Global Modeling of Magnetized Capacitive Discharges

Capacitive reactors for semiconductor processing must simultaneously balance many physical phenomena with engineering constraints to achieve the desired processing properties. Important phenomena include electromagnetic RF propagation, gas ionization, plasma heating, plasma transport, and nonlinear sheath effects. Constraints are driven by process uniformity, radical production, thermal control, and reactor-component lifetime. These phenomena and constraints are often modeled in isolation; however, in a real system, they can interact in ways that are not easily foreseen. It is highly desirable to have global models that can provide relatively quick feedback for the proposed modifications to these systems. While an approach based on fundamental physics models is highly desirable whenever possible, the system can quickly become too complicated for quick design evaluations. In this paper, we explore the interaction between several processes by combining fundamental physics models when reasonable, with simplified, heuristic, or even empirical models for processes that are difficult to model from first principles. The goal is to understand the interaction between these processes in a global system without becoming overly encumbered by details in the individual components of the model. We study the effects of static magnetic field on plasma transport and electromagnetic effects arising at high RF frequency. We also change the RF-coupled power and ionization efficiency in a simplified 2-D model geometry to contrast the various effects. We find that discharges with very high frequency and high plasma density can exhibit localized nulls in the RF fields caused by electromagnetic-propagation effects in the sheath region. We find that relatively low static magnetic fields can modify the radial-plasma density profiles. Good agreement is found between the radial-plasma profiles given by the model and those measured in an experiment where the currents in two concentric coils near the plasma are the only variables.