An empirical formula of E_z in modified Sigmund's formula under the low energy heavy ions bombardment

Based on Yamamura's theory, Zhang took the natural boundary condition into account and proposed the modified Sigmund's formula which agrees well with the experimental results of the sputtering yield and the energy distributions of sputtered atoms. While, the new parameter E_z introduced by Zhang is still unclear. This work mainly studies the experimental results when Ar, Kr and Xe bombard different targets to obtain the best fitted E_z, and proposes an empirical formula of it. Two factors that may impact on E_z are discussed: mass ratio and the correction factor of electronic stopping 'Ψ'. Putting Ψ into the periodic table, we found that the values of Ψ in the same congeners are similar and have the trend of 'W' shape. The row number (n) and column number (m) of the elements in the periodic table are used to fit the 'W' shape. The parabolic model is used to approximate the sputtering yield when E < E_z. Finally, the sputtering yield and the energy distributions of some common elements are used to verify the calculation method of E_z. The results show that the obtained formula can be applied to the situation of low energy heavy ion sputtering and to supplement Zhang's model.