Phonons In Superlattices Research Articles

Study of coherent folded acoustic phonons in semiconductor superlattices by pump-probe technique

We report on the time-resolved study of coherent folded longitudinal acoustic phonons propagating in GaAs/AlAs superlattices using a two-color pump-probe technique with violet pump and near-IR probe pulses. From comparing the frequencies of the observed coherent phonons with the dispersion relations, we find that the wavevectors of the propagating coherent folded acoustic phonons depend on the wavevector of the probe light: q=2 k probe.

Surface vibrational modes and reflection times of phonons in finite-size superlattices

We study theoretically the interaction of vibrational modes localized at a surface of a superlattice with acoustic phonons injected from a substrate. We calculate both numerically and analytically the phase time of the phonons reflected from the superlattice. We find sharp enhancements in the phase time, suggesting their strong interactions. The results indicate that the existence of the surface vibrational modes can be examined by a time-resolved phonon reflection experiment.

Coherent Zone-Folded Longitudinal Acoustic Phonons in Semiconductor Superlattices: Excitation and Detection

Coherent zone-folded acoustic phonons are excited in GaAsyAlAs superlattices by femtosecond laser pulses via resonant impulsive stimulated Raman scattering in both forward and backward scattering directions. The relative amplitudes of three distinct modes of first and second backfolded order match well with scattering intensities calculated within an elastic continuum model. The detection of the coherent acoustic modes is based on the modulation of the interband transitions via the acoustic deformation potential and exhibits a strong enhancement at interband transitions. [S0031-9007(98)08288-X]

Non-local dielectric screening and electric fields associated with optical vibrations in superlattices

We develop a simple and straightforward technique for extracting information about the electrostatic fields created by optical phonons in superstructures directly from microscopic three-dimensional lattice dynamics calculations. Local fields with a mesoscopic scale of variation associated with long-wavelength phonons in superlattices are derived using an 11-parameter rigid-ion force-field model. The classification of local fields, their connection to and distinctions from those obtained from the conventional dielectric continuum approaches is discussed. We also develop an alternative approach based on spatially dependent non-local microscopic dielectric screening in semiconducting superstructures. The analytical properties of long-wavelength phonon frequencies and associated electric fields find an explanation in terms of an eigenvalue problem for the non-local frequency-dependent microscopic dielectric matrix. Rigorous expressions for eigenfields and eigenpotentials are derived in the exactly solvable model of the dispersionless continuum. A simple and practical approximation with a short-range (elastic) dispersion included shows an excellent agreement with lattice dynamical calculations for .

Phonons and Free Carriers in a Strained Hexagonal GaN-AlN Superlattice Measured by Infrared Ellipsometry and Raman Spectroscopy

AbstractPhonon and free-carrier effects in a strained hexagonal (α) {GaN}l-{AlN}m superlattice (SL) heterostructure (l = 8 nm, m = 3 nm) are studied by infrared spectroscopic ellipsometry (IRSE) and micro (µ)-Raman scattering. Growth of the heterostructures was performed by metal-organic vapor phase epitaxy (MOVPE) on (0001) sapphire. An unstrained 1 µm-thick α-GaN layer was deposited prior to the SL. SL phonon modes are identified combining results from both IRSE and µ-Raman techniques. The shift of the GaN-sublayer phonon modes is used to estimate an average compressive SL stress of σxx ∼ - 4.3 GPa. The IRSE data reveal a free-carrier concentration of ne ∼ 5×1018 cm−3 within the undoped SL GaN-sublayers. According to the vertical carrier confinement, the free-carrier mobility is anisotropic, and the lateral mobility ( µ⊥ ∼ 400 cm2/Vs, polarization E⊥c-axis) exceeds the vertical mobility (µ∥ ∼ 24 cm2/Vs, E∥c) by one order of magnitude.

Anisotropy of optical phonons in semiconductor superlattices: Raman scattering experiments

Experiments on Raman scattering in the “forward” geometry, permitting observation of anisotropy of the optical phonons, are performed on specially prepared short-period GaAs/AlAs superlattice structures with the substrates removed and the surfaces covered with an antireflective layer. The experimental data agree well with the computational results obtained for the angular dispersion of optical phonons in superlattices on the basis of a modified continuum model.

