Final-state summation in photoelectron diffraction

A formula was derived to perform the summation over the l_c±1 final states of the dipole transition matrix element and the scattering path operator. This formula shows that often it seems more convenient to speak about l_c+1 and l_c±1 channels instead of the l_c+1 and the l_c−1 channel. Using this formula and restricting the considerations on the first order scattering and the plane wave approximation, explicit formulas were given for the photoelectron intensity, the circular dichroism and the spin polarization in terms of products of the vectors involved in the problem: photon wavevector, photon polarization, magnetization, electron wave vector, and orientation of the spin detector. Additionally the scattering part contains the position vectors of the scatterers with respect to the emitter. These formulas are discussed as well for magnetic as for nonmagnetic samples and for s, p, d and f core states. General expressions are given for the peak rotation. Also it is possible to write down explicitly the dependence on absolute value and the phases of the complex radial matrix elements.     

Optical theorem for multipole sources in wave diffraction theory

The optical theorem is generalized to the case of local body excitation by multipole sources. It is found that, to calculate the extinction cross section, it is sufficient to calculate the scattered field derivatives at a single point. It is shown that the Purcell factor, which is a rather important parameter, can be represented in analytic form. The result is generalized to the case of a local scatterer incorporated in a homogeneous halfspace.     

Buried interfaces studied by photoelectron diffraction

Angle- and energy-scanned photoelectron diffraction data can be used to investigate structures below surfaces. The modulations in photoelectron intensity result from diffraction of the emitted electron wave at neighbor atoms. In the past, scanned-energy photoelectron diffraction had been mainly used to determine the adsorption site of molecules at surfaces. Recent data show, however, that the technique can also be employed to obtain information about the upper substrate layer(s). At low kinetic energies, backward scattering is strong and in scanned-angle photoelectron diffraction the recorded patterns result from backward- and multiple-scattering effects. For a structural analysis, the intensity modulations have to be compared with the results for simulations performed for model clusters. As an example, recent angle-scanned photoelectron diffraction patterns recorded for the technologically important silicon oxide/silicon interface were compared with simulations. At the Si(001) surface orientation, the interface is extended over a few layers, whereas at the Si(111) surface orientation the transition is rather abrupt and occurs within one or two layers. Received: 9 September 2002 / Accepted: 2 October 2002 / Published online: 5 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-231/755-3657, E-mail: carsten.westphal@physik.uni-dortmund.de     

A multiple-scattering approach to X-ray photoelectron diffraction

We present an alternative method for multiple scattering calculations of X-ray photoelectron diffraction from periodic surfaces. The technique uses a time-reversed RHEED wave function as the final state in a one-step model of the photoemission process. We apply the method to the Ni(001)c(2×2)S system and find an excellent agreement with the experimental data for vertical height of the S overlayer of 1.35±0.05 Å above the top Ni layer. Our calculations display a much better agreement with the experimental data than has been previously reported.     

Quantitative X-ray photoelectron diffraction studies of single-crystal silicates

The interpretation of angle-resolved X-ray photoelectron intensity measurements on single crystals which contain an element in more than one structurally distinct location, each of which is individually characteristic of a different element, to yield directly quantitative information concerning the extent of isomorphous substitution in such crystals is described. These principles are applied to quantify the distribution of aluminum between tetrahedrally and octahedrally coordinated sites in four 2:1 layered silicates. An accuracy of ? 5% is demonstrated by comparison with a less direct surface analytical route to the same information.     

Global search algorithms in surface structure determination using photoelectron diffraction

Three different algorithms to effect global searches of the variable-parameter hyperspace are compared for application to the determination of surface structure using the technique of scanned-energy mode photoelectron diffraction (PhD). Specifically, a new method not previously used in any surface science methods, the swarm-intelligence-based particle swarm optimisation (PSO) method, is presented and its results compared with implementations of fast simulated annealing (FSA) and a genetic algorithm (GA). These three techniques have been applied to experimental data from three adsorption structures that had previously been solved by standard trial-and-error methods, namely H₂O on TiO₂(110), SO₂ on Ni(111) and CN on Cu(111). The performance of the three algorithms is compared to the results of a purely random sampling of the structural parameter hyperspace. For all three adsorbate systems, the PSO out-performs the other techniques as a fitting routine, although for two of the three systems studied the advantage relative to the GA and random sampling approaches is modest. The implementation of FSA failed to achieve acceptable fits in these tests.     

用耦合波方法研究取样光栅的衍射特性

介绍了利用耦合波理论编写计算光栅衍射特性程序的基本思想和主要步骤.利用编写的程序计算并分析了一种用于激光取样光栅TE波和TM波的衍射特性.     

X-ray photoelectron diffraction study of ultrathin PbTiO3 films

Full hemispherical X-ray photoelectron diffraction (XPD) experiments have been performed to investigate at the atomic level ultrathin epitaxial c-axis oriented PbTiO₃ (PTO) films grown on Nb-doped SrTiO₃ substrates. Comparison between experiment and theory allows us to identify a preferential ferroelectric polarization state in a 60 ? -thick PTO film. Multiple scattering theory based on a cluster-model [ Phys. Rev. B , 075404 (2001)] is used to simulate the experiments.     

Strongly Z-dependent Auger and photoelectron diffraction in MgO(001)

We have measured angular distributions of Mg KL_2,3L_2,3 Auger and O 1s core-level photoemission intensities at high angular resolution for MgO(001). We find substantial differences in the two types of scans over many regions of k space, despite the very similar local structure of Mg and O in the rocksalt lattice. These diffraction scans are quantitatively predicted by spherical-wave, single-scattering theory, assuming an s wave for the Mg KL_2,3L_2,3 Auger transition. The differences that are observed between Mg KL_2,3L_2,3 Auger and O 1s diffraction scans are shown to be due purely to differences in the elastic scattering phase shifts for Mg and O atoms in the solid.     

General coupled-wave diffraction theory

Coupled-wave theory is developed in full generality for unrestricted grating and polarization geometries. The analysis applies to composite gratings modulated dielectrically, magnetically, and in absorptivity; and is also developed for gratings nonuniform with depth.     

Geometrical theory of diffraction

Geometrical theory of diffraction (GTD) is an alternative model of diffraction propounded first by Thomas Young in 1802. GTD has a long history of nearly 150 years over which many eminent people enriched this model which has now become an accepted tool in the calculation of diffraction patterns. In the conventional Helmholtz-Kirchhoff theory the diffracted field is obtained by computing the net effect of the waves emitted by all points within the area of the aperture. But GTD reduces this problem to one of computing the net effect of waves from a few points on the boundary of the aperture or obstacle, thus simplifying considerably the labour involved in computations. Also the theory can easily be modified to include polarization effects. This has been done specifically by Keller (1962) who exploited the Sommerfeld solution of diffraction of electromagnetic waves at a half plane, making the theory more versatile than the Kirchhoff scalar wave theory. Interestingly the geometry of difffracted rays is predictable from a generalized Fermat principle. According to this the total path chosen by light from the source to the point of observation via the diffracting boundary is an extremum. Historically it should be stated that many of the salient features of GTD were established by a school led by Raman which was active from 1919–1945. Later when Keller (1962) revived GTD independently, he and others who followed him rediscovered many of the results of the Raman school. We have stressed wherever necessary the contributions of the Indian School. We have also discussed certain geometries where GTD can be effectively used. We get some new and interesting results, which can be easily understood on GTD, but are difficult to interpret on the conventional theory of diffraction.