Energy losses of ions implanted in matter
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Energy losses of ions implanted in matter J. H. Liang and K. Y. Liao Department of Nuclear Engineering and Engineering Physics, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China (Received 6 September 1995; accepted 25 April 1996)
A set of simple and accurate formulae for the first four moments of nuclear and electronic energy losses is proposed. A new variable is introduced to include the finite maximum-impact-parameter effect in the nuclear stopping process, which is assumed to be infinite in most studies. A critical energy at which the electronic energy loss is equal to the nuclear energy loss is also defined. It determines whether the nuclear or the electronic stopping process is the dominant mechanism in terms of incident-ion energy. The critical energy increases for heavy ions implanted in heavy target materials during the first moment of energy loss. The second moment of electronic energy loss is important only for light ions implanted at high ion energies. The third and fourth moments of nuclear energy loss are much larger than those of the electronic energy loss for all ion-target combinations. Theoretical predications of the projected ranges and range stragglings for gold ions implanted in carbon films are close to the experimental data when these proposed four moments of nuclear and electronic energy losses are considered.
I. INTRODUCTION
Slowing down of energetic ions in matter has been the subject of great theoretical and experimental interest for several decades. In general, the nature of ion-target interaction involves all the interacting electrons and nuclei. As suggested by Bohr,1 the energy losses of ions implanted in matter can be separated into two independent processes: nuclear and electronic. In essence, nuclear stopping is defined as the transfer of energy from an incident ion to a target atom due to elastic collisions influenced by Coulomb fields that are partially screened by existing electrons. Electronic stopping is considered to be the energy loss incurred by ions through subjecting the target medium to excitation and ionization. Ion energy loss mechanisms play important roles in obtained implanted-ion profiles which may indicate substantial modification of target materials properties. These surface or near-surface modifications may yield either positive benefits or severe problems for scientific and industrial concerns. Characterizing the Pearson distribution of implanted-ion profiles2–5 requires knowing the statistical range projections including projected range Rp , range straggling DRp , skewness, g, and kurtosis b. However, obtaining kurtosis to any useful degree accuracy requires in turn knowing the nuclear and electronic energy losses for the first four moments. It is therefore the aim of this work to propose a set of simple and accurate formulae for nuclear and electronic energy loses up to the first four moments. In particular, in addition to incident-ion energy, a new maximum-reduced-impactparameter variable t
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