On the shapes of high-resolution Rutherford backscattering spectra

Abstract

This paper describes a detailed calculation of the shape of the energy spectrum of backscattered 2 MeV alpha particles from a sample of pure gold. The incident beam energy analyzer and the scattered-particle detector are assumed to have an energy resolution of 0.05%. The rise of the step function is found not to be symmetric about the midpoint. Instead, the upper half of the rise is steeper than the lower half, resulting in the midpoint of the rise occuring almost one keV outside the surface rather than at the surface as is customarily assumed. The reasons for this asymmetric shape are (1) that the beam energy spread broadens as a function of depth in the target (with the result that in the summation process, the energy distributions far from the surface contribute more to the yield at the surface than vice versa) and (2) that the actual beam-energy distributions corresponding to average losses less than about 15 keV are asymmetric, with the most probable energy loss being less than the average energy loss, again leading to an enhancement of the scattering spectrum corresponding to at-surface or near-surface interactions at the expense of the height of the distribution corresponding to interactions in the deeper layers. A major significance of this displacement of the midpoint of the rise is that the depth of a shallow layer of some impurity material in gold under such high-resolution conditions could be misinterpreted by about 12 Å.