On the validity of the classical plasma conductivity in capacitive RF discharges

Abstract

The plasma conductivity is an important input parameter for various plasma models. It is typically obtained from a simplified version of the electron momentum balance equation, where only a single inertia term and a simplified description of the collisional momentum transfer are included. The electric field is assumed to be a harmonic function of the driving frequency, higher harmonics of the current and spatial variations are neglected. Through particle-in-cell/Monte Carlo collision (PIC/MCC) simulations and analysis of the electric field generation based on velocity moments of the Boltzmann equation, the validity of this classical model is studied in capacitively coupled plasmas (CCPs). We find that these assumptions/simplifications result in significant inaccuracies of the conductivity in many cases. In single frequency CCPs, a deviation of more than an order of magnitude from the effective PIC-conductivity obtained from the simulations is found at low pressures in the discharge center and at the maximum sheath edge. In the center, this deviation is caused by neglecting the temperature gradient term in the momentum balance equation and adopting an approximation of the Ohmic term in the classical model, while at the maximum sheath edge it is induced by neglecting the density gradient term that accounts for the effect of the ambipolar electric field. The inaccuracy in the discharge center is reduced at higher pressures where the Ohmic term dominates and the approximations made in the classical model are more applicable. Better performance of the classical model is also found under conditions at which the inertia term included in the model plays an important role. Generally, neglecting higher harmonics of the current and spatial variations of plasma parameters is found to cause strong inaccuracies. Thus, the classical model can result in an inaccurate calculation of the power absorbed by electrons. Our results indicate that its applicability must be evaluated for a given set of conditions before using it to avoid introducing errors to plasma models.