Comparing experiment with theory of X-ray absorption in thin SiGe films

In energy-dispersive X-ray spectrometry (EDXS) the chemical concentration of an element within a small region illuminated by an electron beam is calculated from the measured intensities of X-rays produced by the primary electrons. In the ratio method developed by Cliff & Lorimer [1] and later refined by others, the X-ray intensity of a certain line is compared to that of a standard element (often Si K-line) so that the chemical concentration of an element j can be calculated as xj=(Ij kj,SiK aj ej /Aj)/(∑n In kn,SiK an en /An) (eqn. 1) where I denotes intensity, k is the k-factor with respect to weight %, a the absorption, e the efficiency of the detector for the corresponding X-ray line, A the atomic weight and the index n runs over all elements detected. The k-factors in this equation are sensitivity factors that depend on the primary voltage and the X-ray fluorescence yield of the corresponding element, compared to the standard. The division by atomic weights is only necessary if the k-factors refer to weight % (rather than atomic %). We can define an effective k-factor with respect to silicon as a standard by k*j=kj,SiK aj (eqn. 2) which represents a thickness-dependent k-factor [2] that also depends on the take-off angle of the detector used, as the X-rays have to traverse a length through the specimen given by the ratio o