For EDS quantification, in addition to the general considerations (see page3826), two other factors should also be taken into account if the interesting feature is much smaller than the specimen thickness [1]. Those factors are the electron beam broadening and the top-bottom effect, which is due to the depth position of the feature within the specimen as X-rays travel through the layer before reaching the EDS detector as shown in Figure 3121a.

Figure 3121a. Schematic illustration of X-ray path in the specimen.

In this case, in order to reach the detector the X-rays have to travel a path D=d/sinθ. Therefore, the X-ray intensity I for a specific element will decay exponentially,
        I = A exp(-D/λ) ---------------------------- [3121]
where,
        λ -- The wavelength of X-ray.

As an example, Figure 3121b presents calculated various X-ray intensities as a function of depth d for a case of 2 nm thin layers within 200 nm of GaAs.

Figure 3121b. Calculated various X-ray intensities as a function of depth d within 200 nm of GaAs (b = 2 nm). [1]

[1] T. Walther, Simple method to improve quantification accuracy of energy-dispersive X-ray spectroscopy in an analytical transmission electron microscope by specimen tilting, EMC 2008: Vol 2: Materials Science, edited by Silvia Richter and Alexander Schwedt.