Surface Optical Modes Research Articles

Surface vibrational properties

An overview is given of the principal types of surface vibrational modes that occur at a clean surface of a solid and the means whereby they can be studied experimentally. The modes that are discussed include long-wavelength surface acoustic modes (Rayleigh waves), short-wavelength surface acoustic modes, long-wavelength surface optical modes (surface polaritons), and short-wavelength surface optical modes. Typical dispersion curves illustrating the various types of modes are presented. Mention is also made of surface vibrational modes associated with adsorbed species on solid surfaces. Experimental techniques that are discussed include inelastic electron and helium atom scattering, Raman and Brillouin scattering, acoustic wave reflection, and attenuated total reflection. Other vibrational properties considered are surface specific heat and surface mean square displacements (Debye–Waller factor).

Theory of electron energy loss spectroscopy at the surface of a planar stratified medium, application to semiconductor superlattices

The nonretarded, macroscopic surface and interface optical vibrational modes of a layered material are theoretically investigated via their electron energy loss spectrum (EELS) in the reflection geometry. For this purpose, a continued-fraction representation of the relevant effective dielectric function of an arbitrarily stratified medium is obtained. For a semi-infinite superlattice two distinct types of vibrational excitations are predicted. The first gives rise to weak EELS continua and consists in Bloch-like interface modes propagating throughout the layered medium. The second type is responsible for strong EELS lines outside the above continua and is associated with evanescent, Fuchs-Kliewer-like surface modes of the superlattice. Application to a model GaAs/InAs superlattice is given for illustration.

Observation of surface optical phonons in NaF(001) by inelastic He-atom scattering.

Previous time-of-flight experiments at 20-meV He beam energies, which provided the dispersion curve of Rayleigh surface phonons, have been extended to 90-meV energies on NaF(001) along $〈100〉$. Despite a large multiphonon background from the Rayleigh phonons it has been possible to detect small peaks due to optical surface phonons. The results provide the first direct experimental evidence in the dispersion curves of microscopic surface optical modes.

Localized states and long-range ordering in one-dimensional transverse Ising model

The question of localized states in the one-dimensional Ising model with a transverse field for arbitrary boundary conditions is strictly discussed. An analytical discussion of the occurrence of acoustic and optical surface modes for finite as well as semi-infinite chaim is performed. We also analyze the influence of the surface states on the long-range ordering.

Surface-polaron first-order phase-transition-like behavior

A simple unitary-transformation formalism, successfully applied to the bulk polaron problem, is used in order to investigate the ground-state properties of an electron near a surface of a semi-infinite material and interacting with the surface optical modes. The method has the advantage of being applicable to the whole range of the electron---surface-phonon coupling. A first-order phase-transition---like behavior from the quasifree to the self-trapping electron state as the coupling constant exceeds a certain critical value is observed. The characteristic features of this phase transition such as rapid changes of the ground-state energy, the effective mass, the mean number of surface phonons in the cloud around the electron, and the spatial localization of the electron perpendicular to the surface at the critical coupling constant, are seen. In the present calculation, the coupling of the electron to the bulk excitation modes is not treated.

The spectroscopy of surface vibrations in ionic crystals by inelastic scattering of atoms

The recent progress in the production of highly monochromatic atomic beams is paving the way for a full determination of the surface vibrational structure. Account is given of the recent determination of Rayleigh wave dispersion curves from angular distributions exploiting the kinematical focussing effect. A short review is then presented on the direct measurement of surface phonon dispersion curves, first achieved by Brusdeylins, Doak and Toennies in alkali halides, from time-of-flight (TOF) spectra of scattered He atoms. A comparison is made with the existing theories of surface phonons in ionic crystals. The one phonon energy loss spectra of He scattering from LiF(001) calculated for a hard corrugated surface model are found to be in general good agreement with the experimental TOF spectra. From such a comparison evidence is obtained that: (i) one-phonon processes are predominant, and (ii) in addition to Rayleigh waves important contributions to the inelastic scattering come from the surface projected density of bulk phonons. Important effects due to inelastic resonances with surface bound states are put in evidence and explained by simple kinematical arguments. The possible observation of surface optical modes in NaF(001) is finally discussed.

