V. Bortolani

Surface and gap intrinsic localized modes in one-dimensional III-V semiconductors

A theoretical investigation has been made of intrinsic localized vibrational modes in an anharmonic one-dimensional diatomic lattice with alternating force constants coupling successive neighbours. This system simulates a row of atoms in the 111 direction of a III-V semiconductor. Specific calculations have been carried out for GaN, because it has a large gap between acoustic and optical branches. We study small-amplitude atom vibrations (up to 0.4 A), accessible to experimental detection, in order to legitimize the expansion of the full potential to include cubic and quartic terms. We consider then nearest-neighbour interactions through harmonic as well as cubic and quartic anharmonic interactions to study the interplay between cubic and quartic terms in the frequencies of the localized modes. The force constants were determined empirically by fitting the longitudinal branches in the -L direction of GaN. We have studied both gap and surface intrinsic localized modes. Zinc-blende-structure chains are of particular interest, because the lack of inversion symmetry prevents the classification of the modes as even or odd parity. Nevertheless, modes were found that closely resemble the even- or odd-parity modes of an NaCl-structure chain. Their frequencies lie inside the gap for GaN. The absence of inversion symmetry permits a variety of surface modes to exist, depending on whether the bond at the surface is strong or weak and the atom at the surface is light or heavy. All surface mode frequencies for GaN lie inside the gap as found with the use of the full potential.

Theory of Brillouin scattering from surface acoustic phonons in supported films

The theory of the Brillouin scattering from the surface of a semi-infinite medium, developed previously, is extended to coated surfaces of cubic materials. The Brillouin cross section is obtained for any scattering geometry and for p and s polarisation of the incident and scattered light. The formulae for the cross section contain contributions from the ripple and the elasto-optic scattering mechanisms for the film as well as for the substrate. The theory is applied to a silica film deposited on crystalline silicon and the behaviour of the cross section against the film thickness is investigated. The authors find that there are strong interference effects among the various contributions to the cross-section, so that the intensity of the spectral lines dramatically oscillates by changing the thickness. Although in general the ripple scattering mechanism is the dominant one it is found that the elasto-optic coupling in the silica film is not negligible and sometimes is even prevailing. The discrete phonon spectrum (Rayleigh, Sezawa, Lamb modes) and the continuous spectrum (resonances, mixed modes) are both studied.

Surface phonon calculations for noble metals: Comparison with he-surface scattering experiments

Abstract We evaluate the surface phonon dispersion relations of Ag(111) and Au(111) within a force constants parametrization of the bulk dynamics. By changing the surface force constants we are able to explain all the salient features appearing in the experimental time of flight spectra of a 7.9 meV He beam. The parallel momentum Q has been considered along the [110] and [112] directions of the surface Brillouin ozne. We show that the peaks of the time of flight spectra are related to the Rayleigh wave, to the pseudo Rayleigh wave and to a new resonance of longitudinal character.

Third order perturbation theory and lattice dynamics of simple metals

The dynamical matrix of simple metals is set up by evaluating the total electron energy to third order in the electron ion pseudopotential. In this way three body unpaired non central forces arising from the off diagonal elements of the dielectric matrix are explicitly introduced. Since the usual on Fermi sphere approximation to a nonlocal pseudopotential gives a completely unreliable estimate of third order contributions and a full non local calculation is not feasible, a procedure is given to construct an average local potential, which disposes of most of the non locality and allows for a realistic calculation of the contributions of the unpaired forces to the lattice dynamics of simple metals. The phonon frequencies and the elastic constants of Li, Na, Al and Pb are evaluated. The results show that third order corrections are very important for Pb, while for the other metals they are about 10%. This indicates that three-body central forces are essential in order to describe the lattice dynamics of lead, while for Li, Na and Al a good description is obtained by considering only a central pairwise interaction between the ions.

