On the use of the backward Fokker–Planck equation to calculate range profiles

Abstract

A new mathematical model for range calculations of implanted impurities – the backward Fokker–Planck equation – is derived from the backward Boltzmann transport equation using decomposition of the scattering integral for small energy transfers in nuclear collisions. The present model describes ion transport processes dominated by collisions with small energy transfer such as the diffusion-like motion of the angular direction. Furthermore, we extend the present model to take into account single collisions events in high-energy implantation.