Calculated Dispersion Curves Research Articles

Periodic Green's functions analysis of SAW and leaky SAW propagation in a periodic system of electrodes on a piezoelectric crystal

A method of periodic Green's functions with a propagation factor exp(i/spl beta/x), unknown in advance, is used to calculate dispersion curves and attenuation coefficients for Rayleigh- and leaky- waves propagating in a periodic system of thin electrodes on a piezoelectric surface. To describe the charge distribution on the electrodes both a step approximation and Chebyshev polynomials are used, the last being more adequate in most cases. Numerically determined values of the Green's function are used and interpolated either linearly or using a modified variant of Ingebrigtsen's formula. Such basic parameters as stopband width, stopband center frequency, wave velocity and attenuation in the stopband are found. These parameters can be used in the coupling-of-modes (COM) analysis and design of SAW devices. The analysis includes bulk wave radiation and scattering. The dependence of the corresponding attenuation coefficient on frequency is determined. Results obtained allow the determination directly and properly of the COM parameters and the design of SAW devices having large number of electrodes most precisely and rapidly. Numerical results for Rayleigh waves on YZ-LiNbO/sub 3/ and leaky waves on 36/spl deg/YX-LiTaO/sub 3/ substrates are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Thin film characterization using generalized Lamb waves and harmonic generation

A non-destructive method for the local characterization of the mechanical and adhesion properties of a thin film on a semi-infinite substrate is proposed. A numerical inversion procedure based on the simplex algorithm was developed and tested for the dispersion relation of generalized Lamb waves propagating in a thin film on a substrate. A continuous wave scanning acoustic microscope was used to propagate these surface modes in the specimen and to measure the dispersion curves. This procedure allows the determination of the following parameters of the film: longitudinal wave velocity, transverse wave velocity, density and thickness. Possibilities of this method are studied and tested on several metallic samples. An application to interface characterization is suggested. By comparison of the position and shape of experimental and calculated dispersion curves for various boundary conditions (delamination, weak and perfect interface) at the interface on the one hand and by observation of the harmonic generation phenomena due to the high non-linearity of weakly bonded interfaces on the other hand, qualitative information on the adhesion of the film on the substrate could be obtained.

Quantum well excitonic polaritons : coupling of quantum well excitons to electromagnetic waveguide modes

The calculated dispersion curves of excitonic polaritons in GaAs quantum wells provide up to now not even a qualitative explanation for the time-of-flight experiments by Ogawa et al. [Phys. Rev. Lett. 64, 796 (1990)] which clearly show the existence of a mode with photon-like dispersion above the excitonic resonance. We show that this discrepancy can be removed by realizing that the QW constitutes a dielectric waveguide. The solution of the coupled system consisting of the exciton and the electromagnetic waveguide eigenmodes yields a drastically modified dispersion for the T and Z polariton as compared to previous calculations

Electronic structure of erbium disilicide.

The calculation of the electronic structure of ideal ${\mathrm{ErSi}}_{2}$ has been performed using the linear-muffin-tin-orbital method. Tight-binding parameters were then obtained by fitting to the calculated dispersion curves and applied to two nonstoichiometric ${\mathrm{ErSi}}_{1.7}$ structures corresponding to different vacancy orderings along the c crystal axis. Comparison is made with experimental photoemission data and the relative stability of the different phases is discussed as well as the low value of the Schottky barrier at the ${\mathrm{ErSi}}_{2}$-Si interface.

Acoustic-microscopy measurements of the elastic properties of TiN/(VxNb1-x)N superlattices.

