Deterministic Boltzmann solver for Electron Kinetics in Plasma Reactors for Microelectronics Applications

Vladimir Kolobov ( vik-AT-cfdrc-DOT-com.gif ), and Robert Arslanbekov
CFD Research Corporation, Huntsville, AL 35805, USA

We have developed kinetic module in the commercial CFD-ACE+ software package and applied it for simulations of plasma reactors for microelectronics applications. The kinetic module solves the Boltzmann Transport Equation (BTE) using either two-term Spherical Harmonics Expansion (SHE) or elliptic representation (ER) of the Probability Distribution Function (PDF). Both methods reduce the 6D BTE to one or two coupled equations in a four-dimensional space (3 spatial coordinates + energy) offering a very good compromise between physical accuracy and numerical efficiency. We will describe the design of the kinetic module, its current status and applications to electron kinetics in gas discharges. The kinetic module is coupled to other modules in CFD-ACE+ enabling self-consistent kinetic simulations of plasmas. In the SHE model, a Fokker-Planck equation is solved for the Electron Energy Probability Function (EEPF) providing macroscopic characteristics (electron density, fluxes, rates of electron induced chemical reactions, etc). Using these quantities, the transport of ions and neutrals in plasmas is simulated using continuum model. The electromagnetic fields are calculated by solving Maxwell equations in the potential formulation (scalar electric and vector magnetic potentials). We shall present several samples of hybrid kinetic simulations of plasma reactors including Inductively Coupled Plasma (ICP), Capacitively Coupled Plasma (CCP), and classical DC glow discharges. The developed Boltzmann solver expands the applicability of plasma models to low gas pressures and enhances accuracy and fidelity of plasma simulations. Work supported by NSF SBIR Phase II Project DMI-0091572 http://www.cfdrc.com