Surface resonant phonons of Ag(110)

Abstract A study of the dynamics of the Ag(110) surface in the ḡGȲ direction is presented. The experimental TOF spectra show the existence of two low frequency modes with high scattering intensity and a dispersionless high frequency mode with a smaller intensity. The theoretical analysis based on a force constant model that contains long-range central interactions and short-range angular forces explains accurately both the dispersions and the scattering intensities of the three modes in terms of resonant and localized vibrations related to the modifications of the surface force constants caused by the different role played by the many-body forces in the surface region.

Debye-Waller factor for He/Pt(111)

Abstract We report accurate measurements of the dependence of the specular reflectivity on surface temperature and on incident angle, for He scattering off Pt(111). The usual Debye-Waller formula with a Beeby correction fits the data, provided that the effective well depth is adjusted. We show that a full calculation of the Debye-Waller exponent also reproduces the data. The inelastic atom-surface interaction and the surface phonon spectrum used in the calculation are the ones that reproduce the time-of-flight data obtained in separate experiments. No further adjustable parameters are needed.

Surface Brillouin scattering from acoustic phonons. II. Application to semiconductors

The theory of Brillouin scattering from corrugated surfaces developed previously has been applied to semiconductors. The available spectra measured with 5145 AA light has been used for evaluating the elasto-optic constants (k11, k12, k44) of the medium. For GaAs k11=42.5, k12=51 and k44=25.5. This is the first determination of these constants in GaAs at this wavelength, where other techniques are not applicable. For silicon k11=53, k12=25 and k44=23. It is also shown that in opaque semiconductors the elasto-optic coupling depends strongly on the surface orientation.

Theory of inelastic Ne scattering from the Ni(111) surface

The recent inelastic Ne scattering data for Ni(111) by Feuerbacher and Willis are theoretically analyzed in the framework of the distorted wave Born approximation. A Ne-surface soft potential model is inferred from two-body Ne-Ni interactions and the many-body effects due to the phonon-induced surface electron charge redistribution are qualitatively described by three-body forces. The surface-projected phonon densities for the Ni(111) surface are calculated from a force constant model including three-body forces. The cut-off produced by the softness of the Ne-Ni potential accounts for the observed cross-over from Rayleigh-wave to bulk phonon scattering regimes. The one-phonon picture correlates well with experiments for outgoing angles slightly apart from the specular condition (Rayleigh-wave regime) whereas for larger deviations from the specular condition (bulk phonon regime) multiphonon contributions are important.

Theory of intrinsic localized modes in diatomic chains: beyond the rotating wave approximation

Intrinsic localized modes in the gap of a diatomic chain with free ends are discussed in detail by going beyond the rotating wave approximation. We include in the time dependence of the displacements terms up to cos (2ωt). We consider a finite chain of particles interacting with nearest-neighbour interactions. We study amplitudes of the intrinsic localized modes smaller than 0.25 A. In this range of amplitudes the full potential can be well represented by an expansion in powers of the displacements up to fourth-order terms. The use of a force constant model allows us to simplify the problem. As a test case we consider a chain of LiI atoms. We found intrinsic localized modes in the gap. The amplitudes of the first harmonic term (cos (ωt)) are of even or odd parity, whereas we prove that the amplitudes of the static part and those of the second harmonic can have only even symmetry. The main result of the paper is that the amplitudes associated with the second harmonic are two or three orders of magnitude less than those of the first harmonic. Furthermore, the frequency of the localized modes are modified by less than 1% by the inclusion of the second harmonic.

Inelastic scattering of helium atoms from the phonons of the reconstructed Au(111) surface

We present inelastic atom-surface phonon scattering time-of-flight spectra for the reconstructed Au(111) surface. The shapes of the spectra are compared with calculated reflection coefficients based on a simplified lattice dynamical model for the reconstructed surface. The force constants were determined from a best fit of the surface phonon dispersion curves and the lateral atom-atom interactions in the surface layer were found to be 30% of the bulk value. The theoretical spectra reproduce the overall lineshape of the experimental spectra and reveal additional features which can be attributed to the reconstruction of the surface layer with respect to the substrate.