Fluid modelling of capacitively coupled radio-frequency discharges: a review

This paper reviews the basis and the successes with the fluid modelling of capacitively coupled radio-frequency discharges, produced within a parallel-plate cylindrical setup at (single) 13.56–80MHz frequencies, 6x10−2–6 Torr pressures and 50–1000V rf-applied voltages, in SiH4-H2, H2 and N2. The two-dimensional, time-dependent model used in the simulations accounts for the production, transport and destruction of the charged particles (via the electron and ion continuity and momentum-transfer equations, and the electron mean energy transport equations), and of the excited species and/or radicals (via their rate balance equations, including very complete kinetic descriptions with several collisional–radiative production/destruction mechanisms, coupled to the two-term electron Boltzmann equation), accounting also for the self-consistent development of the rf field (via the solution to Poisson’s equation). The charged particle transport equations are solved with and without corrective flux terms (due to inertia and friction effects), whose influence on results is discussed. In the case of silane–hydrogen mixtures, the model further includes a phenomenological description of the plasma–substrate interaction to calculate the deposition rate of a-Si :H thin films. In general, the model gives good predictions for the self-bias voltage, the coupled power and the intensities of radiative emission transitions (both average and spatially resolved), underestimating the electron density by a factor of 3–4.