In thin TEM specimens quantification of X-ray analysis is generally done with the Cliff-Lorimer method neglecting X-ray absorption in the specimen.  This assumption is valid for X-ray transitions with similar energies but can, even for specimens thinner than 100 nm, lead to appreciable error when low and high energy peaks are combined for the quantification.  These considerations become more important for 360º X-ray tomography for which pillar shaped specimens are used with larger diameter than the thickness of normal plan-parallel TEM specimens.

In this work the absorption effects are compared for pillar and 2º wedge shaped specimens prepared for a Si₇₅Ge₂₅ layer on Si and capped for the TEM specimen preparation with a 150 nm SiO₂ layer and ion deposited Pt in the FIB.  The EDS analysis is made in a Titan³ 60-300 instrument with SuperX EDS detector at 120 kV.  Quantification is done with linescans extracted from EDS maps using the Bruker Esprit software. The considered X-ray peaks are SiK at 1.739 keV, GeL at 1.188 keV and GeK at 9.885 keV. The orientation of the specimens relative to the 4 detectors is shown in Fig. 1. 

The quantitative linescan across the radius of the pillar is shown on Fig. 2a vs specimen thickness as calculated based on the diameter of the pillar.  The outer layer is oxidized due to air exposure of the specimen after the FIB preparation.  Next an amorphous SiGe layer is present due to the 30kV FIB preparation.  The Ge concentration calculated with GeK & SiK and GeL & SiK differs slightly which can be attributed to absorption of the low energy X-rays.  But in both cases the Ge concentrations are nearly constant through the full diameter of the pillar (except in the oxide which is Si-rich), i.e. it can be concluded that even for transitions with large difference of energy, the absorption is not dependent on the specimen thickness.  This is a result of the shape of the pillar as is illustrated on Fig. 3a which shows a section through the pillar in the plane across the electron beam direction and 2 opposite detectors.  In the center of the pillar, i.e. for maximum specimen thickness, the path lengths of the X-rays through the specimen vary with depth along the beam axis.  On average the depth dependence can be approximated by the lengths at half thickness, i.e. in total for the 4 detectors it is 4*l_c. At the thinnest edge of the pillar the X-rays travel a longer distance l_e through the pillar, i.e. in total for all detectors 2*l_e.  Both total lengths are nearly equal and this holds also for positions between center and edge, i.e. for intermediate thickness. Therefore, as observed on Fig. 2a, the strength of the absorption is independent of thickness. 

In a plan-parallel specimen with thickness equal to the diameter of the pillar the path lengths of the X-rays are much longer (Fig. 3b).  Taking half depth as the average length, the total length is 4*l_p, which is more than 2 times larger than the total lengths in the pillar case.  Due to the wedge shape of the specimen the length to the detectors on left and right side slightly differ (not shown on the figure).  Moreover, for the plan parallel specimen the total absorption path length is directly proportional to the specimen thickness.  Therefore the absorption increases with specimen thickness and the Ge concentration increases with thickness when using transitions with large energy difference (GeK & SiK) and decreases in the case of GeL combined with SiK (Fig. 2b).  Extrapolated to zero thickness the concentrations coincide, i.e. the difference of the calculated concentrations with GeK and GeL is due to absorption.  The calculated concentrations in the pillar with diameter 320 nm are similar to the concentrations in the wedge specimen near 150 nm thickness as can be expected based on the ratio of the absorption path lengths in the two cases.

Exact calculation of the path lengths in the pillars requires an integration over the thickness along the electron beam direction.  The strength of the absorption in the direction of the different detectors also depends on the different layers that are crossed, i.e. the capping stack above the SiGe or the Si substrate below the SiGe.  Therefore a full quantitative estimate of the absorption is not easily possible. 

It can be concluded that absorption effects are constant throughout the diameter of a pillar specimen and are about a factor of 2 weaker than for plan-parallel specimens with thickness equal to the diameter of the pillar.

1. Y. Qiu, V.H. Nguyen, A. Dobbie, M. Myronov, T. Walther, J. Phys. Conf. Ser. 471, 012031 (2013).

Figures:

Fig. 1. Configuration of the pillar (a) and wedge (b) specimen relative to the 4 EDS detectors.

Fig. 2. Ge concentration profile calculated with GeK&SiK or GeL&SiK as function of specimen thickness for the 320 nm pillar (a) and for the wedge samples (b). Two wedge samples are analyzed, prepared with 30 kV Ga or with an additional 5 kV Ga clean to reduce the thickness of the amorphized layer.

Fig. 3. Schematic of the X-ray paths through the specimen in the direction to the detectors.

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