Numerical schemes for 1D capacitively coupled plasma fluid simulation

Capacitively coupled plasmas (CCP) are widely used in semiconductor manufacturing, where fluid models provide an efficient approach to the simulation of the low-temperature discharge. The model considered in this work couples the electron and the ion continuity equations, the electron energy equation and the Poisson's equation for the electric potential. We investigate the numerical schemes for the simulation of the 1D-CCP. In particular, a semi-implicit Scharfetter-Gummel (SG) scheme is adopted for the Poisson's equation, while the remaining equations are solved using the implicit SG schemes. The proposed strategy can be naturally extended to the 2D cases. Several alternative schemes are also discussed and tested. Numerical experiments compare these methods in terms of the admissible time step $Δt$, total simulation time, accuracy against a reference solution and robustness of the scheme. We propose a numerical scheme for the 1D-CCP and, to the best of our knowledge, provide the first detailed numerical analysis of such a scheme for CCP.