Ranges of heavy ions in solids

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Abstract
In the present work, applying the Thomas-Fermi-Firsov potential, the approximated formulae for calculations of elastic energy losses of heavy ions in solids were obtained. It is found that the elastic energy losses of low-energy atoms are not constants. With the increase of the ion energy E the elastic loss grows, and at a definite energy maximal values are obtained. Under a further increase of E the elastic energy losses of the ions are slowly decreased. The energy E corresponding to the maximum of the energy loss of an ion is increased with the increase of the atomic numbers of the colliding atoms (Z1, Z2). The elastic energy losses of the heavy ions were calculated in silicon. The inelastic energy losses of the ions are determined by the Lindhard-Scharff-Schiott (LSS) theory. The equations for calculations of total and mean projected ranges of low energy ions in solids were obtained. The heavy ion ranges in silicon (Z1 = 54-83) in the energy region of 20-100 keV were calculated. It is shown that ranges of the low-energy ions (E < 20 keV) in silicon are 1.5-2 times larger than those calculated with the Lindhard formulae. With the energy increase of the heavy ions deviation decreases up to 20% (at E = 100 keV). The calculation results are in good agreement with the experimental data.