A self-consistent model for the production and growth of nanoparticles in low-temperature plasmas

Abstract

A theoretical global model is presented for describing the kinetics of generation and growth of clusters and nanoparticles in low-pressure plasmas, where important processes for clusters and grains are collisions with monomers, electrons, and ions and particle coagulation and loss because of diffusion and gas flow drag. Simple equations are given for calculations of monomer density, particle-size distribution function, critical cluster size, the rate of particle production and particle density and mean size, and plasma characteristics (the densities and average energies of “cold” and “hot” electrons and the density of positively charged ions). The model is self-consistent; that is, the above-mentioned properties of clusters, nanoparticles, electrons, and ions are calculated jointly from coupled equations as functions of a small number of radio frequency (RF) discharge parameters (discharge geometry; absorbed electric power; voltage across the RF sheath; gas pressure; composition; and flow rate). Comparisons are made with the experimental data on SiH4-Ar mixtures.