On the work function and the charging of small (r ≤ 5 nm) nanoparticles in plasmas

Abstract

The growth of nanoparticles (NPs) in plasmas is an attractive technique where improved theoretical understanding is needed for quantitative modeling. The variation of the work function W with size for small NPs, rNP≤ 5 nm, is a key quantity for modeling of three NP charging processes that become increasingly important at a smaller size: electron field emission, thermionic electron emission, and electron impact detachment. Here we report the theoretical values of the work function in this size range. Density functional theory is used to calculate the work functions for a set of NP charge numbers, sizes, and shapes, using copper for a case study. An analytical approximation is shown to give quite accurate work functions provided that rNP > 0.4 nm, i.e., consisting of about >20 atoms, and provided also that the NPs have relaxed close to spherical shape. For smaller sizes, W deviates from the approximation, and also depends on the charge number. Some consequences of these results for nanoparticle charging are outlined. In particular, a decrease in W for NP radius below about 1 nm has fundamental consequences for their charge in a plasma environment, and thereby on the important processes of NP nucleation, early growth, and agglomeration.