Holographic LEED


Holographic Low Energy Electron Diffraction (holographic LEED), first proposed by D. K. Saldin and P. L. De Andres, Phys. Rev. Lett. 64, 1270 (1990), is a technique for the direct recovery of the 3D structure of the atomic environment around adsorbate atoms on a surface by an analysis of the diffuse LEED patterns produced when low energy electrons are incident on the surface. Using computer algorithms, a 3D real-space image is reconstructed directly from the measured data of the diffraction pattern. The electrons reaching a detector directly after scattering from an adsorbate atom constitute a holographic reference wave. Those parts of this reference wave that are subsequently scattered by substrate atoms constitute an object wave. The diffuse LEED pattern is formed by the interference of these two waves, and thus constitutes a hologram.

Two striking examples of atomic adsorption sites recovered from experimental diffuse LEED patterns may be seen by clicking on this link . The method used, later called Compensated Object- and Reference-wave Reconstruction by an Energy-dependent Cartesian Transform (CORRECT), was first proposed in the paper by D. K. Saldin and X. Chen, Phys. Rev. B 52, 2941 (1995).

The representation of the experimental data on a Cartesian grid in reciprocal space allows an extension of the method to fractional-order LEED data from ordered surfaces. A prime example of this was the use of the CORRECT algorithm to rapidly determine the local atomic structure around prominent adatoms on the SiC(111) – (3×3) surface. The identification of this element of the surface by K. Reuter et al. Phys. Rev. Lett. 79, 4818 (1997). was a vital first step in the complete solution of the structure some months later by the same authors by conventional LEED methods.

More recent refinements of the reconstruction algorithm are described in the paper by A. Seubert, D. K. Saldin, and K. Heinz, J. Phys.: Condens. Matter 12, 5527 (2000).

A limitation of the holographic method with an atomic reference-wave source is seen in the above determination of the SiC(111) – (3×3) structure. The scanning tunneling microscopy (STM) image below suggested the presence of a single prominent adatom in each surface unit cell


This implies that a holographic inversion algorithm should be able to reconstruct the positions of nearby atoms relative to the adatom from the I/E data of the fractional-order Bragg spots. The results are shown below.


Although this determines the relative positions of just 6 atoms of the surface unit cell, it makes a large impact on practical iterative model building as it rules out whole classes of structures. Indeed, this element of the structure enabled the relative positions of the remaining atoms to be determined within another 6 months or so. The final structure is shown below.


For structures such as this one with a large unit cell, it would be much more useful if there existed a direct method that could reveal the structure of an entire large surface unit cell.
In fact we have developed just such a method. It is based on a different identification of a reference wave. The idea is applicable to surface x-ray diffraction and also to LEED and is a much more complete solution to the inverse problem in these two fields.