Single-scattering cluster calculations and Fourier-transform analyses of normal photoelectron diffraction

Abstract

The results of single-scattering cluster (SSC) calculations of normal photoelectron diffraction (NPD) from the S $1s$ level in $c(2\ifmmode\times\else\texttimes\fi{}2)\mathrm{S}$ on Ni(001) are compared with multiple-scattering (MS) calculations by Tong and co-workers over the energy range 100 to 600 eV. It is found that the kinematical $\ensuremath{\chi}(E)$ curves are in good agreement with the multiple-scattering curves over the energy range \ensuremath{\sim} 160 to \ensuremath{\sim} 400 eV but in poor agreement elsewhere. The range of agreement between the SSC and MS curves can be directly associated with a relatively strong peak in the backscattering amplitude over essentially the same 160- to 400- eV range. The SSC curve for an adsorbate vertical height of $z=1.35$ \AA{} is also in good agreement with experimental data of Hussain and co-workers over the range of \ensuremath{\sim} 170-430 eV. Thus, it appears that this simple SSC model can be fruitfully used in analyzing NPD data, even if it may not be quantitative enough for refined structural determinations. The effects of cluster size are examined within the single-scattering model, and it is suggested that approximately eight Ni layers are needed to describe NPD at electron energies \ensuremath{\gtrsim} 300 eV. Inclusion of instrumental angular broadening is also found to be significant, and in particular increases the agreement between SSC and MS curves. Fourier-transform analysis of both the single- and multiple-scattering curves shows that peaks in the magnitude of the Fourier transform are most directly related to path-length differences between the direct wave and various scattered waves and not to perpendicular interlayer distances as previously suggested. These results thus indicate that the Fourier transformation of normal photoelectron diffraction data is not a particularly reliable method of obtaining surface structural information unless a very limited number of path-length differences are strongly predominant in the scattering.