Paper PS2-ThM2
Three-Dimensional Modeling of Capacitively-Coupled Plasmas with Asymmetric Reactor Elements

Thursday, October 23, 2008, 8:20 am, Room 306

Much of the focus in past plasma uniformity studies has been on center-to-edge non-uniformity, which can generally be addressed through careful plasma reactor design and process optimization. As plasma processing uniformity requirements grow more stringent, there is an increasing emphasis on the characterization of asymmetric reactor elements which may give rise to azimuthal non-uniformities. The complexity of these systems can make experimental analysis of isolated components difficult, however, which has provided an impetus for the development of a three-dimensional fluid plasma model. Herein, we describe the model and its use in the investigation of several azimuthally asymmetric elements in typical plasma processing reactors. In our three-dimensional model, charged species densities are computed by solving continuity equations for all species using the drift-diffusion approximation. The coupled set of charged species continuity equations and Poisson equation, which governs the electrostatic fields, is solved implicitly in time. The electron temperature is determined by solving the electron energy equation. The model also includes the full set of Maxwell equations in their potential formulation, Kirchhoff equations for the external circuit, and continuity equations for neutral species, along with non-uniform mesh generation to better resolve regions of interest. Using this model, we have investigated several azimuthally asymmetric components with the potential to perturb the plasma density, ion flux at the wafer, and electric fields. Ar is the feed gas in all simulations. For 13.56 MHz capacitively coupled plasma (CCP) discharges with peak plasma densities near the electrode edges, asymmetric elements include discontinuities of various sizes and locations in the reactor wall (e.g., diagnostic ports, slit valve) as well as the presence of off-axis circular plates surrounding the lower electrode. For 162 MHz CCP discharges with densities typically peaking in the reactor center, the impact of electrode planes aligned off-normal to each other is investigated, for several degrees of tilting and at different electrode gaps. Fourier analysis is used as appropriate to quantify the degree of perturbation induced by each asymmetric component.