Roughness induced surface acoustic resonances

The vibrational and electronic spectra of a semi-infinite crystal with a planar surface is modified in presence of surface inhomogeneities or roughness such as ridges or grooves, quantum wires or tips… Using a Green's function formalism, we present an exact numerical method for obtaining the variation of the density of states associated with the adsorption of a ridge on a flat surface or with a groove cut into an otherwise planar surface. This general method is applied to the determination of the acoustic resonances of shear horizontal polarization associated with such deterministic surface protuberances or indentations. The positions and widths of the peaks in the total or local densities of states give the frequencies and lifetimes of the resonances, which may be more or less pronounced features depending on the relative parameters of the substrate and ridge materials. We also investigate the modifications of these acoustic surface shape resonances due to the interaction between two such defects. This calculation can also be transposed to the study of electronic structure of a wire near a flat surface, in the framework of an effective mass model.     

Electronic structure of some mesoscopic systems: II. Electronic composites

We study the electronic properties of a mesoscopic system composed of an array of straight, infinite rods made of an isotropic medium and embedded in a regular way in an isotropic background. Such a composite system has two-dimensional periodicity in the plane perpendicular to the rods. Using a Fourier series expansion, the corresponding Schrödinger equation is solved within the effective-mass approximation. The electronic band structure is computed for the wave vector in the transverse plane, and is illustrated by dispersion curves along the principal directions of the two-dimensional Brillouin zone as well as by the histograms of the density of states. The main result is the appearance of absolute energy gaps in the two-dimensional band structure.     

Simple models of adsorbed polymers: Vibrational properties

The vibrational properties of polymers adsorbed on surfaces are investigated within the frame of two simple models. First the surface is modelled as a one-dimensional infinite harmonic chain. Polymeric “ molecules ” are represented as harmonic chains of finite length. The coupling between the polymers and the surface is treated within the frame of the Interface Response Theory. Upon adsorption of polymers, resonant vibrational modes appear as well defined peaks in the variation of the density of states of the system. The effect of the interaction between adsorbed polymers via phonons is investigated and shown to lead to antiresonances in the spectral density of states and the formation of gaps in the density of states as the surface coverage is increased. A second more realistic model is introduced where the same finite harmonic chains (polymers) are grafted on a two dimensional [001] surface cut through a cubic harmonic crystal. Again the variation in density of states exhibits resonant modes between the polymers and the substrate. However, in this case, the interaction between polymers is short range. Adsorption of a film of polymers produces resonant modes which remain well-defined features within the substrate bulk band.     

Elastic properties of finite three-dimensional solid phononic-crystal slabs

We study theoretically, by means of layer-multiple scattering techniques, the propagation of elastic waves through finite slabs of phononic crystals consisting of metallic spheres in polyester matrix, embedded in air. We focus on the study of modes localized on the surfaces of the structure, investigating the physical parameters which influence and determine their appearance. Our results reveal the existence of absolute phononic frequency gaps in these finite structures, and point out the possibility, under an appropriate choice of the parameters, of tunable regions of frequency free of propagating and/or surface-localized modes. This could be very useful in the design of devices related to frequency filtering, waveguiding, etc.     

Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals

Experimental measurements of acoustic transmission through a solid-solid two-dimensional binary-composite medium constituted of a triangular array of parallel circular steel cylinders in an epoxy matrix are reported. Attention is restricted to propagation of elastic waves perpendicular to the cylinders. Measured transmitted spectra demonstrate the existence of absolute stop bands, i.e., band gaps independent of the direction of propagation in the plane perpendicular to the cylinders. Theoretical calculations of the band structure and transmission spectra using the plane wave expansion and the finite difference time domain methods support unambiguously the absolute nature of the observed band gaps.     

