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EFTEM spectrum imaging at high-energy resolution
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Ultramicroscopy 106 (2006) 1129–1138 www.elsevier.com/locate/ultramic
EFTEM spectrum imaging at high-energy resolution Bernhard Schaffer, Gerald Kothleitner, Werner Grogger Research Institute for Electron Microscopy, Graz University of Technology, Steyrergasse 17, A-8010 Graz, Austria Received 16 June 2005; received in revised form 18 December 2005; accepted 5 April 2006
Abstract This paper deals with the application of high-energy resolution EFTEM image series and the corrections needed for reliable data interpretation. The detail of spectral information gained from an image series is largely determined by the intrinsic energy resolution. In this work we show that energy resolution values of as low as 0.8 eV in spectra extracted from EFTEM image series can be obtained with a small energy-selecting slit. At this resolution level aberrations of the energy filter, in particular the non-isochromaticity, can no longer be neglected. We show that the four most prominent factors for EFTEM image series data correction—spatial drift, non-isochromaticity, energy drift and image distortion—must not be treated independently but have to be corrected in unison. We present an efficient algorithm for this correction, and demonstrate the applied correction for the case of a GaN/AlN multilayer sample. r 2006 Elsevier B.V. All rights reserved. Keywords: EFTEM spectrum imaging; Spectral aberration; Sample drift; Energy drift; Non-isochromaticity; Data correction
1. Introduction Energy filtering transmission electron microscopy (EFTEM) is nowadays a well-established method in many areas of materials research [1]. Image contrast and resolution in bright field images can be enhanced by using only elastically scattered electrons (zero-loss filtering) [2,3], and electrons in the low energy-loss region often show distinct material contrast (contrast tuning) [4]. Furthermore, elemental information can be quickly mapped at high spatial resolution by combination of a few EFTEM images (elemental maps, jump ratio images) [5]. However, the ‘full’ spectral information can only be reconstructed from a larger series of EFTEM images taken with a sufficiently small energy-selecting slit, avoiding large energy gaps between the images. This method is known as ‘Electron Spectroscopic Imaging’ (ESI) [6], ‘Image Spectroscopy’ [7,8], ‘Imaging-Spectrum’ [9] and ‘EFTEM Spectrum Imaging’ (EFTEM SI) [10]. The full 3-dimension dataset gained by the method contains an electron energy-loss (EEL) spectrum for each point of the sampled. This opens up the large range of data analysis methods Corresponding author. Tel.: +43 316 873 8330; fax: +43 316 811596.
E-mail address: [email protected] (B. Schaffer). 0304-3991/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2006.04.028
originally developed for EELS spectroscopy, e.g. plural scattering deconvolution, accurate background subtraction, quantification by multiple least-squares (MLS) fitting, separation of overlapping edges, more accurate sample thickness determination, automated elemental identification, and more. As this information is available for all image pixels, mapping of various associated physical and chemical information becomes possible as shown by numerous authors [7,8,11,12]. In comparison to the alternative method of EELS SI, which uses a focused scanning beam for sequential acquisition of the spectra (STEM EELS SI) [13], EFTEM SI offers high spatial resolution over a larger field of view (many pixels along spatial axes) at comparably short acquisition times. It is therefore often the preferred method when the spatial distributions of spectral features (e.g. ionization edges, plasmon peaks, etc.) need to be mapped over larger sample areas. However, STEM EELS SI offers better energy resolution and collects information over larger energy-loss ranges in one step (many pixels along energy axis). It is therefore most commonly used to investigate subtle spectral changes in small sample areas [14,15]. The aim of this work was to further improve the method of EFTEM SI with respect to energy resolution. The intrinsic energy resolution of an EFTEM SI is a
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convolution of the system’s total energy resolution (the sum of the energy width of the electron beam, the high tension stability, the spectrometer energy resolution, etc.) with the energy selecting slit width. Considering a total system’s energy resolution of 1 eV or better, the energy resolution of the series is then largely determined by the slit width, which in most cases lies in the range of a few to some tens of eV. Some imaging filters allow slit widths smaller than 1 eV to be used so that the energy resolution of the EFTEM SI is no longer limited by the slit and then becomes comparable to the energy resolution of EELS spectra. With the higher energy resolution, additional EELS analysis can be performed and used for mapping, e.g. chemical shift maps, plasmon peak position maps, dielectric constant maps by Kramers–Kronig analysis, etc. Fig. 1 shows another benefit of having better EFTEM energy resolution. In this picture four plasmon ratio maps are compared. Such maps were produced by dividing two EFTEM images acquired at the energy-losses of the GaN and AlN plasmon peaks, respectively. The first three maps (Fig. 1A–C) were produced from datasets acquired with different energy selecting slit widths of 10, 5 and 1 eV, respectively. The datasets were fully corrected for the combined effect of spatial drift, energy drift and nonisochromaticity (NIC), using the novel algorithms described in this work. The fourth map was produced from the same data as the third map, but without data correction except for spatial drift. All images are displayed with the same contrast limits. It can be clearly seen that for best image contrast a small slit width (1 eV) is superior to larger slit widths (5 eV, 10 eV). However, at energy resolutions in the range of the spectrometer aberrations, their influence can no longer be neglected as can be seen from the uncorrected data (Fig. 1D).
This work focuses on the correction of high-energy resolution EFTEM SI data, which becomes essential for reliable data analysis and interpretation. To our best knowledge, it presents the first algorithm, which corrects the combined effect of spatial drift, energy drift and NIC. 2. Data correction The information contained in an image series can be best visualized in 3-dimensional information space, where x and y are spatial coordinates of the sample and z is the EEL axis as suggested by Jeanguillaume et al. [16]. An EFTEM SI is a discrete subset of this information space as shown in Fig. 2A. Any data point of the EFTEM SI contains the integrated intensity of a small subset of the information space centered at given spatial coordinates and energy-loss with dimensions according to the spatial and energy resolution of the EFTEM SI. In analogy to ‘pixel’, which is the commonly known acronym for ‘picture element’, such a data point in a discrete 3-dimensional data set is called ‘voxel’ as acronym for ‘volume picture element’. Ideally, an EFTEM SI is a cuboid built as a stack of horizontal slices (EFTEM images). However, the real shape of a measured EFTEM SI in information space is more or less deformed due to system instabilities and spectrometer lens aberrations. Nevertheless, these deformations are often neglected and the EFTEM SI is treated as an orthogonal block leading to serious errors if used for further data evaluation without corrections. The most influential factors are shown in Figs. 2C–F, leading to a combined deformation shown in Fig. 2B. The deformed EFTEM SI is falsely interpreted as the cuboid shown by the dashed line according to the nominal values of the EFTEM SI acquisition.
Fig. 1. Plasmon ratio maps (20.8 eV image dived by a 19.5 eV image) of a GaN/AlN stack acquired with different energy selecting slit widths (A: 10 eV; B: 5 eV; C and D: 1 eV). The maps are displayed with the same contrast settings and were produced from fully corrected data except image D, where no nonisochromaticity correction was performed.