The spectroscopy of surface vibrations by atom scattering

The recent progress in the production of highly monochromatic atomic beams is opening new perspectives in surface physics, having paved the way for a full determination of the surface vibrational structure. After a discussion on the possible determination of Rayleigh wave dispersion curves from angular distributions exploiting the kinematical focussing effect, a short review is presented on the direct measurement of surface phonon dispersion curves, first achieved by Brusdeylins, Doak and Toennies in alkali halides, from time-of-flight (TOF) spectra of scattered He atoms. A comparison is made with the existing theories of surface phonons in ionic crystals. The state of the art in the theory of inelastic processes is briefly illustrated in order to discuss the theoretical interpretation of TOF spectra. The one-phonon energy loss spectra of He scattering from LiF(001) calculated for a hard corrugated surface model are found to be in general good agreement with the experimental TOF spectra. From such a comparison evidence is obtained that: i) one-phonon processes are predominant, and ii) in addition to Rayleigh waves important contributions to the inelastic scattering come from the surface-projected density of bulk phonons. Important effects due to inelastic resonances with surface bound states are put in evidence and explained by simple kinematical arguments. The possible observation of surface optical modes in NaF(001) is finally discussed.

Self-trapping of an electron by the surface modes

A generalized form of the Feynman's path integral method is used in order to calculate the ground-state energy and the effective mass of an electron interacting with the surface optical modes for the whole range of the coupling constant. A phase-transition-like behaviour from nearly free electron to a self-trapping electron as the coupling constant exceeds a certain critical value α c ∼3.8 is observed.

THE SPECTROSCOPY OF SURFACE PHONONS BY INELASTIC ATOM SCATTERING

The recent great advance in the production of highly inonochromatic atcmic beams is opening new pers2ectives in surface physics, having made way to a full determination of the surface vibrational structure. After a short review of the earlier att- empts to detect surface phonons from the angular distributions of scattered atoms, we re2ort on the direct measurement of surface phonon dispersion curves, first achieved by Brusdeylins, Doak and Toennies in alkali halides, from time-of-flight (TOF) spectra of scattered He atoms. A comparison is made with the existing theo- ries of surface phonons in ionic crystals. The state of the art in the theory of inelastic scattering processes is briefly illu- strated in order to discuss the theoretical inter2retation of TOF spectra. The one-phonon energy-loss spectra of He scattered from LiF(001) calculated for a hard corrugated surface model are found to be in good agreement with TOF spectra at all the incidence angles. Evidence is given that, in addition tl ayleigh waves, important contributions to the inelastic scatte g come from the surface- projected density of bulk phonons. The possible observation of optical surface modes in KCl(001) is finally discussed.

Observation of surface optical phonons on TiO2(100)

Surface vibrations on a Ti${\mathrm{O}}_{2}$(100) surface have been investigated with high-resolution electron-energy-loss spectroscopy at a resolution of 10 meV. The energy-loss spectra are interpreted in terms of single- and multiple-phonon excitation of long-wavelength Fuchs-Kliewer surface optical modes. The observed frequencies are in good agreement with the predictions of dielectric response theory.

Dynamics of a finite harmonic oscillator chain with a surface impurity

A method is presented for constructing the normal modes and spectrum of a finite harmonic oscillator chain to which a polyatomic surface impurity is attached. This scheme is a generalization of an earlier theory due to Puszkarski. Special attention is devoted to localized surface modes and to the identification of the circumstances which cause them to occur. Diagnostic calculations have been performed in order to learn how an adsorbed diatomic molecule alters the normal modes and eigenfrequencies of the lattice. Examples are provided of cases where these effects are slight and of others where the perturbation generates localized optical and/or acoustic surface modes.

Dynamics of a finite harmonic oscillator chain with a surface impurity

Abstract A method is presented for constructing the normal modes and spectrum of a finite harmonic oscillator chain to which a polyatomic surface impurity is attached. This scheme is a generalization of an earlier theory due to Puszkarski. Special attention is devoted to localized surface modes and to the identification of the circumstances which cause them to occur. Diagnostic calculations have been performed in order to learn how an adsorbed diatomic molecule alters the normal modes and eigenfrequencies of the lattice. Examples are provided of cases where these effects are slight and of others where the perturbation generates localized optical and/or acoustic surface modes.

Surface polaritons in semi-infinite crystals

Recent progress in the field of optical surface modes in semi-infinite crystals is reviewed. The basic equations for surface polaritons originating from phonons, plasmons, excitons and magnons are given. Their observation by ATR, the resulting information and possible applications are discussed.

The optical surface modes of metal spheres

A theoretical study of optical surface plasmon modes of metal spheres is made within the framework of a free-electron spatially dispersive dielectric function model which includes retardation effects. Dispersion equations for homogeneous and inhomogeneous spheres are derived for the lth spherical harmonic. The radiative properties of the modes are investigated as a function of l and surface structure which is included by means of a double step-function profile. The real part of the frequency has the same magnitude, and trend with sphere radius, as the current experimental results.

