Waves In Superlattices Research Articles

Elastic waves in polytype superlattices

We study the shear horizontal and sagittal elastic waves in polytype superlattices, formed by the periodic repetition of three different constituent materials. We use the surface Green function matching method for N non-equivalent interfaces in order to obtain the dispersion relations and the density of states. In this way it is possible to obtain the spatial localization of the different modes. The influence of the variation of the thickness of the constituent materials on the dispersion relation of the elastic modes is studied.

Selection rules for light scattering by folded acoustic phonons in low-index Si-based superlattices

We consider the propagation of acoustic waves in Si-based heterojunctions (HJs), quantum wells (QWs) and superlattices (SLs) grown in arbitrary directions, and present a general formalism for obtaining wave velocities, selection rules, and efficiency of Raman scattering (RS) and Brillouin scattering (BS) by folded acoustic-phonons. Results based on nine different directions for the phonon wavevector are tabulated.

Surface and interface optical waves in superlattices: transverse electric localized and resonant modes

We investigate the existence and behaviour of localized and resonant optical waves associated with the surface of a semi-infinite superlattice or its interface with a substrate, considering the case of transverse electric modes. In this paper, we present an analytic determination of the response function (Green function) for a semi-infinite superlattice with or without a cap layer, and for a superlattice in contact with a substrate. This calculation enables us to obtain both local and total densities of states as functions of the frequency and the wavevector (parallel to the interfaces). Besides the surface and interface localized modes which occur as delta peaks inside the gaps, one can also obtain resonant states as well defined peaks of the density of states inside the bulk bands of the superlattice. In particular, we emphasize the different types of mode induced by a cap layer. In addition, we show that the creation of a semi-infinite superlattice gives rise to delta peaks of weight -1/4 in the density of states at every edge of the superlattice bulk bands.

Band model approach to the theory of the dynamic susceptibility and spin waves in superlattices

AbstractThe transverse dynamic susceptibility of periodic layered systems is calculated within the framework of the multiband model by using the equation of motion method. The presented formalism can be applied to systems with ferro‐or antiferromagnetic coupling between the layers. Numerical calculations are performed for the superlattice composed of ferromagnetic and nonmagnetic materials. Spin waves are investigated and the magnon spectrum is found.

Selection Rules for Light Scattering by Folded Acoustic Phonons in Superlattices Grown in Arbitrary Directions

The propagation of acoustic waves in superlattices grown in arbitrary directions is considered, and a general formalism for obtaining wave velocities, selection rules and efficiency of light scattering by folded acoustic phonons is presented. Results based on nine different directions of the phonon wavevector are tabulated. Some errors found in the literature are corrected. The piezoelectric contributions to the phonon frequencies and scattering intensities are analysed. It is shown that their influence is the greatest for propagation along [111]. Changes in the elastic stiffness and Pockels coefficients due to the piezoelectric effect in GaAs are shown to be of the order of 0.1% and 1%, respectively.

Surface elastic waves in superlattices: Sagittal localized and resonant modes.

Surface elastic waves in superlattices: Sagittal localized and resonant modes.

Surface and interface s-polarized optical waves in superlattices

The existence of localized and resonant optical waves associated with the surface of a semi-infinite superlattice or its interface with a substrate is reported, considering the case of s-polarization (transverse electric modes). These modes appear as well defined peaks of the density of states, either inside the minigaps or inside the bulk bands of the superlattice. The density of states, function of the frequency ω, and the wave vector k ∥ (parallel to the interface), are obtained from an analytic determination of the response function for a semiinfinite superlattice with or without a cap layer.

Propagation of elastic waves in semiconductor superlattices under the action of a laser field.

Propagation of elastic waves in semiconductor superlattices under the action of a laser field.

Acoustic waves in finite superlattices.