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EFTEM SI are correct, but the associated coordinates are not. xy are the coordinates of the sample and e is the true energy-loss value. The most prominent deformations are caused by: (1) Spatial drift: During acquisition sample drift may occur as a result of instabilities of the microscope stage or specimen. Consequently, two images of the series might not show the same area of the sample and are shifted in x- and y-direction from their original position in information space. Spatial drift is the same for all voxels of one image acquisition. As the acquisition of one image out of an EFTEM SI is assigned to a nominal energy-loss value (the central value of the acquired energy range), the spatial drift can be expressed as a function of this nominal energy-loss: Dxydrift ¼ f drift ðem Þ.
Fig. 2. Schematics of EFTEM image series (data blocks) in the information space. An ideal data block (A) is orthogonal and holds image information in horizontal slices and spectral information in vertical columns. A real data block (B) is deformed and may show both gaps and overlaps. It is falsely presented as an orthogonal block (dashed line). The deformations due to spatial drift (C), energy drift (D), image distortion (E) and non-isochromaticity (F) are illustrated.
In our mathematical picture, each voxel of the measured EFTEM SI has its individual displacement vector pointing from the nominal position to the correct position in information space. For simplicity reasons the lateral coordinates x and y are noted as one coordinate xy only. I m ðxym ; em Þ ¼ Iðxy; eÞ ¼ Iðxym þ Dxy; em þ DeÞ.
(1)
Im is the measured EFTEM SI data block. It holds intensity values for the nominal coordinates xym and em. xym are the coordinates of the CCD camera (assumed to be identical with the coordinates of the sample) and em is the nominal energy-loss. Due to the deformations listed below those coordinates are shifted away by Dxy and De from their correct position in information space. Therefore, the measured EFTEM SI at the voxel (xym, em) gives the intensity I at the ‘true’ but unknown position ðxy; eÞ in information space instead of the wanted intensity at the coordinates ðxym ; em Þ. In other words, the intensities of the
(2)
The function fdrift is the spatial drift for each EFTEM SI slice of nominal energy-loss em. It can be determined directly from the images of the series by finding the shift vector, which produces an optimum overlap of the image content. This can be done manually or with the help of automated routines based on cross-correlation [17]. During acquisition of a single image, sample drift may lead to a blurring and loss of spatial resolution. (2) Energy drift: The energy reference point of the spectrometer, determined as the zero-loss peak (ZLP) position at the energy selecting slit plane, may change over time. High-voltage instabilities and thermal effects influencing for instance the prism current stability can produce a systematic drift of a few eV during acquisition times of several minutes. The nominal energy-loss then deviates from the real energy-loss of the electrons. A representation in information space describes the images slices as being shifted along the zdirection from their original position. Thus, energy drift can lead to both overlaps and gaps in the sampled energy space. As for the spatial drift, energy drift is the same for all voxels of one image within the EFTEM SI. It can therefore be expressed as a function of the nominal energy-loss, too: Deedrift ¼ f edrift ðem Þ.
(3)
The function fedrift describes the energy drift of the system. In general, it cannot be determined from the measured EFTEM SI, but needs additional measurements. The position of the ZLP provides a good measure for the energy drift, if it is determined before and after each single EFTEM image. However, for practical reasons a ZLP position measurement/readjustment after each single image acquisition of the EFTEM SI is not feasible. In most cases a reasonable approximation of the energy drift can be obtained by determining the ZLP position before and after the whole series and assuming a linear drift in between. In
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EFTEM, the ZLP position is measured by rapid acquisition of an EFTEM image series across zero-loss energy and assigning the image with maximum intensity to the zero-loss value. (3) NIC: Electrons detected at the borders of an EFTEM image might not have exactly the same energy as those in the center of the image. Due to lens aberrations in the spectrometer the iso-energy planes are not completely flat but curved. Modern post-column energy filter designs correct lens aberrations up to third- and fourth-order but a residual NIC in the magnitude of typically 1 eV over the full field-of-view defined by the CCD remains. While this can be safely ignored for elemental mapping where energy selecting slit widths and desired energy resolutions are equal or above 5 eV, it has to be taken into account for high-energy resolution work. In its representation in information space, the NIC leads to a bending of the slices. The NIC for a given magnification is a function of the CCD coordinates only. It is therefore independent of the nominal energy-loss and equal for all individual slice acquisitions of an EFTEM SI. DeNIC ¼ f NIC ðxym Þ.
(4)
The function fNIC describes the NIC-figure as a function of the CCD coordinates. For post-column systems it is typically measured by scanning the ZLP across the slit edge, while recording images with the sample removed. Selecting an energy range with the slit vignettes the image in a shape that represents a slice through the aberration figure of the filter. Consequently the sum of images represents the NIC surface over the field-of-view (FOV) calibrated in energy units [18]. This method is used in the tuning routines of the Gatan Imaging Filter (GIF), which also outputs the NIC figure. Alternatively, one can acquire an image series over the energy-loss of a known feature, e.g. the ZLP, and create a map of the maxima positions (at the energy-loss axis) for instance by fitting an appropriate function. Sigle et al. [19] suggested to use the plasmon peak of a thin, homogeneous carbon film for high accuracy measurements. (4) Image distortion: Lens aberrations of the imaging filter may introduce a small lateral image distortion. While it might play a role for analysis of diffraction patterns computed from lattice images or seamless montage of multiple digital images frames, it is often small enough to be ignored. In the EFTEM SI representation in information space, image distortion appears as lateral deformation of the slices, which is the same for all individual slice acquisitions of an EFTEM SI and therefore independent of the nominal energy-loss. Dxydis ¼ f dis ðxym Þ.
(5)
The image distortion fdis is a function of the CCD coordinates. It can be measured by imaging an object of known shape, e.g. a mask aperture with a regular array
of holes at known positions. Comparison of the mask’s image on the CCD with the known positions of the holes yields the distortion over the entire image field. With all the aberrations characterized, it is now possible to correct an EFTEM SI. In a first step, the intensities of the uncorrected EFTEM SI need to be mapped to their ‘true’ positions in information space (deformed cube in Fig. 2B). In a second step, the correct intensities at the nominal positions are calculated from this deformed cube (dashed cube in Fig. 2B). The mapping of intensities can be mathematically expressed as the following variable transformation using Eq. (2)–(5): xym ! xy0m ¼ xym þ Dxy ¼ xym þ f drift ðem Þ þ f dis ðxym Þ, (6) em ! e0m
¼ em þ De ¼ em þ f edrift ðem Þ þ f NIC ðxym Þ,
I m ðxym ; em Þ ! I 0m ðxy0m ; e0m Þ
¼ I m ðxym ; em Þ.
