| AVS 55th International Symposium & Exhibition | |
| Plasma Science and Technology | Thursday Sessions |
| Session PS2-ThM |
| Session: | Plasma Modeling |
| Presenter: | A. Balakrishna, Applied Materials, Inc. |
| Authors: | A. Balakrishna, Applied Materials, Inc. S. Rauf, Applied Materials, Inc. K. Collins, Applied Materials, Inc. |
| Correspondent: | Click to Email |
Plasma etching is a complicated process where plasma dynamics, gas and surface chemistry, and fluid flow all have significant influence on the processing results. Flow effects in commercial plasma etching reactors cannot be accurately captured in 2D models or 3D plasma-only models. While 3D flow-only models have been used to evaluate the redistribution of important plasma species and to suggest hardware improvements, this approach limits the understanding of the influence of fluid flow on the plasma. In particular, hardware changes made to improve flow symmetry impact plasma distribution, and vice versa. We have developed an integrated 3D flow and plasma model to enable this concurrent optimization. In this model, the Navier-Stokes equations in cylindrical coordinates were solved using a finite volume method. The equations were discretized using flux balances on each computational cell. The pressure distribution was computed using the SIMPLE method,2 which corrects the flow and pressure fields to fulfill mass conservation. The calculated flow distribution was passed to the plasma model, which includes the full set of Maxwell equations in their potential formulation. The vector potential is solved in the frequency domain after each cycle, with current sources computed using results from the previous cycle. The coupled set of equations governing the scalar potential 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 3D fluid-plasma model was used to understand the operation of capacitively coupled plasmas operating at 13.56 and 160 MHz in this paper. Both electropositive (Ar) and electronegative (O2) gases were considered. Comparison of the solutions with and without fluid flow interaction allowed us to separate the effects of flow and plasma on species distribution in the chamber. At sufficiently high flow rates, azimuthal flow non-uniformities were reflected in the plasma species distributions.
1J. Kenney, S. Rauf and K. Collins, AVS 2008.
2S.V. Patankar and D.B. Spalding, Int. J. Heat Mass Transfer, vol. 15, pp. 551-559 (1972).