Verification of an aspect-ratio scaling law for radio-frequency capacitively coupled plasmas

Abstract Establishing reliable scaling laws for plasma discharges is essential for the design of plasma devices, the development of processing recipes, and the advancement of plasma modeling. Within the extended Paschen framework, the breakdown voltage in radio-frequency (RF) capacitively coupled plasmas (CCPs) depends on the ratio of driving frequency to neutral pressure and on the gap-to-radius aspect ratio. The former relation has been well validated by experiments and numerical simulations, showing that the breakdown voltage remains constant when the frequency-to-pressure ratio is fixed. However, direct verification of the aspect-ratio scaling has been limited because systematic modification of electrode gap and radius is impractical in hardware. Here we present a numerical verification of the aspect-ratio scaling using two-dimensional fluid simulations over a wide pressure range for pure helium and argon-oxygen mixtures. Across pressures and chemistries, breakdown voltages converge when the aspect ratio is held constant, demonstrating geometric similarity in RF discharges, elucidating the role of reactor geometry in ignition, and revealing the explicit dependence of discharge characteristics on the aspect ratio. Furthermore, an aspect-ratio criterion governing the transition between discharge modes is identified. These results confirm the universality of the scaling under practical RF discharge conditions. This study provides a robust, physics-based scaling framework for the design and optimization of CCP reactors, supporting predictive design workflows, diagnostics, and more efficient process transfer.