Coherent control of acoustic phonons in semiconductor superlattices

Coherent acoustic phonons are generated in GaAs/AlAs superlattices by excitation with femtosecond laser pulses. Several modes of the acoustic phonon spectrum are observed, in agreement with the effect of zone folding in the mini-Brillouin zone of the superlattice. By applying successive pump pulses we are able to silence the first back-folded mode near q=0, while selectively enhancing the coherent amplitude of higher order backfolded modes. This increase in the spectroscopic sensitivity opens the way to detailed time resolved studies of higher order acoustic modes in superlattices.

Dielectric susceptibility model for optical phonons in superlattices

The form of the long-wavelength optic-phonon modes in semiconductor superlattices is described using a dielectric susceptibility model. This model only requires knowledge of the frequencies and eigenvalues for LO and TO modes propagating along the superlattice growth direction $z.$ From these, the principal-axis dielectric susceptibilities ${\ensuremath{\varepsilon}}_{\mathrm{zz}}(\ensuremath{\omega})$ and ${\ensuremath{\varepsilon}}_{\mathrm{xx}}(\ensuremath{\omega})$ can be obtained, and so a full description of the optic phonons is possible for any phonon propagation direction. Calculations of confined LO and TO mode frequencies and displacements are made for GaAs/AlAs superlattices. The susceptibilities and mode displacements are compared using a simple continuum model and a microscopic linear-chain model. The susceptibilities are also used to model nonresonant Raman-scattering spectra, and are shown to give results that are in close agreement with published micro-Raman measurements.

Isotope scattering of phonons in superlattices

The elastic scattering rate of acoustic phonons in periodic superlattices due to isotopic atoms is calculated in the isotropic, continuum approximation. Unlike the case in bulk solids, the scattering rate depends on both the propagation direction and mode of phonons. Numerical examples are given for AlAs/GaAs and Al/W superlattices for propagation along the normal to the layer interfaces. We find that the scattering of longitudinal phonons is much weaker than that of transverse phonons for wide ranges of frequencies.

Anomalous transmission of phonons in superlattices at oblique propagation: an analysis based on finite difference equations

Anomalous mode-converted transmission of phonons is studied based on the new formulas for the transmitted amplitudes of phonons propagating oblique to the layer interfaces of superlattices. A transfer matrix which well describes the transmission of the coupled longitudinal and transverse phonons in an isotropic model is introduced. With the use of this transfer matrix we can derive finite difference equations which govern the transmitted amplitudes of both the longitudinal and transverse phonons. These equations can be solved exactly for periodic superlattices and approximately for certain aperiodic superlattices. The results are applied to the study of the unusual intermode oscillations in phonon transmission in both periodic superlattices and aperiodic superlattices with variable thickness of bilayers.

Brillouin scattering from longitudinal acoustic phonons in superlattices with diffuse interfaces

The computation of the Brillouin cross section for scattering of light off longitudinal acoustic (LA) bulk phonons in a superlattice with diffuse interfaces between the layers is presented for the case of normal incidence. Unlike in previous work concerning the problem of diffuse interfaces, both the modulation of the acoustic and elasto-optic parameters, and the modulation of the refractive index are taken into account. The acoustic phonon spectrum is computed by means of numerical solution of a self-adjoint Liouville equation, and the dispersion relation is obtained using a wavevector selection rule. The transmitted (zeroth-order) electromagnetic wave, and the consequent fluctuating polarization vector field radiating Brillouin light are computed numerically for generic depth profiles of elastic, elasto-optic, and dielectric (optic) properties of the medium. The back-scattered light wave in the superlattice is obtained to first order in perturbation theory. The Brillouin differential cross section is computed by summing over the density of phonon states satisfying the wavevector selection rule. As an application, we present some results for the GaAs - AlAs superlattice, providing evidence for the differences from the case with diffuse and sharp interfaces.

Generating coherent THz phonons with light pulses

We present an overview of experimental work and discuss the theory of femtosecond-pulse generation of coherent optical phonons. Recent developments and differences between solids and molecular systems are emphasized. Theoretically, we focus on Raman mechanisms for the coherent driving force providing a comprehensive approach for the description of both below-gap and resonant excitation. The survey covers also polaritons and folded acoustic phonons in superlattices as well as a comparison with spontaneous Raman scattering.

Acoustic SH phonons in a superlattice with (111) interfaces

Transmission rates and dispersion relations of SH phonons in a (111) superlattice are calculated. Unlike the case of a (100) superlattice, phonon stop bands appear inside the folded Brillouin zone in general rather than at the center and edges. A superlattice structure factor is introduced appropriately for phonon reflection or Bragg conditions in the superlattice. More importantly, the transfer matrix contains information not only about the dispersion relation, but also about the condition for frequency bands or stop bands in the dispersion relation, and the extinction rule for the Bragg reflection. The locations of the stop bands inside of the folded zone are defined as a function of frequency and incidence angle of the phonons.

