Symmetry breaking in high frequency, symmetric capacitively coupled plasmas

Two radially propagating surface wave modes, “symmetric,” in which the upper and lower axial sheath fields (Ez) are aligned, and “anti-symmetric,” in which they are opposed, can exist in capacitively coupled plasma (CCP) discharges. For a symmetric (equal electrode areas) CCP driven symmetrically, we expected to observe only the symmetric mode. Instead, we find that when the applied rf frequency f is above or near an anti-symmetric spatial resonance, both modes can exist in combination and lead to unexpected non-symmetric equilibria. We use a fast 2D axisymmetric fluid-analytical code to study a symmetric CCP reactor at low pressure (7.5 mTorr argon) and low density (∼3 × 1015 m−3) in the frequency range of f = 55 to 100 MHz which encompasses the first anti-symmetric spatial resonance frequency fa but is far below the first symmetric spatial resonance fs. For lower frequencies such that f is well below fa, the symmetric CCP is in a stable symmetric equilibrium, as expected, but at higher frequencies such that f is near or greater than fa, a non-symmetric equilibrium appears which may be stable or unstable. We develop a nonlinear lumped circuit model of the symmetric CCP to better understand these unexpected results, indicating that the proximity to the anti-symmetric spatial resonance allows self-exciting of the anti-symmetric mode even in a symmetric system. The circuit model results agree well with the fluid simulations. A linear stability analysis of the symmetric equilibrium describes a transition with increasing frequency from stable to unstable.Two radially propagating surface wave modes, “symmetric,” in which the upper and lower axial sheath fields (Ez) are aligned, and “anti-symmetric,” in which they are opposed, can exist in capacitively coupled plasma (CCP) discharges. For a symmetric (equal electrode areas) CCP driven symmetrically, we expected to observe only the symmetric mode. Instead, we find that when the applied rf frequency f is above or near an anti-symmetric spatial resonance, both modes can exist in combination and lead to unexpected non-symmetric equilibria. We use a fast 2D axisymmetric fluid-analytical code to study a symmetric CCP reactor at low pressure (7.5 mTorr argon) and low density (∼3 × 1015 m−3) in the frequency range of f = 55 to 100 MHz which encompasses the first anti-symmetric spatial resonance frequency fa but is far below the first symmetric spatial resonance fs. For lower frequencies such that f is well below fa, the symmetric CCP is in a stable symmetric equilibrium, as expected, but at higher frequencies such ...