Quantitative annular dark field electron microscopy using single electron signals

One of the difficulties in analyzing atomic resolution electron microscope images is that the sample thickness is usually unknown or has to be fitted from parameters that are not precisely known. An accurate measure of thickness, ideally on a column-by-column basis, parameter free, and with single atom accuracy, would be of great value for many applications, such as matching to simulations. Here we propose such a quantification method for annular dark field scanning transmission electron microscopy by using the single electron intensity level of the detector. This method has the advantage that we can routinely quantify annular dark field images operating at both low and high beam currents, and under high dynamic range conditions, which is useful for the quantification of ultra-thin or light-element materials. To facilitate atom counting at the atomic scale we use the mean intensity in an annular dark field image averaged over a primitive cell, with no free parameters to be fitted. To illustrate the potential of our method, we demonstrate counting the number of Al (or N) atoms in a wurtzite-type aluminum nitride single crystal at each primitive cell over the range of 3-99 atoms.