X-ray absorption in pillar shaped transmission electron microscopy specimens

Ultramicroscopy 177 (2017) 58–68

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X-ray absorption in pillar shaped transmission electron microscopy specimens H. Bender a,∗, F. Seidel a, P. Favia a, O. Richard a, W. Vandervorst a,b a b

Imec, Kapeldreef 75, 3001 Leuven, Belgium Instituut voor Kern- en Stralingsfysica, KU Leuven, 3001 Leuven, Belgium

a r t i c l e

i n f o

Article history: Received 12 October 2016 Revised 11 January 2017 Accepted 5 March 2017 Available online 7 March 2017 Keywords: Pillar TEM specimen X-ray absorption EDS X-ray tomography Transmission electron microscopy SiGe HfO2

a b s t r a c t The dependence of the X-ray absorption on the position in a pillar shaped transmission electron microscopy specimen is modeled for X-ray analysis with single and multiple detector configurations and for different pillar orientations relative to the detectors. Universal curves, applicable to any pillar diameter, are derived for the relative intensities between weak and medium or strongly absorbed X-ray emission. For the configuration as used in 360° X-ray tomography, the absorption correction for weak and medium absorbed X-rays is shown to be nearly constant along the pillar diameter. Absorption effects in pillars are about a factor 3 less important than in planar specimens with thickness equal to the pillar diameter. A practical approach for the absorption correction in pillar shaped samples is proposed and its limitations discussed. The modeled absorption dependences are verified experimentally for pillars with HfO2 and SiGe stacks. © 2017 Elsevier B.V. All rights reserved.

1. Introduction In thin transmission electron microscopy (TEM) specimens quantification of X-ray analysis is generally done with the CliffLorimer method neglecting X-ray absorption in the lamellae [1]. This assumption is valid for X-ray lines 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 [2–6]. These considerations become more important for X-ray tomography using pillar shaped specimens that often have diameters larger than the thickness of standard planar TEM specimens. A methodology to correct for X-ray absorption in 3D STEMEDS tomography is recently discussed by Burdet et al. [7] based on a voxel-by-voxel calculation of the variation of the absorption along the X-ray track towards the detectors. The procedure is shown to be essential to correctly reconstruct the O and C distribution in core/shell nanowires with diameters on the order of 200 nm. Slater et al. [8] consider the maximum X-ray path length as criterion to decide whether the variation of the X-ray signal with tilt fulfills the projection requirement for tomography reconstruction in AgAu nanoparticles. They showed that for nanoparticles of only 40 nm diameter, this condition is still reached for the Au M line at 2.1 keV but not for the lower energy O K and C K lines. In the EDS reconstruction of II-VI multishell ZnTe/CdTe ∗

Corresponding author. E-mail address: [email protected] (H. Bender).

http://dx.doi.org/10.1016/j.ultramic.2017.03.006 0304-3991/© 2017 Elsevier B.V. All rights reserved.

nanowires (diameter <100 nm) by discrete tomography using the a prior knowledge of the symmetry of the wires, the absorption of O and Mg is estimated to be less than 10% and taken into account for these elements in the ζ -factor quantification procedure [9]. To include a full nano-electronic device with gate and contact structures in a pillar TEM sample requires, also for advanced technologies, diameters exceeding 100 nm [10,11]. Such structures typically consist of a wide range of materials among which light elements that show strong X-ray absorption. Furthermore, in future technologies the active devices themselves also take cylindrical nanowires shapes [10,12-14], therefore further requiring the need to understand the absorption effects in pillar shaped morphologies. Modern energy dispersive X-ray spectroscopy (EDS) systems are based on window-less Si drift detectors (SDD) that allow high count rates and have good sensitivity for low energy X-rays. Detection efficiency is further improved by increasing the X-ray collection angle by increasing the detector diameter and the use of multiple (2 or 4) detectors around the sample [15–17]. The latter can, depending on specimen and sample holder configuration, lead to important shadowing effects of the signal towards the different detectors [8,18–22]. In the 4-detectors geometry, the angular dependence of the shadowing for single tilt tomography holders with maximum tilt angles of ±70° shows a reduction of the X-ray intensities at 0° tilt to about 25% compared to the largest tilt angles [8,19,20]. As the signal shadowing is occurring by almost complete absorption in the heavy metal parts of the holder, the relative in-

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Fig. 1. Section in the plane of the electron beam and 2 opposite X-ray detectors for a planar (a) and a cylindrical pillar (b) specimen consisting of a single material in the configuration of Fig. 2d and a respectively. The electron beam is incident along the y direction. The X-ray path lengths in the middle of a layer with thickness tl sandwiched between a substrate and cap material is shown for a planar specimen (c) and for a pillar (d). In the pillar the position of the layer shifts through the elliptical section while scanning along the diameter of the pillar.

tensities of high and low energy peaks is however not affected [8]. A time varied acquisition is proposed to compensate for the angular dependence of the X-ray intensities in such holders. In lowbackground double tilt holders the shadowing is reduced and the maximum count rates are obtained for 0° tilt [8,21] but in this type of holders the relative signal ratios of high and low energy peaks show an angular dependence due to different absorption strength of the signals in the Be-parts of the holder. This dependence can lead to incorrect quantification [8,21,22]. By a modified design of these holders the shadowing at 0° is strongly reduced [23]. With sufficiently high, free-standing pillar shaped specimens in 360° tomography holders shadowing effects are fully absent for all tilt angles. In that case the intensity ratio of high to low energy peaks is expected to be constant, unless absorption effects are induced by the structures in the pillar. In this work the absorption effects in free standing pillar shaped specimens are modeled for different orientations of the pillar relative to the detectors in a 4-detectors EDS configuration. Universally applicable curves for the dependence along the pillar diameter of the relative intensities of weak and medium or strongly absorbed X-ray lines are derived. The practical application for absorption correction in pillar shaped specimens is discussed. The results are compared with experimental data acquired for pillars showing strong and medium absorbing effects, i.e. stacks with HfO2 and SiGe respectively. The modeling can directly be extended to dual or single detector configurations as used in other types of microscopes. 2. Sample shape dependence of X-ray absorption In plane specimens (Fig. 1a) the X-ray intensity I(y) in the direction of the detector will be attenuated by absorption as can be described by the Lambert–Beer law [1]:

I (y ) = I0 e−l (y )/λ

(1)

with l (y ) = y/ sin α the X-ray absorption path length through the sample from the emission point towards the detector, α the take-

off angle and λ the X-ray mean free path which can be calculated for a given matrix and X-ray energy from the tabulated X-ray mass attenuation coefficients μ/ρ [24–27] and the density ρ as:

λ = ((μ/ρ ) · ρ )−1

(2)

Integration over the specimen thickness t yields:



t

It = ∫ I0 e−l (y )/λ dy = I0 λ sin α 1 − e−t/(λ

sin α )



(3)

0

For pillar samples the specimen section in the plane of the electron beam and two opposite detectors is in general an ellipse (Fig. 1b). Therefore the X-ray path lengths l(x, y) are dependent on the position x, y in the section and are, except for x = 0, different for detectors on the left and right side. Hence the integration over the specimen thickness becomes:

It (x ) =

t+(x )

∫ I0 e−l (x,y)/λ dy

t−(x )

(4)

The path length l(x, y) at each position x0 ,y0 can be calculated by determining the intersection point of the straight line to the detector y = a x + b and the ellipse x2 /a2 + y2 /b2 = 1. The parameters of the line are given by a = tan α and b = y0 − tan α x0 with α the take-off angle of the detector. The path lengths l(x, y) and the integrated intensities It (x) are calculated numerically for the different detectors in a 4-detector EDS configuration for pillar specimens either aligned across or rotated 45° relative to the TEM specimen holder (Fig. 2a and b). The case of the pillar aligned across the holder is symmetry-equivalent with the one for a pillar along the axis of the holder as is the case in 360° tomography holders (Fig. 2c). The detector numbering is taken from the user interface of the TEM system and consistent with the tilt dependence of the signals. For a detector with 26 mm2 active area at a distance of 12 mm [8,18,21] the semi-opening angle is ∼14°. The opening angle of the detector is not taken into account in the calculations, i.e. it is assumed that the center of the detector well represents the average over its area. As will be seen in the comparison with the experimental data this is not always

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Fig. 2. Configuration of the specimens in the TEM specimen holder: a) pillar orthogonal to the axis of the TEM specimen holder (referred to as 0° configuration in the text), b) pillar 45° rotated, c) pillar in a 360° tomography holder and d) plane specimen aligned along the tilt axis. Detector positions and numbering relative the TEM specimen are schematically indicated.

a valid assumption. The modeling with the 45° rotated pillar combining only detectors 2 and 4 or detectors 1 and 2 corresponds to alternative EDS configurations as available on the market with 2 opposite or 2 orthogonally mounted detectors, respectively (but take-off angles are different than in the present calculations). 2.1. Pillar shaped sample aligned across the specimen holder With the pillar oriented orthogonal to (Fig. 2a) or parallel (Fig. 2c) with the direction of the specimen holder the 4 detectors are situated symmetrically at 45° azimuthal angle relative to the axis of the pillar and with a take-off angle α = 18° above the sample [8,21]. Assuming a perfectly cylindrically shaped pillar sample, the section through the pillar in the plane of the electron beam √ direction and 2 opposite detectors is an ellipse with a/b = 2 (Fig. 1b) where a and b are the lengths of the semi-major and semi-minor axes of the ellipse and b is equal to the radius of the pillar. The sections for the 2 sets of opposite detectors are equivalent in this case. The calculated path lengths to the detectors on the left side of the pillar (detector 1 or 4) are represented as function of the electron beam position x and depth y in the pillar in Fig. 3 using normalized dimensions, i.e. the radius r of the pillar set equal to 1. Due to the symmetry, the dependence for the detectors on the right side is flipped compared to Fig. 3. The intensities integrated over the local pillar thickness using Eq. (4) are shown for a left detector and summed for all 4 detectors in Fig. 4 for normalized λ/r in the range 0.2, i.e. strong absorption or large diameter, to 500, i.e. weak absorption. For a single detector the asymmetry of the intensity distribution across the pillar becomes more pronounced for increasing absorption strength while for weakly absorbed X-rays (λ/r ≥ 50) the intensity distribution nearly scales with the local thickness of the pillar and hardly changes anymore for λ/r above 50. Therefore λ/r = 50 is further considered as the reference condition for absence of significant absorption. For the

Fig. 3. Calculated X-ray path lengths through the pillar towards the detectors on left side (Detector 1 or 4) as a function of the position in the pillar oriented across the axis of the sample holder (Fig. 2a). Subsequent curves correspond to a step along the thickness direction of y= 0.05. Positions and lengths are in normalized units with the radius of the pillar equal to 1.

combined detectors the intensity distribution flattens in the center for medium absorption and gets strongly reduced in the center compared to the edges for strong absorption conditions. Based on the data in Fig. 4 the relative intensities for different combinations of weak and stronger absorbed X-rays can be calculated (Fig. 5). For medium absorbed X-rays (λ/r = 50 versus > 5 ) the absorption shows a weak dependence along the diameter for single detectors but the absorption effect for the combined detectors is almost independent of position, i.e. independent of local thickness of the pillar so that a constant absorption correction can be applied across the diameter of the pillar for quantification based on measurements with all four detectors. For strong absorption conditions (λ/r = 50 versus 1 ) this is not the case anymore and a position

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Fig. 4. Intensity integrated over local pillar thickness as function of normalized position along the diameter of the pillar for normalized λ/r in the range 0.2–500 for the pillar aligned across the sample holder: a) for detector on the left side (Detector 1 or 4) and b) for all 4 detectors.

