Z-contrast atom counting using the few-layer graphene sheets

Upon the development of the quantitative scanning transmission electron microscopy (QSTEM), individually counting the gold atom has been achieved. The correlation of the signals to the atom quantity (N), i.e. calibration, is its crucial work. One has to seek the ultra-fine mass standards, where the size-selected gold clusters rank the best recently. However, practically this is difficult for light elements, since STEM intensity is proportional to Z
^α
, where Z is atomic number of the elements and α is in the range of 1.5-1.9 depending on the detector collection angle, sample thickness, and the Debye-Waller factor of the atomic species. As a result, the light elements would have a much weaker image contrast than that of heavy elements. This could be even more difficult for the carbon particles supported by the Formvar films. Graphene layers are featured by large scale uniformity and discrete layer steps, which shed light on precision calibration of the carbon atomic scales. To establish direct correlation between the STEM intensity with the number of layers in graphene sheets, we apply an independent layer counting method by utilizing dark lines in bright field TEM images at the edge of graphene sheets [2]. We search over a large area of the sample for the freely suspending graphene sheets (for example, the area indicated by the arrows in Fig. 1a)[3]. Fig. 1b displays a typical example of such an edge, where the layer number can be counted in the high-resolution bright field image and the STEM intensity is also obtained. The calibration in the few-layer range gives Fig. 1c, where a linear relationship is apparent. The calibration performed over an extended thickness presents a precise exponential growth. The behaviour can be described by the incoherent scattering picture of single scattering. This leads to accurate measurement of the electron mean free path (The error is reduced to 5 percent). The calibration relation works from individual up to millions of carbon atoms.