A New Formula for Energy Spectrum of Sputtered Atoms Due to Low-Energy Light Ions

Abstract

A new formula has been derived to describe the energy spectrum of sputtered atoms from a target material bombarded by light ions. We assume that sputtered atoms bombarded by low-energy light ions are mainly primary knock-on atoms which are created by large-angle backscattered light ions. The escape processes of recoil atoms are estimated on the basis of the Falcone-Sigmund model. The new formula has the dependence on the incident energy of a projectile. We have compared the new formula with simulation results calculated with ACAT code for a Fe target material bombarded by 50 eV, 100 eV and 500 eV D + ions. Good agreements are found for 50 eV and100 eV D + ions.

Modeling of dc magnetron plasma for sputtering: Transport of sputtered copper atoms

“…The flux velocity distribution of the sputtered particles f sp ͑ sp , sp ; r t ͒ is estimated as a function of initial ejection energy and angle from the surface normal. The energy spectrum of the sputtered Cu f sp ͑ sp ; r t ͒ will be estimated by the formula of Kenmotsu et al 22 modified for a system between a light incident ion with low energy and a heavy target atom, which produces a single knock-on collision cascade in the target material. The angular distribution of the sputtered particles f sp ͑ sp ; r t ͒ is assumed to follow the cosine law.…”

An extended formula for the energy spectrum of sputtered atoms from a material irradiated by light ions

“…(15-II) to calculate Y N (E inc , E 1 ). Kenmotsu [3], Thompson [1] and Falcone [4] formulas are also referred to for comparison, where each spectrum is normalized to give a sputtered energy distribution function as discussed above. We have normalized the truncated Thompson formula (which includes a cut-off factor) and the conventionally used untruncated Thompson formula (which does not have a cut-off factor), by setting the maximum of sputtered energy at cE inc À U.…”

“…We introduce a primary recoil density F p (E, E 0 ) in the way that F p (E, E 0 )dE 0 is the average number of primary recoil atoms created with energy E 0 in a collision cascade or sequence initiated by a light ion with initial energy E. For a collision between a light ion and a heavy target atom, from Eqs. (1) and (2) of Paper I, the integral equation for F P (E, E 0 ) can be reduced to the following equation [3,6]:…”

“…As discussed in Paper I, almost all light ions at near-normal incidence are subject to randomization because they are backscattered near 180°by target atoms, and primary recoil atoms produced then by those ions are nearly isotropic [3,11]. Then we can assumê F ðE inc ; e; E 0 ; e 0 ; xÞ %F ðE inc ; E 0 ; xÞ=4p.…”

“…This deviation can be understood from the fact that light ions cannot produce such a cascade, but rather a single or multiple collision sequence. Considering that an elastic energy loss is greater than an inelastic one for ions with energy of about a few hundred eV, we derived a formula for the energy spectrum of sputtered atoms due to light ions (H + , D + , T + , He + ) by assuming that the primary knock-on atoms created near the surface with large-angle backscattered ions are the main candidates for ejection and by neglecting inelastic energy loss in Paper I [3]. In what follows, we derive an extended formula which can be applied to an energy region ranging from several tens of eV to keV, by considering both elastic and inelastic energy losses.…”