Elastic waves at the (0 0 1) and (1 1 0) surfaces of AlN, GaN and InN

We have studied the acoustic waves in the (0 0 1) and (1 1 0) surfaces of AlN, GaN and InN. We have employed the surface Green function matching method and different sets of calculated elastic constants available in the literature for these materials, because no experimental values are available. Important differences are found for the velocities of the bulk and surface acoustic waves coming from these sets of elastic constants, in such a way that they could be easily measured by ultrasonic and Brillouin techniques. These results together with the expressions obtained here for the velocities of the acoustic waves in high symmetry directions could be used to determine the elastic coefficients of these materials.     

Elastic interaction between a point defect and a step

The elastic interaction energy between a point defect or an adatom and a step is calculated. The defect is represented by a localized dipole force while the presence of the step is modelled by a distribution of dipole forces on half of the surface plane. The interaction energy changes sign when the defect goes through the plane perpendicular to the surface and containing the edge of the step. For an adatom, this energy behaves like the inverse of its distance to the edge of the step ; it is attracted to the step on one terrace and repelled from it on the other terrace.     

Interaction of Love waves with coupled cavity modes in a 2D holey phononic crystal

The interaction of Love waves with square array of pillars deposited on a cavity defined in a 2D holey phononic crystal is numerically investigated using Finite Element Method. First, the existence of SH surface modes is demonstrated separately for phononic crystals that consist of square arrayed holes, or rectangular arrayed Ni pillars, respectively in, or on, a SiO₂ film deposited on a ST-cut quartz substrate. The coupling between SH modes and torsional mode in pillars induces a transmission dip that occurs at a frequency located in the range of the band-gap of the holey phononic crystal. Second, a cavity is constructed by removing lines of holes in the holey phononic crystal and results in a transmission peak that matches the dip. The optimal geometrical parameters enable us to create a coupling of the cavity mode and the localized pillar mode by introducing lines of pillars into the cavity, which significantly improved the efficiency of the cavity without increasing the crystal size. The obtained results will pave the way to implement advanced designs of high-performance electroacoustic sensors based on coupling modes in phononic crystals.     

Density of states of superlattices with multiple layers per period

Density-of-states (DOS) investigations of polytype superlattices (SLs), whose period consists of more than two different layers, are presented. Local DOS (LDOS) is computed as a function of both the electron energy and the space coordinate, which illustrates — in a direct way — the spatial localization, over the SL period, of states forming the energy minibands. A few examples of AlGaAs-based polytype SLs with a coupled-well, step-well and δ-doped basis are analysed, indicating that various LDOS distributions within SL minibands can be arranged. By changing the basis geometry, the electronic DOS can either be selectively confined to a particular SL layer or extend over the whole SL period, which provides a means of modifying the spatial overlap of states from different SL minibands and thus, tuning the respective interband transitions. In particular, polytype SLs with similar miniband structures may exhibit essentially different LDOS features and, consequently, the different transport and optical characteristics. Therefore, it is emphasized that — for a particular device application of a complex-basis SL — not only the electronic level structure should be appropriately designed, but also the corresponding space-charge distributions should be carefully considered.     

Sonic stop-bands for cubic arrays of rigid inclusions in air

Extensive band structures have been computed for cubic arrays of rigid spheres and cubes in air. Complete stop bands are obtained for the face-centered-cubic (fcc) structure; however, there is no gap for the body-centered-cubic (bcc) and simple-cubic (sc) structures. These gaps start opening up for a filling fraction of (27%) for spherical (cubic) inclusions and tend to increase with the filling fraction, exhibiting a maximum at the close-packing. We also propose a tandem structure that allows the achievement of an ultrawideband filter for environmental or industrial noise in the desired frequency range. This work is motivated by the recent experimental measurement of sound attenuation on the sculpture, by Eusebio Sempere, exhibited at the Juan March Foundation in Madrid (Nature 378, 241 (1995)) and complements the corresponding theoretical work (Appl. Phys. Lett. 70, 3218 (1997)). Received: 24 October 1997 / Revised: 1 December 1997 and 26 January 1998 / Accepted: 6 March 1998