Effect of phase angle on plasma characteristics in electrically asymmetric capacitive discharge

Abstract

In addition to the separate control of the ion energy and ion flux, the so-called electrical asymmetry effect (EAE) also plays an important role in improving the plasma radial uniformity. In this work, a two-dimensional fluid model combined with a full set of Maxwell equations is used to investigate the plasma characteristics in an electrically asymmetric capacitive discharge sustained by multiple consecutive harmonics. The effects of the phase angle θn on the dc self-bias (Vdc) and on the plasma radial uniformity for different numbers of consecutive harmonics k are discussed. The simulation results indicate that the phase angles of different harmonics θn have different influences on the dc self-bias Vdc. For instance, Vdc varies almost linearly with θ1 with a period π in dual frequency discharge, and the period is 2π for other discharge conditions. Besides, the modulation of Vdc becomes less obvious by changing the phase angle of the highest harmonic θk, especially for k>3. In addition, both the axial component of the power density Pz and the radial component of the power density Pr vary with θn, thus the plasma radial uniformity can be adjusted. When the total power density at the radial edge becomes comparable to that in the discharge center, the plasma distribution becomes uniform. For instance, when k=2, the plasma radial uniformity is the best at the phase angle θ1=π/2 and θ2=π. However, for k=3, the best radial uniformity is observed at θ1=3π/2, and the nonuniformity degree α is only 0.41% under this condition. It is worth noting that at k=8, the maximum of α is seven times higher than the minimum by changing the phase angles θ1 and θ2, which means that the plasma radial uniformity can be adjusted effectively. However, the modulation induced by θk(k>3) becomes less obvious, especially for k=8. Indeed, the electron density shows an edge-high profile, and the radial uniformity is always bad for all θ8 investigated. The results obtained in this work can help us to gain an insight into the optimization the plasma process by utilizing the EAE.