The elastic constants of (${\mathrm{V}}_{0.6}$${\mathrm{Nb}}_{0.4}$)N and (${\mathrm{V}}_{0.3}$${\mathrm{Nb}}_{0.7}$)N films have been determined from anisotropic surface acoustic wave (SAW) dispersion data measured by line-focus acoustic microscopy. Using the acoustic microscope, measurements of SAW velocities have also been carried out on the TiN/(${\mathrm{V}}_{0.6}$${\mathrm{Nb}}_{0.4}$)N (001) and TiN/(${\mathrm{V}}_{0.3}$${\mathrm{Nb}}_{0.7}$)N (001) and (111) superlattice films, all grown on cubic-crystalline MgO substrates. The phase velocities, measured as functions of the angle of propagation, display the expected anisotropic natures of (001) and (111) cubic symmetries. Dispersion curves of SAW's propagating along the symmetry axes have been obtained by measuring wave velocities for various film thicknesses and frequencies. From the elastic constants of homogeneous TiN, (${\mathrm{V}}_{0.6}$${\mathrm{Nb}}_{0.4}$)N, and (${\mathrm{V}}_{0.3}$${\mathrm{Nb}}_{0.7}$)N films, the effective elastic constants of TiN/(${\mathrm{V}}_{0.6}$${\mathrm{Nb}}_{0.4}$)N and TiN/(${\mathrm{V}}_{0.3}$${\mathrm{Nb}}_{0.7}$)N superlattice films and the corresponding phase velocities of SAW's have been calculated. The calculated dispersion curves show very good agreement with the experimental results. The dependence of the elastic properties of the superlattices on the TiN fraction, on the superlattice period, and on the crystallographic orientation has been investigated. The results show no elastic anomalies within measurement errors, indicating that previously reported hardness enhancements were not related to elastic property changes.

Raman study of CeO2: Second-order scattering, lattice dynamics, and particle-size effects.

Polarized Raman-scattering spectra are obtained from oriented single crystals of ${\mathrm{CeO}}_{2}$. Second-order features are assigned to phonon overtones from the X and L points on the Brillouin-zone boundary on the basis of selection rules and by analogy to another fluorite structure compound, ${\mathrm{BaF}}_{2}$, in which the phonon dispersion curves are known. Complete selection rules for second-order scattering from these high-symmetry points are determined. A rigid-ion model is constructed for the phonon dispersion curves by fitting several of these features and the known zone-center optical modes. The ${\mathit{F}}_{2\mathit{g}}$ Raman-active mode at 465 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in ${\mathrm{CeO}}_{2}$ shifts and broadens with decreased particle size [G. W. Graham, W. H. Weber, C. R. Peters, and R. Usmen, J. Catalysis 130, 310 (1991)]. It is shown using the calculated dispersion curves that this particle-size effect cannot be explained with the spatial-correlation model.

Determination of acoustic phonon dispersion curves in layer silicates by inelastic neutron scattering and computer simulation techniques

Inelastic neutron scattering and computer modelling techniques have been used to study acoustic phonons in several layer silicate minerals. Experimental measurements have been made on four layer silicate minerals; namely samples of muscovite, Fe-bearing muscovite, margarite and chlorite. The longitudinal acoustic modes propagating along the [0, 0, ξ] direction of muscovite and Fe-bearing muscovite were found to be the same, within experimental error. The longitudinal and transverse acoustic modes propagating along [0, 0, ξ] of muscovite have been calculated using computer simulation techniques based on lattice dynamics. The experimental and calculated longitudinal modes of muscovite are in excellent agreement, thereby demonstrating the complementary nature of both techniques. The shape of both experimental and calculated dispersion curves was found to be approximately sinusoidal, indicating that interatomic forces act principally between nearest-neighbour atoms.

Magnetoplasma reflectivity and polaritons in semiconductor superlattices

The expressions for the effective-medium dielectric tensor of a superlattice comprising doped semiconductor layers in the presence of a magnetic field are derived. They are applied to calculations of reflectivity, bulk and surface polariton dispersion curves and attenuated total reflection (ATR). Numerical results are presented for an n-p and for an n-n' superlattice, the latter being a model for delta -doped GaAs.

Exact algebraic dispersion relations for wave propagation in hot magnetized plasmas

A new model is presented for the treatment of wave propagation along an external magnetic field in a hot collisionless plasma. The analysis is based on the so-called polynomial distribution functions along the magnetic field, and takes account of enhanced fractions of high-energy particles, which are characteristic of rarefied and magnetized astrophysical plasmas, in comparison with the bi-Maxwellian distributions. These new distributions permit the derivation of general dispersion relations that are exactly valid for waves with Im (ω) &gt; 0, and represent good approximations for those with Im (ω) &gt; 0. Furthermore, the explicit form of the dispersion relations is shown to be valid for distribution functions of different shapes. Because of their algebraic structure, the solution of the dispersion relations can be shown to be equivalent to the determination of the roots of complex-valued polynomials. The cold plasma, the Maxwellian plasma and the so-called quasi-Maxwellian plasma appear in this formalism as asymptotic and special cases. The reliability of the model is demonstrated with the calculation of dispersion curves, growth and damping rates for several standard modes, and by comparing it with previous calculations carried out using explicit Maxwellian distributions. Finally, the tendency of the solar wind to generate ion-cyclotron waves is investigated as a first, new application.

Magnetic properties of Fe 2Na 3(PO 4) 3—I. Calculation of magnon dispersion curves in a complex structure

A model capable of reproducing the magnon excitations observable in the anti-ferromagnetic phase of Fe 2Na 3(PO 4) 3 is proposed. This model takes into account all the super-super-exchange interactions between the spins of the four Fe 3+ of the unit cell and the neighboring spins. It is assumed that spins are collinear. The calculation method of the magnon dispersion curves is based on Saenz's formalism, and the analytical derivation of the magnon energies is performed for ideal hexagonal symmetry. Numerical calculations of magnon dispersion curves and spin deviations vs exchange interactions are reported, both in the hexagonal and triclinic symmetries. It appears that four modes can be distinguished in the triclinic symmetry. Magnetic structure stability considerations demonstrate that exchange interaction frustrations are consistent with the anti-ferromagnetic structure of the compound; it is shown that magnon dispersion curves are strongly dependent on the presence of frustrated exchange interactions.

Elastic properties of a-Ge:H/Si and a-Ge: H/SiO 2 heterostructures

Brillouin light scattering from Rayleigh and Sezawa surface acoustic modes in a-Ge: H films depositedf on both c-Si(100) and fused silica substrates has been exploited for studying the elastic properties of these heterostructures. Their effective elastic constants have been determined from a fit of the calculated dispersion curves to the measured sound velocities. We have found that the effective shear modulus C 44 is much lower that that of crystalline Ge. The decrease observed is of about ∼ 38% when the film is supported by c-Si and of about ∼ 44% when supported by fused silica. No appreciable modification of the effective elastic constant C 11, with respect to crystalline Ge, has been observed.

Self-consistent-screening calculation of interatomic force constants and phonon dispersion curves from first principles.

We have developed a method for the calculation of phonon dispersion curves for crystals. The method is based upon linear-response theory and makes no assumptions about the form of the ion-electron interaction or the representation of the wave functions used in the determination of the electronic structure. To demonstrate the accuracy of our method, we present a calculation of the interatomic force constants and the phonon dispersion curves of aluminum from first principles. In this calculation, the bare ion-electron interaction is taken as a nonlocal ab initio pseudopotential. We compare the results of the present method with total-energy frozen phonon results, and with experiment, where the agreement is excellent.

The Theoretical Calculation of Elastic Constants and Phonon Dispersion Curves of Ca0.86Sr0.14CuO211The project supported by National Natural Science Foundation of China throught Grant No. 1880710.

The lattice dynamical properties of Ca0.86Sr0.14CuO2 are studied with a shell model. Its elastic constants and phonon dispersion curves are predicted. The calculated optical mode frequencies in Γ point are in reasonable agreement with infrared spectra, except an A2u symmetry mode around 180 cm-1. Our calculated results can serve as guide for further experimental investigation.

