无定形靶中离子注入的R,Rp,△Rp的理论计算

本文在Thomas-Fermi势能基础上,导出了全射程R的解析解:R=2/aE^1/2-A₁(arctg(2E^1/2-f)/△^1/2+arctg f/△^1/2)+B₁ln((E^1/2-f)²)/(E-fE^1/2+d) ·d/f²],其中A₁,B₁,f,d和△均为与离子及靶的质量、原子序数有关的常数。结合导出的η=R/(R_p)(R_p指投影射程)比值的双曲线函数关系 η=F(μ)A₂(μ)+(B₂(μ))/(ε^1/2+C)],和ω=R_p/△R_p(△R_p指投影射程的标准偏差)比值的线性关系ω=A₃(μ)ε^1/21/2+B₃(μ),可简便而又准确地计算R,△R_p,R_p.这里F(μ),A₂(μ),B₂(μ), B₃(μ)和A₃(μ)为μ的代数函数,μ为离子与靶的质量比,C是经验常数.并对η等关系式的物理意义作了讨论。上述公式的计算结果与Gibbons的数值解结果及有关实验结果作了比较,表明可用于元素半导体如Si、二元化合物如GaAs以及三元化合物如SiO₂等;既对较轻离子适用,也对重离子适用,具有一定的普适范围。

THEORETICAL ESTIMATES OF R, Rp AND △Rp, OF THE ION IMPLANTATION IN AMORPHOUS TARGETS

Based on Thomas-Fermi potential, we derived an analytical expression of the total range R=2/aE^1/2-A₁(arctg(2E^1/2-f)/△^1/2+arctg f/△^1/2)+B₁ln((E^1/2-f)²)/(E-fE^1/2+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=R_p/△(R_p) =F(μ)·A₂(μ)+(B₂(μ))/(ε^1/2+C)], and linear function ω=R_p/△R_p=A₃(μ)ε^1/21/2+B₃(μ), R,R_p and △R_p can be calculated easily and accurately. Here, R_p and △B_p 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.