The spatial resolution of aberration-corrected annular dark field scanning transmission electron microscopy was studied as function of the vertical position z within a sample. The samples consisted of gold nanoparticles (AuNPs) positioned in different horizontal layers within aluminum matrices of 0.6 and 1.0 µm thickness. The highest resolution was achieved in the top layer, whereas the resolution was reduced by beam broadening for AuNPs deeper in the sample. To examine the influence of the beam broadening, the intensity profiles of line scans over nanoparticles at a certain vertical location were analyzed. The experimental data were compared with Monte Carlo simulations that accurately matched the data. The spatial resolution was also calculated using three different theoretical models of the beam blurring as function of the vertical position within the sample. One model considered beam blurring to occur as a single scattering event but was found to be inaccurate for larger depths of the AuNPs in the sample. Two models were adapted and evaluated that include estimates for multiple scattering, and these described the data with sufficient accuracy to be able to predict the resolution. The beam broadening depended on z1.5 in all three models.

We present high-precision measurements of pure element stable isotope pairs that demonstrate mass has no influence on the backscattering of electrons at typical electron microprobe energies. The traditional prediction of average backscatter intensities in compounds was pragmatically based on elemental mass fractions. Our isotopic measurements establish that this approximation has no physical basis. We propose an alternative model to mass fraction averaging, based on the number of electrons or protons, termed “electron fraction,” which predicts backscatter yield better than mass fraction averaging. We also present an improved backscatter (electron loss) factor based on a modified electron fraction average for the ZAF atomic number correction that provides a significant analytical improvement, especially where large atomic number corrections are required.