Modeling of Capacitively Coupled Plasmas Using Fluid Ion + Particle-in-Cell Electron Plasma Model

Low pressure (< 50 mTorr) capacitively coupled plasmas (CCP) are widely used for plasma processing in the semiconductor industry.  Kinetic effects play an important role in electron dynamics in these plasmas.  Fluid plasma models are often inadequate in capturing the behavior of these plasmas.  Full particle-in-cell (PIC) multi-dimensional models are more accurate but computationally very expensive and limited to simple chemistries.  A hybrid scheme for modeling low-pressure CCPs is described in this paper where electrons are modeled using PIC while ions and neutral species are treated as fluid.  Coupling between the fluid and PIC modules is done at every time step, where electron density from the PIC model is used during the solution of the Poisson equation.  The resulting model provides a good compromise between accuracy and computational speed, and it is suitable for industrial plasma system design applications.  One and 2-dimensional simulations of Ar and O₂ plasmas are discussed in this paper.  Single frequency, dual-frequency, and CCPs biased using non-sinusoidal waveforms are considered.  Plasma modeling results from this hybrid code are compared to corresponding results from fluid and full PIC simulations.  This comparison highlights the importance of using the appropriate boundary conditions and transport approximations for ions in fluid or hybrid plasma models.