Deterministic Boltzmann solver for Electron Kinetics in Plasma Reactors for
Microelectronics Applications
Vladimir Kolobov (

), 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