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Comparison of detectability limits for elemental mapping by EF-TEM and STEM-XEDS
Micron 34 (2003) 173–183 www.elsevier.com/locate/micron
Comparison of detectability limits for elemental mapping by EF-TEM and STEM-XEDS Masashi Watanabea,*, David B. Williamsa, Yoshitsugu Tomokiyob b
a Department of Materials Science and Engineering, Lehigh University, Bethlehem, PA 18015, USA Department of Engineering Science for Electronics & Materials, Kyushu University, Kasuga 816-8580, Japan
Abstract The analytical sensitivity in terms of the signal-to-noise ratio (SNR) was investigated for elemental mapping by a transmission electron microscope equipped with an energy filter (EF-TEM) and a scanning transmission electron microscope with an X-ray energy dispersive spectrometer (STEM-XEDS). To compare the detectability limits of the elemental maps by the two techniques, homogeneous Cu– 0.98 ^ 0.34 wt% Mn and Cu – 4.93 ^ 0.49 wt% Mn thin specimens were used. Elemental maps can be considered as either an image or a spectrum. Therefore, the detectability limits of the elemental maps were characterized by the spectral SNR. To evaluate the detectability limits of the elemental maps with statistical confidence limits such as 1s; 2s and 3s; the SNR values were reviewed from the statistical point of view. In STEM-XEDS mapping, the spectral SNR values improve as the specimen thickness increases since the signal intensity increases. Conversely, the spectral SNR in EF-TEM mapping is maximized at a certain thickness and then reduces as the thickness increases. To compare the two mapping techniques with regard to the analytical sensitivity, a method to estimate the minimum mass fraction (MMF) from measured signal and background intensities was developed. In this experimental approach, the MMF value can be evaluated by selecting the appropriate SNR value corresponding to the statistical confidence limits. In comparing the estimated MMF values from the two mapping approaches, EF-TEM mapping can be more sensitive than STEM-XEDS mapping up to specimen thicknesses , 20 – 30 nm in the 1s confidence limit and ,, 50 nm in the 3s limits. However, as the specimen thickness increases, the XEDS maps provide better detectability limits in the Cu– Mn dilute alloy specimens. q 2003 Elsevier Ltd. All rights reserved. Keywords: Analytical sensitivity; Spectral signal-to-noise ratio; Confidence limits for detection; Minimum mass fraction
1. Introduction The elemental mapping approach can be the best way to analyze nano-scale features in materials such as fine precipitates and interfaces/boundaries, since two dimensional fluctuations in composition around such small features, which may be easily missed by point or line-scan analyses, can be revealed in images of elemental distributions. Currently, such elemental distributions can be obtained by a transmission electron microscope equipped with an energy filter (EF-TEM), or a scanning transmission electron microscope with an X-ray energy dispersive spectrometer (STEM-XEDS) and/or an electron energyloss spectrometer (STEM-EELS). The spatial resolution of the fixed beam EF-TEM technique can reach sub-nanometer ranges and the major sources of degradation of the spatial resolution are the chromatic aberration due to the width of the energy-selecting slit (Berger and Kohl, 1993; Krivanek * Corresponding author. 0968-4328/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0968-4328(03)00028-3
et al., 1995; Botton and Phaneuf, 1999; Egerton, 1999; Bentley et al., 2001; Wittig et al., 2001; Omura et al., 2002). The spatial resolution of the STEM-based techniques is mainly governed by the focused probe size and the beam broadening in the specimen. So, there are basically no major differences in the spatial resolution of the STEM-based techniques between the mapping mode and the point/line analysis modes. When a STEM equipped with a fieldemission gun source is used, sub-nanometer spatial resolution is also achievable in the STEM-EELS technique, as demonstrated by Browning et al. (1997). In the STEMXEDS technique, conversely, the spatial resolution reaches a few nanometers since much larger beam currents which enlarge the incident probe sizes are required to gather sufficient signal intensity within a reasonable acquisition time (Carpenter et al., 1999; Keast and Williams, 2000; Williams et al., 2002). Although the spatial resolution of elemental mapping can reach the sub-nanometer level in EELS-based mapping and a few nanometers in STEM-XEDS mapping, the analytical
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sensitivity in elemental mapping may become worse than that of conventional spot analysis and/or line scan approaches. This is true especially in the STEM-based techniques since the acquisition time at a single pixel (dwell time) is much shorter than for the point analysis (typically , 60– 100 s/total acquisition) or line-scan analysis approach (typically , 3 –20 s/individual acquisition). In principle, the acquisition time for elemental mapping in either the EFTEM or the STEM-based methods can simply be increased. However, total mapping times can take many minutes or hours, which are significantly longer than a conventional point analysis or line profiling and this may provide more chances for contamination build-up and/or irradiation damage. In addition, the longer acquisition could cause many kinds of drifts during mapping, e.g. spatial drift, energy drift, beam current drift, etc. since the long-term stability is not sufficient even in current instruments. It should be noted that some of these drifts are now correctable during acquisition or post processing. However, it is not very easy to cure all of drifts in elemental mapping even using current software. Furthermore, one of the major limitations in elemental mapping either by EF-TEM or by STEM is that obtainable net signal intensities are not significant enough. The EELS signals can be measured with great collection efficiency. However, most EELS signals consist of huge backgrounds and net signals from characteristic edges are, relatively, much lower than the background. For XEDS, although the characteristic peak signals are more intense than the background, the measured signals are extremely low due to the poor collection efficiency. Therefore, the intensity fluctuation in the elemental maps may not reflect the compositional fluctuations but could be lost within the statistical noise. In this study, comparative elemental maps of dilute amounts of Mn in Cu have been taken by EF-TEM and STEM-XEDS, to analyze the detection sensitivities of elemental mapping, with statistical certainty. In order to evaluate the detectability limits of elemental maps, the standard methods were applied in elemental mapping by two techniques: the simple energy window method for STEM-XEDS mapping and the three-window method for EF-TEM mapping. In addition, only the specimen thickness and the binning pixel number were changed as the experimental parameters, since these parameters are also related to the spatial resolution of analysis. However, there are also several experimental parameters, which can affect the detectability limit, such as the probe current, the probe size and the dwell time for STEM-XEDS and the illumination current, the objective-aperture size and the acquisition time for EF-TEM. In addition, the energy window setting also affects the detectability limit seriously, especially when elemental mapping is conducted for minor amounts (, 10 wt%) of elements. In this study, these parameters, except for the specimen thickness and the binning pixel number were fixed in order to simplify the relationship between the detectability limits and the spatial
resolution. To investigate the detectability limit in elemental mapping completely, these experimental parameters should also be taken into account.
2. Definition of evaluation parameters for detectability limits of elemental maps Basically, an elemental map is an image with a relatively low signal intensity. Therefore, in experimental data, useful signals can be hidden by the contributions of systematic and/or random noises and analytical sensitivity can be degraded. So, in order to evaluate the detectability from experimental data, especially for EELS spectra and for EFTEM maps, the signal-to-noise ratio (SNR) has usually been applied (Egerton, 1996). If the SNR value is significant, i.e. higher than a certain threshold value, the signal of interest (in the case of an EELS spectrum, the edge intensity above the background) is judged as detectable. This concept of the SNR is originally based on Rose’s work (Rose, 1948, 1970): Rose defined the SNR to evaluate the visibility (not detectability) of images with relatively low signals and proposed that SNR ¼ 5 was a sufficient threshold limit to distinguish the signal from noise in an image. This limit is well known as the Rose criterion. In several studies, the SNR value was used as a figure of merit to optimize the microscope conditions for EF-TEM elemental mapping (Berger and Kohl, 1993; Berger et al., 1994; Kothleitner and Hofer, 1998; Moore et al., 1999). Obviously, SNR is one of the most suitable parameters to describe the detectability limits of elemental maps. However, several SNR values have been used as the threshold for detectability, e.g. SNR ¼ 5 (Rose criterion) (Berger and Kohl, 1993; Berger et al., 1994) or 3 (Trebbia, 1988; Colliex et al., 1989; Egerton, 1996), in previous studies. This inconsistency in the SNR value for detectability evaluation is mainly because the SNR value has not been defined with a certain statistical confidence level. Recently, SNR was reconsidered as a statistically meaningful measure for the detectability evaluation (Natusch et al., 1999). The definition of the SNR for elemental maps is briefly described below, based on a spectrometric approach, and the statistical description of SNR is also reviewed. Then, the detectability limits of the elemental maps will be discussed with statistical confidence limits. 2.1. Spectral SNR There are several ways to describe the SNR of elemental maps because the definition of the noise component varies. The noise can be defined by taking the square root of the variance of the signal as originally demonstrated for images by Rose (1948, 1970). However, the noise component in the elemental maps is affected not only by the variance of the net signal but also by any fluctuations in the background, since background subtraction is required. Therefore, uncertainties arising from background subtraction should be taken
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into account for the SNR of elemental maps. Egerton (1996) defined the spectral SNR SNR ¼
Is ðIs þ hIb Þ1=2
ð1Þ
where Is and Ib are the signal and background intensities, respectively, and h is a dimensionless parameter associated with background subtraction and given as: h¼1þ
varðIb Þ Ib
ð2Þ
The value of h typically ranges between 2 and 30 depending on background fitting and energy regions (Kothleitner and Hofer, 1998), especially for XEDS h ¼ 2 (Trebbia, 1988; Colliex et al., 1989). For EF-TEM elemental mapping with the three-window background, subtraction of h is given as (Berger and Kohl, 1993) 3 E 2 ðEb1 þ Eb2 Þ=2 2 h¼ þ2 s ð3Þ 2 Eb2 2 Eb1 where Es ; Eb1 and Eb2 are the energy positions for the signal (post edge) window and the two background (pre-edge) windows, respectively. Note that Eq. (3) assumes only a small amount of extrapolation, i.e. Es q Es 2 Eb1 (Berger and Kohl, 1993). The spectral SNR defined in Eq. (1) only takes into account the generated signals. However, the detector (such as a CCD camera), which was used, for recording EF-TEM elemental maps may also introduce additional noise. Therefore, Eq. (1) should be modified using the signal and background intensities at each pixel, Is ðjÞ and Ib ðjÞ with consideration of the detector noise (Berger and Kohl, 1993): SNR ¼
ðDQEÞ1=2 kIs ðjÞl ½kIs ðjÞl þ hkIb ðjÞl1=2
ð4Þ
where DQE is the detector quantum efficiency. For the CCD camera, the DQE value was reported as , 0.6 at the incident beam energy of 200 keV (Zuo, 1996). In this study, this value was used to determine the spectral SNR for the EFTEM elemental maps. For STEM-XEDS elemental maps, it is assumed that DQE is unity. It should be noted that SNR ¼ 3 is preferably chosen as the threshold limit to judge the detectability in an EELS spectrum, instead of employing the Rose criterion. Since these SNR values were arbitrarily chosen, obviously there is no correlation between the SNR values and the statistical confidence limits to define the detectability limit. Therefore, the threshold SNR value for the detectability limit should be defined as a meaningful measure, in a statistical manner. 2.2. Statistical description of SNR for minor-element analysis The spectral SNR described in Eqs. (1) and (4) means that the signal in a spectrum is assumed to obey a Gaussian
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distribution. This is a reasonable assumption whenever signal intensities are high enough. However, this assumption may fail if the signal intensity becomes extremely low, e.g. analysis of minor elements in a specimen. This is because the signal intensity is always positive although the Gaussian distribution is defined in the infinite region (2 1 to þ 1) (Trebbia, 1988). Therefore, Tixier (1979) modified the criterion for minor-element analysis by introducing a non-central x2 distribution. Let r denote a normally distributed variable with a unit standard deviation and a zero mean, and then a random variable obeying the noncentral x2 distribution with a degree of freedom of one is expressed as (Pearson and Hartley, 1976)
x 02 ¼ ðr þ l1=2 Þ2
ð5Þ
where l is the non-centrality parameter and defined as (SNR)2 in this case (Tixier, 1979). So, the distribution is deviated from zero with a magnitude of (SNR). This concept was originally applied for XEDS (Tixier, 1979) and for EELS (Trebbia, 1988). When a minor element with lower composition is analyzed, two risks are always involved: the first-kind ðg1 Þ is the probability of concluding that the minor element is detected in spite of the absence of the elements at the analyzed point and the second-kind ðg2 Þ is the probability of concluding that the minor element is not detected while the element is actually present (Tixier, 1979). Recently, Natusch et al. (1999) evaluated both the risks from the non-central x2 probability density distribution as a function of SNR. Then, the confidence limits for SNR were derived by minimizing the sum of both the risks ðg1 þ g2 Þ; based on the regular Gaussian standard deviation. According to Natusch et al. (1999), the SNR values of 3 and 5 are equivalent to 82 and 98% of probability of detection, respectively. Let s denote the standard deviation of the regular Gaussian distribution. Then, the confidence limits of 68% ð^sÞ; 95% ð^2sÞ and 99% ð^3sÞ; which are commonly employed in error analysis, correspond to SNR ¼ 2.4, 4.3 and 6.2, respectively. It should be mentioned that these SNR values for the corresponding confidence limits can vary when only one of the two risks (most likely the g2 risk only) is taken into account, as noted by Natusch et al. (1999). However, it is still better to incorporate both risks when the detectability is estimated from the SNR.
