Particle-in-Cell (PIC) modeling of electron and ion kinetics in single vs multi frequency plasma discharges

Semiconductor device fabrication process yield for high aspect ratio applications is influenced heavily by controllable near-wafer sheath dynamics. Understanding the time-dependent sheath dynamics is critical to obtain the optimal spatial uniformity of ion flux and energy-angle distributions. Characterizing the nonlinear sheath behavior with hybrid fluid-particle plasma models is insufficient due to the several assumptions that go into approximating the sheath behavior. However, a particle-in-cell (PIC) model, in general, has fewer assumptions by allowing general velocity distribution functions for charged plasma species and can self-consistently handle the nonlinear and transient effects. In this work, the kinetic aspects of electron heating and ion transport are discussed using a high-performance two-dimensional (2D) PIC simulation parallelized with a graphics processing unit (GPU). Analysis of the electron dynamics and ion sheath transport are presented for plasma with substrate bias in single and/or mixed RF frequency operation modes. Phase resolved ion angular and energy distributions (IEAD) show a higher degree of spatial non-uniformity in sheath near wafer edge for low frequency bias source. The effects of wafer focus ring material coupled with driving frequency on the ion dynamics near wafer edge to minimize the extreme wafer edge tilt will be discussed.