Analysing gold nanorod STEM-in-SEM signals at 20 and 30 keV beam energies using a simulation combining explicite diffraction calculations with Monte Carlo strategies

Abstract text (incl. figure legends and references)

Environmental and health care issues demand for a quantification of the size of nanoparticles (NP) necessitating the characterization of the geometrical dimensions and shapes. NP of simple geometries such as rods and spheres reveal varying STEM-in-SEM signals for identical thickness, even identical particles, depending on a varying history of exposure [1], see Fig. 1.

Models of the geometry and as well physical models of the beam-sample interaction are required to interpret the transmission signals to defer size information.

We have measured gold nanorods (Au-NRs) using a SEM in transmission mode with beam energies of 20 and 30 keV, a beam current of 50 pA and various dwell times. The Au-NRs have been prepared on a carbon support film of a thickness of 12.5 ± 2.5 nm. Simulations have been carried out using ELSEPA [2] to calculate the scattering amplitudes, thus cross sections, of elastic scattering with a muffin tin radius for gold of 0.147 nm and using cross sections for inelastic scattering coming with JMONSEL [3] according to Shinotsuka et al. [4]. Both types of cross-sections have been implemented as concrete physics C++ classes into the framework of Geant4 [5]. The complex waves with their elastic scattering amplitudes of "independent" gold atoms, their potentials being limited within a sphere (muffin tin) and the atoms being positioned at the gold lattice have been superimposed to calculate the Laue diffraction.

The propagation of beam electrons as trajectories with paths and vertices, with the vertices being the positions where scattering events occur, has been simulated by a Monte Carlo (MC) model. The path lengths s are diced according to the mean free path L by s = -L log(R) with R being a uniformly distributed random number, such that vertices are randomly positioned without any crystal lattice relationship. The signal of the bright field detector simulated by such MC simulations complies with the second scan taken 12 seconds after the first, see in Fig. 1 the blue, purple dash-dotted and yellow curves. A sequence of scans show changing signals of the identical particle. Some NR even have stripes of varying intensity that lie parallel to the scanning direction. It is assumed that the higher transmission yield is obtained due to channeling effects dependent on crystallization. The polar diagrams of the diffraction images in Fig. 2 depict the resultant distribution of the scattering; left: that of a single atom representing the differential cross section as generally used for MCs; right: the diffraction pattern of a Laue diffraction calculation on a lattice with 704 atoms. Comparing the two intensity distributions reveals that in case of crystal diffraction, the electron's wave amplitudes are channeled into the center of the bright field detector. The probability of interacting inelastically, thus incoherently and mostly scattered outside the bright field detector, is 45.2%. If channeling occurs, expect for the small fraction of intensity of the secondary maxima, most of the remaining 54.8% hit the bright field detector. We have observed 53.8% intensity on the bright field detector, see Fig. 1 red curves.

For a quantitative determination of NP sizes, appropriate physical modeling is required. Therefore, a combination of a Monte Carlo approach accounting for the randomness of size and orientation of crystal domains and of inelastic scattering processes with crystal diffraction is under development.