V. Celli

Scattering of atoms by solid surfaces. I

Abstract A quantum mechanical theory of the scattering of atoms by solid surfaces is presented. The theory is applied to a detailed discussion of elastic scattering (diffraction) processes, and the extension to inelastic scattering (phonon exchange) processes is discussed briefly. A great advantage of the theory is that scattering intensities of any size are easily handled; the moduli of the scattering matrix elements are not restricted to be small. If the results are expanded to lowest order in these moduli, then the “first order distorted wave Born approximation” is recovered. An example of the results obtained is that the intensity of the specularly scattered beam is by no means always larger than other diffracted intensities; this result is in agreement with experiments, and is a decided improvement over the usual first order treatments.

Some aspects of light scattering from a randomly rough metal surface

Two problems involving the interaction of a volume electromagnetic wave with a randomly rough metal surface are studied. In the first part a recently constructed theory of the resonant nonspecular scattering of light from a randomly rough metal surface is fitted to experimental data in a way that permits the extraction of the two-dimensional Fourier transform g(k∥) of the two-point correlation function of the surface profile function from the experimental results. It is found that the resulting correlation function can have its first maximum away from k∥ = 0 and decays to zero with increasing k∥ in a nonmonotonic fashion. This form for g(k∥) has been obtained in recent, independent, experimental determinations of this function. In the second part the scattering of p-polarized light from a randomly rough grating is studied in a case in which the plane of incidence is normal to the grooves of the grating. A diagrammatic method that self-consistently takes into account the diagrams responsible for localization phenomena in other contexts is used in this analysis. It is shown that the contribution from these diagrams gives rise to an enhanced scattered intensity in the antispecular direction. As a by-product of this calculation, the localization of surface polaritons by surface roughness is demonstrated and their localization length is determined.

Motion of a Screw Dislocation in a Crystal

The problem of the uniform motion of a screw dislocation in a crystal is treated from the point of view of lattice dynamics. A simple model of cubic lattice with piecewise‐linear nearest‐neighbor interactions is considered in detail and the extension to more realistic interatomic forces is outlined. The external stress necessary to maintain the dislocation in uniform motion is computed as a function of dislocation velocity. This stress has a minimum at one‐half of the sound velocity and motion is quite possible at hypersonic velocities. The calculations are at zero temperature, hence the only dissipative mechanism present is the emission of phonons by the core of the moving dislocation. The theory is relevant to high‐velocity dislocation motion, which is not of the usual thermally activated type.

Pairwise additive semi ab initio potential for the elastic scattering of He atoms from the LiF(001) crystal surface

The interaction potential for the elastic diffractive scattering of low‐energy He atoms from the highly corrugated LiF(001) crystal surface is derived from semi ab initio pair potentials in the framework of the recently developed Tang–Toennies potential model [J. Chem. Phys. 80, 3726 (1984)]. In addition to the sum of all He atom‐crystal ion two‐body potentials the induced dipole potential caused by the electric field of the ion lattice is taken into account, leaving only one free parameter, the C6 dispersion constant of the He–F− interaction. By simple adjustment of this parameter, it is possible to fit all of the experimental bound states of the atom‐surface potential well, to within experimental error. Diffraction probabilities calculated by the close coupling method with this potential are shown to be in good agreement with the available experimental results. Two different empirical potential models based on the Morse potential are also investigated, but do not provide as good a description of the bou...

Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods

Iterative methods offer a practical means for the calculation of wave scattering from two-dimensional surfaces. We present what is to our knowledge the first calculation of the scattering of an electromagnetic beam from a two-dimensional, randomly rough, perfectly conducting surface, using an iterative approach. We also examine a bootstrapping scheme of iteration that can further reduce computing time.

Interaction potential for one‐phonon inelastic He–Cu(111) and He–Ag(111) scattering

The interaction potential for the elastic and inelastic scattering of low‐energy He atoms from the Cu(111) and the Ag (111) crystal surface is derived from the sum of semi ab initio pair potentials modified by a damping function which takes into account the smoothing effect of the conduction electrons at large parallel momentum transfer. By adjusting only two free parameters of the potential model a very good fit to published experimental diffraction intensities and bound state levels is obtained. Without any further adjustment of the potential new experimental data of one‐phonon inelastic reflection coefficients can be reproduced within the experimental error by calculations based on the distorted wave Born approximation. This new potential model has made it possible to study the dependence of the inelastic intensities on potential parameters and different experimental conditions.

Vector theory of light scattering from a rough surface: Unitary and reciprocal expansions

Abstract We present a vector theory of light scattering from a rough surface which is based on the Rayleigh solution to the electromagnetic boundary value problem. The extinction theorem is used in order to obtain the “reduced” Rayleigh equations, which involve only the field outside the medium. These equations may be written in a way that makes the unitarity and reciprocity of the theory readily apparent, and also provides a means of generating approximate solutions that satisfy this requirement. As a result, this formalism provides a convenient starting point for making flux-conserving approximations when treating the scattering of light from a randomly rough surface.

Exact multiple scattering of waves from random rough surfaces

Abstract The exact multiple scattering theory of waves scattered from a random rough surface is presented. We give an iterative series for the mean scattered intensity ( I ( Q ) ) for all order in the statistics. We show that the coherent intensity for large correlation distances approaches the value obtained in the Kirchhoff approximation by Beckmann. Also we prove that a “white noise” surface reflects specularly the whole incident intensity.

Energy-band structure of solids from a perturbation on the “empty lattice”☆☆☆

Abstract A simple perturbation approach is developed to obtain the energy-band structure of solids. The unperturbed Hamiltonian consists of the kinetic part and of a uniform potential; the perturbing operator is the crystal potential plus a term which originates from the requirement that valence and conduction states be orthogonal to the inner states. This amounts to an approximation to the O.P.W. method. Reasons are given for the validity of such a simple scheme and applications are made to the case of the diamond lattice and of the zincblende lattice. It is shown how features of the energy-band structure depend on the symmetry of the lattice, on the lattice parameter and on the “core states” of the atomic components. Numerical results obtained for diamond, silicon and BN are in fair agreement with recent calculations. An energy-band structure consistent with experimental information is obtained for Ge and GaAs by fixing the values of a few parameters.

Monte Carlo calculation of backscattering enhancement for a randomly rough grating

A Monte Carlo calculation of diffuse scattered intensity of p-polarized light from a randomly rough Ag grating shows enhancement in the backward direction, as predicted in perturbation theory by the selective summation of maximally crossed diagrams for the resonantly excited surface polaritons.