Moments approach to compare a particle-in-cell simulation with a fluid model for RF capacitively coupled plasmas

The particle-in-cell (PIC) and fluid simulations are commonly used in low-temperature capacitively coupled plasma (CCP) equipment utilized in semiconductor manufacturing processes. As the PIC simulation calculate the transient motion of all charged particles, the energy distribution functions are computed without assumptions, and all terms of fluid equations can be compared with moments obtained from the PIC simulation. We compare every term of moment equations in the PIC and fluid simulations under the same simulation conditions. Therefore, closures of a fluid model are verified by the PIC simulation, and the role of the viscosity of the pressure tensor is investigated. As a result, we suggest the criterion for valid fluid models in a CCP.