Acoustic waves of shear horizontal polarization are studied in a finite superlattice (SL) deposited on a substrate with or without a surface cap layer, or sandwiched between two materials. Using a Green's function method, we have obtained closed-form expressions of local and total densities of states as a function of the frequency \ensuremath{\omega} and the wave vector ${\mathit{k}}_{\mathrm{\ensuremath{\parallel}}}$ parallel to the layers. Due to the substrate-SL-capping layer interaction, different kinds of localized and resonant discrete modes are found and their properties are investigated.

Plasma Waves in a Finite Superlattice

AbstractDispersion equations for plasma waves in a superlattice with a finite number of conducting layers are obtained. It is shown that the existence of surface‐like plasma waves in a finite superlattice is possible under definite conditions which represent the generalization of the well‐known restrictions for the surface waves in semiinfinite superlattices. Results are demonstrated for the case of a superlattice containing N = 3 layers.

Band structure for the propagation of elastic waves in superlattices

A 2×2 transfer matrix approach is used to study the elastic response of multilayered systems. Superlattices with a period of n layers are considered to calculate the dispersion relations of the normal modes for both longitudinal and transverse waves, and the reflectivity of longitudinal modes for finite and semi-infinite structures. Numerical results of the dispersion relation for a two- and three-layer period superlattice are presented to show the band structure of wave propagation. For transverse waves, it is considered that the single layer may support surface modes and it is found that their interaction with those of the adjacent layers also yield a band structure. The calculated reflectivity of longitudinal elastic waves for the semi-inifinite superlattices resembles the allowed and forbidden regions of the dispersion relations. The theoretical reflectivity curves of sound waves are compared with the experimental results for the three-layer systems. A good agreement between theory and experiment is obtained.

Dynamic localization of acoustic waves in superlattices.

The absorption and change in velocity of acoustic wave interacting with electrons in a superlattice irradiated by an infrared laser field are investigated. Near the roots of the equation ${\mathit{s}}_{0}$/\ensuremath{\Delta}d=\ensuremath{\Vert}${\mathit{J}}_{0}$(eFd/\ensuremath{\Omega})\ensuremath{\Vert} (2\ensuremath{\Delta} and d are the miniband width and period of the superlattice, F, and \ensuremath{\Omega} are amplitude and frequency of the laser field, and ${\mathit{s}}_{0}$ is the sound velocity) a strong renormalization of sound velocity and intense absorption peaks are predicted. These phenomena have a straightforward relation with the dynamic localization of electrons and are called dynamic localization of acoustic waves.

Surface and interface elastic waves in superlattices: Transverse localized and resonant modes.

Localized and resonant transverse elastic waves associated with the surface of a semi-infinite superlattice or its interface with a substrate are investigated. These modes appear as well-defined peaks of the vibrational density of states, either inside the minigaps or inside the bulk bands of the superlattice. The densities of states, which are calculated as a function of the frequency \ensuremath{\omega} and the wave vector ${\mathbf{k}}_{\mathrm{\ensuremath{\parallel}}}$ (parallel to the interfaces), are obtained from an analytic determination of the response function for a semi-infinite superlattice with or without a cap layer, and also for a superlattice in contact with a substrate. Besides, we show that the creation from the infinite superlattice of a free surface or of the substrate-superlattice interface gives rise to \ensuremath{\delta} peaks of weight (-1/4) in the density of states, at the edges of the superlattice bulk bands. Then when one considers together the two semi-infinite superlattices obtained by cleavage of an infinite one along a plane parallel to the interfaces, one always has as many localized surface modes as minigaps, for any value of ${\mathbf{k}}_{\mathrm{\ensuremath{\parallel}}}$. Although these results are obtained for transverse elastic waves with polarization perpendicular to the saggital plane (containing the propagation vector ${\mathbf{k}}_{\mathrm{\ensuremath{\parallel}}}$ and the normal to the interfaces), they remain valid for the longitudinal waves in the limit of ${\mathbf{k}}_{\mathrm{\ensuremath{\parallel}}}$=0. Specific applications of these analytical results are given in this paper for Y-Dy or GaAs-AlAs superlattices. The effect of a Si surface cap layer on the surface of this last superlattice is also investigated.

