Deterministic Boltzmann solver for electron kinetics in plasma reactors for microelectronics applications
A kinetic module has been developed in the commercial software package CFD-ACE+ and applied to simulations of plasma reactors for microelectronics applications. The kinetic module solves the Boltzmann transport equation (BTE) using two-term spherical harmonics expansion (SHE) of the probability distribution function (PDF). This method reduces the 6D BTE to a Fokker Planck equation in a four-dimensional space (three spatial coordinates+energy) offering a very good compromise between physical accuracy and numerical efficiency. This paper describes the design of the kinetic module and its current status and applications to electron kinetics in gas discharges. The kinetic module is coupled to other modules in CFD-ACE+ for self-consistent kinetic simulations of plasmas. The FokkerPlanck 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 a continuum model. The electromagnetic fields are calculated by solving Maxwell equations in the potential formulation (scalar electric and vector magnetic potentials). Several examples of hybrid kinetic simulations of plasma reactors are described including inductively coupled plasma (ICP), and classical DC glow discharges in electropositive and electronegative gases. The developed Boltzmann solver expands the applicability of computational plasma models to low gas pressures and enhances accuracy and fidelity of plasma simulations.
plasma reactors kinetic module cfd-ace+