(7) (8)
Dashed variables are the corrected variables. I 0m is the correct, but no longer orthogonal and equally spaced data. It is important to note that I 0m is not yet the corrected EFTEM SI. However, inserting Eqs. (6)–(8) into Eq. (1) reveals that I 0m is identical with the intensities in information space (and therefore correct): I 0m ðxy0m ; e0m Þ ¼ I m ðxym ; em Þ ¼ Iðxym þ Dxy; em þ DeÞ ¼ Iðxy0m Dxy þ Dxy; e0m De þ DeÞ ¼ Iðxy0m ; e0m Þ, I 0m I.
ð9Þ
The corrected EFTEM SI should be an orthogonal cuboid with equidistant sampling intervals according to the nominal values of the acquisition. It is calculated from I 0m . Fig. 2B shows that due to the discrete nature of the measured data, some interpolation of the corrected data might be necessary to take into account the ‘holes’ and ‘overlaps’ in information space as well as the sampling intervals. As each individual voxel of the uncorrected EFTEM SI has its own displacement vector, the direct implementation of Eqs. (6)–(8) would be a voxel-by-voxel algorithm, shifting the intensity of each uncorrected voxel to its correct position and finally interpolating the corrected EFTEM SI with the given sampling intervals (image scale and dispersion). Considering the huge amount of data (typically more than five million voxels) voxel-based algorithms are impractically slow. Assuming one voxel operation would be carried out in only 0.01 s, the full correction of a typical EFTEM SI (256 256 pixels, 80 energy steps) would still take more than 14.5 h. Individual corrections of spatial drift, energy drift and NIC are considerably faster as larger subsets of the EFTEM SI can be corrected at once. Spatial and energy drift correction shift whole slices at once, while the NIC
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correction shifts entire columns. It has therefore been suggested in the literature to perform a NIC correction prior to a spatial and energy drift correction [19]. However, this suggestion cannot be performed straightforwardly without introducing extra errors. After the NIC correction, voxels from one slice no longer stem from a single acquisition and therefore no longer share a common drift vector. This can be seen by inserting Eq. (7) without the energy drift term into Eq. (2): Dxydrift ¼ f drift ðe0m Þ ¼ f drift ðem þ f NIC ðxym ÞÞ ¼: f 0drift ðxym ; em Þaf drift ðem Þ.
ð10Þ
f 0drift is the new spatial drift function. After the NIC correction it is a function of all three coordinates and is not identical to the measured drift fdrift prior to the NIC correction. A similar argument holds for the opposite case. After a spatial drift correction, the new coordinates are no longer identical with the CCD coordinates and consequently the NIC figure becomes a function of all three coordinates: DeNIC ¼ f NIC ðxy0m Þ ¼ f NIC ðxym þ f drift ðem ÞÞ ¼: f 0NIC ðxym ; em Þaf NIC ðxym Þ.
ð11Þ
In other words, after a spatial drift correction a common NIC figure can no longer be found. This is illustrated in Fig. 3. Doing a spatial drift correction and a subsequent NIC correction inevitably introduces an error. This error increases with larger spatial drift and a more strongly warped NIC figure, but it depends on the sample. In energy regions of pronounced intensity changes (e.g. sharp peaks or edge onsets) or at sample regions with strong contrast changes (e.g. interfaces or precipitates) the effect is most pronounced.
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3. Combined spatial drift and NIC correction The aim of the data correction is to regain a good approximation of the real, orthogonal data block from the measured data block. The deformation vector for each voxel can be measured as described previously. Voxel-by-voxel algorithms are inefficiently slow, but from Eqs. (6) and (11) it can be derived that a correction of the lateral deformations (spatial drift and image distortion) can be performed slice-by-slice prior to a correction of the energy deformations (energy drift and NIC). The function of the energy deformation De then has to be adjusted accordingly. The combined EFTEM SI correction algorithm therefore consists of the following steps (see Fig. 4). If image distortion needs to be corrected for, it has to be done first. Each acquisition slice of the EFTEM SI is dewarped and the same process is applied to the NIC figure. In the words of our mathematical picture, a variable transformation of distorted CCD coordinates to corrected ones is performed. In the next step, spatial drift is determined from this image distortion corrected EFTEM SI. Now a second data block (EC) is generated, which will hold the information for the energy correction. This ECblock is first filled by the same (dewarped) NIC figure for each slice. If energy drift is to be corrected as well, the energy shift for each slice of the EFTEM SI is added to the corresponding slice of the EC-block. Finally, the same spatial drift correction is applied to both the data block and the EC-block to obtain a distortion/spatial drift corrected data block and a shifted EC-block. Each voxel of the data block now has a corresponding voxel in the ECblock carrying displacement information for the z-axis (energy-loss). The EC-block represents the sum of the functions fNIC and fedrift in Eq. (7). In the last step of the algorithm, the fully corrected EFTEM SI block is reconstructed slice by slice. For each
Fig. 3. Schematic illustrating the problem of successively correcting sample drift and non-isochromaticity (NIC). Pixels along a column do not show the same z-displacement (energy) after shifting the slices of the data block in x- and y-direction (spatial). Small arrows indicate required energy shift due to NIC.
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Fig. 4. Schematics of the combined correction algorithm. In a first step, spatial drift correction is performed and the same drift is applied to a block holding NIC figures and energy drift values (EC). In the second step, the two blocks are used to reconstruct the fully corrected EFTEM SI slice-by-slice. For each energy plane, the EC block is used to define a weighting mask for the data block. The weighted sum of the intensities yields the corrected energy plane.
slice the algorithm evaluates the relevant subset of the data block only. This subset is defined by the nominal energyloss of the slice plus/minus the maximum possible energy displacement and by the energy step size of the EFTEM SI. It holds all images that might contribute intensity to the slice. The corresponding subset of the EC-block is used to calculate the relative amount of intensity of each image, which contributes to the corrected slice. The fully corrected slice is the sum of all weighted intensities of the EFTEM SI subset.
4. Experimental All experiments were performed on an FEI Tecnai F20/ STEM microscope operated at 200 kV and equipped with an FEG electron source and a monochromator [20]. The microscope has a super twin objective lens (CC ¼ 1.2 mm; CS ¼ 1.2 mm). A high-resolution imaging filter from Gatan Inc. (HR-GIF) with a 1024 1024 CCD camera was attached to the microscope [21]. The HR-GIF is fully corrected for aberrations up to the third-order and partially
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Fig. 5. (A) Spatial drift in x- and y-direction during the experiment. Drift is given in pixels of the recorded images for better comparison with the nonisochromaticity (NIC) figure. (B) NIC figure measured by the tuning routine of the GIF (values in eV).
