Transmission Electron Diffraction from a Surface

Transmission electron driffraction (TED) is a technique wich is well-suited to solving atomic structures for surfaces. The mean free path of electrons at typical energies used in transmission electron microscopes (100-500 keV) is ~100 nm implying that scattering from the surface layers of a few angstroms is relatively kinematical. This is not true of LEED data as the low electron energies involved (tens of eV) result in a mean free path of ~0.1 nm yielding data which is highly dynamical and not well suited to the Direct Methods algorithms for recovering phases (and hence structures) from diffraction patterns. Conversely, x-rays interact extraordinarily weakly with matter having a mean free path in the hundreds of microns which translates into long collection times for surface diffraction.

If the surface reconstruction layers of the crystal were free-standing, the effective sample would be so thin (a few angstroms) that the diffraction could be considered rather kinematical to first order. However, the reconstruction actually occurs on both the top and botom surface of a bulk crystal and the surface diffraction intensities are modulated by the dynamical effects of the bulk. However, these effects can be minimized by a careful selection of crystal orientation.

When the sample is tilted a few degrees away from the zone axis, the quality of the diffraction data from the surface improves substantially for two key reasons:

1. As the thickness of the reconstructed surface layer is substantiall smaller than the total bulk thickness, the shape function of the surface in the z-direction (i.e. the relrods) for the surface are much larger than those of the bulk. As a result, when the crystal is tilted away from the zone axis, the intensity of the surface reflections is increased with respect to the bulk. The bulk reflections still dominate those from the surface, but any amount of enhancement is welcome as the bulk reflections are ~10⁴ stronger than the surface reflections when on-zone.
   
   
   

    

2. The dynamical contribution of the bulk is enhanced in strong-scattering orientations such as a low-index zone aaxis or a two-beam condition. If an of-zone tilt is carefully chosen such that strong bulk scattering is avoided, the coupling of the dynamical effects in the bulk and the (mostly) kinematical conttribution from the surface can be minimized and treated to first order as simply an increase in noise. This is illustrated in the context of the Si(111)-7x7 reconstruction in the figure below.
   
   
   
   Twesten, R.D., J.M. Gibson, Ultramicroscopy 53 223 (1994)
   
   a) Diffraction pattern of the Si(111)-7x7 surface in the strongly scattering, highly dynamical two-beam condition. Note the losss of the expected 6-fold symmetry in the surface reflections.

   b) Diffraction pattern from the same surface in an orientation 4.5 degrees from the zone axis avoiding strong excitation of the bulk reflections to minimize bulk dynamical effects. The expected 6-fold symmetry has returned.

Selected Papers on Transmission Surface Diffraction

1. K. Takayanagi, Y. Tanishiro, M. Takahashi, et al., Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 3, 1502 (1985).
2. K. Takayanagi, Y. Tanishiro, S. Takahashi, et al., Surface Science 164, 367 (1985).
3. L. D. Marks, T. S. Savage, J. P. Zhang, et al., Ultramicroscopy 38, 343 (1991).
4. R. D. Twesten and J. M. Gibson, Ultramicroscopy 53, 223 (1994).
5. A. Subramanian and L. D. Marks, Ultramicroscopy 98, 151 (2004).