3. Experimental In this study, homogeneous Cu – 0.98 ^ 0.34 wt% Mn (1% Mn) and Cu– 4.93 ^ 0.49 wt% Mn (5% Mn) thin specimens were used. The compositions of these alloys were determined from the bulk samples by using a JEOL superprobe 733 electron probe microanalyzer. The Cu – Mn system was originally employed for estimation of the minimum mass fraction (MMF) by Michael (1987). In our
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previous paper (Watanabe and Williams, 1999), several Cu – Mn thin specimens were also used to evaluate the analytical sensitivity of X-ray microanalysis in terms of the MMF and the minimum detectable mass (MDM). Since the Cu – Mn alloys can be homogenized via a standard diffusion anneal and there are no reports about the formation of fine-scale precipitates or clusters in this alloy system (Watanabe and Williams, 1999), it is assumed that any intensity fluctuations in the elemental maps are not caused by compositional differences at least. To acquire STEM-XEDS elemental maps, a VG HB 603 STEM at Lehigh University was used. This STEM is optimized for X-ray microanalysis with maximum X-ray collection efficiency (Lyman et al., 1994) and the analytical sensitivity in terms of the MDM is 2 –3 atoms in an analyzed volume (Watanabe and Williams, 1999). The STEM was operated at 300 kV with an incident probe size of , 1.6 nm (full-width at tenth maximum) and a probe current of , 0.5 nA. The X-ray maps of the Mn Ka peak and background intensities were gathered in 128 £ 128 pixels with a dwell time of 0.2 s (total acquisition time: , 1 h with dead time) by the simple energy window method and then the background intensity was subtracted from the peak map. Fig. 1(a) shows an X-ray spectrum measured from the Cu – 0.98 wt% Mn thin specimen at , 50 nm. The shadowed areas in the spectrum represent the energy windows for the Mn Ka peak (5.89 keV) and the backgrounds (5.58 and 6.71 keV). In this study, the width of the energy window was set to 180 eV, corresponding to about 1.2 times the fullwidth at half maximum. The magnification for mapping was carefully chosen to accomplish oversampling. The size of a single pixel in each map was 1.25 £ 1.25 nm2 which is smaller than the incident beam diameter. More details of the experimental conditions for X-ray mapping can be found elsewhere (Williams et al., 1998; Carpenter et al., 1999). The specimen thickness at each individual measured area was determined by the z-factor method (Watanabe et al., 1996). The z-factor method can provide specimen thickness
at the measured point, from X-ray intensities of Mn Ka and Cu Ka lines. The EF-TEM elemental maps were obtained in a JEM2010FEF at Kyushu University equipped with an in column omega-type energy filter. Maps were recorded by a Gatan MSC-794 1k slow-scan CCD camera, binning 8 £ 8 pixels together to increase the intensity of the map. So, the acquired maps are 128 £ 128 pixels with a single pixel dimension of 0.9 £ 0.9 nm2 (which closely matches that of the XEDS maps). It should be noted that the readout value from the CCD camera (even after corrections of the gain variation and the dark current) is not the actual number of electrons. To calculate spectral SNR values and compare them with XEDS results fairly, the number of electrons detected by the CCD camera should be used instead of the simple CCD readout values. In this study, the conversion factor from the CCD readout to the number of electrons was determined by comparing the readout value from the CCD camera with the incident beam current directly measured by a Faraday cap in the instrument. The conversion factor is 1.22 electrons/count in this CCD camera. The Mn L2;3 edge map was obtained at 200 kV with an incident electron current of , 3.5 nA at the CCD camera, which is close to the highest illumination condition for in this instrument. For background subtraction, the three-window method (e.g. Egerton, 1996) was applied. Each map was recorded for 200 s and hence the total acquisition time becomes 800 s because the dark current measurement takes the same acquisition time as the image. An EELS spectrum around the Mn L2;3 edge taken from the Cu – 0.98 wt% Mn thin specimen at , 50 nm is shown in Fig. 1(b). The energy windows (30 eV) for the three-window method were selected at 585 and 615 eV for the pre-edge images and 655 eV for the post edge image. In EF-TEM elemental mapping, the objective-aperture size is one of the key parameters since not only the spatial resolution but also the measured map intensity (hence the SNR) are strongly dependent on the collection angle, b: In general, the spatial resolution can be maximized at a certain objective-aperture
Fig. 1. (a) An XEDS spectrum and (b) an EELS spectrum measured from the Cu–0.98 wt% Mn specimen at ,50 nm. The energy windows for elemental mapping are described in both the spectra.
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size depending on operating conditions such as the accelerating voltage, the slit width for elemental mapping, the chromatic aberration coefficient, etc. (Berger and Kohl, 1993; Krivanek et al., 1995; Botton and Phaneuf, 1999; Omura et al., 2002) and the map intensity increases as the objective-aperture size increases (Berger and Kohl, 1993; Moore et al., 1999). As mentioned in Section 2, the SNR value may be degraded as the signal intensity reduces in an image with extremely weak signal intensities. In this study, the objective-aperture size of 15.4 ^ 1.5 mrad, which is slightly larger than the optimum aperture size to achieve the highest spatial resolution (Omura et al., 2002), was employed to increase the signal intensity in elemental maps in spite of sacrificing the spatial resolution. The specimen thickness for the EF-TEM technique at the analyzed region was measured by the log-ratio method (Egerton, 1996) with the experimentally determined meanfree path (l ¼ 106:3 ^ 4:1 nm).
4. Results 4.1. STEM-XEDS mapping The Mn maps from STEM-XEDS were obtained by using the energy window method (Williams and Carter, 1996). The background intensities were estimated by averaging two background intensities at lower and higher energy regions around the Mn Ka peak, as shown in Fig. 1(a). Then the averaged background intensity was subtracted from the peak map. Fig. 2 shows the Mn Ka maps (a: IMn ) and the corresponding background maps (b: BMn ) from the 5% Mn specimen, measured at several thickness regions. The intensity of the Mn map simply increases as the specimen thickness increases and the distribution of the Mn intensity seems homogeneous. In comparison with the intensity in the corresponding background maps, the intensity of the IMn map is much higher. Using the Mn Ka maps and the corresponding background maps, the spectral SNR was determined. Fig. 3 shows
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the spectral SNR of (a) 5% Mn and (b) 1% Mn calculated from Eq. (4) with DQE ¼ 1 and h ¼ 2; plotted against the specimen thickness. The three horizontal solid lines represent the confidence limits of 1s; 2s and 3s; as described in the previous sections. For comparison, the Rose criterion, which represents SNR ¼ 5, is also drawn as a dashed line. In Fig. 3, the determined SNR values are plotted with different gray levels, corresponding to the values of the confidence limit (below 1s : black; between 1s and 2s : dark gray, between 2s and 3s : light gray and above 3s : white). The notations of 1 £ 1, 2 £ 2 and 4 £ 4 in Fig. 3 indicate the SNR values calculated from a single pixel (1.25 £ 1.25 nm2), from binned 2 £ 2 pixels (2.50 £ 2.50 nm2) and from binned 4 £ 4 pixels (5.00 £ 5.00 nm2), respectively, and the error bars indicate the 99% confidence limit ð^3sÞ: As shown in Fig. 3, the spectral SNR increases as the specimen thickness increases since the signal intensities are higher at thicker regions. Furthermore, the SNR value can be improved by adding several pixels together at the expense of the spatial resolution. In the 5% Mn specimen, the measured SNR value based on the single pixel data reaches the 1s criterion at t . 20 nm and finally meets 3s at t . 110 nm. When the intensity is binned together in 2 £ 2 pixels, the SNR value passes the 3s criterion at t . 40 nm. The SNR value from the 1% Mn specimen never satisfies even the 1s criterion with the single pixel data in the thickness range in this study. By binning 4 £ 4 pixels together, the SNR for the 1% Mn specimen can exceed 1s at t . 10 nm and 3s at t . 50 nm. Even by binning 2 £ 2 pixels, SNR passes 1s at t . 30 nm but never meets 2s in this thickness range. To obtain reasonable signals from lower amounts of elements, therefore, the spatial resolution needs to be degraded either by adding pixels or by measuring from thicker regions (which again degrades the spatial resolution due to beam broadening). 4.2. EF-TEM mapping Several Mn L2;3 edge maps obtained from the 5% Mn specimen by the EF-TEM technique are shown in Fig. 4(a).