for the fourth-order. The energy-selecting slit of the spectrometer installed at our lab can be closed down to widths of 0.1 eV as determined experimentally. With a given energy resolution of roughly 0.6 eV for the 5 mm GIF entrance aperture, a slit width of 0.4 eV was chosen as a good compromise between energy resolution and intensity. An alternating stack of GaN and AlN layers produced by molecular beam epitaxy (MBE) was used as a test sample [22]. A cross-section of the sample was prepared by focused ion beam (FIB) milling using a Nova200 NanoLab DualBeam FIB from FEI. The final lamella was thinned to a thickness of approximately 45 nm. After checking the exact slit width of 0.4 eV in spectroscopy mode, we acquired 70 EFTEM images with a size of 512 512 pixel (2 2 hardware binning) in the energy range of 14.0–27.8 eV (0.2 eV steps) with a 100 mm objective aperture (13.83 mrad collection half-angle). We used a customized script for acquisition, which included automatic adjustment of exposure time for each image in order to optimally utilize the CCD’s dynamic range. The total acquisition time of the series was roughly 15 min. During this time total sample drift of approximately 120 nm corresponding to 140 pixels on the CCD at the chosen magnification was observed in x-direction while sample drift in y-direction was less than 26 nm (30 pixels) as shown in Fig. 5A. Energy drift was determined by performing a ZLP alignment prior and after the EFTEM SI acquisition. The total energy drift during the acquisition time was less than 1 eV and therefore not corrected for. Image distortion was measured by the automatic tuning routine of the GIF, yielding a distortion at the fractional percent level, which was 0.6% over the entire FOV and hence was not corrected for. To better study the NIC influence, we slightly mistuned the HR-GIF during the acquisition to produce a more pronounced energy bending of the NIC-figure of approximately 2 eV peak-to-peak comparable to imaging filters without higher-order aberration correction.
Fig. 6. EELS zero-loss peak spectra extracted from the EFTEM SI of the GaN/AlN multilayer sample at a single point and over the whole FOV before and after NIC correction. Energy resolution over the FOV determined as FWHM of the peak is improved from 1.1 eV (before correction) to 0.8 eV (after the correction), which is the same as in a single extracted spectrum.
To compare the NIC from the tuning routine with a NIC figure derived from an EFTEM SI, we also acquired an EFTEM image series with the sample removed. This series was acquired in the energy range from 5 to +5 eV with an energy step of 0.2 eV and a slit width of 0.4 eV yielding an energy resolution of 0.8 eV measured as full-width at half-maximum (FWHM) of the ZLP extracted from the EFTEM SI in a single pixel. Fitting the ZLP with a Gaussian, we derived a NIC figure, which matched very well the figure from the tuning
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routine (Fig. 5B). This derived NIC-figure was used for the correction of the EFTEM SI of the sample. Fig. 6 compares extracted ZLPs from this EFTEM SI with and without NIC correction. The energy resolution measured as FWHM of the extracted ZLP from the whole FOV was 1.1 eV before and 0.8 eV after NIC correction, comparing well to the ZLP extracted from a single point. A third EFTEM SI data set with an intrinsic energy drift of 5 eV during the total acquisition time of 30 min was used
to demonstrate a data correction including energy drift correction. The EFTEM SI was acquired with a slit width of 1 eV in the energy range from 5 to 25 eV. All other parameters were kept constant. The energy drift was measured by ZLP alignment before and after the acquisition and the total energy drift was linearly interpolated over time. As the exact time of each image acquisition of the EFTEM SI was stored by our acquisition routine, an energy drift value could be assigned to each slice of the EFTEM SI to be used for the correction.
Fig. 7. Plasmon ratio maps (1) extracted from purely drift corrected data (A), successively NIC and then drift corrected data (B) and fully combined corrected data (C). Vertical line profiles (2) and horizontal line profiles (3) were extracted from the indicated areas to demonstrate the uniform contrast after full correction. A defect in the AlN layer (indicated by the arrow) is completely obscured after incorrect data correction (B).
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5. Results and discussion The aim of the experiment was to demonstrate the need of a NIC correction for high-energy resolution data and to compare the described combined data correction with a correction where spatial drift and NIC correction have been carried out successively one after the other. To show the effect, the collected data was treated in three ways. First, the data block was corrected for spatial drift only (‘DC-block’). Second, the data block was first NIC corrected simply by shifting the columns in z- (energy-loss) direction according to the NIC information and then, in a second step, corrected for spatial drift (‘NDC-block’). In the third example, we used the combined spatial drift and NIC correction to produce a fully corrected data block (‘FC-block’). From these three data blocks we calculated plasmon ratio maps by dividing an extracted image at energy-loss of the AlN plasmon peak maximum (20.8 eV) by the image at the energy-loss of the GaN plasmon peak maximum (19.5 eV). For better statistics the two images where extracted as the sum of 5 slices giving the energy range from 20.3 to 21.3 eV for the AlN and 19.0 to 20.0 eV for the GaN, respectively. The ratio maps and thereof extracted line profiles are shown in Fig. 7. Gradients which can be assigned to the missing NIC correction, can be found in the map created from the DC-block (Fig. 7A), while the map created from the FC-block (Fig. 7C) is completely smooth, giving clear evidence that NIC correction is meaningful for high-energy resolution studies. Additionally, the contrast in the fully corrected results is slightly improved. The comparison with the ‘NDC-block’ results (Fig. 7B) shows that the independently performed NIC- and drift correction did not succeed. The effect of the NIC could not be completely removed, as clearly shown in the vertical line profile. In addition extra artifacts were introduced caused by mixing drift- and NIC-contributions. The interfaces of the layers are smoothed out by the slight drift in y-direction, and the strong specimen drift in x-direction completely obscured the defect in the top layer (arrows in Fig. 7). The results clearly demonstrate that a NIC correction cannot be performed independently of the spatial drift correction for the EFTEM SI method. The effect of a complete data correction including energy drift is shown in Fig. 8. Extracted GaN spectra from the EFTEM SI with and without energy drift correction are compared to an EELS spectrum acquired from the same sample position, showing that the extracted spectrum fits very well to the EELS spectrum after energy drift correction. 6. Conclusion Carrying out filtering experiments with ultra-narrow slit widths at the experimental energy-resolution limit of a modern EFTEM microscope requires a simultaneous
Fig. 8. EELS spectra of GaN extracted from an EFTEM SI with and without energy drift correction compared to the spectrum acquired in spectroscopy mode.
correction of both the spectral aberrations, the spatial drift, and the energy drift intrinsic to an EFTEM SI image stack. Investigation of a test sample consisting of alternating GaN/AlN layers showed that extra artifacts are introduced if the spatial drift correction is performed independently from the NIC correction, and we attempted to give a mathematical explanation of the reason. To our knowledge, we described and demonstrated the first effective algorithm to perform a combined correction including also the energy drift correction. We also suggested how the algorithm must be adapted to additionally correct image distortion due to spectrometer lens aberrations. Using our routines we obtained a final energy resolution of the EFTEM SI of 0.8 eV using an energy selecting slit width of 0.4 eV and an energy step size of 0.2 eV.
Acknowledgements The authors would like to thank Dr. Achim Trampert from the Paul Drude Institute for Solid State Electronics (Berlin, Germany) for providing the test sample and DI Andreas Domaingo from the Institute of Theoretical and Computational Physics (TU Graz, Austria) for fruitful discussions. We also like to thank Prof. Ferdinand Hofer for supervising this project. Finally, we gratefully acknowledge financial support by the SFB—‘Electroactive Materials’ of the Austrian Science Foundation FWF, Vienna.
