An Analytical Scattering Model for Low Energy Annular Dark Field Transmission Scanning Electron Microscopy
Taylor J. Woehl, Jason D. Holm, Robert R. Keller
Here we employ an analytical electron scattering model to show that the decrease in ADF t-SEM contrast of gold nanoparticles on carbon films is consistent with a competition between mass-thickness and atomic number contrast. Images of gold nanoparticles on lacey carbon TEM grids were acquired in an SEM (30 keV) with an ADF detector masked by an annular aperture to define inner and outer collection angles. We varied the distance between the sample and detector to systematically vary the ADF collection angles and found that the contrast of the gold nanoparticles decreased as a function of the ADF inner collection angle. The contrast of the nanoparticles was lower overall for nanoparticles on the thicker lacey carbon support. To model the experimental contrast, we developed an analytical electron scattering model that includes collection angle dependent elastic and inelastic electron scattering as well as geometric considerations for the ADF detector. With this model we calculated the nanoparticle contrast by determining the number of electrons transmitted to a solid angle defined by the inner and outer collection angles, for both the nanoparticle and the substrate. The theoretical contrast was compared to the experimental images using the carbon support thickness as an adjustable parameter, as we could not accurately determine this thickness. With this fitting parameter, there was good agreement between the model predictions and experimental contrast. The model indicated that the decrease in contrast with decreasing collection angle was due to increased mass-thickness contrast from the carbon support relative to the atomic number contrast of the gold nanoparticles. The discrepancy in the carbon support thickness is likely due to multiple scattering in the nanoparticles. We expect this analytical scattering model will be important for determining artifact-free imaging conditions for ADF t-SEM imaging.