Fig. 2. (a) The Mn Ka peak maps and (b) the corresponding background maps from the Cu –4.93 wt% Mn specimen at several thicknesses, obtained by STEMXEDS in the VG HB 603 STEM.
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Fig. 3. The spectral SNR determined from the Mn Ka peak and the corresponding background maps with DQE ¼ 1 and h ¼ 2; plotted as a function of the specimen thickness: (a) the Cu –4.93 wt% Mn thin specimen and (b) the Cu –0.98 wt% Mn thin specimen. The curved lines indicate the results of polynomial fitting of the data. The three horizontal solid lines represent 1s; 2s and 3s from the bottom and the horizontal dashed line indicates the Rose criterion. The error bars represent the 99% confidence limit ð^3sÞ:
In Fig. 4, the corresponding background maps determined by the three-window are also shown in Fig. 4(b). It should be mentioned that the actual number of electrons were used for all the results from EF-TEM mapping, instead of using the CCD readout count. So, the gray scale in Fig. 4 corresponds to the number of electrons (however, the term of ‘intensity’ is still used in this study to avoid any confusion). In contrast to the STEM-XEDS maps, signal intensities are much lower than the backgrounds and the distributions of signal intensity are much noisier, despite the fact that signal intensities in the EF-TEM maps (at the corresponding thickness regions) are much higher than in the XEDS maps. These intensity fluctuations in the Mn L2;3 edge maps may be caused by diffraction contrast (Reimer, 1995). More importantly, the signal intensity of the Mn map at 81 nm is higher than that at 113 nm, as shown in Fig. 4. This thickness dependence of the signal intensity is not shown in the XEDS map, either. The decrease of the signal
intensity in the EF-TEM maps is due to plural scattering (Egerton, 1996). As shown in Fig. 4, in the EELS-based approaches background intensities are much higher than signal intensities from low concentration of elements. So, the influence of the background intensities on the analytical sensitivity can be more significant. Fig. 5 shows the spectral SNR of the (a) 5% Mn and (b) 1% Mn specimens with the same format as Fig. 3, calculated from the Mn L2;3 edge and the corresponding background maps using Eq. (4). In this calculation, DQE was set to 0.6 (Zuo, 1996) and the h parameter was evaluated as 8.22 using Eq. (3) with the energy window setting for the Mn L2;3 edge as described previously. In Fig. 5, the notations of 1 £ 1, 2 £ 2, 4 £ 4 and 8 £ 8 indicate the SNR values calculated from a single pixel (0.90 £ 0.90 nm 2), from binned 2 £ 2 pixels (1.80 £ 1.80 nm 2), from binned 4 £ 4 pixels (3.60 £ 3.60 nm 2), and from binned 8 £ 8 pixels
Fig. 4. (a) The Mn L2;3 edge maps and (b) the corresponding background maps from the Cu –4.93 wt% Mn specimen at several thicknesses, obtained by EFTEM in the JEM-2010F EF-TEM.
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Fig. 5. The spectral SNR determined from the Mn L2;3 edge and the corresponding background maps with DQE ¼ 0.6 and h ¼ 8:22; plotted as a function of the specimen thickness: (a) the Cu –4.93 wt% Mn specimen and (b) the Cu–0.98 wt% Mn specimen. The curved lines indicate the results of polynomial fitting of the data.
(7.20 £ 7.20 nm2). The spectral SNR from the EF-TEM elemental maps has a different thickness dependence to the XEDS elemental maps. That is, SNR is maximized at , 50 nm ð, 0:5lÞ for 5% Mn and around 20 – 30 nm ð0:2 – 0:3lÞ for 1% Mn. This thickness dependence of SNR has also been reported for EELS spectra (Leapman, 1992; Egerton, 1996). This effect arises because the signal intensity does not linearly increase as thickness increases due to a drastic increase in the background intensity from plural scattering. So, there is an optimum thickness to maximize SNR in EF-TEM mapping. In both the specimens, SNR never passes 1s without binning. By binning several pixels together, the SNR value is improved, e.g. results by 2 £ 2 binning and 4 £ 4 binning reach 2s between 20 and 100 nm and 3s between 30 and 70 nm, respectively, for the 5% Mn specimen. Furthermore, the peak position of the SNR value is not affected by pixel binning. In the 1% Mn specimen, the spectral SNR data even from 8 £ 8 binned pixels cannot reach 3s although the results can be improved by binning pixels. Since spectral SNR peaks at a certain thickness range, opportunities to detect elements with lower composition in the EF-TEM mapping approach will be
enhanced by exploring relatively thinner regions instead of thicker regions in contrast to XEDS mapping.
5. Discussion 5.1. Comparison of spectral SNR in STEM-XEDS and EF-TEM mapping For comparison, the spectral SNR results of a single pixel (1 £ 1) in the STEM-XEDS (Fig. 3) and EF-TEM maps (Fig. 5) were re-plotted together in Fig. 6. If the results from the single pixels are compared, the XEDS technique provides higher spectral SNR over all the thickness ranges for both specimens in typical acquisition conditions. In the total acquisition time, STEM-XEDS mapping is , 4 £ longer than EF-TEM mapping (STEM-XEDS: , 1 h, EFTEM: 800 s). However, these results should be compared at the same electron dose. In STEM-XEDS mapping, the total incident dose is , 6.2 £ 108 electrons in each pixel with the beam current of 0.5 nA for the dwell time of 0.2 s. On the other hand, the total dose can be calculated as about
Fig. 6. Comparison of the spectral SNR of the STEM-XEDS and the EF-TEM maps: (a) the Cu–4.93 wt% Mn specimen and (b) the Cu–0.98 wt% Mn specimen. The spectral SNR values determined from the single pixel shown in Figs. 3 and 5 are re-plotted with open symbols. The closed symbols indicate the spectral SNR values of the EF-TEM maps adjusted to the same electron dose as the STEM-XEDS maps.
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2.5 £ 108 electrons for the EF-TEM approach, by assuming that the incident beam current (3.5 nA) homogeneously illuminates 128 £ 128 pixels (, 2.0 £ 1024 nA per pixel) for 200 s. So, the electron dose per pixel in STEM-XEDS mapping is still , 2.5 times higher than that in EF-TEM mapping. The closed symbols in Fig. 6 indicate the spectral SNR values from the EF-TEM maps adjusted to the same electron dose as the STEM-XEDS maps. The adjusted SNR values from the EF-TEM maps are as high as those from the XEDS maps in the thickness range below 30 nm (which corresponds to , 0:3l) for both the specimens. However, the STEM-XEDS mapping becomes more sensitive as the specimen thickness increases above the value which provides the maximum SNR in EF-TEM mapping. Leapman and Hunt (1991) compared the detectability limit of both techniques theoretically and experimentally by using only small amounts of elements on thin carbon support films. They concluded that the EELS technique has better performance in detection of trace amounts for light elements (atomic number , 10) and for several transition elements (atomic number , 25) if L edges are used. As shown in Fig. 6, however, the analytical sensitivities of both the mapping approaches are almost same in thin regions (,, 0:3l and the STEM-XEDS technique becomes more sensitive as the specimen thickness increases. The major reason for the difference in the results of the analytical sensitivity is the difference in the type of specimens. In contrast to the thin carbon films (Leapman and Hunt, 1991), regular self-supporting alloy thin films were used in this study, and such thin films generate more background intensities. Therefore, the higher background intensity in the Cu – Mn specimens degrades the spectral SNR in the EF-TEM maps. As a spectrometry technique, the signal-collection capability of the EELS-based approach is essentially higher than that of XEDS. There are two major factors that may degrade the SNR of EF-TEM maps, which do not appear in the regular EELS spectrum. As shown in Fig. 2(a), the intensity distribution of the STEM-XEDS elemental maps seems very homogeneous. Conversely, the EF-TEM elemental maps show more fluctuations despite the maps being much more intense, as shown in Fig. 4(a). These intensity fluctuations in the EF-TEM maps are caused by diffraction contrast. Since the objective-aperture is required to maintain high spatial resolution in EF-TEM mapping, the contributions of the diffraction contrast to the elemental maps are unavoidable in crystalline materials. Obviously, the diffraction contrast degrades the SNR of the elemental maps. The second factor that degrades the sensitivity of the EFTEM maps is the background subtraction method. In EFTEM mapping, the spectral SNR is governed by the background term in Eq. (4). So, if the background term including the h parameter can be reduced, the spectral SNR is improved. In this study, the three-window method was applied for background subtraction. This three-window
method is one of the most popular approaches for EF-TEM mapping but one of the worst approaches to subtract the background from EELS spectra because the background intensity is extrapolated from two background regions below the edge by fitting a power-law function. Since the two parameters of the power-law function are determined from only two background intensities, any fluctuations in intensities of the two backgrounds can introduce serious errors in the extrapolated background. The errors that arise from background subtraction can be reduced by applying the EF-TEM spectrum-imaging method, in which a series of energy-loss images is recorded with a much narrower slit width around the inner-shell edge of interest and then the power-law fit is applied using multiple-backgrounds just as in the regular background subtraction for a spectrum (Ko¨rtje, 1994; Mayer et al., 1997; Plitzko and Mayer, 1999; Bentley et al., 2001; Thomas and Midgley, 2001). Obviously, the accuracy of the background subtraction can be significantly improved (and hence the h value can be reduced), by applying multiple-background windows instead of two windows. In fact, the SNR of a Cu elemental map was improved from 2.3 to 4.6 by applying the EF-TEM spectrum-imaging method instead of the three-window method (Thomas and Midgley, 2001). In addition to those degrading factors, there is another possible disadvantage in EF-TEM mapping. In this study, the EF-TEM maps were obtained with almost maximum illumination conditions in the system for relatively long acquisition time (200 s for each image, 800 s for total). Since the illumination is already maximized, increase of the acquisition times by , 2.5 £ is the only way to obtain the same electron dose as the STEM-XEDS maps. Thus, 500 s would be required for each image and 2000 s for total acquisition. In practice, however, it is not practical to obtain the elemental maps with such acquisition in EF-TEM, mainly because of spatial drift, energy drift and current drift. Among these drifts, the spatial drift can be the most crucial. However, the current version of EF-TEM control software does not have the capability to correct the spatial drifts when a single image is been recorded. 5.2. Evaluation of practical detectability limit from spectral SNR The detectability limits in terms of the MMF or the MDM can be estimated theoretically via a number of models proposed both for XEDS (Ziebold, 1967; Joy and Maher, 1977) and EELS (Colliex et al., 1989; Egerton, 1996). These theoretical approaches must take into account the signal generation and the detection efficiency in specific instruments. Unfortunately, because there are still uncertainties in cross-sections for the signal generation and it is not very easy to evaluate spectrometer efficiencies, the detectability limits determined theoretically may result in over and/or underestimation of the experimental values. Therefore, a simple approach to evaluate the detectability