Laser generation and detection of surface acoustic waves: Elastic properties of surface layers

A noncontact all-optical method for surface photoacoustics is described. The surface acoustic waves (SAWs) were excited employing a KrF laser and detected with a Michelson interferometer using a 633-nm HeNe laser. Due to an active stabilization scheme developed for the interferometer a surface displacement of 0.2 Å could be detected. The materials investigated included pure materials such as polycrystalline aluminum, and crystalline silicon; films of gold, silver, aluminum, iron, and nickel on fused silica; and a-Si:H on Si(100). In the case of pure materials the shape of the acoustic pulse and the phase velocity were determined. The dispersion of the SAW phase velocity observed for the film systems was used to extract information on the film thickness, density, and transverse and longitudinal sound velocity. Models for the theoretical treatment of film systems and the calculation of dispersion curves are presented.

Vector circuit method applied for chiral slab waveguides

Eigenvalue equations for the propagation constants of lightwaves in open chiral slab waveguides are derived. The analysis makes use of vector circuit modeling of a chiral slab, the method which has been previously applied for calculating reflection and transmission of electromagnetic waves in chiral multilayer structures. The general eigenvalue equation for the guide which is valid for arbitrary boundary impedance conditions on the slab interfaces is derived, and three special cases are analyzed in detail: an open chiral dielectric slab with dielectric half spaces of the opposite sides of the slab, a chiral slab on an ideally conducting surface, and a chiral slab on an ideal magnetic surface. The theory is visualized by calculated dispersion curves indicating the chirality effect on the wave propagation characteristics.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Ab initio calculations of phonon dispersion curves. Application to Nb and Mo

The technique for the phonon dispersion calculations in transition metals using ab initio pseudopotentials is discussed. The phonon dispersion curves along the (ξ, 0, 0) direction are calculated for Nb and Mo. The Al phonon spectra are also calculated to check the technique used. The analysis of the results appears to confirm the dominant role of the low-band contribution in the formation of the dip in the Nb longitudinal phonon branch.

Rayleigh waves and leaky SAWs in periodic systems of electrodes: periodic Green functions analysis

A new method using periodic Green functions is developed and used to calculate dispersion curves and attenuation coefficients for Rayleigh waves and for leaky waves propagating in periodic systems of thin electrodes on piezoelectric substrates. Such basic parameters as stopband width, centre frequency of the stopband, attenuation in the stopband and resulting bulk-wave scattering are found for Rayleigh waves in YZ-LiNbO3 and leaky waves on 36° YX-LiTaO3 substrate with shorted or open electrodes.

Resonances in the surface-phonon spectrum of an sp-bonded metal.

We report He-atom time-of-flight measurements and microscopic calculations of surface-phonon spectral densities and dispersion curves, revealing the presence of ``anomalous'' resonances in the phonon spectrum for low-index surfaces of Al. These resonances are similar to those observed in d-electron metals, for which they have been attributed to sp-d hybridization effects. For sp-bonded Al the resonances are not related to a ``softening'' of a single force constant, but rather to cumulative effects of changes in the entire surface force field.

Dispersion curves and fields for a chiral slab waveguide

The paper discusses wave propagation and field distributions in slab dielectric waveguides having homogeneous isotropic chiral material. The analysis is based on field expansions in the guide and in the upper and lower half spaces. Enforcing the boundary conditions at the waveguide interfaces result in eigenvalue equations for the hybrid propagating and guided modes. The theory is illustrated by calculating dispersion curves and field distributions for weakly guiding chiral slab waveguides.

Elastic properties of CuCo multilayers

The acoustic phonon modes of sputter-deposited CuCo multilayers were studied using Brillouin scattering. These are the first such measurements to be made on an f.c.c.-f.c.c. multilayer system. The multilayer samples had a fixed atomic percentage of cobalt (53 at.%). The effective elastic constants of the multilayer samples, which were obtained by comparing the data with calculated dispersion curves for the phonon modes, were independent of the multilayer modulation wavelength.