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Ultramicroscopy 106 (2006) 1129–1138 www.elsevier.com/locate/ultramic
EFTEM spectrum imaging at high-energy resolution Bernhard Schaffer, Gerald Kothleitner, Werner Grogger Research Institute for Electron Microscopy, Graz University of Technology, Steyrergasse 17, A-8010 Graz, Austria Received 16 June 2005; received in revised form 18 December 2005; accepted 5 April 2006
Abstract This paper deals with the application of high-energy resolution EFTEM image series and the corrections needed for reliable data interpretation. The detail of spectral information gained from an image series is largely determined by the intrinsic energy resolution. In this work we show that energy resolution values of as low as 0.8 eV in spectra extracted from EFTEM image series can be obtained with a small energy-selecting slit. At this resolution level aberrations of the energy filter, in particular the non-isochromaticity, can no longer be neglected. We show that the four most prominent factors for EFTEM image series data correction—spatial drift, non-isochromaticity, energy drift and image distortion—must not be treated independently but have to be corrected in unison. We present an efficient algorithm for this correction, and demonstrate the applied correction for the case of a GaN/AlN multilayer sample. r 2006 Elsevier B.V. All rights reserved. Keywords: EFTEM spectrum imaging; Spectral aberration; Sample drift; Energy drift; Non-isochromaticity; Data correction
1. Introduction Energy filtering transmission electron microscopy (EFTEM) is nowadays a well-established method in many areas of materials research [1]. Image contrast and resolution in bright field images can be enhanced by using only elastically scattered electrons (zero-loss filtering) [2,3], and electrons in the low energy-loss region often show distinct material contrast (contrast tuning) [4]. Furthermore, elemental information can be quickly mapped at high spatial resolution by combination of a few EFTEM images (elemental maps, jump ratio images) [5]. However, the ‘full’ spectral information can only be reconstructed from a larger series of EFTEM images taken with a sufficiently small energy-selecting slit, avoiding large energy gaps between the images. This method is known as ‘Electron Spectroscopic Imaging’ (ESI) [6], ‘Image Spectroscopy’ [7,8], ‘Imaging-Spectrum’ [9] and ‘EFTEM Spectrum Imaging’ (EFTEM SI) [10]. The full 3-dimension dataset gained by the method contains an electron energy-loss (EEL) spectrum for each point of the sampled. This opens up the large range of data analysis methods Corresponding author. Tel.: +43 316 873 8330; fax: +43 316 811596.
E-mail address: [email protected] (B. Schaffer). 0304-3991/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2006.04.028
originally developed for EELS spectroscopy, e.g. plural scattering deconvolution, accurate background subtraction, quantification by multiple least-squares (MLS) fitting, separation of overlapping edges, more accurate sample thickness determination, automated elemental identification, and more. As this information is available for all image pixels, mapping of various associated physical and chemical information becomes possible as shown by numerous authors [7,8,11,12]. In comparison to the alternative method of EELS SI, which uses a focused scanning beam for sequential acquisition of the spectra (STEM EELS SI) [13], EFTEM SI offers high spatial resolution over a larger field of view (many pixels along spatial axes) at comparably short acquisition times. It is therefore often the preferred method when the spatial distributions of spectral features (e.g. ionization edges, plasmon peaks, etc.) need to be mapped over larger sample areas. However, STEM EELS SI offers better energy resolution and collects information over larger energy-loss ranges in one step (many pixels along energy axis). It is therefore most commonly used to investigate subtle spectral changes in small sample areas [14,15]. The aim of this work was to further improve the method of EFTEM SI with respect to energy resolution. The intrinsic energy resolution of an EFTEM SI is a
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convolution of the system’s total energy resolution (the sum of the energy width of the electron beam, the high tension stability, the spectrometer energy resolution, etc.) with the energy selecting slit width. Considering a total system’s energy resolution of 1 eV or better, the energy resolution of the series is then largely determined by the slit width, which in most cases lies in the range of a few to some tens of eV. Some imaging filters allow slit widths smaller than 1 eV to be used so that the energy resolution of the EFTEM SI is no longer limited by the slit and then becomes comparable to the energy resolution of EELS spectra. With the higher energy resolution, additional EELS analysis can be performed and used for mapping, e.g. chemical shift maps, plasmon peak position maps, dielectric constant maps by Kramers–Kronig analysis, etc. Fig. 1 shows another benefit of having better EFTEM energy resolution. In this picture four plasmon ratio maps are compared. Such maps were produced by dividing two EFTEM images acquired at the energy-losses of the GaN and AlN plasmon peaks, respectively. The first three maps (Fig. 1A–C) were produced from datasets acquired with different energy selecting slit widths of 10, 5 and 1 eV, respectively. The datasets were fully corrected for the combined effect of spatial drift, energy drift and nonisochromaticity (NIC), using the novel algorithms described in this work. The fourth map was produced from the same data as the third map, but without data correction except for spatial drift. All images are displayed with the same contrast limits. It can be clearly seen that for best image contrast a small slit width (1 eV) is superior to larger slit widths (5 eV, 10 eV). However, at energy resolutions in the range of the spectrometer aberrations, their influence can no longer be neglected as can be seen from the uncorrected data (Fig. 1D).
This work focuses on the correction of high-energy resolution EFTEM SI data, which becomes essential for reliable data analysis and interpretation. To our best knowledge, it presents the first algorithm, which corrects the combined effect of spatial drift, energy drift and NIC. 2. Data correction The information contained in an image series can be best visualized in 3-dimensional information space, where x and y are spatial coordinates of the sample and z is the EEL axis as suggested by Jeanguillaume et al. [16]. An EFTEM SI is a discrete subset of this information space as shown in Fig. 2A. Any data point of the EFTEM SI contains the integrated intensity of a small subset of the information space centered at given spatial coordinates and energy-loss with dimensions according to the spatial and energy resolution of the EFTEM SI. In analogy to ‘pixel’, which is the commonly known acronym for ‘picture element’, such a data point in a discrete 3-dimensional data set is called ‘voxel’ as acronym for ‘volume picture element’. Ideally, an EFTEM SI is a cuboid built as a stack of horizontal slices (EFTEM images). However, the real shape of a measured EFTEM SI in information space is more or less deformed due to system instabilities and spectrometer lens aberrations. Nevertheless, these deformations are often neglected and the EFTEM SI is treated as an orthogonal block leading to serious errors if used for further data evaluation without corrections. The most influential factors are shown in Figs. 2C–F, leading to a combined deformation shown in Fig. 2B. The deformed EFTEM SI is falsely interpreted as the cuboid shown by the dashed line according to the nominal values of the EFTEM SI acquisition.
Fig. 1. Plasmon ratio maps (20.8 eV image dived by a 19.5 eV image) of a GaN/AlN stack acquired with different energy selecting slit widths (A: 10 eV; B: 5 eV; C and D: 1 eV). The maps are displayed with the same contrast settings and were produced from fully corrected data except image D, where no nonisochromaticity correction was performed.