M. Watanabe et al. / Micron 34 (2003) 173–183
limits from measured signal intensities will be described in this section. If it is assumed that the net signal intensity of a minor element from a specimen is directly proportional to the composition of the element, a value of the measured signal intensity divided by the compositional fraction (weight fraction or atomic fraction) corresponds to the signal intensity from the pure element. Since the signal intensity normalized by the compositional fraction becomes constant in the same experimental conditions, the following equation holds I Is ¼ s;min C CMMF
ð6Þ
where C is the weight fraction of the minor element in the specimen and Is;min and CMMF are the minimum signal intensity detectable and the corresponding weight fraction (i.e. MMF), respectively. Therefore, the MMF value of the minor element can be determined using a measured signal intensity from a specimen with known composition, if Is;min is known: CMMF ¼
Is;min C Is
ð7Þ
It should be mentioned that the above equation applies only when the difference between CMMF and C is relatively small, experimental conditions including the specimen thickness are similar and atomic numbers of the minor and major elements are similar. So, the Mn signals from the Cu – Mn specimens used in this study are ideal to evaluate the detectability limits using Eq. (7). The key to evaluate the CMMF values from Eq. (7) is determination of Is;min : This term can be derived from Eq. (4): 2
Is;min ¼
4
2
ðSNRÞ þ ½ðSNRÞ þ 4ðDQEÞðSNRÞ hIb 2ðDQEÞ
which corresponds to 6 and 38 counts for the 1s and 3s definition, respectively, even if there is no background and DQE ¼ 1. By substituting Eq. (8) into Eq. (7), the detectability limit CMMF can be estimated from measured signal and background intensities with a selection of the appropriate SNR value: CMMF ¼
ðSNRÞ2 þ ½ðSNRÞ4 þ 4ðDQEÞðSNRÞ2 hIb 1=2 C 2ðDQEÞIs
ð8Þ
Note that Eq. (8) is equivalent to the expression derived by Trebbia (1988) when DQE ¼ 1. According to Eq. (9), the minimum signal intensity should be at least (SNR)2,
ð9Þ
Fig. 7 shows the CMMF value calculated using a single pixel data of (a) STEM-XEDS and (b) EF-TEM maps obtained from the 1% and 5% Mn specimens, plotted against specimen thickness. The CMMF values were determined with h ¼ 2 and DQE ¼ 1 for the STEMXEDS results and h ¼ 8:22 and DQE ¼ 0.6 for the EFTEM results, respectively. The CMMF can be defined with a selection of the SNR value. So, two definitions of the CMMF values with SNR ¼ 2.4 ð1sÞ and 6.2 ð3sÞ are shown in Fig. 7. The CMMF values from XEDS maps are improved as thickness increases since the signal intensity increases. The results evaluated from the two different specimens are superimposed, which implies that the assumptions for Eq. (9) described above are also appropriate for XEDS data. The CMMF values evaluated with the 3s confidence limit are about five times higher than those with the 1s limit. In the range of the specimen thickness . , 100 nm, the evaluated MMF can reach to about 1 wt% in the 1s definition and to 5 wt% in the 3s definition, respectively. Note that the detectability limit for the XEDS signal is well defined as (Romig and Goldstein, 1979; Michael, 1987; Watanabe and Williams, 1999): CMMF ¼
1=2
181
3ð2Ib Þ1=2 C Is
ð10Þ
In comparison with the CMMF values from Eq. (9) in the XEDS case (h ¼ 2 and DQE ¼ 1), Eq. (10) produces slightly lower values than those in the 1s confidence limit although Eq. (10) is defined as the 3s confidence limit.
Fig. 7. The MMF values evaluated using Eq. (9) for (a) STEM-XEDS maps and (b) EF-TEM maps plotted against the specimen thickness. The MMF values were calculated from the measured intensities at the single pixel in the 1 and 5% Mn specimens for two statistical criteria (1s and 3s confidence limits).
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Therefore, the MMF definition based on the SNR is more severe than the conventional criterion for XEDS. For EF-TEM mapping, conversely, the CMMF values slightly degrade with an increase in specimen thickness as shown in Fig. 7(b). Obviously, the higher background intensity causes this degradation of MMF for EF-TEM mapping. This thickness dependence of CMMF indicates that there may be a chance to detect minor elements by exploring relatively thinner regions in the EF-TEM mapping approach. In contrast to the results evaluated from the XEDS maps, the CMMF values from two different specimens vary in EF-TEM mapping: CMMF from the 5% Mn specimen is better than that from the 1% Mn specimen. As described above, Eq. (9) can be wrong when the estimated composition range is too far from the composition of the minor element. Therefore, the results from the 1% Mn specimen may be less reliable because the composition of the other specimen (5 wt%) is closer to the estimated CMMF values. In addition, the signal intensity is lower in the 1% Mn specimen. In the thickness range below , 40 nm, the MMF value evaluated from the 5% Mn specimen can be , 6 wt% in the 1s definition and , 20 wt% in the 3s definition in the acquisition conditions for EF-TEM mapping. Estimated CMMF values with the 1s and 3s confidence limits from the STEM-XEDS and EF-TEM maps of the 5% Mn specimen are plotted together in Fig. 8. To make fair comparison, the MMF values from the EF-TEM maps are adjusted to the same electron dose for STEM-XEDS mapping as in Fig. 6. EF-TEM mapping can be more sensitive than STEM-XEDS mapping up to a specimen thickness , 20– 30 nm in the 1s confidence limit and , , 50 nm in the 3s limit. However, as the specimen thickness increases, the XEDS maps provide better detectability limits. As mentioned above, elemental mapping by the EELS-based approaches should be performed in reasonably thin regions (e.g. , 0:3t=l) to improve the analytical sensitivity.
Fig. 8. Comparison of CMMF of STEM-XEDS and EF-TEM maps. For fair comparison, the results from EF-TEM mapping were adjusted to the same electron dose as the STEM-XEDS maps.
6. Conclusions In this study, the detectability limits of the EF-TEM and STEM-XEDS elemental maps from thin, homogeneous Cu – 0.98 ^ 0.34 wt% Mn and Cu –4.93 ^ 0.49 wt% Mn thin specimens were evaluated using the spectral SNR. In STEM-XEDS mapping, the SNR improves as the specimen thickness increases, since the signal intensity increases accordingly. Conversely, the SNR in EF-TEM mapping is maximized at a certain thickness. The analytical sensitivity of both mapping approaches was compared by using the MMF values, which were estimated from the measured signal and background intensities with a selection of the spectral SNR value. By comparing the two mapping techniques using estimated MMF, it is shown that the EFTEM mapping is more sensitive when the specimen is thinner than the peak thickness obtained from the SNR of EF-TEM maps. However, the sensitivity of STEM-XEDS mapping becomes higher as the specimen thickness increases in the Cu – Mn thin specimens. To detect trace amounts of elements, it is better to use thicker specimens ð., 0:3t=lÞ in STEM-XEDS mapping. Conversely, in EFTEM mapping, detection of trace amounts of elements is best achieved in thinner specimens ð,, 0:3t=lÞ:
Acknowledgements The authors acknowledge Dr M.G. Burke at BechtelBettis Labs. Inc. for useful discussions and DBW wishes to acknowledge the support of the National Science Foundation through grant DMR 0304738.
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M. Watanabe et al. / Micron 34 (2003) 173–183 Egerton, R.F., 1996. Electron Energy-Loss Spectroscopy in the Electron Microscope, second ed., Plenum Press, New York. Egerton, R.F., 1999. Spatial resolution of nanostructural analysis by electron energy-loss spectroscopy and energy-filtered imaging. J. Electron Microsc. 48, 711 –716. Joy, D.C., Maher, D.M., 1977. Sensitivity limits for thin specimen X-ray analysis. In: Johari, O., (Ed.), Scanning Electron Microscopy, vol. 1. IITRI, Chicago, IL, pp. 325 –334. Keast, V.J., Williams, D.B., 2000. Quantification of boundary segregation in the analytical electron microscope. J. Microsc. 199, 45–55. Ko¨rtje, K.-H., 1994. Image-EELS: simultaneous recording of multiple electron energy-loss spectra from series of electron spectroscopic images. J. Microsc. 174, 149–159. Kothleitner, G., Hofer, F., 1998. Optimization of the signal to noise ratio in FETEM elemental maps with regard to different ionization edge types. Micron 29, 349–357. Krivanek, O.L., Kundmann, M.K., Kimoto, K., 1995. Spatial resolution in EFTEM elemental maps. J. Microsc. 180, 277–287. Leapman, R.D., 1992. EELS quantitative analysis. In: Disko, M.M., Ann, C.C., Fultz, B. (Eds.), Transmission Electron Energy Loss Spectrometry in Materials Science, Minerals, Metals & Materials Society, Warrendale, PA, pp. 47–83. Leapman, R.D., Hunt, J.A., 1991. Comparison of detection limits for EELS and EDXS. Microsc. Microanal. Microstruct 2, 231– 244. Lyman, C.E., Goldstein, J.I., Williams, D.B., Ackland, D.W., Von Harrach, S., Nicholls, A.W., Statham, P.J., 1994. High-performance X-ray detection in a new analytical electron microscope. J. Microsc. 176, 85–98. Mayer, J., Eigenthaler, U., Plitzko, J.M., Dettenwanger, F., 1997. Quantitative analysis of electron spectroscopic image series. Micron 28, 361 –370. Michael, J.R., 1987. In: Williams, D.B., (Ed.), Practical Analytical Electron Microscopy in Materials Science, second ed., Philips Electron Optics Publishing Group, Mahwah, NJ, p. 83. Moore, K.T., Howe, J.M., Veblen, D.R., Murray, T.M., Stach, E.A., 1999. Analysis of electron intensity as a function of aperture size in energyfiltered transmission electron microscope imaging. Ultramicroscopy 80, 221–236. Natusch, M.K.H., Humphreys, C.J., Menon, N., Krivanek, O.L., 1999. Experimental and theoretical study of the detection limits in electron energy-loss spectroscopy. Micron 30, 173–183. Omura, T., Watanabe, M., Tomokiyo, Y., 2002. Quantitative evaluation of zero-loss and core-loss images by using EF-TEM. J. Electron Microsc. 51 (Suppl.), S87–S96. Pearson, E.S., Hartley, H.O., 1976. Biometrika Tables for Statisticians, vol. II. Biometrika Trust, London.