Study of phonons in semiconductor superlattices by Raman scattering spectroscopy and microscopic model calculation

Raman spectroscopy is used to study phonons in a series of thin (AlAs) m /(GaAs) n superlattices (SLs) grown by molecular beam epitaxy (MBE). The influence of buffer layer type on the interface roughness of heterostructures is carefully evaluated. The accuracy of optical phonons and the degree of peak sharpness of GaAs-like confined modes are examined via off-resonance Raman spectroscopy. Theoretical calculations of phonons in thin (AlAs) m /(GaAs) n superlattices (i.e. samples with m, n ≤ 12) are reported for various directions of propagation by using a rigid-ion model. Optical phonons acquire significant dispersive character when the wavevector q forming an angle θ with the growth axis of the superlattice is changed from θ = 0 to π/2, i.e. from [001] to [100]. The frequency gaps in the angular dispersions due to mode anti-crossing behavior observed recently by Zunke et al. using micro-Raman spectroscopy and studied by a continuum model are found to be in reasonably good agreement with our lattice dynamical model calculations.

Far infrared attenuated total reflection spectroscopy for investigating superlattice phonon parameters

We report on low-temperature (77 K) far infrared attenuated total reflection (ATR) spectroscopic measurements on a short period GaAs/AlAs superlattice, and discuss the optics of the modes observed. We assess the significance of the ATR technique for determining superlattice phonon parameters. We model the results using a linear chain model that incorporates the effects of interface roughness; it appears that this model is correctly modelling the phonon response.

Confined Phonons in Metallic Superlattices: Raman Study of Co/Ru.

The Raman-active transverse-optic (TO) phonon mode of Ru was measured in a series of Co/Ru superlattices. The changes in the frequency of the TO vibration, interpreted within the framework of confined phonons, are in excellent agreement with published dispersion curves for bulk Ru obtained from inelastic neutron-scattering experiments. Interpretations of the frequency shifts of the Ru TO mode as due to phonon-folding or lattice-strain effects are ruled out by the data. {copyright} {ital 1996 The American Physical Society.}

Going beyond the mean-field approximations of alloys and alloy superlattices: a few puzzles solved?

We discuss a few examples of cases in which the widely used mean-field approaches to alloys and alloy superlattices may not give complete solutions. These examples include the anomalously large Stokes and anti-Stokes real space-charge transfer over thick alloy barriers and the spatial extent of optical phonons in alloys and alloy superlattices, which have remained unsolved or controversial. We argue, both theoretically and experimentally, that approaches that fully account for inhomogeneities, partial ordering, and disorder effects in the alloys as well as the proper understanding of coupled quantum-mechanical systems do give answers to these important puzzles.

Enhancement of mode-converted transmission of phonons in superlattices

We study the transmission and reflection of phonons incident on a superlattice at an oblique angle. For frequencies in the vicinity of an anti-crossing frequency in the superlattice phonon dispersion relation we find that the wave energy oscillates back and forth between the different polarizations as the wave propagates through the superlattice. These oscillations are analogous to the Pendellösung effect for electrons and X-rays.

Resonant-mode conversion and transmission of phonons in superlattices.

We study the transmission and reflection of phonons incident on a superlattice at an oblique angle. For frequencies in the vicinity of an anticrossing frequency in the superlattice phonon-dispersion relation we find that the wave energy oscillates back and forth between the different polarizations as the wave propagates through the superlattice. These oscillations are analogous to the Pendell\"osung effect for electrons and x rays. \textcopyright{} 1996 The American Physical Society.

Resonant Acoustic PhononRaman Scattering in Magnetic and Electric Fields

The Raman efficiency for scattering of acoustic phonons in semiconductor quantum wells and superlattices exhibits strong resonances at interband critical points of the electronic structure. Owing to Landau or Stark quantization of electron and hole states in an external magnetic or electric field, such resonances can be tuned with respect to the excitation energy and detailed investigations of their character are possible. Layer thickness fluctuations and interface roughness in real samples are the origin of disorder-induced resonant acoustic phonon Raman scattering which manifests itself in a continuous emission background where modes from the whole mini-Brillouin zone participate. In such scattering processes, crystal momentum conservation is relaxed. The fundamental properties of this effect are summarized and its application to studies of quantum well and superlattice electronic structure is illustrated.