A Novel Approach to Simulate the Potential at the Center Axis of Poisson's Equation in Cylindrical Co-Ordinates for Plasma Immersion Ion Implantation Processes

摘要

A novel and practical method is developed to resolve the three dimensional Poisson's and Laplace's equation at the center axis in cylindrical coordinates. The method employs the rectangular xyz co-ordinates to solve the potential φ along the center axis. The new approach is tested by comparing the potential distribution of a biased cylindrical duct simulated by two dimensional l' Hospital rule. The capability of the method to model non-symmetry field structure is verified by simulating the potential distribution inside the cylindrical duct with only a three quarter of the wall biased with a positive voltage.