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Plitzko, J.M., Mayer, J., 1999. Quantitative thin film analysis by energy filtering transmission electron microscopy. Ultramicroscopy 78, 207– 219. Reimer, L., 1995. Electron spectroscopic imaging. In: Reimer, L., (Ed.), Energy-Filtering Transmission Electron Microscopy, Springer, Berlin, pp. 347–400. Romig, A.D. Jr, Goldstein, J.I., 1979. Detectability limit and spatial resolution in STEM X-ray analysis: application to Fe–Ni alloys. In: Newbury, D.E., (Ed.), Microbeam Analysis, 1979, San Francisco Press, San Francisco, CA, pp. 124–156. Rose, A., 1948. Television pickup tubes and the problem of vision. Adv. Electron. 1, 131– 166. Rose, A., 1970. Quantum limitations: to vision at low light levels. Image Technol. 12, 13– 15. see also pp. 30–31. Thomas, P.J., Midgley, P.A., 2001. Image-spectroscopy. I. The advantages of increased spectral information for compositional EFTEM analysis. Ultramicroscopy 88, 179 –186. Tixier, R., 1979. Microanalyse X des lames minces en microscopie electronique. J. Microsc. Spectrosc. Electron 4, 295–304. Trebbia, P., 1988. Unbiased method for signal estimation in electron energy loss spectroscopy, concentration measurements and detection limits in quantitative microanalysis: method and programs. Ultramicroscopy 24, 399– 408. Watanabe, M., Williams, D.B., 1999. Atomic-level detection by X-ray microanalysis in the analytical electron microscope. Ultramicroscopy 78, 89–101. Watanabe, M., Horita, Z., Nemoto, M., 1996. Absorption correction and thickness determination using z factor in quantitative X-ray microanalysis. Ultramicroscopy 65, 187 –198. Williams, D.B., Carter, C.B., 1996. Transmission Electron Microscopy, Plenum Press, New York. Williams, D.B., Watanabe, M., Carpenter, D.T., 1998. Thin film analysis and chemical mapping in the analytical electron microscope. Mikrochim. Acta 15 (Suppl.), 49 –57. Williams, D.B., Papworth, A.J., Watanabe, M., 2002. High resolution X-ray mapping in the STEM. J. Electron Microsc. 51 (Suppl.), S113–S126. Wittig, J.E., Al-Sharab, J.F., Bentley, J., Evans, N.D., Nolan, T.P., Sinclair, R., 2001. Quantitative EFTEM of Cr grain boundary segregation in CoCrTa. Microsc. Microanal. 7 (Suppl. 2), Springer, New York, pp. 298– 299. Ziebold, T.O., 1967. Precision and sensitivity in electron microprobe analysis. Anal. Chem. 39, 858–861. Zuo, J.M., 1996. Electron detection characteristics of slow-scan CCD camera. Ultramicroscopy 66, 21–33.
Comparison of detectability limits for elemental mapping by EF-TEM and STEM-XEDS Masashi Watanabea,*, David B. Williamsa, Yoshitsugu Tomokiyob b
a Department of Materials Science and Engineering, Lehigh University, Bethlehem, PA 18015, USA Department of Engineering Science for Electronics & Materials, Kyushu University, Kasuga 816-8580, Japan
Abstract The analytical sensitivity in terms of the signal-to-noise ratio (SNR) was investigated for elemental mapping by a transmission electron microscope equipped with an energy filter (EF-TEM) and a scanning transmission electron microscope with an X-ray energy dispersive spectrometer (STEM-XEDS). To compare the detectability limits of the elemental maps by the two techniques, homogeneous Cu– 0.98 ^ 0.34 wt% Mn and Cu – 4.93 ^ 0.49 wt% Mn thin specimens were used. Elemental maps can be considered as either an image or a spectrum. Therefore, the detectability limits of the elemental maps were characterized by the spectral SNR. To evaluate the detectability limits of the elemental maps with statistical confidence limits such as 1s; 2s and 3s; the SNR values were reviewed from the statistical point of view. In STEM-XEDS mapping, the spectral SNR values improve as the specimen thickness increases since the signal intensity increases. Conversely, the spectral SNR in EF-TEM mapping is maximized at a certain thickness and then reduces as the thickness increases. To compare the two mapping techniques with regard to the analytical sensitivity, a method to estimate the minimum mass fraction (MMF) from measured signal and background intensities was developed. In this experimental approach, the MMF value can be evaluated by selecting the appropriate SNR value corresponding to the statistical confidence limits. In comparing the estimated MMF values from the two mapping approaches, EF-TEM mapping can be more sensitive than STEM-XEDS mapping up to specimen thicknesses , 20 – 30 nm in the 1s confidence limit and ,, 50 nm in the 3s limits. However, as the specimen thickness increases, the XEDS maps provide better detectability limits in the Cu– Mn dilute alloy specimens. q 2003 Elsevier Ltd. All rights reserved. Keywords: Analytical sensitivity; Spectral signal-to-noise ratio; Confidence limits for detection; Minimum mass fraction
1. Introduction The elemental mapping approach can be the best way to analyze nano-scale features in materials such as fine precipitates and interfaces/boundaries, since two dimensional fluctuations in composition around such small features, which may be easily missed by point or line-scan analyses, can be revealed in images of elemental distributions. Currently, such elemental distributions can be obtained by a transmission electron microscope equipped with an energy filter (EF-TEM), or a scanning transmission electron microscope with an X-ray energy dispersive spectrometer (STEM-XEDS) and/or an electron energyloss spectrometer (STEM-EELS). The spatial resolution of the fixed beam EF-TEM technique can reach sub-nanometer ranges and the major sources of degradation of the spatial resolution are the chromatic aberration due to the width of the energy-selecting slit (Berger and Kohl, 1993; Krivanek * Corresponding author. 0968-4328/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0968-4328(03)00028-3
et al., 1995; Botton and Phaneuf, 1999; Egerton, 1999; Bentley et al., 2001; Wittig et al., 2001; Omura et al., 2002). The spatial resolution of the STEM-based techniques is mainly governed by the focused probe size and the beam broadening in the specimen. So, there are basically no major differences in the spatial resolution of the STEM-based techniques between the mapping mode and the point/line analysis modes. When a STEM equipped with a fieldemission gun source is used, sub-nanometer spatial resolution is also achievable in the STEM-EELS technique, as demonstrated by Browning et al. (1997). In the STEMXEDS technique, conversely, the spatial resolution reaches a few nanometers since much larger beam currents which enlarge the incident probe sizes are required to gather sufficient signal intensity within a reasonable acquisition time (Carpenter et al., 1999; Keast and Williams, 2000; Williams et al., 2002). Although the spatial resolution of elemental mapping can reach the sub-nanometer level in EELS-based mapping and a few nanometers in STEM-XEDS mapping, the analytical
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sensitivity in elemental mapping may become worse than that of conventional spot analysis and/or line scan approaches. This is true especially in the STEM-based techniques since the acquisition time at a single pixel (dwell time) is much shorter than for the point analysis (typically , 60– 100 s/total acquisition) or line-scan analysis approach (typically , 3 –20 s/individual acquisition). In principle, the acquisition time for elemental mapping in either the EFTEM or the STEM-based methods can simply be increased. However, total mapping times can take many minutes or hours, which are significantly longer than a conventional point analysis or line profiling and this may provide more chances for contamination build-up and/or irradiation damage. In addition, the longer acquisition could cause many kinds of drifts during mapping, e.g. spatial drift, energy drift, beam current drift, etc. since the long-term stability is not sufficient even in current instruments. It should be noted that some of these drifts are now correctable during acquisition or post processing. However, it is not very easy to cure all of drifts in elemental mapping even using current software. Furthermore, one of the major limitations in elemental mapping either by EF-TEM or by STEM is that obtainable net signal intensities are not significant enough. The EELS signals can be measured with great collection efficiency. However, most EELS signals consist of huge backgrounds and net signals from characteristic edges are, relatively, much lower than the background. For XEDS, although the characteristic peak signals are more intense than the background, the measured signals are extremely low due to the poor collection efficiency. Therefore, the intensity fluctuation in the elemental maps may not reflect the compositional fluctuations but could be lost within the statistical noise. In this study, comparative elemental maps of dilute amounts of Mn in Cu have been taken by EF-TEM and STEM-XEDS, to analyze the detection sensitivities of elemental mapping, with statistical certainty. In order to evaluate the detectability limits of elemental maps, the standard methods were applied in elemental mapping by two techniques: the simple energy window method for STEM-XEDS mapping and the three-window method for EF-TEM mapping. In addition, only the specimen thickness and the binning pixel number were changed as the experimental parameters, since these parameters are also related to the spatial resolution of analysis. However, there are also several experimental parameters, which can affect the detectability limit, such as the probe current, the probe size and the dwell time for STEM-XEDS and the illumination current, the objective-aperture size and the acquisition time for EF-TEM. In addition, the energy window setting also affects the detectability limit seriously, especially when elemental mapping is conducted for minor amounts (, 10 wt%) of elements. In this study, these parameters, except for the specimen thickness and the binning pixel number were fixed in order to simplify the relationship between the detectability limits and the spatial
resolution. To investigate the detectability limit in elemental mapping completely, these experimental parameters should also be taken into account.
