Spatially averaged ion temperature model for low-temperature plasma sources

Although the ion temperature can considerably affect bulk plasma parameters and ion angle distribution functions arriving at the substrate, limited experiments have been conducted on this phenomenon because ion temperature measurement is difficult. Furthermore, only a few simulations have been performed under specific conditions. Therefore, in this study, a novel method was developed to calculate the ion temperature using a global model. The spatially averaged ion temperature equation was derived by integrating the ion temperature over space. Continuity and electron temperature equations were used in a self-consistent manner to solve the equation. We investigated radio-frequency inductively coupled Ar, N2, and Cl2 discharges in the pressure range of 5-20 mTorr and power range of 200-1000 W. The obtained results were highly consistent with experimental and two-dimensional simulation results.