Model for ion-induced nucleation based on properties of small ionic clusters

Abstract

A method is presented for calculating ion-induced nucleation rates. Whereas classical ion-induced nucleation theory makes the approximation that small ionic clusters are charged droplets whose properties equal their values for the bulk liquid, the method presented gives a nucleation rate in the form of a summation over discrete cluster properties. The summation converges rapidly around the critical cluster size, which is often as small as a few atoms. This approach allows the direct utilization of experimental and/or computational data for cluster properties. Sample calculations are presented for nucleation of silicon particles via condensation of neutral silicon vapor onto silicon anions for conditions representative of microelectronics processing plasmas. As the temperature increases the predicted nucleation rates show a transition from the collision-limited regime to the condensation–evaporation regime, where nucleation rates drop sharply with temperature. The value of the temperature where this occurs depends on the condensible vapor concentration.