Experimental Demonstration of the Similarity Law for Low-pressure Capacitive Radio-frequency Discharge

Similarity laws can be employed for correlating discharges at different dimensional scales with predictable discharge parameters, and thus can aid the design and construction of discharge devices, such as lowpressure capacitive radio-frequency (rf) discharge chambers which are commonly used for plasma etching in the field of chip fabrication. In this work, the similarity law of low-pressure rf discharge was experimentally explored based on the measurement of the voltage-ampere characteristics and phaseresolved optical emission spectroscopy (PROES). By simultaneously tuning the combined parameters pd, $f / p$ and $p R$, where p is gas pressure, f is driving frequency, d is gap distance and R is the radius of electrodes, two similar rf discharge systems were experimentally prepared. By applying the equivalent circuit model to the rf discharge system and measuring the equivalent parameters of the stray capacitance and inductance, the voltage-current characteristics between the electrodes were determined. The voltagecurrent characteristics of the discharges under similarity conditions were found to be the same across a range of the varied experimental parameters, which confirm the discharge similarities. By keeping the rf power the same in the similar discharges, the spatial-temporal evolutions of the excitation rate, through PROES under two groups of pressure conditions, were found to be approximately identical. This work experimentally validates of similarity laws in low-pressure rf discharges based on the electrical measurement, which may further promote the application of similarity laws in gas discharge investigations.