Statistical methods for the correction of tip convolution effects in STM imaging of nanometer size particles in metal—C: H films

Abstract

Metal containing amorphous hydrogenated carbon films are protective coating materials with very low friction coefficients, high hardness and wear resistance, combined with an adjustable electrical conductivity. The structure of these films, consisting of nanometer size metallic particles in a hydrogen—carbon matrix, was investigated by means of scanning tunneling microscopy (STM) in order to determine particle size and particle distance distributions. In doing so, tip convolution effects lead to apparent particle enlargement and particle hiding, falsifying radii and distance determination. In order to correct these errors (1) a statistical method is presented which allows off-line tip radius determination by analysing apparent particle radii, (2) a simple Monte Carlo model is proposed to compute fractions of hidden particles and their influence on particle distance distributions. Both methods are applied to STM measurements of Au-C:H and Pt-C:H samples of different metal content and the result is compared with results of small angle X-ray scattering (SAXS), transmission electron microscopy (TEM) and X-ray diffraction (XRD).