Experimental method for determining Cliff–Lorimer factors in transmission electron microscopy (TEM) utilizing stepped wedge-shaped specimens prepared by focused ion beam (FIB) thinning

An experimental method to determine the Cliff–Lorimer factor has been developed utilizing an ultra-wide double-wedge (UWDW) FIB membrane geometry with terraced steps that increase in thickness in increments of approximately 30 nm. Pure elements are deposited as thin films onto a single-crystal Si substrate and energy dispersive X-ray spectroscopy (EDS) is performed on each of the terrace steps. The linear relationship that exists between X-ray counts and specimen thickness can be established and the Cliff–Lorimer factor (k-factor) determined. This method for experimental k-factor determination can be used as an alternative to intimately mixed standards, when they are difficult to obtain. The following general relation was developed to determine the k-factor by this method: kβ−α=(mα/mβ)(ρβ/ρα) where mα and mβ are the slopes of X-ray intensity vs. thickness plots for elements α and β, respectively; and ρα and ρβ are the mass densities of elements α and β. A polycrystalline Ni thin film on a single crystal Si substrate was used to test this method. The theoretical k-factor calculated for Ni and Si was kNi–Si=1.50. Two k-factors were determined for the UWDW membrane using the appropriate microscope and detector conditions: kRightNi–Si=1.51 for the terrace steps to the right of the specimen membrane, and kLeftNi–Si=1.56 for the terrace steps on the left side. These results agree to within 0.44% and 2.67%, respectively, of the calculated theoretical value.