Methods for modeling microwave plasma system stability

Abstract

Today’s modern commercial semiconductor plasma processes require, more than ever, stable and repeatable energy delivery. One of the challenges to utilizing microwaves for plasma processing is an inherent instability that sometimes renders “repeatable energy delivery” difficult to achieve. This instability often manifests itself as a propensity for the plasma to extinguish or rapidly change to a lower density as system components are adjusted to facilitate optimal energy transfer from the microwave generator to the plasma. This article presents two modeling methods for demonstrating microwave powered plasma system stability, both based on simple plasma system component mathematical models. Each component of a microwave plasma system was first represented with simple equations. These individual plasma system component equations were combined into a single closed-loop ‘plasma system’ Matlab Simulink model. Simulation output was compared directly against actual measured operating parameters of a microwave cavity plasma reactor (MCPR). The individual plasma system component equations were also combined into a single differential “system” equation or “state” equation. This state equation was then tested with a graphical method to further illustrate characteristics of system stability. The Simulink model and the graphical control analysis clearly demonstrated major trends of actual MCPR stability performance, showing the extent to which the actual system could be perturbed before stability was lost, and that the observed instabilities appear to be primarily caused by first order effects of system component interactions.