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Fig. 6. Universal curves of the relative intensities for single detectors 4 and 3 (or 1) (a) and for all 4 detectors (b) as function of normalized position along the diameter of the pillar for a 45° rotated pillar position. Different combinations of weakly absorbed X-rays (λ/r = 50 ) with increasingly stronger absorbed X-rays (λ/r = 10, 5 and 1 ) and (λ/r = 10, 5, 2 and 1 ) are shown in a and b respectively.

dependent correction must be applied. The curves are universally valid and allow, for a given material and pillar diameter, to decide on the importance of the absorption effects for different X-ray lines based on the corresponding mean free path λ. 2.2. Pillar specimen 45° rotated relative to the specimen holder For a pillar specimen rotated 45° relative to the axis of the specimen holder (Fig. 2b), the two sections through 2 opposite detectors are no longer equivalent. The section across detectors 2 and 4 is a circular section for which the path lengths can be calculated in similar way as above but with a/b = 1. The section across detectors 1 and 3 corresponds, for each electron beam position along the radius of the pillar, to a section similar to the one for a plane specimen (i.e. a/b = ∞). The relative intensities to the different detectors for different combinations of weak and stronger absorbed X-rays are shown in Fig. 6 as function of the electron beam position along the diameter of the pillar. For detectors 2 and 4 the dependence is similar as for the case of the pillar aligned across the holder, but the absorption effects are weaker because the X-ray path lengths are shorter in the smaller circular section than in the elliptical one. On the other hand the absorption effects towards the detectors 1 or 3 are much stronger as the path lengths are much larger. Combined for the four detectors the absorption effects are therefore stronger and also more important for medium absorbed X-rays (Fig. 6b versus Fig. 5b). Fig. 5. Universal curves of the relative intensities for single detector 1 or 4 on the left side (a) and for all 4 detectors (b) as function of normalized position along the diameter of the pillar for the pillar mounted across the sample holder. Different combinations of weakly absorbed X-rays (λ/r = 50 ) with increasingly stronger absorbed X-rays (λ/r = 10, 5, 2 and 1 ) are considered.

2.3. Plane specimen For a plane specimen the orientation in the sample holder is not important as long as the material is uniform around the analysis point over a minimum distance r  = t/ tan α , a condition which

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complicate the milling sequence in particular when a special feature is targeted to be included in the pillar. The slope of the cone results in distortion of the elliptical section on Fig. 1b, i.e. the path lengths to the top side of the pillar will slightly decrease and to the substrate side will increase. In the case of the 45° mounting this will only affect the path lengths to detectors 1 and 3. For analysis with a single detector this asymmetry will have a small effect but for analysis with all 4 detectors it will be mainly cancelled out and the dependences on Figs. 5b and 6b will still be reasonably valid. The multidetector analysis is anyhow the targeted mode of use for the system as it allows to improve the S/N and sensitivity and hence the slightly conical shape is not a limitation. Uniform bulk materials are in general of less interest for analysis with tomography pillars unless e.g. for lattice defect or crystal grain studies. Target samples for chemical tomography however, generally include 3D features in the pillar volume. Due to the deposition of these features on a substrate or by the built-up of the stacks in a semiconductor device, a nearly layered configuration will often be present in which these features are embedded. As a result the X-rays travel through a range of materials which to a large extent can be considered as substrate/layer or feature/cap material. For a layered structure with layer thickness tl in a planar cross-sectional specimen, the average ratio of the X-ray path length in the layer ll to the total path length l in the specimen can be calculated for the 0° mounting configuration in the center of the layer as (Fig. 1c):

Fig. 7. Intensity integrated over normalized thickness (a) as function of thickness for normalized λ/r in the range 1 to 500 in a plane specimen, and relative intensities (b) for different combinations of weak and stronger absorbed X-rays. Specimen thickness of the plane specimen is normalized to the radius of the pillar.

is however, in particular for cross-sectional samples and layered structures often not fulfilled. With an 18° take-off angle, r ࣃ 3 · t in the center of the detector while for the lowest position of the detection cone r ࣃ 14 · t and hence the X-ray path length through the specimen foil is large even for very thin samples. For weakly absorbed X-rays (i.e. large normalized λ/r) the intensity will scale with the thickness while for strongly absorbed X-ray lines the intensity becomes dependent on the thickness (Fig. 7a), i.e. the signal mainly escapes from the top part of thick samples and therefore reduces with increasing thickness. The relative intensities of weak and stronger absorbed X-rays show nearly a linear dependence on thickness (Fig. 7b). Due to the geometry of the specimens, the absorption effects in the center of a pillar in 0° orientation are only as strong as in a planar specimen with a thickness nearly a factor 2.9 thinner (normalized thickness ∼0.7 on Fig. 7b vs center position on Fig. 5b with normalized thickness equal to 2), i.e. pillars may be much thicker before absorption effects become important. This is due to the longer X-ray path in a planar sample compared to a pillar with diameter equal to the thickness of the planar sample as can be qualitatively visualized from Fig. 1. For the 45° mounting orientation the factor is 1.8 using the 4 detectors simultaneously while it is 3.6 when considering only the detectors 2 and 4. 2.4. Impact of experimental conditions In experiments the sample shape and mounting conditions may differ from the idealized configuration in the modeling. In the simulations, the pillar samples are assumed to have a cylindrical shape and to consist of a single uniform material. Due to the top down circular FIB milling the actual shape is conical with a typical slope of <4°. Fully eliminating this slope would require a small sample tilt and a series of segmented milling steps which would strongly

