Stability Criteria for Radiofrequency Plasmas at Low Pressure

Uniformity is critical in plasma processing of semiconductors where instabilities can give rise to destructive arcing, striations and plasmoids that can permanently damage equipment or lead to scrapped wafers. The formation of self-organized striations in the direction parallel to the radiofrequency current in low pressure, high voltage plasmas has been experimentally reported
¹
. A fluid description, typically called the nonlocal moment model
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, which uses the drift-diffusion approximation and includes the thermoelectric transport term, shown to be critical for the evolution of plasmoids in planar capacitively coupled plasmas (CCPs)
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, is used. The plasma instabilities leading to and the conditions under which these striations occur are analyzed in a planar inductively and capacitively coupled argon plasma. This analysis will be extended to Ar with CF
4
gas admixtures. The ionization rates and transport coefficients are derived from an electron energy distribution function calculated using a multi-term Boltzmann equation solver, MultiBolt. A linear stability analysis is performed to derive a stability criterion as a function of discharge parameters for uniform plasma processing. The application to practical plasma conditions and system operating parameters, such as pressure and power, is explored to identify process windows where the uniform plasma is stable.