Discharge similarity and scaling networks for low-pressure capacitively coupled radio-frequency CF₄ plasmas

Capacitively coupled radio frequency (rf) discharges are widely used for plasma etching and surface processing in the field of semiconductor industry. Understanding the discharge similarity and scaling networks for characterizing discharge properties with control parameters simultaneously tuned is essential for practical applications. In this work, we confirm the validity of similarity laws for low-pressure capacitive rf discharges in CF₄ via fully kinetic particle-in-cell (PIC) simulations. It is found that the spatiotemporal distributions of electron density under similarity conditions are shown to be scale-invariant; however, a violation of the similarity law for the positive and negative ion densities is observed. The validity of the similarity relations for charged species depends on whether the linear or nonlinear collisions are dominant. We also experimentally established a similarity-based scaling network for capacitive rf CF₄ discharges by applying phase-resolved optical emission spectroscopy and Langmuir-probe diagnosis. Control parameters, including gas pressure, gap distance, and driving frequencies, are progressively tuned toward similarity conditions in this network. This establishment of the complete set of scaling pathways is vital for precise prediction and parametric study of rf discharge plasmas.