Simplified LSS Theory

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 r_s of the nuclear stopping power S_n to the total stopping power in each energy region, related S_n to energy straggling, and succeeded in obtaining a simplified analytical model. We showed that the range and the ratio r_s have a universal dependence on the energy, normalized with respect to the reference energy E₁ where S_n 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.