√ ll t t = 2 tan α l = 0.46 l l t t

(5)

with t the specimen thickness. It implies that in a planar specimen, the layer thickness must be approximately double of the specimen thickness to have, for X-rays generated at half the layer thickness, only absorption in the material of the layer. In that condition Xrays generated deeper in the specimen will still partially travel √ through the substrate and cap layer. For the 45° mounting the 2 must be omitted in the formula for detectors 1 and 3 while the ratio ll /l equals unity for the detectors 2 and 4. The range of the Xray cones cutting a planar cross-section specimen is schematically illustrated on Fig. 8 for typical conditions as will be investigated in Section 3. It obviously shows that for thick specimens or thin layers, the absorption effects will be dominated by the substrate and cap layer materials. For pillar samples the total X-ray path length l varies with depth in a non-linear way so that an analytical formula for ll /l cannot be derived. The schematic of Fig. 8 however shows that also for pillars the absorption in the substrate and cap will be dominant if the layer is much thinner than the pillar diameter. For the 45° mounting configuration, the X-ray path length inside the pillar will be much longer for detectors 1 and 3 than for detectors 2 and 4 (Fig. 8b). The signal will only cross the material of the layer in the latter case (depending on layer thickness and pillar size), but will mainly cross the substrate and cap layer for detectors 1 and 3. Although less than for the 0° configuration, with a 4-detector acquisition the absorption effects will therefore also be dominated by the substrate and cap. The assumption in the modeling that the pillar is exactly oriented in the 0° configuration relative to the detectors will with the 360° tomography holder quite easily be fulfilled for well prepared pillars. The 45° mounting is for the 4-detector EDS spectrometer not possible with such holder but it is the configuration that will be obtained in the alternative 2-detector EDS system on the market (with opposite detectors 2 and 4 only). Again the alignment will be determined by the accuracy of the mounting of the pillar on the stub of the holder. For pillars on top of a Cu grid with which both the 0 and 45° configuration can be obtained as will be discussed in Section 3, the alignment must be controlled by the manual mounting of the grid in the holder. Although the error might

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Fig. 8. Illustration of the intersection of a planar cross-sectional specimen with the X-ray cones towards the detectors in the 0° (a) and 45° (b) mounting configuration for a sample consisting of a substrate/100 nm layer/cap stack. The average range of the X-rays through the specimen is indicated by the circles for a specimen thickness t of 50 nm (inner) and 150 nm (outer). The projected volume of a pillar specimen with 300 nm diameter is overlaid by the orange box. The t = 300 nm circle on (b) corresponds to the range in the center of the pillar in the 1-3 direction.

be larger, it can be kept easily below few degrees as can be verified by the TEM image. Deviations of the alignment will result in gradual shift of the dependences of Fig. 5b towards the ones on Fig. 6b. For small misalignment angle this will not have noticeable impact. Also β -tilt will be small for well mounted pillars and will therefore not create strong deviations of the modeling. The detector opening is neglected in the calculations, i.e. a single take-off angle corresponding to the center of the detector is assumed. For the elliptical or circular section of the pillar in the plane of the opposite detectors (Fig. 1b), the cut by the cone of the X-rays towards the detector shows for most emission points in the pillar volume only a small asymmetry. Hence integration over the opening of the cone will not strongly differ from the result for the central axis. Only in a small rim at the bottom of the pillar the asymmetry is much stronger but in the integration over the thickness of the pillar this has only little impact. For plane specimens and for detector 1 and 3 in the 45° mounting configuration, the asymmetry is more important but still the impact on the relative intensities is small. As will be shown in the experimental comparison the only position where the effect of neglecting the detector opening angle is noticeable is at the thinnest edges of the pillar for detectors 1 and 3 for the 45° configuration because half of the cone to the detector is there still cutting the pillar whereas its central axis is almost fully out of the pillar volume. In general it can be concluded that neglecting the opening angle of the detectors is an acceptable simplification. Whereas shadowing of the X-rays in the direction of the detectors occurs in single tilt tomography [8,19,20] and low-background double tilt [8,21,22] holders, it can be fully avoided with 360° tomography holders. As illustrated on Fig. 9b, pillars mounted on top of the conical stub used in such holders will be, independent of sample tilt, totally free of shadowing towards all four detectors by the stub as well as the sample holder. The stubs have a 30° semiangle and rounded top so that for a pillar of at least 10 μm high this condition is reached (exact dimensions will depend on geometry and roundness of the stub). Such dimension is typical used for tomography pillars.

Fig. 9. HAADF-STEM image of a typical pillar mounted on top of a Cu grid (a) and SEM image of a pillar mounted on top of a stub for the 360° tomography holder (b). Zoom of the HfO2 layer in the pillar sample mounted at 0° (c) and 45° (d) rotated positions. Composition line scans are extracted from EDS maps along the diameter of the pillar. The V-shapes indicate the actual projected opening angle towards the detectors at some typical positions to illustrate the intersection with the pillar sample (the actual cone has an 18° take-off angle and 14° semi-angle).

