Pseudo-surface Mode Research Articles

Off-axis phonon and photon propagation in porous silicon superlattices studied by Brillouin spectroscopy and optical reflectance

Brillouin light scattering experiments and optical reflectance measurements were performed on a pair of porous silicon-based optical Bragg mirrors which had constituent layer porosity ratios close to unity. For off-axis propagation, the phononic and photonic band structures of the samples were modeled as a series of intersecting linear dispersion curves. Zone-folding was observed for the longitudinal bulk acoustic phonon and the frequency of the probed zone-folded longitudinal phonon was shown to be dependent on the propagation direction as well as the folding order of the mode branch. There was no conclusive evidence of coupling between the transverse and the folded longitudinal modes. Two additional observed Brillouin peaks were attributed to the Rayleigh surface mode and a possible pseudo-surface mode. Both of these modes were dispersive, with the velocity increasing as the wavevector decreased.

Surface and bulk polaritons in a PML-type magnetoelectric multiferroic with canted spins:TE and TM polarization

We present a theory for surface polaritons on ferroelectric–antiferromagnetic materials withcanted spin structure. A small uniform canted moment is allowed, resulting in a weakferromagnetism directed in the plane parallel to the surface. Surface and bulk polariton modesfor a semi-infinite film are calculated for the case of transverse electric (TE) and transversemagnetic (TM) polarization. Example results are presented using parameters appropriate forBaMnF4. We find that the surface modes are non-reciprocal for the TE polarization due to themagnetoelectric interaction, and the non-reciprocity can be controlled by an appliedelectric field. Example results for attenuated total reflection (ATR) are calculated. Themagnetoelectric interaction also gives rise to ‘leaky’ surface modes in the case of TMpolarization. These are pseudo-surface waves that exist in the pass band, and dissipateenergy into the bulk of the material. We show that these pseudo-surface mode frequenciesand properties can be modified by temperature and the application of external electric ormagnetic fields.

Elastic Properties of Zinc Blende MnTe

The Brillouin light scattering was used to investigate elastic properties of the zinc blende, MBE-grown MnTe layer that was deposited on a (001) GaAs substrate covered by CdTe buffer layer. The three elastic constants of the zinc blende MnTe, namely c11, c12, and c44, were directly determined for the first time from the frequency of the Rayleigh mode, of the pseudo-surface mode, and of the shear horizontal bulk mode traveling parallel to the layer surface. The value of c11 was checked using the frequency of longitudinal bulk waves propagating at different angles from the normal of the layer plane. This value was also independently determined by results of the folding of acoustic phonons, observed for MnTe/CdTe superlattices by the Raman scattering. Finally, the bulk modulus given by the formula B=(c11+2c12)/3 was determined for zinc blende MnTe by ab initio calculations making use of the density functional theory and atomic pseudopotentials; spin polarization of MnTe was taken into account. A satisfactory agreement between theoretical and experimental values was obtained.

Elastic properties of β-SiC films by Brillouin light scattering

Brillouin light scattering has been used to investigate elastic properties of a monocrystalline and of 〈111〉 textured polycrystalline 3C polytype silicon carbide films that have been deposited on silicon substrate by chemical vapor deposition. Taking advantage from the detection of different acoustic modes, a complete elastic characterization of the films has been achieved. The three unknown elastic constants of the monocrystalline 3C-SiC, namely, c11=395 GPa, (c11−c12)/2=136 GPa, and c44=236 GPa have been selectively determined, respectively, from the frequency of the longitudinal and of the shear horizontal bulk modes traveling parallelly to the film surface. These determinations are in agreement with the frequency of the observed Rayleigh surface mode, of the pseudosurface mode, and of the bulk waves propagating at different angles from the normal of the single crystal film plane and consistent with existing theoretical calculations of β-SiC elastic constants. Finally, the calculated Voigt average values of the effective elastic constants for the 〈111〉 textured 3C-SiC polycrystalline film using the single crystal constants provides a good agreement with our experimental results (C11=500 GPa, C33=535 GPa, C44=165 GPa, C66=210 GPa, and C13=50 GPa) and compare fairly well with the α-SiC published one. These results confirm that the elastic constants of silicon carbide are slightly influenced by the polytypism.

Angular dispersion of surface acoustic waves on (001), (110), and (111) GaAs

The generalized surface, pseudosurface, and high-frequency pseudosurface acoustic waves propagating on (001), (110), and (111) surfaces of GaAs have been examined using Brillouin spectroscopy. The phase velocities of the surface acoustic waves were measured as a function of their propagating directions over the entire angular periods on the respective basal planes. Unlike the single dispersion curve arising from the branching from the generalized surface mode to the pseudosurface mode, commonly observed for anisotropic cubic crystals, two separate and distinct dispersion branches were recorded for these surface modes on the (001) surface. The complete dispersion branch of high-frequency pseudosurface acoustic waves on the (110) surface has been determined.