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EFTEM SI are correct, but the associated coordinates are not. xy are the coordinates of the sample and e is the true energy-loss value. The most prominent deformations are caused by: (1) Spatial drift: During acquisition sample drift may occur as a result of instabilities of the microscope stage or specimen. Consequently, two images of the series might not show the same area of the sample and are shifted in x- and y-direction from their original position in information space. Spatial drift is the same for all voxels of one image acquisition. As the acquisition of one image out of an EFTEM SI is assigned to a nominal energy-loss value (the central value of the acquired energy range), the spatial drift can be expressed as a function of this nominal energy-loss: Dxydrift ¼ f drift ðem Þ.
Fig. 2. Schematics of EFTEM image series (data blocks) in the information space. An ideal data block (A) is orthogonal and holds image information in horizontal slices and spectral information in vertical columns. A real data block (B) is deformed and may show both gaps and overlaps. It is falsely presented as an orthogonal block (dashed line). The deformations due to spatial drift (C), energy drift (D), image distortion (E) and non-isochromaticity (F) are illustrated.
In our mathematical picture, each voxel of the measured EFTEM SI has its individual displacement vector pointing from the nominal position to the correct position in information space. For simplicity reasons the lateral coordinates x and y are noted as one coordinate xy only. I m ðxym ; em Þ ¼ Iðxy; eÞ ¼ Iðxym þ Dxy; em þ DeÞ.
(1)
Im is the measured EFTEM SI data block. It holds intensity values for the nominal coordinates xym and em. xym are the coordinates of the CCD camera (assumed to be identical with the coordinates of the sample) and em is the nominal energy-loss. Due to the deformations listed below those coordinates are shifted away by Dxy and De from their correct position in information space. Therefore, the measured EFTEM SI at the voxel (xym, em) gives the intensity I at the ‘true’ but unknown position ðxy; eÞ in information space instead of the wanted intensity at the coordinates ðxym ; em Þ. In other words, the intensities of the
(2)
The function fdrift is the spatial drift for each EFTEM SI slice of nominal energy-loss em. It can be determined directly from the images of the series by finding the shift vector, which produces an optimum overlap of the image content. This can be done manually or with the help of automated routines based on cross-correlation [17]. During acquisition of a single image, sample drift may lead to a blurring and loss of spatial resolution. (2) Energy drift: The energy reference point of the spectrometer, determined as the zero-loss peak (ZLP) position at the energy selecting slit plane, may change over time. High-voltage instabilities and thermal effects influencing for instance the prism current stability can produce a systematic drift of a few eV during acquisition times of several minutes. The nominal energy-loss then deviates from the real energy-loss of the electrons. A representation in information space describes the images slices as being shifted along the zdirection from their original position. Thus, energy drift can lead to both overlaps and gaps in the sampled energy space. As for the spatial drift, energy drift is the same for all voxels of one image within the EFTEM SI. It can therefore be expressed as a function of the nominal energy-loss, too: Deedrift ¼ f edrift ðem Þ.
(3)
The function fedrift describes the energy drift of the system. In general, it cannot be determined from the measured EFTEM SI, but needs additional measurements. The position of the ZLP provides a good measure for the energy drift, if it is determined before and after each single EFTEM image. However, for practical reasons a ZLP position measurement/readjustment after each single image acquisition of the EFTEM SI is not feasible. In most cases a reasonable approximation of the energy drift can be obtained by determining the ZLP position before and after the whole series and assuming a linear drift in between. In
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EFTEM, the ZLP position is measured by rapid acquisition of an EFTEM image series across zero-loss energy and assigning the image with maximum intensity to the zero-loss value. (3) NIC: Electrons detected at the borders of an EFTEM image might not have exactly the same energy as those in the center of the image. Due to lens aberrations in the spectrometer the iso-energy planes are not completely flat but curved. Modern post-column energy filter designs correct lens aberrations up to third- and fourth-order but a residual NIC in the magnitude of typically 1 eV over the full field-of-view defined by the CCD remains. While this can be safely ignored for elemental mapping where energy selecting slit widths and desired energy resolutions are equal or above 5 eV, it has to be taken into account for high-energy resolution work. In its representation in information space, the NIC leads to a bending of the slices. The NIC for a given magnification is a function of the CCD coordinates only. It is therefore independent of the nominal energy-loss and equal for all individual slice acquisitions of an EFTEM SI. DeNIC ¼ f NIC ðxym Þ.
(4)
The function fNIC describes the NIC-figure as a function of the CCD coordinates. For post-column systems it is typically measured by scanning the ZLP across the slit edge, while recording images with the sample removed. Selecting an energy range with the slit vignettes the image in a shape that represents a slice through the aberration figure of the filter. Consequently the sum of images represents the NIC surface over the field-of-view (FOV) calibrated in energy units [18]. This method is used in the tuning routines of the Gatan Imaging Filter (GIF), which also outputs the NIC figure. Alternatively, one can acquire an image series over the energy-loss of a known feature, e.g. the ZLP, and create a map of the maxima positions (at the energy-loss axis) for instance by fitting an appropriate function. Sigle et al. [19] suggested to use the plasmon peak of a thin, homogeneous carbon film for high accuracy measurements. (4) Image distortion: Lens aberrations of the imaging filter may introduce a small lateral image distortion. While it might play a role for analysis of diffraction patterns computed from lattice images or seamless montage of multiple digital images frames, it is often small enough to be ignored. In the EFTEM SI representation in information space, image distortion appears as lateral deformation of the slices, which is the same for all individual slice acquisitions of an EFTEM SI and therefore independent of the nominal energy-loss. Dxydis ¼ f dis ðxym Þ.
(5)
The image distortion fdis is a function of the CCD coordinates. It can be measured by imaging an object of known shape, e.g. a mask aperture with a regular array
of holes at known positions. Comparison of the mask’s image on the CCD with the known positions of the holes yields the distortion over the entire image field. With all the aberrations characterized, it is now possible to correct an EFTEM SI. In a first step, the intensities of the uncorrected EFTEM SI need to be mapped to their ‘true’ positions in information space (deformed cube in Fig. 2B). In a second step, the correct intensities at the nominal positions are calculated from this deformed cube (dashed cube in Fig. 2B). The mapping of intensities can be mathematically expressed as the following variable transformation using Eq. (2)–(5): xym ! xy0m ¼ xym þ Dxy ¼ xym þ f drift ðem Þ þ f dis ðxym Þ, (6) em ! e0m
¼ em þ De ¼ em þ f edrift ðem Þ þ f NIC ðxym Þ,
I m ðxym ; em Þ ! I 0m ðxy0m ; e0m Þ
¼ I m ðxym ; em Þ.
(7) (8)
Dashed variables are the corrected variables. I 0m is the correct, but no longer orthogonal and equally spaced data. It is important to note that I 0m is not yet the corrected EFTEM SI. However, inserting Eqs. (6)–(8) into Eq. (1) reveals that I 0m is identical with the intensities in information space (and therefore correct): I 0m ðxy0m ; e0m Þ ¼ I m ðxym ; em Þ ¼ Iðxym þ Dxy; em þ DeÞ ¼ Iðxy0m Dxy þ Dxy; e0m De þ DeÞ ¼ Iðxy0m ; e0m Þ, I 0m I.