2. Definition of evaluation parameters for detectability limits of elemental maps Basically, an elemental map is an image with a relatively low signal intensity. Therefore, in experimental data, useful signals can be hidden by the contributions of systematic and/or random noises and analytical sensitivity can be degraded. So, in order to evaluate the detectability from experimental data, especially for EELS spectra and for EFTEM maps, the signal-to-noise ratio (SNR) has usually been applied (Egerton, 1996). If the SNR value is significant, i.e. higher than a certain threshold value, the signal of interest (in the case of an EELS spectrum, the edge intensity above the background) is judged as detectable. This concept of the SNR is originally based on Rose’s work (Rose, 1948, 1970): Rose defined the SNR to evaluate the visibility (not detectability) of images with relatively low signals and proposed that SNR ¼ 5 was a sufficient threshold limit to distinguish the signal from noise in an image. This limit is well known as the Rose criterion. In several studies, the SNR value was used as a figure of merit to optimize the microscope conditions for EF-TEM elemental mapping (Berger and Kohl, 1993; Berger et al., 1994; Kothleitner and Hofer, 1998; Moore et al., 1999). Obviously, SNR is one of the most suitable parameters to describe the detectability limits of elemental maps. However, several SNR values have been used as the threshold for detectability, e.g. SNR ¼ 5 (Rose criterion) (Berger and Kohl, 1993; Berger et al., 1994) or 3 (Trebbia, 1988; Colliex et al., 1989; Egerton, 1996), in previous studies. This inconsistency in the SNR value for detectability evaluation is mainly because the SNR value has not been defined with a certain statistical confidence level. Recently, SNR was reconsidered as a statistically meaningful measure for the detectability evaluation (Natusch et al., 1999). The definition of the SNR for elemental maps is briefly described below, based on a spectrometric approach, and the statistical description of SNR is also reviewed. Then, the detectability limits of the elemental maps will be discussed with statistical confidence limits. 2.1. Spectral SNR There are several ways to describe the SNR of elemental maps because the definition of the noise component varies. The noise can be defined by taking the square root of the variance of the signal as originally demonstrated for images by Rose (1948, 1970). However, the noise component in the elemental maps is affected not only by the variance of the net signal but also by any fluctuations in the background, since background subtraction is required. Therefore, uncertainties arising from background subtraction should be taken
M. Watanabe et al. / Micron 34 (2003) 173–183
into account for the SNR of elemental maps. Egerton (1996) defined the spectral SNR SNR ¼
Is ðIs þ hIb Þ1=2
ð1Þ
where Is and Ib are the signal and background intensities, respectively, and h is a dimensionless parameter associated with background subtraction and given as: h¼1þ
varðIb Þ Ib
ð2Þ
The value of h typically ranges between 2 and 30 depending on background fitting and energy regions (Kothleitner and Hofer, 1998), especially for XEDS h ¼ 2 (Trebbia, 1988; Colliex et al., 1989). For EF-TEM elemental mapping with the three-window background, subtraction of h is given as (Berger and Kohl, 1993) 3 E 2 ðEb1 þ Eb2 Þ=2 2 h¼ þ2 s ð3Þ 2 Eb2 2 Eb1 where Es ; Eb1 and Eb2 are the energy positions for the signal (post edge) window and the two background (pre-edge) windows, respectively. Note that Eq. (3) assumes only a small amount of extrapolation, i.e. Es q Es 2 Eb1 (Berger and Kohl, 1993). The spectral SNR defined in Eq. (1) only takes into account the generated signals. However, the detector (such as a CCD camera), which was used, for recording EF-TEM elemental maps may also introduce additional noise. Therefore, Eq. (1) should be modified using the signal and background intensities at each pixel, Is ðjÞ and Ib ðjÞ with consideration of the detector noise (Berger and Kohl, 1993): SNR ¼
ðDQEÞ1=2 kIs ðjÞl ½kIs ðjÞl þ hkIb ðjÞl1=2
ð4Þ
where DQE is the detector quantum efficiency. For the CCD camera, the DQE value was reported as , 0.6 at the incident beam energy of 200 keV (Zuo, 1996). In this study, this value was used to determine the spectral SNR for the EFTEM elemental maps. For STEM-XEDS elemental maps, it is assumed that DQE is unity. It should be noted that SNR ¼ 3 is preferably chosen as the threshold limit to judge the detectability in an EELS spectrum, instead of employing the Rose criterion. Since these SNR values were arbitrarily chosen, obviously there is no correlation between the SNR values and the statistical confidence limits to define the detectability limit. Therefore, the threshold SNR value for the detectability limit should be defined as a meaningful measure, in a statistical manner. 2.2. Statistical description of SNR for minor-element analysis The spectral SNR described in Eqs. (1) and (4) means that the signal in a spectrum is assumed to obey a Gaussian
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distribution. This is a reasonable assumption whenever signal intensities are high enough. However, this assumption may fail if the signal intensity becomes extremely low, e.g. analysis of minor elements in a specimen. This is because the signal intensity is always positive although the Gaussian distribution is defined in the infinite region (2 1 to þ 1) (Trebbia, 1988). Therefore, Tixier (1979) modified the criterion for minor-element analysis by introducing a non-central x2 distribution. Let r denote a normally distributed variable with a unit standard deviation and a zero mean, and then a random variable obeying the noncentral x2 distribution with a degree of freedom of one is expressed as (Pearson and Hartley, 1976)
x 02 ¼ ðr þ l1=2 Þ2
ð5Þ
where l is the non-centrality parameter and defined as (SNR)2 in this case (Tixier, 1979). So, the distribution is deviated from zero with a magnitude of (SNR). This concept was originally applied for XEDS (Tixier, 1979) and for EELS (Trebbia, 1988). When a minor element with lower composition is analyzed, two risks are always involved: the first-kind ðg1 Þ is the probability of concluding that the minor element is detected in spite of the absence of the elements at the analyzed point and the second-kind ðg2 Þ is the probability of concluding that the minor element is not detected while the element is actually present (Tixier, 1979). Recently, Natusch et al. (1999) evaluated both the risks from the non-central x2 probability density distribution as a function of SNR. Then, the confidence limits for SNR were derived by minimizing the sum of both the risks ðg1 þ g2 Þ; based on the regular Gaussian standard deviation. According to Natusch et al. (1999), the SNR values of 3 and 5 are equivalent to 82 and 98% of probability of detection, respectively. Let s denote the standard deviation of the regular Gaussian distribution. Then, the confidence limits of 68% ð^sÞ; 95% ð^2sÞ and 99% ð^3sÞ; which are commonly employed in error analysis, correspond to SNR ¼ 2.4, 4.3 and 6.2, respectively. It should be mentioned that these SNR values for the corresponding confidence limits can vary when only one of the two risks (most likely the g2 risk only) is taken into account, as noted by Natusch et al. (1999). However, it is still better to incorporate both risks when the detectability is estimated from the SNR.
3. Experimental In this study, homogeneous Cu – 0.98 ^ 0.34 wt% Mn (1% Mn) and Cu– 4.93 ^ 0.49 wt% Mn (5% Mn) thin specimens were used. The compositions of these alloys were determined from the bulk samples by using a JEOL superprobe 733 electron probe microanalyzer. The Cu – Mn system was originally employed for estimation of the minimum mass fraction (MMF) by Michael (1987). In our
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previous paper (Watanabe and Williams, 1999), several Cu – Mn thin specimens were also used to evaluate the analytical sensitivity of X-ray microanalysis in terms of the MMF and the minimum detectable mass (MDM). Since the Cu – Mn alloys can be homogenized via a standard diffusion anneal and there are no reports about the formation of fine-scale precipitates or clusters in this alloy system (Watanabe and Williams, 1999), it is assumed that any intensity fluctuations in the elemental maps are not caused by compositional differences at least. To acquire STEM-XEDS elemental maps, a VG HB 603 STEM at Lehigh University was used. This STEM is optimized for X-ray microanalysis with maximum X-ray collection efficiency (Lyman et al., 1994) and the analytical sensitivity in terms of the MDM is 2 –3 atoms in an analyzed volume (Watanabe and Williams, 1999). The STEM was operated at 300 kV with an incident probe size of , 1.6 nm (full-width at tenth maximum) and a probe current of , 0.5 nA. The X-ray maps of the Mn Ka peak and background intensities were gathered in 128 £ 128 pixels with a dwell time of 0.2 s (total acquisition time: , 1 h with dead time) by the simple energy window method and then the background intensity was subtracted from the peak map. Fig. 1(a) shows an X-ray spectrum measured from the Cu – 0.98 wt% Mn thin specimen at , 50 nm. The shadowed areas in the spectrum represent the energy windows for the Mn Ka peak (5.89 keV) and the backgrounds (5.58 and 6.71 keV). In this study, the width of the energy window was set to 180 eV, corresponding to about 1.2 times the fullwidth at half maximum. The magnification for mapping was carefully chosen to accomplish oversampling. The size of a single pixel in each map was 1.25 £ 1.25 nm2 which is smaller than the incident beam diameter. More details of the experimental conditions for X-ray mapping can be found elsewhere (Williams et al., 1998; Carpenter et al., 1999). The specimen thickness at each individual measured area was determined by the z-factor method (Watanabe et al., 1996). The z-factor method can provide specimen thickness
at the measured point, from X-ray intensities of Mn Ka and Cu Ka lines. The EF-TEM elemental maps were obtained in a JEM2010FEF at Kyushu University equipped with an in column omega-type energy filter. Maps were recorded by a Gatan MSC-794 1k slow-scan CCD camera, binning 8 £ 8 pixels together to increase the intensity of the map. So, the acquired maps are 128 £ 128 pixels with a single pixel dimension of 0.9 £ 0.9 nm2 (which closely matches that of the XEDS maps). It should be noted that the readout value from the CCD camera (even after corrections of the gain variation and the dark current) is not the actual number of electrons. To calculate spectral SNR values and compare them with XEDS results fairly, the number of electrons detected by the CCD camera should be used instead of the simple CCD readout values. In this study, the conversion factor from the CCD readout to the number of electrons was determined by comparing the readout value from the CCD camera with the incident beam current directly measured by a Faraday cap in the instrument. The conversion factor is 1.22 electrons/count in this CCD camera. The Mn L2;3 edge map was obtained at 200 kV with an incident electron current of , 3.5 nA at the CCD camera, which is close to the highest illumination condition for in this instrument. For background subtraction, the three-window method (e.g. Egerton, 1996) was applied. Each map was recorded for 200 s and hence the total acquisition time becomes 800 s because the dark current measurement takes the same acquisition time as the image. An EELS spectrum around the Mn L2;3 edge taken from the Cu – 0.98 wt% Mn thin specimen at , 50 nm is shown in Fig. 1(b). The energy windows (30 eV) for the three-window method were selected at 585 and 615 eV for the pre-edge images and 655 eV for the post edge image. In EF-TEM elemental mapping, the objective-aperture size is one of the key parameters since not only the spatial resolution but also the measured map intensity (hence the SNR) are strongly dependent on the collection angle, b: In general, the spatial resolution can be maximized at a certain objective-aperture
Fig. 1. (a) An XEDS spectrum and (b) an EELS spectrum measured from the Cu–0.98 wt% Mn specimen at ,50 nm. The energy windows for elemental mapping are described in both the spectra.
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size depending on operating conditions such as the accelerating voltage, the slit width for elemental mapping, the chromatic aberration coefficient, etc. (Berger and Kohl, 1993; Krivanek et al., 1995; Botton and Phaneuf, 1999; Omura et al., 2002) and the map intensity increases as the objective-aperture size increases (Berger and Kohl, 1993; Moore et al., 1999). As mentioned in Section 2, the SNR value may be degraded as the signal intensity reduces in an image with extremely weak signal intensities. In this study, the objective-aperture size of 15.4 ^ 1.5 mrad, which is slightly larger than the optimum aperture size to achieve the highest spatial resolution (Omura et al., 2002), was employed to increase the signal intensity in elemental maps in spite of sacrificing the spatial resolution. The specimen thickness for the EF-TEM technique at the analyzed region was measured by the log-ratio method (Egerton, 1996) with the experimentally determined meanfree path (l ¼ 106:3 ^ 4:1 nm).
