductor Planar Phonon Cavity

Extending the idea of optical microcavities to sound waves, we propose a phonon cavity consisting of two semiconductor superlattices enclosing a spacer layer. We show that acoustical phonons can be confined in such layered structures when the spacer thickness is an integer multiple of the acoustic half-wavelength at the center of one of the superlattice folded minigaps. We report Raman scattering experiments that, taking profit of an optical microcavity geometry, demonstrate unambiguously the observation of a phonon-cavity confined acoustical vibration in a $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{A}\mathrm{s}$ based structure. The experimental results compare precisely with photoelastic model calculations of the Raman spectra.

Figure 1

Scheme of the proposed phonon cavity embedded within an optical cavity. The phonon “mirrors” consist of 11 period $74\AA /38\AA$ $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{A}$s SL’s, and enclose a $50\AA$ $\mathrm{A}{\mathrm{l}}_{\mathrm{0.8}}\mathrm{G}{\mathrm{a}}_{\mathrm{0.2}}\mathrm{A}\mathrm{s}$ spacer. The phonon-cavity structure, on the other hand, constitutes the $\lambda$ spacer of an optical microcavity enclosed by 20 BR $\mathrm{G}{\mathrm{a}}_{\mathrm{0.8}}\mathrm{A}{\mathrm{l}}_{\mathrm{0.2}}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{A}\mathrm{s}$ pairs on the bottom and 16 on top.

Figure 2

Calculated phonon reflectivity (top) and Raman spectrum (bottom) in the spectral region around the first zone-center minigap for the phonon cavity embedded within a photon cavity depicted in Fig. 1. The separate contributions of the forward scattering (FS) and backscattering (BS) terms is also shown.

Figure 3

Calculated phonon amplitude corresponding to the confined phonon-cavity mode. The curve is shown superimposed to a scheme of the phonon structure characterized by the material’s photoelastic constant.

Figure 4

Experimental Raman spectrum in the spectral range corresponding to the acoustical folded-phonon first center-zone minigap (Exp), obtained with laser wavelength $\lambda =833\mathrm{n}\mathrm{m}$. Also shown are calculated Raman curves corresponding to (i) the nominal structure (Nominal), and (ii) a phonon cavity with random disorder $\pm 4\%$ of the SL layer’s thickness (Disorder).