Mathematical Analysis of the Physical Properties of High- and Low-Frequency Capacitively Coupled Plasma

This study investigates the behavior of dual-frequency capacitively coupled plasma (DF-CCP) systems using numerical methods. The model determines a system of equations involving four variables: electrostatic potential, electron density, ion density, and electron temperature. These physical quantities are mathematically expressed using the finite-difference method, along with the corresponding conservation equations. Finally, the solution of this four-variable system of equations is obtained using a fully coupled Jacobian-based solution with Newton–Raphson iteration. In this study, the 3-D plasma distribution has been calculated for a system using 13.56-MHz radio frequency (RF) and 2-kHz low-frequency (LF) power sources. The results show how combining these different frequencies affects the plasma properties in the volume. This 3-D model allows us to observe the effects of applying a specific frequency to each electrode. Such dual-frequency configurations may offer new possibilities for tuning plasma parameters and provide greater control over process conditions in industrial applications.