The derivation of second-order extended Lindhard-Scharff-Schiott theory
(E2LSS) has shown that it is possible to predict accurate ion implantation moment
parameters for a projected range of Rp , a straggling parameter ΔRp , and a lateral
straggling parameter pt ΔR . Starting from E2LSS theory, we divided the energy region and
introduced the ratio rs of the nuclear stopping power Sn to the total stopping power in
each energy region, related Sn to energy straggling, and succeeded in obtaining a simplified
analytical model. We showed that the range and the ratio rs have a universal dependence
on the energy, normalized with respect to the reference energy E1 where Sn the electron
stopping power at that energy equals. The simplified model can be applied to any
combination of ion and substrate atoms, similarly to E2LSS. The simplified model
reproduces E2LSS over a wide range of ion implantation conditions and can be used to
generate Gaussian profiles easily and obtain physical intuition for ion implantation profiles.
Keywords: Ion implantation, LSS theory, projected range, straggling, nuclear stopping
power, electron stopping power, Gaussian function, range, lateral straggling, screening
length, reduced energy, universal nuclear stopping power, SIMS, B, As, P, Sb.