ð9Þ
The corrected EFTEM SI should be an orthogonal cuboid with equidistant sampling intervals according to the nominal values of the acquisition. It is calculated from I 0m . Fig. 2B shows that due to the discrete nature of the measured data, some interpolation of the corrected data might be necessary to take into account the ‘holes’ and ‘overlaps’ in information space as well as the sampling intervals. As each individual voxel of the uncorrected EFTEM SI has its own displacement vector, the direct implementation of Eqs. (6)–(8) would be a voxel-by-voxel algorithm, shifting the intensity of each uncorrected voxel to its correct position and finally interpolating the corrected EFTEM SI with the given sampling intervals (image scale and dispersion). Considering the huge amount of data (typically more than five million voxels) voxel-based algorithms are impractically slow. Assuming one voxel operation would be carried out in only 0.01 s, the full correction of a typical EFTEM SI (256 256 pixels, 80 energy steps) would still take more than 14.5 h. Individual corrections of spatial drift, energy drift and NIC are considerably faster as larger subsets of the EFTEM SI can be corrected at once. Spatial and energy drift correction shift whole slices at once, while the NIC
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correction shifts entire columns. It has therefore been suggested in the literature to perform a NIC correction prior to a spatial and energy drift correction [19]. However, this suggestion cannot be performed straightforwardly without introducing extra errors. After the NIC correction, voxels from one slice no longer stem from a single acquisition and therefore no longer share a common drift vector. This can be seen by inserting Eq. (7) without the energy drift term into Eq. (2): Dxydrift ¼ f drift ðe0m Þ ¼ f drift ðem þ f NIC ðxym ÞÞ ¼: f 0drift ðxym ; em Þaf drift ðem Þ.
ð10Þ
f 0drift is the new spatial drift function. After the NIC correction it is a function of all three coordinates and is not identical to the measured drift fdrift prior to the NIC correction. A similar argument holds for the opposite case. After a spatial drift correction, the new coordinates are no longer identical with the CCD coordinates and consequently the NIC figure becomes a function of all three coordinates: DeNIC ¼ f NIC ðxy0m Þ ¼ f NIC ðxym þ f drift ðem ÞÞ ¼: f 0NIC ðxym ; em Þaf NIC ðxym Þ.
ð11Þ
In other words, after a spatial drift correction a common NIC figure can no longer be found. This is illustrated in Fig. 3. Doing a spatial drift correction and a subsequent NIC correction inevitably introduces an error. This error increases with larger spatial drift and a more strongly warped NIC figure, but it depends on the sample. In energy regions of pronounced intensity changes (e.g. sharp peaks or edge onsets) or at sample regions with strong contrast changes (e.g. interfaces or precipitates) the effect is most pronounced.
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3. Combined spatial drift and NIC correction The aim of the data correction is to regain a good approximation of the real, orthogonal data block from the measured data block. The deformation vector for each voxel can be measured as described previously. Voxel-by-voxel algorithms are inefficiently slow, but from Eqs. (6) and (11) it can be derived that a correction of the lateral deformations (spatial drift and image distortion) can be performed slice-by-slice prior to a correction of the energy deformations (energy drift and NIC). The function of the energy deformation De then has to be adjusted accordingly. The combined EFTEM SI correction algorithm therefore consists of the following steps (see Fig. 4). If image distortion needs to be corrected for, it has to be done first. Each acquisition slice of the EFTEM SI is dewarped and the same process is applied to the NIC figure. In the words of our mathematical picture, a variable transformation of distorted CCD coordinates to corrected ones is performed. In the next step, spatial drift is determined from this image distortion corrected EFTEM SI. Now a second data block (EC) is generated, which will hold the information for the energy correction. This ECblock is first filled by the same (dewarped) NIC figure for each slice. If energy drift is to be corrected as well, the energy shift for each slice of the EFTEM SI is added to the corresponding slice of the EC-block. Finally, the same spatial drift correction is applied to both the data block and the EC-block to obtain a distortion/spatial drift corrected data block and a shifted EC-block. Each voxel of the data block now has a corresponding voxel in the ECblock carrying displacement information for the z-axis (energy-loss). The EC-block represents the sum of the functions fNIC and fedrift in Eq. (7). In the last step of the algorithm, the fully corrected EFTEM SI block is reconstructed slice by slice. For each
Fig. 3. Schematic illustrating the problem of successively correcting sample drift and non-isochromaticity (NIC). Pixels along a column do not show the same z-displacement (energy) after shifting the slices of the data block in x- and y-direction (spatial). Small arrows indicate required energy shift due to NIC.
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Fig. 4. Schematics of the combined correction algorithm. In a first step, spatial drift correction is performed and the same drift is applied to a block holding NIC figures and energy drift values (EC). In the second step, the two blocks are used to reconstruct the fully corrected EFTEM SI slice-by-slice. For each energy plane, the EC block is used to define a weighting mask for the data block. The weighted sum of the intensities yields the corrected energy plane.
slice the algorithm evaluates the relevant subset of the data block only. This subset is defined by the nominal energyloss of the slice plus/minus the maximum possible energy displacement and by the energy step size of the EFTEM SI. It holds all images that might contribute intensity to the slice. The corresponding subset of the EC-block is used to calculate the relative amount of intensity of each image, which contributes to the corrected slice. The fully corrected slice is the sum of all weighted intensities of the EFTEM SI subset.
4. Experimental All experiments were performed on an FEI Tecnai F20/ STEM microscope operated at 200 kV and equipped with an FEG electron source and a monochromator [20]. The microscope has a super twin objective lens (CC ¼ 1.2 mm; CS ¼ 1.2 mm). A high-resolution imaging filter from Gatan Inc. (HR-GIF) with a 1024 1024 CCD camera was attached to the microscope [21]. The HR-GIF is fully corrected for aberrations up to the third-order and partially
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Fig. 5. (A) Spatial drift in x- and y-direction during the experiment. Drift is given in pixels of the recorded images for better comparison with the nonisochromaticity (NIC) figure. (B) NIC figure measured by the tuning routine of the GIF (values in eV).
