Two-Dimensional Implicit PIC/MC Simulations For Radio-Frequency Capacitively Coupled Plasmas

Low pressure capacitively coupled plasmas (CCP) are commonly used as etching and deposition devices in the microelectronics, flat panel display and solar cells industries. Nu-merical simulations have played essential roles both in the fundamental researches for CCP, and in the optimization for industrial reactors. Numerical simulations can not only give the high-dimensional results with full kinetics, but also greatly reduce the cost and time in developing novel industrial reactorsTwo kinds of methods are commonly used:fluid model and PIC/MC (Particle-in-cell/Monte Carlo) model. Fluid model runs fast with good stability, and is easy to couple with chemical reaction models. Two-dimensional or three-dimensional, fully electromagnetic fluid model has been realized, and is widely used in the optimization for industrial CCP discharge devices. However, due to the inherent drawbacks of fluid model, it can not consider the non-local, non-thermal equilibrium behaviors in CCP. PIC/MC model is a fully kinetics method without any of above shortcomings. However, PIC/MC model is very computation-ally costly, the most PIC/MC simulations are done in one-dimension. Two-dimensional simulation results are rare, some of which use super computers. Therefore, the development of high-speed two-dimensional PIC/MC model in axisymmetric geometry are urgent for CCP simulations. This dissertation contains two parts, first part is the algorithms for PIC/MC model, including chaptersâ…¡and Chaptersâ…¢; second part is the simulation results of CCP, including the Chapterâ…£, Chapters V and VI.For the the algorithms of PIC/MC model, the general PIC/MC model is presented in chaptersâ…¡. The weighting scheme, particle pushing and field solving are outlined, as well as the MC algorithm for particle sampling, determining the collision type and the post-collision velocity. Implicit PIC/MC algorithms in two dimensional and axisymmetric geometry are given in Chaptersâ…¢. Different algorithms are analyzed and benchmarked. It is shown that uniform grids and weighted particles are required for axisymmetric geometry simulations. The introduction of weighted particle will lead to a number of difficulties that must be handled carefully. It is concluded that the charge-conserved weighting renormalization. and z-r2 weighting is the best algorithms for weighted particles. At the same time, global X-Y-Z coordinates and semi-nultigrid method is the most optimal way for particle pushing and Poisson solver, respectively. Implicit scheme can eliminate of space and time step restrictions in explicit PIC/MC model, so the code can run 100 times faster than the explicit code, thus significantly increasing the application ability of the PIC/MC model, and makes the PIC/MC simulations for the industrial reactors possible.For the CCP simulations, in Chapterâ…£. one-dimensional explicit PIC/MC model is used to simulate the effect of gap lengths in CCP. It was found when the discharge pressure, frequency and spacing to meet certain conditions, the dominant plasma heating mechanism changes from the one sheath collisionless heating into two sheath collisionless heating. The plasma density may be significantly enhanced at small gap lengths. Hysteresis will be intro-duced in this process. In Chapter V, radial geometry effects and self bias voltage effects are studied with two dimensional implicit PIC/MC model in axisymmetric geometry. Simulations show that self-bias voltage depends on the electrode area ratios. If the reactor radial size is comparable to the electron mean free path, the plasma density and the electron heating rate will increase significantly. Ion flux and energy distributions to the rf powered electrode are also calculated. Comparing the the results of fluid model, the PIC/MC model can include all the kinetics effect and numerical-diffusion-free. In Chapterâ…¥, an altered configuration for dual-frequency (DF) CCP is proposed. In this configuration, two pairs of electrodes are arranged oppositely, and the discharge is perpendicularly driven by two rf sources. With PIC/MC model in planar geometry, we have demonstrated this configuration can remove the harmful electromagnetic and DF coupling effects in conventional DF-CCP.