Nanoparticle growth by collection of ions: Orbital motion limited theory and collision-enhanced collection

Abstract

The growth of nanoparticles in plasma is modeled for situations where the growth is mainly due to the collection of ions of the growth material. The model is based on the classical orbit motion limited (OML) theory with the addition of a collision-enhanced collection (CEC) of ions. The limits for this type of model are assessed with respect to three processes that are not included: evaporation of the growth material, electron field emission, and thermionic emission of electrons. It is found that both evaporation and thermionic emission can be disregarded below a temperature that depends on the nanoparticle material and on the plasma parameters; for copper in our high-density plasma this limit is about 1200 K. Electron field emission can be disregarded above a critical nanoparticle radius, in our case around 1.4 nm. The model is benchmarked, with good agreement, to the growth of copper nanoparticles from a radius of 5 nm-20 nm in a pulsed power hollow cathode discharge. Ion collection by collisions contributes with approximately 10% of the total current to particle growth, in spite of the fact that the collision mean free path is four orders of magnitude longer than the nanoparticle radius.