Numerical modeling of high-energy ion implantation using Fokker – Planck equations

Abstract

The model of transport for high energetic ions in solids based on numerical solving of the boundary value problem for the Fokker – Planck equation is considered. The Fokker – Planck equation has a second order both on energetic and angular variables. We derived the difference scheme approximating the boundary value problem. It was shown, that the difference scheme is satisfied the grid maximum principle. There is estimated the stability of the difference solutions with respect to the initial data. We present the results of computational experiments on modeling of bismuth and phosphorus ion transport under ion implantation into the silicon with the initial energy of 1 and 50 MeV. We compared depth distribution profiles of stopped particles obtained using both the presented model and the model without angular scatte ring with the data of statistical simulations.

Keywords

• the high-energy ion implantation
• the fokker – planck equation
• difference schemes
• stability