Ion scattering spectroscopy intensities for supported nanoparticles: The hemispherical cap model

Abstract

Nanoparticles of one element or compound dispersed across the surface of another substance form the basis for many materials of great technological importance, like catalysts, fuel cells, sensors and biomaterials. Nanoparticles also often grow during thin film deposition. The size and number density of such nanoparticles are important, often estimated with electron or scanning tunneling microscopies. However, these are slow and often unavailable with sufficient resolution for particles near 1nm. Because the probe depth of low-energy ion scattering spectroscopy (LEIS) with He+ and Ne+ is so shallow (less than one atom), it provides quantitative information on the fraction of the surface that is covered by such nanoparticles. Combined with the total amount per unit area, this fraction provides the average particle thickness. When the ions are incident or detected at some angle away from the surface normal, macroscopic screening effects cause interpretation of LEIS signals in terms of area fraction covered to be complicated. In this paper, we report a geometric analysis of particles with the shape of hemispherical caps so that LEIS signals obtained in any measurement geometry can also be used to quantitatively determine the area fraction, average particle thickness and diameter, or number density of particles.