Analytical model of Micro Hollow Cathode Discharges

In the framework of the optimization of a boron nitride deposition process based on a Micro Hollow Cathode Discharge (MHCD), a model of the cathodic region has been developed to understand how the reactive species are created in the plasma source before being transported in the deposition chamber. The key feature of the model is to correctly calculate the ionization profile resulting from energetic electrons generated in the sheath and entering the plasma region with significant energy. To simplify the problem, a pure argon discharge in a 1D planar geometry is first considered. The model is decomposed into two separated regions: (i) the quasi-neutral region in the center and (ii) the cathode sheath region near the surface. The two models are coupled at the plasma-sheath interface, where the electric field, the discharge current and the ionization rate must be continuous. The model is validated through comparison with Particle-In-Cell (PIC) simulations. Once the physics of this simplified geometry is understood and validated, a second symmetrical sheath is added to mimic the MHCD configuration. This complete model is then compared to experimental findings on the electron density and sheath thickness variations.