Electrode Shape Optimization Using Continuum Sensitivity Analysis in Unipolar Space-Charge System

Abstract

This study proposes an electrode shape optimization strategy with a space-charge distribution. Previous studies on electrode shape optimization did not consider field distortion through a space-charge. Here, a non-dimensional charge transport equation and a Poisson equation are numerically solved in a fully coupled system using a standard finite element method for transient analysis. The proposed method can be used to generate or smoothen the target field of a particular part in a strongly inhomogeneous field, such as dry etching reactor. The deformations of the design parameters are determined based on the velocity field calculated through a sensitivity analysis and are expressed using the level set method. To verify its feasibility, the proposed method was tested on a planer diode model. The results show that the optimized shape is well matched with the analytical solution. Application models, such as a sharp pin-plane model, were also tested to demonstrate the utility of the proposed method.