4. Results 4.1. STEM-XEDS mapping The Mn maps from STEM-XEDS were obtained by using the energy window method (Williams and Carter, 1996). The background intensities were estimated by averaging two background intensities at lower and higher energy regions around the Mn Ka peak, as shown in Fig. 1(a). Then the averaged background intensity was subtracted from the peak map. Fig. 2 shows the Mn Ka maps (a: IMn ) and the corresponding background maps (b: BMn ) from the 5% Mn specimen, measured at several thickness regions. The intensity of the Mn map simply increases as the specimen thickness increases and the distribution of the Mn intensity seems homogeneous. In comparison with the intensity in the corresponding background maps, the intensity of the IMn map is much higher. Using the Mn Ka maps and the corresponding background maps, the spectral SNR was determined. Fig. 3 shows
177
the spectral SNR of (a) 5% Mn and (b) 1% Mn calculated from Eq. (4) with DQE ¼ 1 and h ¼ 2; plotted against the specimen thickness. The three horizontal solid lines represent the confidence limits of 1s; 2s and 3s; as described in the previous sections. For comparison, the Rose criterion, which represents SNR ¼ 5, is also drawn as a dashed line. In Fig. 3, the determined SNR values are plotted with different gray levels, corresponding to the values of the confidence limit (below 1s : black; between 1s and 2s : dark gray, between 2s and 3s : light gray and above 3s : white). The notations of 1 £ 1, 2 £ 2 and 4 £ 4 in Fig. 3 indicate the SNR values calculated from a single pixel (1.25 £ 1.25 nm2), from binned 2 £ 2 pixels (2.50 £ 2.50 nm2) and from binned 4 £ 4 pixels (5.00 £ 5.00 nm2), respectively, and the error bars indicate the 99% confidence limit ð^3sÞ: As shown in Fig. 3, the spectral SNR increases as the specimen thickness increases since the signal intensities are higher at thicker regions. Furthermore, the SNR value can be improved by adding several pixels together at the expense of the spatial resolution. In the 5% Mn specimen, the measured SNR value based on the single pixel data reaches the 1s criterion at t . 20 nm and finally meets 3s at t . 110 nm. When the intensity is binned together in 2 £ 2 pixels, the SNR value passes the 3s criterion at t . 40 nm. The SNR value from the 1% Mn specimen never satisfies even the 1s criterion with the single pixel data in the thickness range in this study. By binning 4 £ 4 pixels together, the SNR for the 1% Mn specimen can exceed 1s at t . 10 nm and 3s at t . 50 nm. Even by binning 2 £ 2 pixels, SNR passes 1s at t . 30 nm but never meets 2s in this thickness range. To obtain reasonable signals from lower amounts of elements, therefore, the spatial resolution needs to be degraded either by adding pixels or by measuring from thicker regions (which again degrades the spatial resolution due to beam broadening). 4.2. EF-TEM mapping Several Mn L2;3 edge maps obtained from the 5% Mn specimen by the EF-TEM technique are shown in Fig. 4(a).
Fig. 2. (a) The Mn Ka peak maps and (b) the corresponding background maps from the Cu –4.93 wt% Mn specimen at several thicknesses, obtained by STEMXEDS in the VG HB 603 STEM.
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Fig. 3. The spectral SNR determined from the Mn Ka peak and the corresponding background maps with DQE ¼ 1 and h ¼ 2; plotted as a function of the specimen thickness: (a) the Cu –4.93 wt% Mn thin specimen and (b) the Cu –0.98 wt% Mn thin specimen. The curved lines indicate the results of polynomial fitting of the data. The three horizontal solid lines represent 1s; 2s and 3s from the bottom and the horizontal dashed line indicates the Rose criterion. The error bars represent the 99% confidence limit ð^3sÞ:
In Fig. 4, the corresponding background maps determined by the three-window are also shown in Fig. 4(b). It should be mentioned that the actual number of electrons were used for all the results from EF-TEM mapping, instead of using the CCD readout count. So, the gray scale in Fig. 4 corresponds to the number of electrons (however, the term of ‘intensity’ is still used in this study to avoid any confusion). In contrast to the STEM-XEDS maps, signal intensities are much lower than the backgrounds and the distributions of signal intensity are much noisier, despite the fact that signal intensities in the EF-TEM maps (at the corresponding thickness regions) are much higher than in the XEDS maps. These intensity fluctuations in the Mn L2;3 edge maps may be caused by diffraction contrast (Reimer, 1995). More importantly, the signal intensity of the Mn map at 81 nm is higher than that at 113 nm, as shown in Fig. 4. This thickness dependence of the signal intensity is not shown in the XEDS map, either. The decrease of the signal
intensity in the EF-TEM maps is due to plural scattering (Egerton, 1996). As shown in Fig. 4, in the EELS-based approaches background intensities are much higher than signal intensities from low concentration of elements. So, the influence of the background intensities on the analytical sensitivity can be more significant. Fig. 5 shows the spectral SNR of the (a) 5% Mn and (b) 1% Mn specimens with the same format as Fig. 3, calculated from the Mn L2;3 edge and the corresponding background maps using Eq. (4). In this calculation, DQE was set to 0.6 (Zuo, 1996) and the h parameter was evaluated as 8.22 using Eq. (3) with the energy window setting for the Mn L2;3 edge as described previously. In Fig. 5, the notations of 1 £ 1, 2 £ 2, 4 £ 4 and 8 £ 8 indicate the SNR values calculated from a single pixel (0.90 £ 0.90 nm 2), from binned 2 £ 2 pixels (1.80 £ 1.80 nm 2), from binned 4 £ 4 pixels (3.60 £ 3.60 nm 2), and from binned 8 £ 8 pixels
Fig. 4. (a) The Mn L2;3 edge maps and (b) the corresponding background maps from the Cu –4.93 wt% Mn specimen at several thicknesses, obtained by EFTEM in the JEM-2010F EF-TEM.
M. Watanabe et al. / Micron 34 (2003) 173–183
179
Fig. 5. The spectral SNR determined from the Mn L2;3 edge and the corresponding background maps with DQE ¼ 0.6 and h ¼ 8:22; plotted as a function of the specimen thickness: (a) the Cu –4.93 wt% Mn specimen and (b) the Cu–0.98 wt% Mn specimen. The curved lines indicate the results of polynomial fitting of the data.
(7.20 £ 7.20 nm2). The spectral SNR from the EF-TEM elemental maps has a different thickness dependence to the XEDS elemental maps. That is, SNR is maximized at , 50 nm ð, 0:5lÞ for 5% Mn and around 20 – 30 nm ð0:2 – 0:3lÞ for 1% Mn. This thickness dependence of SNR has also been reported for EELS spectra (Leapman, 1992; Egerton, 1996). This effect arises because the signal intensity does not linearly increase as thickness increases due to a drastic increase in the background intensity from plural scattering. So, there is an optimum thickness to maximize SNR in EF-TEM mapping. In both the specimens, SNR never passes 1s without binning. By binning several pixels together, the SNR value is improved, e.g. results by 2 £ 2 binning and 4 £ 4 binning reach 2s between 20 and 100 nm and 3s between 30 and 70 nm, respectively, for the 5% Mn specimen. Furthermore, the peak position of the SNR value is not affected by pixel binning. In the 1% Mn specimen, the spectral SNR data even from 8 £ 8 binned pixels cannot reach 3s although the results can be improved by binning pixels. Since spectral SNR peaks at a certain thickness range, opportunities to detect elements with lower composition in the EF-TEM mapping approach will be
enhanced by exploring relatively thinner regions instead of thicker regions in contrast to XEDS mapping.
5. Discussion 5.1. Comparison of spectral SNR in STEM-XEDS and EF-TEM mapping For comparison, the spectral SNR results of a single pixel (1 £ 1) in the STEM-XEDS (Fig. 3) and EF-TEM maps (Fig. 5) were re-plotted together in Fig. 6. If the results from the single pixels are compared, the XEDS technique provides higher spectral SNR over all the thickness ranges for both specimens in typical acquisition conditions. In the total acquisition time, STEM-XEDS mapping is , 4 £ longer than EF-TEM mapping (STEM-XEDS: , 1 h, EFTEM: 800 s). However, these results should be compared at the same electron dose. In STEM-XEDS mapping, the total incident dose is , 6.2 £ 108 electrons in each pixel with the beam current of 0.5 nA for the dwell time of 0.2 s. On the other hand, the total dose can be calculated as about
Fig. 6. Comparison of the spectral SNR of the STEM-XEDS and the EF-TEM maps: (a) the Cu–4.93 wt% Mn specimen and (b) the Cu–0.98 wt% Mn specimen. The spectral SNR values determined from the single pixel shown in Figs. 3 and 5 are re-plotted with open symbols. The closed symbols indicate the spectral SNR values of the EF-TEM maps adjusted to the same electron dose as the STEM-XEDS maps.
