Screened Rutherford multiple scattering estimates for heavy ion backscattering applications

Abstract

An analytical expression and an integral representation are presented for the contribution, Y ( n) = ϵ ( n) Δω n , of n-event multiple scattering chains to the observed backscattering spectrum in heavy-ion backscattering (HIBS) measurements. The approximations introduced in deriving the results are chosen such that an upper limit is placed on Y ( n) by the expressions. The Rutherford elastic scattering cross section is used to describe individual collisions between incident projectiles and target atoms. Screening of the Rutherford scattering cross section is included in an approximate fashion which maintains the upper limit estimate. Inelastic energy loss between collision events is assumed proportional to the projectile velocity. Specific application of these expressions is made to HIBS detection of trace amounts of heavy atom impurities on a Si surface by 200–400 keV C + beams. The predicted multiple scattering background for this application is compared with the predicted single scattering signal for 10 10 at./cm 2 of Fe, Cu, Zr, Sn, or Au, as a surface impurity. The comparison shows that the multiple scattering background poses no barrier to extending the sensitivity of HIBS detection of impurities in this mass range to levels as low as 10 8 at./cm 2 for the upper part of the energy range considered. Comparison of calculations with and without screening included show that the screening of the Rutherford cross section by atomic electrons is a significant factor in preventing multiple scattering effects from interfacing with HIBS spectrometry at impurity levels in the 10 10 at./cm 2 range.