Spin Waves in Superlattices with Exchange Coupling between Nearest and Next‐Nearest Neighbours

AbstractThe spin‐wave spectrum of infinite ferromagnetic superlattices composed of two b. c. c. materials with exchange coupling between nearest and next‐nearest neighbours is analysed theoretically in the exchange‐dominated region. The appropriate dispersion equations are derived by the transfer matrix method. Some numerical examples are presented for superlattices with (100) interfaces.

Effective elastic constants and phonon spectrum in metallic Ta/Al quasiperiodic superlattices.

The propagation of acoustic waves in superlattices is investigated within the effective-medium model generalized to the quasiperiodic structure. The effective elastic constants are analytically obtained in closed form for superlattices with hexagonal symmetry. These results are used to interpret the observed low-frequency phonon spectra from Ta/Al superlattices with quasiperiodic Fibonacci ordering and the elastic constants ${\mathit{c}}_{11}$ and ${\mathit{c}}_{44}$ for the superlattices are determined by fitting the data with an acoustic model of supported hexagonal films. The relative Brillouin cross section is found to be accurately represented by a pure ripple effect without photoelastic contribution. We show that the measured and calculated ${\mathit{c}}_{11}$ demonstrates a reasonable agreement, but an appreciable discrepancy of \ensuremath{\sim}20% for ${\mathit{c}}_{44}$ is found. The implication of these results is discussed in detail.

Theory of spin waves in ferromagnetic superlattices with nonuniaxial single-ion anisotropy.

Calculations based on linear-response theory and the semiclassical torque equation are presented for the role of nonuniaxial single-ion ansiotropy in two-component magnetic superlattices. A Green-function analysis is developed within the Heisenberg model of a ferromagnetic crystal for the bulk and surface exchange-dominated spin waves in superlattices where one material is a nonuniaxial (or ``easy-plane'') ferromagnet and the other material is a uniaxial (or ``easy-axis'') ferromagnet. The influence of the anisotropy on the spectrum of bulk spin-wave bands and surface branches is illustrated by numerical examples.

Resonant reflectance dips induced by coupled surface plasmon polaritons in thin metal-film/dielectric superlattices

The optical reflectance of metal films changes dramatically as the film thickness becomes thinner than the electron mean free path. We have developed a transfermatrix formalism for deducing the dispersion relations of the electromagnetic waves in infinite and semi-infinite metal-dielectric superlattices by taking into account the presence of the size effect and coupled plasmon waves. This work shows that the resonance frequency occurring at the reflecting dip increases while the bandwidth decreases as the thickness of the dielectric films increases. Reducing the values of p′ and q′ shifts the resonance frequency upward and yields multiple numbers of minimum reflectivity.

Effect of next-nearest-neighbour interactions on spin waves in magnetic superlattices

Results are presented for 3D magnetic superlattices consisting of alternating films of cubic Heisenberg ferromagnets. Taking into account the next-nearest-neighbour (NNN) interactions, an explicit equation for the spin-wave dispersion relation is obtained by means of a transfer matrix method. Numerical results are presented for FCC ferromagnetic films with different values of the exchange constant ratio eta =J(NNN)/J(NN). If eta not=0, for every frequency omega , there are two pairs of allowed values of wavenumbers k and in some frequency range both can be real if eta >or=1. For the superlattice, a comparison with the dispersion relation obtained considering only NN interaction is made and the main physical features are discussed.

Spin waves in superlattices. IV. The exchange-dominated region

Bulk and surface exchange-dominated spin waves in semi-infinite superlattices are considered theoretically within the transfer matrix formalism. The in- and inter-plane exchange constants for two atomic planes at each interface are assumed to differ from appropriate bulk values. The spin-wave spectrum has been calculated numerically for superlattices composed of two different ferromagnetic materials. Considerations are restricted to the case of parallel alignment of the film magnetizations.

特集 金属人工格子の構造，物性とその応用 金属人工格子のスピン波・表面弾性波ブリルアン散乱

特集 金属人工格子の構造，物性とその応用 金属人工格子のスピン波・表面弾性波ブリルアン散乱