Brillouin scattering study of the pseudosurface acoustic mode on the (110) face of cubic crystals having elastic anisotropy ratio above unity

We report the experimental observation of a pseudosurface mode in (110)-cut cubic crystals having the anisotropy ratio η=2C44/(C11−C12)≳1, where C11, C12, and C44 are elastic constants. The measurements have been performed with Brillouin light-scattering spectroscopy for GaAs, InSb, Ge, and InAs crystals. Results are shown for GaAs and InSb. An additional Brillouin satellite has been observed in the bulk velocity range for general propagation directions on the (110) plane; this peak is attributed to the presence of the pseudosurface mode. For all the crystals investigated, we have found that the pseudosurface mode exists for propagation directions within the range θ=±55°, where θ is the azimuthal angle measured from the [001] crystal axis. The results of calculations of the light-scattering cross section and of the propagation velocity of the pseudosurface mode are in a good agreement with the measurements.

Localized surface phonon propagation in CaF2/Si(110) heterostructures

We have studied experimentally the propagation of the surface phonon modes in CaF2/Si(110) heterostructures with h=0, 10 and 200 nm thickness by Brillouin light scattering spectroscopy. The angular azimuthal behaviour or the Rayleigh mode was found to be close to that of the material of the substrate in the case with h=10 nm, and to that of the layer in the case with h=200 nm. In an h=200 nm heterostructure for the azimuthal directions close to (110) it was concluded that the behaviour of the first localized mode is described well by the proper pseudo-surface mode of CaF2 of the (110) plane, whereas higher-mode (i.e. second, third) velocity values were found to be close to that of the material of the substrate. Experimental and calculated velocity values match each other rather well.

Mandelstamm-Brillouin studies of peculiarities of the phonon frequency distribution at cubic crystal (001) surfaces

For z-cut cubic crystals of Si, GaAs, InSb measurements of the peak intensities of Mandelstamm-Brillouin satellites corresponding to surface excitations of the pseudo surface mode (PSM) frequency range were conducted. The angular intensity dependence for various plane of incidence orientations reveal two maxima, for θ2=45°, and for θ2=36° (Si), 33° (GaAs), and 32° (InSb). Here θ is the angle between the (010) plane and the plane of incidence of light. The variations of the PSM satellite linewidth registered experimentally for the first time demonstrate the positions of its minima to be well correlated with θ1,2 in all the cases. The non-monotonous peak intensity and the linewidth of the PSM satellite behavior are explained by PSM attenuation anomalies around θ1,2.

Determination of high-frequency pseudo surface mode velocity in high-T c superconducting RBa 2Cu 3O 7−y ( R= Tm, Er, Ho, Dy, Gd, Eu, Sm, Nd, Pr) single crystal by Mandelstamm-Brillouin light scattering spectra

The registration of Mandelstamm-Brillouin spectral lines corresponding to High Frequency Pseudo Surface Mode (HFPSM) and consequent V HFPSM velocity determination in both orthorhombic and tetragonal structured RBa 2Cu 3O 7−y crystal is reported. For orthorhombic crystal V HFPSM drops from 5.8 to 5.2 km/s with the incrase of R element ionic radius from R= Tm to Pr, and V HFPSM values measured in non-superconducting tetragonal structured crystals are 5–6% lower than in more oxygen saturated orthorhombicc crystals. Similar dependencies from the crystals nature may be assumed also to corresponding bulk longitudinal velocity values.

Studies of Mandelstamm-Brillouin light scattered by the surface of (111)-, (110)-cutted GaAs, and (111)-cutted InSb crystals

Mandelstamm-Brillouin (MB) surface light scattering spectra of light in case of GaAs crystals of (111) and (110) cut demonstrate considerable drop of the intensity of the spectral components caused as by Generalized Surface Wave (GSW), as by High Frequency Pseudo Surface Mode (HFPSM), incident light wave polarization being changed from parallel to normal to the plane of light incidence. New MB peak located at 11.8 GHz was detected for (110) plane scattering. In case of InSb crystal of (111) cut simultaneous registration of MB satellites corresponding to GSW and to Pseudo Surface Mode is reported.

Surface Exciton Polariton in ZnO

The surface exciton polaritons associated with the A, B and C excitons in ZnO are investigated by the attenuated total reflection (ATR) measurements. The concept of the surface admittance is introduced to understand the characteristic nature of the surface polaritons in anisotropic ZnO crystal. The experimental ATR spectra and the dispersion curves for the respective excitons are analyzed taking account of the anisotropic and non-local exciton dielectric functions and of the surface layer effect. The real and virtual surface polariton modes are identified on the B exciton from the experimental dispersion curves for particular geometries. Besides, a pseudo-surface mode is observed as additional ATR dips and is interpreted as the guided-wave mode propagating along an optical wave-guide-like structure, ZnO-surface layer-MgF 2 gap, under specific conditions.