Transport theory of sputtering I: Depth of origin of sputtered atoms

Abstract

Sputter theory employing a sum of two power cross sections has been implemented. Compared with the well known Lindhard power cross section ( V∝ r −1/m), a sum of two such cross sections can give a much better approximation to the Born–Mayer scattering in the low energy region ( m ∼ 0.1). By using both one and two power cross sections, we have solved the linear transport equations describing the sputtering problem asymptotically. As usual, electronic stopping is ignored in the analysis. It has further been proved that Falcone’s theory of the atom ejection process contradicts transport theory. The Andersen–Sigmund relation for partial sputtering yield ratios between two elements in an arbitrary multicomponent target has been derived by both methods. The energy deposited in the target surface layers has been computed for a few typical ion–target combinations. The numerical curves show that both theories generate almost the same results (error <10%) for m=0.2. It is also shown that, if the sputtering yield equals the corresponding one in Sigmund’s theory, the depth of origin of sputtered atoms must be shorter than in Sigmund’s theory for 0.25 > m⩾0. The former even may be only about one half of the latter as long as m=0.