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2.5 £ 108 electrons for the EF-TEM approach, by assuming that the incident beam current (3.5 nA) homogeneously illuminates 128 £ 128 pixels (, 2.0 £ 1024 nA per pixel) for 200 s. So, the electron dose per pixel in STEM-XEDS mapping is still , 2.5 times higher than that in EF-TEM mapping. The closed symbols in Fig. 6 indicate the spectral SNR values from the EF-TEM maps adjusted to the same electron dose as the STEM-XEDS maps. The adjusted SNR values from the EF-TEM maps are as high as those from the XEDS maps in the thickness range below 30 nm (which corresponds to , 0:3l) for both the specimens. However, the STEM-XEDS mapping becomes more sensitive as the specimen thickness increases above the value which provides the maximum SNR in EF-TEM mapping. Leapman and Hunt (1991) compared the detectability limit of both techniques theoretically and experimentally by using only small amounts of elements on thin carbon support films. They concluded that the EELS technique has better performance in detection of trace amounts for light elements (atomic number , 10) and for several transition elements (atomic number , 25) if L edges are used. As shown in Fig. 6, however, the analytical sensitivities of both the mapping approaches are almost same in thin regions (,, 0:3l and the STEM-XEDS technique becomes more sensitive as the specimen thickness increases. The major reason for the difference in the results of the analytical sensitivity is the difference in the type of specimens. In contrast to the thin carbon films (Leapman and Hunt, 1991), regular self-supporting alloy thin films were used in this study, and such thin films generate more background intensities. Therefore, the higher background intensity in the Cu – Mn specimens degrades the spectral SNR in the EF-TEM maps. As a spectrometry technique, the signal-collection capability of the EELS-based approach is essentially higher than that of XEDS. There are two major factors that may degrade the SNR of EF-TEM maps, which do not appear in the regular EELS spectrum. As shown in Fig. 2(a), the intensity distribution of the STEM-XEDS elemental maps seems very homogeneous. Conversely, the EF-TEM elemental maps show more fluctuations despite the maps being much more intense, as shown in Fig. 4(a). These intensity fluctuations in the EF-TEM maps are caused by diffraction contrast. Since the objective-aperture is required to maintain high spatial resolution in EF-TEM mapping, the contributions of the diffraction contrast to the elemental maps are unavoidable in crystalline materials. Obviously, the diffraction contrast degrades the SNR of the elemental maps. The second factor that degrades the sensitivity of the EFTEM maps is the background subtraction method. In EFTEM mapping, the spectral SNR is governed by the background term in Eq. (4). So, if the background term including the h parameter can be reduced, the spectral SNR is improved. In this study, the three-window method was applied for background subtraction. This three-window
method is one of the most popular approaches for EF-TEM mapping but one of the worst approaches to subtract the background from EELS spectra because the background intensity is extrapolated from two background regions below the edge by fitting a power-law function. Since the two parameters of the power-law function are determined from only two background intensities, any fluctuations in intensities of the two backgrounds can introduce serious errors in the extrapolated background. The errors that arise from background subtraction can be reduced by applying the EF-TEM spectrum-imaging method, in which a series of energy-loss images is recorded with a much narrower slit width around the inner-shell edge of interest and then the power-law fit is applied using multiple-backgrounds just as in the regular background subtraction for a spectrum (Ko¨rtje, 1994; Mayer et al., 1997; Plitzko and Mayer, 1999; Bentley et al., 2001; Thomas and Midgley, 2001). Obviously, the accuracy of the background subtraction can be significantly improved (and hence the h value can be reduced), by applying multiple-background windows instead of two windows. In fact, the SNR of a Cu elemental map was improved from 2.3 to 4.6 by applying the EF-TEM spectrum-imaging method instead of the three-window method (Thomas and Midgley, 2001). In addition to those degrading factors, there is another possible disadvantage in EF-TEM mapping. In this study, the EF-TEM maps were obtained with almost maximum illumination conditions in the system for relatively long acquisition time (200 s for each image, 800 s for total). Since the illumination is already maximized, increase of the acquisition times by , 2.5 £ is the only way to obtain the same electron dose as the STEM-XEDS maps. Thus, 500 s would be required for each image and 2000 s for total acquisition. In practice, however, it is not practical to obtain the elemental maps with such acquisition in EF-TEM, mainly because of spatial drift, energy drift and current drift. Among these drifts, the spatial drift can be the most crucial. However, the current version of EF-TEM control software does not have the capability to correct the spatial drifts when a single image is been recorded. 5.2. Evaluation of practical detectability limit from spectral SNR The detectability limits in terms of the MMF or the MDM can be estimated theoretically via a number of models proposed both for XEDS (Ziebold, 1967; Joy and Maher, 1977) and EELS (Colliex et al., 1989; Egerton, 1996). These theoretical approaches must take into account the signal generation and the detection efficiency in specific instruments. Unfortunately, because there are still uncertainties in cross-sections for the signal generation and it is not very easy to evaluate spectrometer efficiencies, the detectability limits determined theoretically may result in over and/or underestimation of the experimental values. Therefore, a simple approach to evaluate the detectability
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limits from measured signal intensities will be described in this section. If it is assumed that the net signal intensity of a minor element from a specimen is directly proportional to the composition of the element, a value of the measured signal intensity divided by the compositional fraction (weight fraction or atomic fraction) corresponds to the signal intensity from the pure element. Since the signal intensity normalized by the compositional fraction becomes constant in the same experimental conditions, the following equation holds I Is ¼ s;min C CMMF
ð6Þ
where C is the weight fraction of the minor element in the specimen and Is;min and CMMF are the minimum signal intensity detectable and the corresponding weight fraction (i.e. MMF), respectively. Therefore, the MMF value of the minor element can be determined using a measured signal intensity from a specimen with known composition, if Is;min is known: CMMF ¼
Is;min C Is
ð7Þ
It should be mentioned that the above equation applies only when the difference between CMMF and C is relatively small, experimental conditions including the specimen thickness are similar and atomic numbers of the minor and major elements are similar. So, the Mn signals from the Cu – Mn specimens used in this study are ideal to evaluate the detectability limits using Eq. (7). The key to evaluate the CMMF values from Eq. (7) is determination of Is;min : This term can be derived from Eq. (4): 2
Is;min ¼
4
2
ðSNRÞ þ ½ðSNRÞ þ 4ðDQEÞðSNRÞ hIb 2ðDQEÞ
which corresponds to 6 and 38 counts for the 1s and 3s definition, respectively, even if there is no background and DQE ¼ 1. By substituting Eq. (8) into Eq. (7), the detectability limit CMMF can be estimated from measured signal and background intensities with a selection of the appropriate SNR value: CMMF ¼
ðSNRÞ2 þ ½ðSNRÞ4 þ 4ðDQEÞðSNRÞ2 hIb 1=2 C 2ðDQEÞIs
ð8Þ
Note that Eq. (8) is equivalent to the expression derived by Trebbia (1988) when DQE ¼ 1. According to Eq. (9), the minimum signal intensity should be at least (SNR)2,
ð9Þ
Fig. 7 shows the CMMF value calculated using a single pixel data of (a) STEM-XEDS and (b) EF-TEM maps obtained from the 1% and 5% Mn specimens, plotted against specimen thickness. The CMMF values were determined with h ¼ 2 and DQE ¼ 1 for the STEMXEDS results and h ¼ 8:22 and DQE ¼ 0.6 for the EFTEM results, respectively. The CMMF can be defined with a selection of the SNR value. So, two definitions of the CMMF values with SNR ¼ 2.4 ð1sÞ and 6.2 ð3sÞ are shown in Fig. 7. The CMMF values from XEDS maps are improved as thickness increases since the signal intensity increases. The results evaluated from the two different specimens are superimposed, which implies that the assumptions for Eq. (9) described above are also appropriate for XEDS data. The CMMF values evaluated with the 3s confidence limit are about five times higher than those with the 1s limit. In the range of the specimen thickness . , 100 nm, the evaluated MMF can reach to about 1 wt% in the 1s definition and to 5 wt% in the 3s definition, respectively. Note that the detectability limit for the XEDS signal is well defined as (Romig and Goldstein, 1979; Michael, 1987; Watanabe and Williams, 1999): CMMF ¼
1=2
181
3ð2Ib Þ1=2 C Is
ð10Þ
In comparison with the CMMF values from Eq. (9) in the XEDS case (h ¼ 2 and DQE ¼ 1), Eq. (10) produces slightly lower values than those in the 1s confidence limit although Eq. (10) is defined as the 3s confidence limit.
Fig. 7. The MMF values evaluated using Eq. (9) for (a) STEM-XEDS maps and (b) EF-TEM maps plotted against the specimen thickness. The MMF values were calculated from the measured intensities at the single pixel in the 1 and 5% Mn specimens for two statistical criteria (1s and 3s confidence limits).
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Therefore, the MMF definition based on the SNR is more severe than the conventional criterion for XEDS. For EF-TEM mapping, conversely, the CMMF values slightly degrade with an increase in specimen thickness as shown in Fig. 7(b). Obviously, the higher background intensity causes this degradation of MMF for EF-TEM mapping. This thickness dependence of CMMF indicates that there may be a chance to detect minor elements by exploring relatively thinner regions in the EF-TEM mapping approach. In contrast to the results evaluated from the XEDS maps, the CMMF values from two different specimens vary in EF-TEM mapping: CMMF from the 5% Mn specimen is better than that from the 1% Mn specimen. As described above, Eq. (9) can be wrong when the estimated composition range is too far from the composition of the minor element. Therefore, the results from the 1% Mn specimen may be less reliable because the composition of the other specimen (5 wt%) is closer to the estimated CMMF values. In addition, the signal intensity is lower in the 1% Mn specimen. In the thickness range below , 40 nm, the MMF value evaluated from the 5% Mn specimen can be , 6 wt% in the 1s definition and , 20 wt% in the 3s definition in the acquisition conditions for EF-TEM mapping. Estimated CMMF values with the 1s and 3s confidence limits from the STEM-XEDS and EF-TEM maps of the 5% Mn specimen are plotted together in Fig. 8. To make fair comparison, the MMF values from the EF-TEM maps are adjusted to the same electron dose for STEM-XEDS mapping as in Fig. 6. EF-TEM mapping can be more sensitive than STEM-XEDS mapping up to a specimen thickness , 20– 30 nm in the 1s confidence limit and , , 50 nm in the 3s limit. However, as the specimen thickness increases, the XEDS maps provide better detectability limits. As mentioned above, elemental mapping by the EELS-based approaches should be performed in reasonably thin regions (e.g. , 0:3t=l) to improve the analytical sensitivity.
Fig. 8. Comparison of CMMF of STEM-XEDS and EF-TEM maps. For fair comparison, the results from EF-TEM mapping were adjusted to the same electron dose as the STEM-XEDS maps.
6. Conclusions In this study, the detectability limits of the EF-TEM and STEM-XEDS elemental maps from thin, homogeneous Cu – 0.98 ^ 0.34 wt% Mn and Cu –4.93 ^ 0.49 wt% Mn thin specimens were evaluated using the spectral SNR. In STEM-XEDS mapping, the SNR improves as the specimen thickness increases, since the signal intensity increases accordingly. Conversely, the SNR in EF-TEM mapping is maximized at a certain thickness. The analytical sensitivity of both mapping approaches was compared by using the MMF values, which were estimated from the measured signal and background intensities with a selection of the spectral SNR value. By comparing the two mapping techniques using estimated MMF, it is shown that the EFTEM mapping is more sensitive when the specimen is thinner than the peak thickness obtained from the SNR of EF-TEM maps. However, the sensitivity of STEM-XEDS mapping becomes higher as the specimen thickness increases in the Cu – Mn thin specimens. To detect trace amounts of elements, it is better to use thicker specimens ð., 0:3t=lÞ in STEM-XEDS mapping. Conversely, in EFTEM mapping, detection of trace amounts of elements is best achieved in thinner specimens ð,, 0:3t=lÞ:
Acknowledgements The authors acknowledge Dr M.G. Burke at BechtelBettis Labs. Inc. for useful discussions and DBW wishes to acknowledge the support of the National Science Foundation through grant DMR 0304738.
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