Experimental and numerical studies on voltage distribution in capacitively coupled very high-frequency plasmas

A non-uniform voltage distribution across a driven electrode results in inhomogeneous film deposition in large-area, very high-frequency (VHF) plasma reactors. Here we perform experimental and numerical studies on the voltage distribution across the electrode. Two kinds of dedicated vacuum chambers are prepared for one- and two-dimensional observations of the voltage and the plasma distributions. A comparison between the measured voltage and the plasma distribution clearly shows a good agreement between the two. In principle the plasma distribution is governed by the standing wave of the voltage on the driven electrode for an at least one-dimensional electrode. A numerical model based on transmission-line modelling is presented for calculating the voltage distribution. The influence of plasma conditions such as the electron density and the sheath length included in the model on the voltage distribution is investigated through comparison of the model predictions with the experimental results. The correlation between the plasma conditions and the propagation constant of the model suggests that the sheath length dominates the wavelength; in contrast, the electron density dominates the decay of the wave propagation. Using the parameters of the plasma conditions estimated from the experimental results, the model can predict the voltage distribution across a ladder electrode of size 45 cm x 55 cm in a large-area VHF plasma reactor.