2.5. Application for absorption correction in pillar samples As follows from the previous discussion, the major deviation from the modeling can be expected due to the non-uniformity of the material inside the pillar. For pillars with relatively large diameter mounted in the 0° configuration and containing a thin layer or small features embedded between a substrate and a cap layer, in first approximation the absorption in the layer or features can

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be neglected. Instead the absorption correction can be calculated in the substrate/capping material with published mass attenuation coefficients for a plane specimen with thickness a factor 3 smaller than the diameter of the pillar. As the absorption is almost constant across the diameter of the pillar for combinations of weak and medium absorbed X-ray lines, such approach will give good results for all X-ray lines and pillar radii that fulfill λ/r > 5 for the lower energy line used for the quantification. A possible criterion for the maximum layer thickness for which this approach is valid can be taken as ll /l < 0.2 for a planar specimen. From (5) and taking into account that the allowed pillar diameter is a factor 3 larger, the criterion for a pillar becomes tl /r < 0.3. As the correction is constant across the diameter, the absorption correction procedure can also be applied for small features situated anywhere in the diameter of the pillar. Only for light elements such approach will generally not be applicable unless very small pillar diameters are used so that λ/r is still >5. For pillars in the 45° configuration, and having not too thin layers across their diameter, the use of only detectors 2 and 4 is advisable in which case the absorption can be calculated in the material of the layer. The corresponding planar thickness for the calculation of the absorption correction is in that case 3.6 times thinner than the pillar diameter. The maximum layer thickness that will fulfill the condition that the X-ray cone is only crossing the material of the layer is for the center of the pillar tl ∼ 2rtan(γd ) = 0.5r with γ d the semi-angle of the detectors (14°). For layer thickness exceeding the tl /r < 0.3 criterion, the modeling can be extended easily to a 3-layer stack substrate/layer/cap layer in which the consecutive contributions towards the different detectors of the absorption in the layer/substrate and layer/cap can be taken into account. For more complicated sample morphologies a full 3D calculation of the X-ray tracks and their attenuation in the different materials is needed which requires a much more heavy calculation which is specific for the particular morphology of the structures in the pillars. Also further refining the calculation by taking into account the opening angles of the detectors will require a much more elaborate modeling. As discussed above, in many cases the proposed simplified procedures will not only be much more straightforward to apply but will also yield a sufficiently accurate absorption correction. 3. Experimental verification 3.1. Experiments Pillar samples are prepared from layer stacks in which strong and medium absorption effects can be expected, i.e. 110 nm metalorganic chemical vapor deposited (MOCVD) polycrystalline HfO2 on Si and 80 nm Si0.75 Ge0.25 epitaxially grown on Si. Rutherford backscattering spectrometry and X-ray diffraction show a Ge content in the SiGe layer of 26.6at%. The cylindrical pillars are prepared by Focused ion beam (FIB) with in-situ lift-out and circular milling. They are about 10 μm high and attached on top of a Cu half grid close to one face of the grid which is subsequently mounted upwards in the TEM to minimize shadowing of the X-ray signal by the sample grid (Fig. 9a). A FEI low background holder is used for the experiments which shows minimal shadowing by the holder at 0° tilt [8,21]. The use of this holder allows to mount the same pillar specimens in the 0° and 45° orientation. For the 0° mounting orientation of the pillar (Fig. 9a and c), the experimental signal intensities of the high energy peak (Hf L) in the center of the pillar are similar for all four detectors indicating that shadowing effects by the grid and sample holder are not important or are at least similar in all detector directions. The layers are capped before thinning by ∼40 nm amorphous Si on the HfO2 and 150 nm CVD SiO2 on the SiGe and a FIB de-

