Low-energy electron scattering in carbon-based materials analyzed by scanning transmission electron microscopy and its application to sample thickness determination.

High-angle annular dark-field scanning transmission electron microscopy (HAADF STEM) at low energies (≤30 keV) was used to study quantitatively electron scattering in amorphous carbon and carbon-based materials. Experimental HAADF STEM intensities from samples with well-known composition and thickness are compared with results of Monte Carlo simulations and semiempirical equations describing multiple electron scattering. A well-defined relationship is found between the maximum HAADF STEM intensity and sample thickness which is exploited (a) to derive a quantitative description for the mean quadratic scattering angle and (b) to calculate the transmitted HAADF STEM intensity as a function of the relevant materials parameters and electron energy. The formalism can be also applied to determine TEM sample thicknesses by minimizing the contrast of the sample as a function of the electron energy.