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In recent years, capacitively coupled plasmas driven by ultra-low frequency source have garnered increasing attention, because they are beneficial for generating ions with high energy and small scattering angle, which aligns well with the current trend in high aspect ratio etching. Since the sheath becomes thicker when a ultra-low frequency source is applied, the secondary electron emission becomes significant. Indeed, these energetic secondary electrons could enhance the ionization process and even influence the discharge mode. In this work, a two-dimensional fluid model is employed to study the influence of secondary electrons on the dual frequency capacitively coupled plasmas under different ultra-low frequency voltages, secondary electron emission coefficients and inter-electrode gaps. The high frequency is fixed at 13.6 MHz, and the ultra-low frequency is fixed at 400 kHz. First, by using the ion energy dependent secondary electron emission coefficient, it is shown that the electron density first decreases and then increases with ultra-low frequency voltage. This is because on one hand, the higher ultra-low frequency voltage leads to thicker sheath, and therefore, the effective discharge volume is compressed. On the other hand, secondary electrons emitted from electrodes could obtain more energy, and thus enhance the ionization process. By comparing with the results obtained with fixed secondary electron emission coefficients, it is found that in the low voltage range, the evolution of the electron density is similar to that with fixed coefficient of 0.1. While, in the high voltage range, the growth of the electron density is even more pronounced than that with fixed coefficient of 0.2, indicating that the enhancement of the secondary electron effect by ultra-low frequency voltage is non-linear. Finally, the impact of discharge gap on the plasma properties has also been discussed. It is shown that with the increase of inter-electrode gap from 2 cm to 4 cm, the maximum ionization rate becomes lower, but the electron density rises significantly, and the plasma radial uniformity is improved. When inter-electrode gap is large, secondary electrons could collide with neutral species fully, and thus their influence on the electron density at high ultra-low frequency voltage is more pronounced. The results obtained in this paper are helpful to understand the influence of ultra-low frequency source on the secondary electron effect, and provide some guidance for the optimization of plasma processing.
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Keywords:
- capacitively coupled plasma /
- fluid model /
- ultra-low frequency power /
- secondary electron
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