Modelling of nanoparticle coagulation and transport dynamics in dusty silane discharges

This paper reports on a self-consistent one-dimensional (1D) hydrodynamic model that investigates the formation, the subsequent growth and transport of nanoparticles in a parallel plate capacitively-coupled radio-frequency silane (SiH₄) discharge. A fully coupled description of the first two stages of particle formation (nucleation and coagulation) is attained by the development of a model which treats the electron kinetics, the gas phase chemistry, the particle formation mechanisms, the nanoparticle charging and transport dynamics, and the coagulation phase together with a self-consistent determination of the plasma properties. In the present paper, we focus on the fast coagulation stage, incorporated by making a self-consistent coupling between the 1D fluid model and an aerosol dynamics model in which an evolution of the nanoparticle size domain is obtained by utilizing a sectional approach to solve the general dynamic equation (GDE). During each coagulation step, the effect of nanoparticle charging and transport is included and solved with the same temporal resolution. The calculated density and charge distribution profiles are presented for particles ranging in size between ∼1 and 50 nm. The concerted action of particle charging and transport is found to severely affect the location of nanoparticle growth due to coagulation. Heating of one of the electrodes immediately induces a thermophoretic force that can be considered as a useful means to control particle contamination.