Paper PS2-WeM3
3-Dimensional Model for Magnetized Capacitively Coupled Plasma Discharges

Wednesday, October 22, 2008, 8:40 am, Room 306

Static magnetic fields are often used in plasma processing systems to improve plasma confinement, modify plasma spatial profile or adjust other plasma characteristics. Aside from some simple magnetic field configurations, magnetized plasmas have a complex spatial structure and significant physics is missed in reduced (0, 1 or 2) dimensional models. A 3-dimensional fluid plasma model is used to understand the operation of magnetized capacitively coupled plasmas operating at 13.56 and 180 MHz in this paper. Both electropositive (Ar) and electronegative (O₂) gases are considered. To simplify interpretation of results, simulations have been done for an axi-symmetric reactor geometry. Static magnetic field is generated using current carrying wires, where several wire configurations that generate converging, diverging and uniform magnetic fields in the plasma region are considered. Our 3-dimensional plasma model includes the full set of Maxwell equations in their potential formulation. The equations governing the vector potential, A, are solved in the frequency domain after each cycle for multiple harmonics of the driving frequency. The coupled set of equations governing the scalar potential, φ, and drift-diffusion equations for all charged species are solved implicitly in time. The model also includes the electron energy equation, Kirchhoff equations for the external circuit, and continuity equations for neutral species. The effect of static magnetic field is included through the charged species transport properties, which become tensor quantities in the presence of a static magnetic field. Without magnetic field, electron density peaks in the center of the chamber when the plasma is generated using a 180 MHz source. The 180 MHz plasma is also symmetric because of considerable distance from the chamber walls. When a static magnetic field parallel to the electrodes is applied, ExB drift in the sheath regions shifts the peak in plasma density off-axis. As the 180 MHz plasma is symmetric, ExB drift occurs in opposite direction in the two sheaths, which leads to an overall shearing of the plasma. Electron density peaks near the electrode edges in the 13.56 MHz plasma and the plasma is highly asymmetric. Application of magnetic field and the resultant ExB drift lead to overall shifting of the low frequency plasma in the ExB direction.