Similarity laws for two-dimensional simulations of low-pressure capacitively coupled radio-frequency discharges

Abstract

Similarity laws (SLs) for low-pressure capacitive radio-frequency plasmas are generalized from one- to two-dimensional (2D) frameworks based on kinetic particle-in-cell simulations. Fundamental discharge parameters, such as the 2D distributions of electron densities and electric fields, are examined to assess the applicability of SLs to such discharges. The discharge characteristics are found to remain invariant when external control parameters are changed according to SLs. Even under conditions where nonlinear electron resonance heating caused by the self-excitation of the plasma series resonance due to the geometric reactor asymmetry plays an important role, the electron kinetics are shown to be invariant. Moreover, the validity of SLs for the ion dynamics is demonstrated. The results advance the applicability of SLs to a 2D cylindrical reactor geometry with azimuthal symmetry, indicating broad application prospects in practice.