Matching an RF Sheath Model to a Bulk Plasma Model

In this paper, we present a combined plasma-sheath model designed for the study of high density discharges, or other systems with thin sheaths. Sheaths in high density plasmas are typically less than 1 mm in thickness. When modeling multidimensional discharges, fully resolving the sheaths can be prohibitively expensive computationally, especially when RF power is coupled capacitively into the discharge. However, the sheath impedance often strongly affects instantaneous and period-averaged plasma potentials, which in turn can strongly influence crucial processing characteristics such as the ion energy and angular distributions impacting surfaces. In the combined plasma-sheath model we present, the sheaths are treated independently from the plasma region, and different length scales are employed for each. The Godyak-Sternberg sheath model [Phys. Rev. A, 42, 2299 (1990)] is used to represent the sheaths. The bulk plasma portion of the discharge is represented using a fluid model. Boundary conditions at the plasma-sheath interfaces transfer information dynamically between the sheath and bulk plasma portions of the model. Results from the combined plasma-sheath model are compared to results from a discharge model that fully resolves the sheaths, with generally good to excellent agreement.