A computational investigation of the effects of varying discharge geometry for an inductively coupled plasma

Abstract

In this paper, a numerical investigation of ionization and density profiles in a low pressure inductively coupled plasma (ICP) discharge is presented. ICP reactors have in recent years become a popular choice for semiconductor processing. To ensure high yields, it is important to optimize process uniformity. Off-axis ionization can result in the hollowing of the density profile of the plasma. Previous numerical studies [Keiter (1996), Beale (1995), Mumken (1999), Kortshagen (1999)] have focused on electron kinetics and the resulting ionization rates as the main factor in producing nonuniform ion density profiles. Here we extend some of the previous work to also examine the effects of the ion transport in detail. Two models are used for the study. The first model is a hybrid model that approximates electron transport by solving the Boltzmann transport equation (BTE) using a spatially dependent two-term spherical harmonic expansion (SHE), and neutral and ion transport with a simple fluid model. The second model is a new kinetic model for ion transport in complex geometry based on the convected scheme (CS). This model uses an "unstructured mesh" and "Long Lived Moving Cells". By using the CS model for ion transport, it is possible to investigate the limitations of the fluid model and issues pertinent to process uniformity which are not accessible to the fluid approximation. As the ratio between ion mean-free path and system size is often looked to as the key parameter for determining the applicability of a fluid model, the two parameters we have varied in this study are the reactor chamber height and the neutral temperature. Ion density profiles produced by the fluid model are qualitatively similar to those of the kinetic ion model, although the kinetic model tends to produce more uniform ion density profiles.