Modification of Semianalytical Finite Element Model for Radio Frequency Sheaths in Single- and Dual-Frequency Capacitively Coupled Plasmas: Incorporating Ion Density Oscillation at Low Frequency

摘要

The semianalytical rf sheath model for single- and dual-frequency capacitively coupled plasmas based on the finite element method has been modified by incorporating ion density oscillation at low frequency into it. Using the new rf sheath model, we have confirmed that the ion density in a one-dimensional dual-frequency (60 MHz/2 MHz) sheath responds to 2 MHz, but not to 60 MHz. The electron density profile affected by the ion density oscillation agrees well with a result from a particle-in-cell, Monte Carlo collision plasma model referred to in this study. This is an indirect but positive proof of the validity of our modified rf sheath model. We have also applied the model to a sheath around a gap between a wafer and a focus ring in a dual-frequency (40 MHz + 3.2 MHz) etching reactor to demonstrate its capability for multidimensional simulation.