Depth of origin and angular spectrum of sputtered atoms

Abstract

A theoretical analysis is presented of the depth of origin of atoms sputtered from a random target. The physical model aims at high energy sputtering under linear cascade conditions and assumes a dilute source of recoil atoms. The initial angular distribution of the recoils is assumed isotropic, and their energy distribution is E −2 like without an upper or lower cutoff. The scattering medium is either infinite or bounded by a plane surface. Atoms scatter according to the m = 0 power cross section. Electronic stopping is ignored. The sputtered flux, differential in depth of origin, ejection energy and ejection angle has been evaluated by Monte Carlo simulation and by five distinct methods of solution of the linear Boltzmann equation reaching from continuous slowing down neglecting angular scattering to the P 3 approximation and a Gram-Charlier expansion going over spatial moments. The continuous slowing down approximation used in previous work leads to results that are identical to those found from a scheme that only ignores angular scattering but allows for energy loss straggling. Moreover, these predictions match more closely with the Monte Carlo results than any of the approximate analytical schemes that take account of angular scattering. The results confirm the common assertion that the depth of origin of sputtered atoms is determined mainly by the stopping of low energy recoil atoms. The effect of angular scattering turns out to be astonishingly small. The distributions in depth of origin, energy, and angle do not depend significantly on whether the scattering medium is a halfspace or an infinite medium with a reference plane. The angular spectrum comes out only very slightly over cosine from the model as it stands, in agreement with previous experience, but comments are made on essential features that are not incorporated in the physical model but might influence the angular spectrum. An improved set of constants matching the standard power cross section to Born-Mayer scattering brings the depth of origin of sputtered atoms into close numerical agreement with results from more realistic simulation models.