for the fourth-order. The energy-selecting slit of the spectrometer installed at our lab can be closed down to widths of 0.1 eV as determined experimentally. With a given energy resolution of roughly 0.6 eV for the 5 mm GIF entrance aperture, a slit width of 0.4 eV was chosen as a good compromise between energy resolution and intensity. An alternating stack of GaN and AlN layers produced by molecular beam epitaxy (MBE) was used as a test sample [22]. A cross-section of the sample was prepared by focused ion beam (FIB) milling using a Nova200 NanoLab DualBeam FIB from FEI. The final lamella was thinned to a thickness of approximately 45 nm. After checking the exact slit width of 0.4 eV in spectroscopy mode, we acquired 70 EFTEM images with a size of 512 512 pixel (2 2 hardware binning) in the energy range of 14.0–27.8 eV (0.2 eV steps) with a 100 mm objective aperture (13.83 mrad collection half-angle). We used a customized script for acquisition, which included automatic adjustment of exposure time for each image in order to optimally utilize the CCD’s dynamic range. The total acquisition time of the series was roughly 15 min. During this time total sample drift of approximately 120 nm corresponding to 140 pixels on the CCD at the chosen magnification was observed in x-direction while sample drift in y-direction was less than 26 nm (30 pixels) as shown in Fig. 5A. Energy drift was determined by performing a ZLP alignment prior and after the EFTEM SI acquisition. The total energy drift during the acquisition time was less than 1 eV and therefore not corrected for. Image distortion was measured by the automatic tuning routine of the GIF, yielding a distortion at the fractional percent level, which was 0.6% over the entire FOV and hence was not corrected for. To better study the NIC influence, we slightly mistuned the HR-GIF during the acquisition to produce a more pronounced energy bending of the NIC-figure of approximately 2 eV peak-to-peak comparable to imaging filters without higher-order aberration correction.
Fig. 6. EELS zero-loss peak spectra extracted from the EFTEM SI of the GaN/AlN multilayer sample at a single point and over the whole FOV before and after NIC correction. Energy resolution over the FOV determined as FWHM of the peak is improved from 1.1 eV (before correction) to 0.8 eV (after the correction), which is the same as in a single extracted spectrum.
To compare the NIC from the tuning routine with a NIC figure derived from an EFTEM SI, we also acquired an EFTEM image series with the sample removed. This series was acquired in the energy range from 5 to +5 eV with an energy step of 0.2 eV and a slit width of 0.4 eV yielding an energy resolution of 0.8 eV measured as full-width at half-maximum (FWHM) of the ZLP extracted from the EFTEM SI in a single pixel. Fitting the ZLP with a Gaussian, we derived a NIC figure, which matched very well the figure from the tuning
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routine (Fig. 5B). This derived NIC-figure was used for the correction of the EFTEM SI of the sample. Fig. 6 compares extracted ZLPs from this EFTEM SI with and without NIC correction. The energy resolution measured as FWHM of the extracted ZLP from the whole FOV was 1.1 eV before and 0.8 eV after NIC correction, comparing well to the ZLP extracted from a single point. A third EFTEM SI data set with an intrinsic energy drift of 5 eV during the total acquisition time of 30 min was used
to demonstrate a data correction including energy drift correction. The EFTEM SI was acquired with a slit width of 1 eV in the energy range from 5 to 25 eV. All other parameters were kept constant. The energy drift was measured by ZLP alignment before and after the acquisition and the total energy drift was linearly interpolated over time. As the exact time of each image acquisition of the EFTEM SI was stored by our acquisition routine, an energy drift value could be assigned to each slice of the EFTEM SI to be used for the correction.
Fig. 7. Plasmon ratio maps (1) extracted from purely drift corrected data (A), successively NIC and then drift corrected data (B) and fully combined corrected data (C). Vertical line profiles (2) and horizontal line profiles (3) were extracted from the indicated areas to demonstrate the uniform contrast after full correction. A defect in the AlN layer (indicated by the arrow) is completely obscured after incorrect data correction (B).
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5. Results and discussion The aim of the experiment was to demonstrate the need of a NIC correction for high-energy resolution data and to compare the described combined data correction with a correction where spatial drift and NIC correction have been carried out successively one after the other. To show the effect, the collected data was treated in three ways. First, the data block was corrected for spatial drift only (‘DC-block’). Second, the data block was first NIC corrected simply by shifting the columns in z- (energy-loss) direction according to the NIC information and then, in a second step, corrected for spatial drift (‘NDC-block’). In the third example, we used the combined spatial drift and NIC correction to produce a fully corrected data block (‘FC-block’). From these three data blocks we calculated plasmon ratio maps by dividing an extracted image at energy-loss of the AlN plasmon peak maximum (20.8 eV) by the image at the energy-loss of the GaN plasmon peak maximum (19.5 eV). For better statistics the two images where extracted as the sum of 5 slices giving the energy range from 20.3 to 21.3 eV for the AlN and 19.0 to 20.0 eV for the GaN, respectively. The ratio maps and thereof extracted line profiles are shown in Fig. 7. Gradients which can be assigned to the missing NIC correction, can be found in the map created from the DC-block (Fig. 7A), while the map created from the FC-block (Fig. 7C) is completely smooth, giving clear evidence that NIC correction is meaningful for high-energy resolution studies. Additionally, the contrast in the fully corrected results is slightly improved. The comparison with the ‘NDC-block’ results (Fig. 7B) shows that the independently performed NIC- and drift correction did not succeed. The effect of the NIC could not be completely removed, as clearly shown in the vertical line profile. In addition extra artifacts were introduced caused by mixing drift- and NIC-contributions. The interfaces of the layers are smoothed out by the slight drift in y-direction, and the strong specimen drift in x-direction completely obscured the defect in the top layer (arrows in Fig. 7). The results clearly demonstrate that a NIC correction cannot be performed independently of the spatial drift correction for the EFTEM SI method. The effect of a complete data correction including energy drift is shown in Fig. 8. Extracted GaN spectra from the EFTEM SI with and without energy drift correction are compared to an EELS spectrum acquired from the same sample position, showing that the extracted spectrum fits very well to the EELS spectrum after energy drift correction. 6. Conclusion Carrying out filtering experiments with ultra-narrow slit widths at the experimental energy-resolution limit of a modern EFTEM microscope requires a simultaneous
Fig. 8. EELS spectra of GaN extracted from an EFTEM SI with and without energy drift correction compared to the spectrum acquired in spectroscopy mode.
correction of both the spectral aberrations, the spatial drift, and the energy drift intrinsic to an EFTEM SI image stack. Investigation of a test sample consisting of alternating GaN/AlN layers showed that extra artifacts are introduced if the spatial drift correction is performed independently from the NIC correction, and we attempted to give a mathematical explanation of the reason. To our knowledge, we described and demonstrated the first effective algorithm to perform a combined correction including also the energy drift correction. We also suggested how the algorithm must be adapted to additionally correct image distortion due to spectrometer lens aberrations. Using our routines we obtained a final energy resolution of the EFTEM SI of 0.8 eV using an energy selecting slit width of 0.4 eV and an energy step size of 0.2 eV.
Acknowledgements The authors would like to thank Dr. Achim Trampert from the Paul Drude Institute for Solid State Electronics (Berlin, Germany) for providing the test sample and DI Andreas Domaingo from the Institute of Theoretical and Computational Physics (TU Graz, Austria) for fruitful discussions. We also like to thank Prof. Ferdinand Hofer for supervising this project. Finally, we gratefully acknowledge financial support by the SFB—‘Electroactive Materials’ of the Austrian Science Foundation FWF, Vienna.
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B. Schaffer et al. / Ultramicroscopy 106 (2006) 1129–1138
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