Based on Thomas-Fermi potential, we derived an analytical expression of the total range R=2/a[E1/2-A1(arctg(2E1/2-f)/△1/2+arctg f/△1/2)+B1ln((E1/2-f)2)/(E-fE1/2+d)·d/f2], where A1, B1, a,f, d, and △ are constants related to mass and atomic number of the ion and the target. Combined with the derived hyperbolic relation η=Rp/△(Rp) =F(μ)·[A2(μ)+(B2(μ))/(ε1/2+C)], and linear function ω=Rp/△Rp=A3(μ)ε1/21/2+B3(μ), R,Rp and △Rp can be calculated easily and accurately. Here, Rp and △Bp are project range and standard deviation respectively, C is an empirical constant, and F(μ), A2(μ), B2(μ), A3(μ) and B3(μ) are all algebric functions of μ, the mass ratio of the ion and the target. By Comparing with numerical solutions of Gibbons et al. and experimental results published in literature, we conclude that our expressions can be used to both light or heavy ion implantation into Si, GaAs or SiO2 target. The physical significance of our expression was discussed also.
下载:
