Effect of finite charging time on particulates in RF discharges

The effect of the finite charging time on spherical and cylindrical particulates in an RF discharge is considered. Using probe theory, analytical expressions for the charging rate under various conditions are derived and compared with numerical solutions. Scaling of the charging time with discharge parameters, in particular the electron temperature, is demonstrated. Using a one-dimensional fluid model for an rf discharge, the equilibrium electric and ion drag forces are compared for spherical and cylindrical particulates. The effect of the finite charging time on the dynamics of particulates of various sizes in the model discharge are discussed. Overall, a long cylindrical particle with the same mass as a spherical particle charges up more slowly to a larger net (negative) charge and has a significantly larger polarization. As a consequence, small cylindrical particles introduced near the electrodes are more likely to escape from the sheath region before becoming fully charged