posited Pt layer. The latter is actually a PtGax Cy mixture with high C content for which the mass absorption will be much lower than for pure Pt. The pillars are finished with 30 keV ion milling and thinned to a diameter ∼260 nm and ∼320 nm at the level of the HfO2 and SiGe layers respectively. Due to the milling the pillar has a cone shape with ∼4° sloped sidewalls (Fig. 9c and d). Plane specimens with a 2° wedge shape are also prepared for the SiGe stacks. These are finished with either 30 or 5 keV ion milling to reduce the thickness of the amorphized layer. EDS X-ray maps and HAADF-STEM images are acquired in a Titan3 G2 60-300 at 120 keV with an electron beam current of 0.8 nA and convergence angle of 18 mrad. Separate maps are acquired with each detector separately and with all four detectors active together. A pixel size and total dwell time of 617 pm and 900 μs for the HfO2 , and 312 pm and 1550 μs for the Si0.75 Ge0.25 sample are used. The samples are O2 /Ar plasma cleaned before the analysis and show no appreciable C-contamination at the end of the measurements. The specimens are aligned along the [110]Si zone axis which requires a specimen tilt <2°. The system is equipped with a Bruker SuperX EDS system with 4 detectors arranged around the sample as indicated in Figs. 2 and 9. For the pillar samples, intensity line scans are extracted from the maps along the diameter (or radius) of the pillar and averaged over almost the full thickness of the layer. For the wedge shaped specimen, maps are acquired at different positions along the wedge and the local thickness is calculated based on the distance to the edge and the opening angle of the wedge. Within the area of the ∼500 × 500 nm2 maps the thickness variation is small so that the data can be averaged over each map. Background subtracted netcounts are determined with the Esprit software. For quantification the built-in Cliff–Lorimer k-factors are used and the Cu stray signal peaks arising from the Cu TEM-grid are deconvoluted. Different databases are available for the mass attenuation coefficients μ/ρ [24–27]. As the tabulated values in reference [24] start only at 1 keV, the data of μ/ρ need to be extrapolated for the O K line. The mean free path λ calculated that way is nearly a factor 2 larger than obtained with the database of Henke and Ebisu [25] and Chantler et al. [27]. For other X-ray lines the λ values generally differ only ∼10%. The considered X-ray lines and the mean free paths λ calculated based on the mass attenuation coefficients μ/ρ as published by Chantler et al. [27] are summarized in Table 1. In general, λ increases for increasing X-ray energy. However, due to the particular position of the absorption edge of Ge L, the X-ray mean free path λ for Si K in Ge, and hence also in SiGex , is smaller than for the Ge L line although that one has a lower X-ray energy. 3.2. Stack with strong absorption: HfO2 The HfO2 layer has a rough surface and shows on HAADFSTEM some variation of channeling contrast in the columnar grains (Fig. 9c). Whereas the Si substrate is amorphized on its outer surface by the 30 keV Ga+ FIB beam, no noticeable damage can be observed in the HfO2 . The EDS line scans are calculated from maps excluding the rough top region of the layer. The ratios of the netcounts of the high energy Hf L with the medium energy Hf M and low energy O K lines are shown in Fig. 10 for acquisition with each detector separately or with all four detectors activated for the pillar mounted 0° (a,b) or 45° rotated (c,d). Linear fits are added to the Hf L/Hf M data and either 2nd order polynomial or exponential fits to the data for Hf L/O K. The regions at the edge of the pillars where the signal ratios become unstable due to the division by almost zero signal are excluded from these fitting. Similar results are obtained for detectors 2, 3 and 4 as shown in Fig. 10a. For the pillar with ∼260 nm diameter the experimental results for Hf L/Hf M and Hf L/O K are to be com-

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Table 1 Considered X-ray lines and mean free paths λ calculated in the relevant materials based on the database in [27]. The normalized λ/r are calculated for the experimental pillar radii. Density (g/cm3 )

SiGe25 3.08

Si 2.33

SiO2 2.2

X-ray mean free path λ

X-ray line

OK Hf M Hf L Ge L Si K Ge K

HfO2 10.10

keV

μm

0.525 1.644 7.898 1.188 1.740 9.874

0.14 0.9 7.4

μm

μm

μm

3.0 1.2 89

0.57 11.3 66 4.9 13.2 125

1.10 5.8 123 2.4 6.8 236

Radius (μm)

HfO2 0.13

SiGe25 0.16

λHfO2 /r

λSiGe /r

λSi /r

19 7 555

4 87 504 30 83 784

1 7 57

Fig. 10. Experimental netcount ratios for the HfO2 pillar mounted at 0° (a,b) and 45° rotation (c,d): a) detector 1 only (similar results for detector 4 and mirrored graphs for detectors 2 and 3 – not shown); b) with all detectors; c) each of the detectors separately, for clarity only the fitted curves are shown for detectors 2, 3, 4 for Hf L/O K and only the results for detector 1 for Hf L/Hf M; and d) with all four detectors. Table 2 Net count ratios from the fitted curves on Fig. 10a and c extrapolated to zero thickness at the side of the pillars towards the detectors. Pillar mounting

Detector Detector Detector Detector

1 2 3 4

Hf L / O K

Hf L / Hf M

0°

45°

0°

45°

2.56 2.08 2.24 2.72

4.0 2.06 4.0 2.21

1.10 0.88 0.95 1.02

1.2 0.91 1.0 0.99

pared with the simulations for the λ/r ratios (Table 1) nearly 50 vs 5 and 50 vs 1 in Figs. 5 and 6. However, the calculations do not take into account the relative X-ray fluorescence yields of the different X-ray lines. Experimental values of this yield normalized to the composition ratio can be obtained from the experimental data for the single detector measurements by extrapolation of the fitted curves to zero thickness at the side of the pillars towards the detectors, i.e. at the positions which are free of absorption (Table 2).

The extrapolated results with the 45° rotated pillar for the Hf L/O K ratio with detector 1 and 3 is about a factor 2 higher than for all other conditions. This is due to the fact that at zero thickness about half of the cone from the emission point towards the detectors is intersecting with the pillar (Fig. 9d), and hence the condition of “zero absorption” is not fulfilled. For all other conditions this cone is fully outside the pillar at the zero thickness positions. For the weak absorption case of Hf L/Hf M this effect is not noticeable in the experimental data. For quantitative comparison of the experimental and calculated graphs, the experimental ones need to be normalized by the zero-thickness ratios which are on average from Table 2 equal to 2.31 ± 0.27 and 0.98 ± 0.08 for Hf L/O K and Hf L/Hf M respectively (excluding the data for detector 1 and 3 with 45° rotation). Overlay of simulations with the λHfO2 /r ratios from Table 1 and the normalized experimental data are shown in Fig. 11. For the pillar in 0° position (Fig. 11a), the experimental ratios are smaller than predicted by the simulations, i.e. the actual absorption is smaller than expected. Similar observation holds for the detectors 1 and 3 in the 45° rotated case. In all cases the deviation is relatively largest for the Hf L/O K ratios. On the other hand,

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Fig. 12. HAADF-STEM image (a) and Si-K, Ge-L and Ge-Kα X-ray counts maps acquired with all detectors of the left half of the pillar oriented orthogonally to the axis of the TEM specimen holder. The compositional line scans are extracted along the radius of the pillar and integrated over the indicated width.

