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

Abstract

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 × 55 cm in a large-area VHF plasma reactor.

Calculation of the electrode shape for suppression of the standing wave effect in large area rectangular capacitively coupled reactors

“…3,4 However, it has been shown that when higher frequency is combined with large area reactor, standing wave effects become the main source of nonuniformity in conventional capacitively coupled parallel plate reactors, 1,[5][6][7][8][9][10] or in reactors using a ladder electrode. 11 Taking into account the wavelength reduction or worsening effect due to the presence of the plasma, 1,7,9 the standing wave nonuniformity already becomes important when the reactor size is about one tenth of the free space wavelength 0 at the excitation frequency ͑ 0 / 10= 2.2 m at 13.56 MHz, but only 0.3 m at 100 MHz͒.…”

Comparison of electrostatic and electromagnetic simulations for very high frequency plasmas

“…Satake et al 22 measured the voltage distribution with VHF excitation by a high frequency voltage probe, and it agreed well with the plasma distribution. Schmidt et al 23 measured the optical emission intensity and ion flux in a cylindrical reactor, proving that the Gaussian-lens electrode could suppress the standing wave nonuniformity.…”

“…In recent years, several theoretical studies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and experimental research [22][23][24][25][26][27][28][29][30] have been published on the plasma characteristics in a CCP sustained by VHF sources. Lieberman et al 6 first employed a uniform slab model to investigate the standing-wave and skin effects in VHF discharges.…”

Generation of Uniform Large-Area VHF Plasmas by Launching a Traveling Wave

“…For sinusoidal waves propagating in rectangular coordinates, the resulting standing wave patterns can be expressed by sinusoidal functions as well . It has been verified in various experimental studies that the result can serve as excellent approximation even when plasma discharge is ignited in a rectangular capacitively coupled plasma (CCP) reactor . If two standing waves (denoted as SW1 and SW2) possess the following mathematical forms: their superposition results in A × cos( ωt − kz ) and A × cos( ωt + kz ), which are both traveling waves, as they are applied to the same electrode or different electrodes of CCP reactors.…”

“…Nevertheless, for VHF plasmas, the standing wave pattern depends on the wavelength ( λ ) of electromagnetic wave in the plasma region, which could be influenced by a variety of experimental parameters, such as frequency, discharge gap, power, pressure, and gas compositions. According to the available literatures, the actual wavelength in plasma ranges from 12 to 60% of that in vacuum …”