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Fibre-Optic Low Energy Electron Diffraction (FO-LEED)

Introduction

Low energy electron diffraction (LEED) is one of the most widely used experimental probes of surface structure. Low energy (50-300 eV) electrons have wavelengths comparable to interatomic distances, and are therefore backscattered by a periodically ordered surface into diffracted beams. At these energies, the mean free path of the electrons in the surface is very short (~1 nm, or 2-3 atomic layers), so LEED is highly surface-specific. The exact positions of the atoms within the surface repeat unit (the "unit mesh") govern the intensities of the diffracted beams. By varying the incident electron beam energy and measuring the diffracted beam intensities to give a set of so-called I/V curves, the arrangement of the atoms within the unit mesh can be determined. We have a well-established experimental programme of surface structure determination using quantitative LEED (LEED I/V), much of it tying in closely with work in the DFT subgroup. The LEED and DFT structural analyses serve to benchmark each other, allowing us to place a particularly high level of confidence in the models we obtain.

The Case for Fibre-Optic LEED

An important issue in LEED is electron-beam damage. Molecules with weak intra-molecular bonding, or species which are weakly bonded to the surface, can dissociate or desorb under the electron beam. Examples of particular interest and importance with which problems occur include water, ammonia, thiols and physisorbed species.

To open up these systems to structural analysis by LEED, we have developed a unique LEED instrument, which operates at very low beam current (~1 nA) in order to minimise damage. Fibre-optic coupling is used for maximum efficiency in capturing the resulting low-intensity LEED patterns, and transferring them to a high-sensitivity, slow-scan CCD camera. This approach has several advantages over approaches based on channel plate detectors, including conventional geometry, low noise and high dynamic range. The apparatus is also equipped with liquid helium sample cooling. This minimises thermal desorption of weakly bonded (e.g. physisorbed) species, allows us to study low-temperature structural phases, and helps to reduce the thermal vibrations that smear out atomic positions.

Analysis

Low energy electrons are strongly scattered in the surface, and LEED is therefore a multiple-scattering process. In any diffraction experiment, phase information is lost in the measurement, as one measures intensity rather than amplitude, so that direct Fourier inversion of the data does not simply return the structure. The problem is even more acute for LEED, because of the multiple scattering, and because the atomic scattering phase shifts are complex and dependent on parameters such as local structure and energy.

LEED analysis therefore proceeds via a trial-and-error process: a trial structure is "guessed", simulated I/V curves based on computer modelling of the multiple scattering process are calculated, and these are compared to the experimental curves, using a reliability factor, or "R-factor", as a quantitative measure of goodness of fit. The trial structure is then refined until the R-factor is optimised. The minimum R-factor value can then be compared with those obtained by refining different trial structures; the structure that gives the lowest R-factor of all is taken to be the correct structure.

We have our own code for LEED I/V data analysis, CLEED (or "Cambridge LEED"). Written in C, and exploiting dynamical memory allocation, CLEED performs a full dynamical scattering calculation for each structure through the refinement process. Efficient code and the use of modern, fast workstations allow the calculations to be run within a reasonable timeframe.

CLEED is under ongoing development. A fully symmetrised version of CLEED allows the symmetry of the LEED pattern to be used to reduce calculation times, while a separate version for kinked-stepped surfaces has been developed, in which the usual layer-doubling approach is not used, avoiding the problems normally encountered with non-low-index surfaces in which the layer spacings are small. Recent advances include the implementation of a global search strategy, simulated annealing, and the incorporation of the t-matrix method for efficient treatment of adsorbed molecular species, including an advanced treatment of thermal vibrations, including anisotropic and anharmonic motions. Many of these developments have been made in close collaboration with Pedro de Andres (Madrid).


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Last updated 25/4/2009 by mb633 -at- cam.ac.uk