3.3. Stack with medium absorption: Si75 Ge25

Fig. 11. Overlay of the normalized experimental data for the Hf L/Hf M and Hf L/O K ratios with the calculated dependences (dashed curves) for 0° (a) and 45° (b,c) oriented pillars and for different single detectors. Similar results are obtained for the symmetry equivalent detectors (not shown).

the experimental data for detector 4 (and detector 2, not shown) for the 45° rotated case correspond very well with the simulations (Fig. 11c). The absorption is stronger in that case because the cone towards the detectors 2 and 4 is at all positions crossing only the HfO2 (Figs. 8b and 9d), while for the pillar aligned at 0° position, part of the X-ray path will go through the Si substrate (for detector 3 and 4) or through the cap layers (detector 1 and 2) in which the absorption is weaker than in the HfO2 . This effect also accounts for the smaller experimental than simulated data for the detectors 1 and 3 in the 45° rotated case. From the comparison for detectors 2 and 4 in the 45° rotated case it can be concluded that the database of Chantler et al. [27] allows a very accurate calculation of the X-ray mean free path λ and hence of the absorption correction. On the other hand, calculations for the oxygen signal in HfO2 , based on the mass attenuation coefficient μ/ρ extrapolated from reference [24] or with the data of reference [25], yield a too low or too high simulated dependence respectively. For X-ray peaks at higher energies the differences between the databases are less important.

The EDS analysis of the SiGe stack is done on a pillar sample mounted in the 0° position and on 2° wedge shaped specimens mounted along the axis of the sample holder. The measurements are performed with all four detectors active simultaneously. Due to the 30 keV finishing of the FIB milling of the pillar an amorphized layer of ∼24 nm is present at the edges in both the SiGe and Si. It shows up on the HAADF-STEM image as well as on the X-ray counts maps as an intensity step due to the absence of channeling effects in the amorphous layer (Fig. 12). On the outer edge of the pillar, a thin oxide layer (2–3 nm) is present caused by the air exposure after the preparation and the O2 /Ar plasma clean of the specimen before the STEM analysis. The oxide is Si-rich and is present all around the pillar. Owing to its small thickness it will not have significant effect on the analysis of the SiGe composition in the pillar. The amorphized layer contains a low level of Ga due to the FIB beam. The maximum concentration is below 1.5at%. At the transition from crystalline to amorphized SiGe a small step is observed in the signal ratios (Fig. 13a). This is more obvious for the X-ray intensity normalized to local pillar thickness (Fig. 13b). The average ratio of the intensity normalized to thickness in the crystalline to the amorphized region is 1.13 for Si K and Ge L, and 1.18 for Ge K. The larger ratio for the higher energy Ge K peak is in agreement with simulation of the X-ray intensity by Chen et al. [28] for Sr K and L peaks in SrTiO3 in channeling and random orientations. As the ratio is similar for Si K and Ge L, the distinction between crystalline and amorphous will vanish after quantification with these X-ray lines but will show up for quantification with the Si K and Ge K peaks as can be observed on the quantified line profiles calculated with the Cliff–Lorimer method neglecting absorption (Fig. 14a). In the crystalline SiGe the signal ratios are independent of position in the pillar (Fig. 13a). The position dependence across the pillar diameter is for the λ/r corresponding to SiGe (Table 1) well represented by the simulation for low vs medium absorption, i.e. λ/r = 50 vs 10 to 5 in Fig. 5b. It implies almost constant signal ratios across the pillar in agreement with the experimental observations. The signal ratios Ge K/Si K and Ge L/Si K in Si75 Ge25 correspond for the 320 nm diameter pillar to λ/r = 555 versus 7 and 19 vs 7

H. Bender et al. / Ultramicroscopy 177 (2017) 58–68

Fig. 13. Net counts ratio (a) and intensity normalized to specimen thickness (b) along the linescan in Fig. 12.

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respectively (Table 1). Hence although the Ge L line has a lower energy than the Si K line, in SiGex the Si will be the stronger absorbed signal relative to both the Ge K and Ge L. Therefore the calculated Ge concentrations should in both cases be higher than the nominal level. However, the quantification in the pillar gives only with Ge K a higher but with Ge L a lower than nominal result (Fig. 14a). To verify that this is not due to the Cliff–Lorimer k-factors, the Ge concentrations are derived from maps on planar wedge samples finished with 30 keV and 5 keV final FIB milling. As a function of specimen thickness the Ge content slightly decreases for quantification with Ge L and Si K and increases more strongly for calculation with Ge K and Si K (Fig. 14b). Extrapolated to zero thickness the Ge content is similar for the quantification with both Ge peaks, i.e. 25.3–25.6 at% which agrees well with the 26.6 at% Ge determined by RBS and XRD for this layer. It shows that the Cliff– Lorimer factors are excellent. As Si K is the stronger absorbing element compared Ge L, the decreasing thickness dependence of the quantification with Ge L and Si K is not consistent with the expectations for Si75 Ge25 . However, as already discussed in Section 2.4, the major part of the X-ray paths towards the detectors actually crosses the Si substrate and SiO2 cap layer while the path length is much shorter in the SiGe layer itself. With increasing specimen thickness the absorption effects get stronger and relatively more dominated by the substrate and cap layer as the total path length l in the sample increases while the path length ll in the layer is constant (Fig. 1c). As a result, the thickness dependence of the absorption effects for quantification with Ge K or Ge L is following the trend as expected for the substrate and cap materials. In Si and SiO2 , the relative ratio of the λ/r for Ge L vs Si K is inverted compared to SiGe (Table 1), i.e. Ge L is the stronger absorbed signal and therefore the thickness dependence shows a negative slope (Fig. 14b). The contribution from the heavier Pt cap layer will be relatively small as it is not directly above the SiGe and it is partially milled away (not shown). The average Ge contents in the 320 nm pillar as determined with Ge K and Ge L peaks (Fig. 14a) correspond to the compositions obtained for the wedge sample at approximately 100 nm thickness. This excellently agrees with the comparison of the simulated absorption effects in pillars relative to planar specimens as discussed before and proofs that absorption corrections as determined for planar specimens of thickness nearly a third of the pillar diameter can be applied for correction of the quantification across the full diameter of the pillar. 4. Conclusions

