Thermoelectric instability trends in argon radiofrequency plasmas

Plasma uniformity is critical in radiofrequency plasma processing for semiconductor manufacturing, where plasma instabilities can further constrain already narrow process windows, making it challenging to achieve desired on-wafer results. These constraints underscore the need for practical models that predict conditions for self-organization and guide process optimization. This study examines thermoelectric instability in planar inductively coupled argon glow discharges and its dependence on gas pressure and gap length. A fluid theoretical framework, grounded in the drift-diffusion approximation, was employed to analyze stability trends and provide a detailed perturbation analysis. The analysis predicts that plasma instabilities emerge within constrained, yet experimentally testable ranges of sub-Torr gas pressures and centimeter-scale gap lengths. Accuracy of these predictions depends strongly on the underlying transport data: incorporating a multiterm Boltzmann solver resolves discrepancies in the literature and demonstrates the inadequacy of two-term solvers. The study also shows that assuming energy transport coefficients to scale as a fixed factor of particle coefficients leads to systematic errors, and that stability outcomes are sensitive to the orientation of electron diffusivity and the choice of ion mobility model. Together, these findings delineate the operating conditions where self-organization is likely and provide a quantitative basis for predicting the growth rates and wave numbers of unstable modes.