Optical surface modes of lattice vibrations

Two simple methods, based on simple crystal models, for estimating the longitudinal optical surface vibration mode frequencies which lie in a LALO gap are examined. One method consists of deriving and solving a single-variable equation for the surface mode frequency, which depends only on the experimental bulk dispersion curves. The other method consists of fitting the known dispersion curves of a simple one-dimensional model, for which the optical surface mode frequency is given by a simple expression, to experimental bulk dispersion curves of more complex crystals. The results are compared with detailed theoretical surface mode calculations. The latter method is found to give better estimates.

Experimental Study of Surface Optical Modes in Ionic Crystal Slabs

AbstractSurface optical vibrations have been revealed and investigated in slabs of a number of alkali halide crystals and crystals of CaF2 and CdF2. The measurements were carried out by the attenuated total reflection technique. The frequency dependence of reflection coefficient has been calculated in accordance with the experimental set‐up. For NaCl and CaF2 crystals dispersion curves of the surface modes have been measured at room and liquid nitrogen temperatures. The comparison of experimental and calculated data shows that the anharmonic term of the dielectric constant should be taken into account in the calculation of the surface modes.

Theory of Inelastic Scattering of Slow Electrons by Long-Wavelength Surface Optical Phonons

The purpose of this paper is to present a quantum-mechanical theory of the inelastic scattering of slow electrons by long-wavelength surface optical phonons for simple models of an ionic crystal and for a nonionic crystal such as silicon. It is argued that a quantum-mechanical approach is necessary for this problem. However, the expression we obtain for the one-phonon cross section is found to be identical to the one that follows from the earlier classical theory of Lucas and co-workers, provided one replaces their parameter ${P}_{0}$ by the quantum-mechanical reflection coefficient for specular reflection. The angular distribution of the scattered electrons and the energy dependence of the one-phonon cross section are discussed for the case of ZnO and silicon, where the surface optical modes have a very different character. For the surface mode in silicon, we define a dipole-moment effective charge, which is nonzero by virtue of the absence of inversion symmetry in the surface region. A quantitative estimate of the magnitude of this parameter is extracted from the data of Ibach.

Surface Modes of Vibration and Optical Properties of an Ionic - Crystal Slab

A formalism is developed for calculating the normal modes of vibration of an ionic-crystal slab having the NaCl structure. The slab consists of a finite number of (100) planes oriented normal to the $z$ axis and is of infinite extent in the $x$ and $y$ directions. The derivation of the dynamical matrix takes into account the free surfaces of the slab as well as the effect of retardation of the Coulomb interaction. Retardation is easily excluded from the theory by letting the speed of light $c$ become infinite in the Coulomb contributions to the dynamical matrix. The unretarded normal-mode frequencies and eigenvectors are calculated for a seven-layer slab for values of the wave vector chosen along the $x$ axis and ranging from zero out to the boundary of the two-dimensional first Brillouin zone. The properties of the optical surface modes are discussed in detail. If an electromagnetic wave is incident upon the slab, the optical properties of the slab can be found by calculating the total electric field which exists in the regions of space on either side of the slab as a superposition of the incident field and the induced field arising from the ionic motion within the slab. For both $P$ and $S$ polarizations of the incident field, peaks in the infrared absorption are found to occur at frequencies corresponding to certain optical modes of the slab. The calculated results offer a qualitative explanation of the transmittance of a thin LiF film as experimentally observed by Berreman.

Surface modes of vibration in an ionic crystal

Optical surface modes of a new type have been found in calculations for the (100) surface of an NaCl crystal. The problem of obtaining rapidly convergent lattice sums in such calculations is discussed.

THE INTERACTION OF PHOTONS AND PHONONS WITH CRYSTAL SURFACES

In the first part of this paper the dielectric tensor eµν(ω) is determined for a thin slab of an ionic crystal of the rocksalt structure, bounded by a pair of parallel [001] surfaces. The result serves as the basis for a calculation of the absorption coefficient of the slab, and a discussion of the feasibility of studying infrared active optical surface modes by the technique of infrared absorption. In the second part a derivation is presented of a formal expression for the inverse relaxation time for the scattering of phonons by the boundaries of a crystal. This expression is evaluated for two simple crystals, and the results are compared briefly with expressions used in calculations of the lattice thermal conductivity of insulating crystals.