Fig. 14. Ge concentration profiles calculated with Ge K and Si K or Ge L and Si K as function of specimen thickness for a pillar sample oriented orthogonal to the axis of the TEM specimen holder (a) and for a wedge sample aligned with the specimen holder (b). The data points in (b) correspond to specimens finished with 30 keV and 5 keV FIB milling, the fitted curves are for the combined datasets. The XRD&RBS reference point is added on a random specimen thickness position for comparison.

The analysis shows that absorption effects in pillar shaped specimens are only as important as in planar specimens of about 3 times smaller thickness, i.e. much thicker pillars are allowed before absorption effects will significantly influence the EDS quantification. This is particularly interesting for 360° tomography investigations of semiconductor nano-devices that, even for most advanced technologies, require pillar diameters >10 0–20 0 nm to include a complete device with e.g. gate and source/drain contacts. With 4-detector acquisition the absorption effects are almost independent of position along the diameter of the pillar for medium absorbed X-ray lines so that a constant absorption correction can be considered. Only for strongly absorbed X-rays, e.g. O K, the signal in the center of the pillar becomes, also with 4-detector investigations, significantly reduced compared to the edges of the pillar. The absorption effects depend on the orientation of the pillar relative to the detectors. In 0° oriented pillars, the X-rays will partially travel through the cap layers and substrate if the layer is thinner than the diameter of the pillar. If the layer is much thinner (e.g. the SiGe25 sample), the absorption is dominated by the

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substrate and cap materials. This is also the case in planar samples that are analyzed in a 0° mounted configuration. Absorption dominated by the analyzed material will only occur for detectors 2 and 4 in a 45° rotated configuration for layers thicker than ∼r/2. Using only these detectors in that case the absorption correction can be calculated for the pillar based on a planar specimen with thickness 3.6 times smaller than the pillar diameter. For practical application, in the 0° mounting configuration, if the layer thickness and pillar radius fulfill the criterion tl /r < 0.3, acceptable absorption correction can be expected by calculating the absorption correction in the material of the substrate or cap of a planar specimen with thickness 3 times smaller than the pillar diameter instead of in the material of the layer itself. For Xray lines and pillars for which λ/r > 5 this will lead to accuracy of the correction better than 20% and this correction can then be applied across the full diameter of the pillar. For thickness that do not fulfill the tl /r < 0.3 criterion, the model needs to be extended to a 3-layer structure substrate/layer/cap so that the absorption contributions in the different materials can be taken into account. For thin layers or small features embedded between a substrate and cap layer this approach can be applied for any position of the features across the diameter of the pillar. For more complicated 3D structures, e.g. full semiconductor nano-devices, estimate of the absorption corrections requires a modeling of the full 3D configuration in the pillar which requires more extended and lengthy calculations that are specific for the particular morphology in the pillar volume and which calculate the consecutive absorption of the X-rays travelling through the different materials. In many sample configurations the simplified approach as discussed in this work will lead to sufficiently accurate absorption corrections in a much more straightforward way. A further refinement of the modeling could take into account the opening angle of the detection cones towards the detectors. In particular on the thinnest edges of the pillar this is shown to have experimentally considerable effect but more in the center the average effect of neglecting the opening angle will be minor. The simulation of the strength of the absorption effects with tabulated mass attenuation coefficients μ/ρ corresponds very well to the experimental data for the configurations that probe only the considered material in the cone towards the detector (detector 2 and 4 in 45° rotated pillar orientation). The uncertainty on μ/ρ between different databases is only important for the lowest energy X-ray lines. On the other hand, pillars cut in bulk materials could allow to experimentally determine these parameters more accurately. Advantages of pillars over wedge samples for such application are the better control of the thickness in the thinnest edges and the ease to prepare samples without any shadowing effects from other parts of the specimen or sample holder towards the detectors when using a 360° tomography holder. Acknowledgment Dr Yang Qiu, imec, Belgium (presently at South University of Science and Technology, Shenzhen, China), is acknowledged for discussion on EDS quantification and tomography, and Dr Clement Porret, imec, Belgium, for providing the SiGe epi sample and the RBS and XRD calibrations. References [1] G. Cliff, G.W. Lorimer, The quantitative analysis of thin specimens, J. Microsc. 103 (1975) 203–207, doi:10.1111/j.1365-2818.1975.tb03895.x. [2] Z. Horita, T. Sano, M. Nemoto, Simplification of X-ray absorption correction in thin-sample quantitative microanalysis, Ultramicroscopy 21 (1987) 271–276. [3] E. Van Cappellen, The parameterless correction method in X-ray microanalysis, Microsc. Microanal. Microstruct. 1 (1990) 1–22.

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