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Local crystal structure analysis with several picometer precision using scanning transmission electron microscopy
ARTICLE IN PRESS Ultramicroscopy 110 (2010) 778–782
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Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
Local crystal structure analysis with several picometer precision using scanning transmission electron microscopy Koji Kimoto a,n, Toru Asaka b, Xiuzhen Yu a, Takuro Nagai a, Yoshio Matsui a, Kazuo Ishizuka c,a a
National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan Japanese Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta, Nagoya 456-8587, Japan c HREM Research, Inc., 14-48 Matsukazedai, Higashimatsuyama, Saitama 355-0055, Japan b
a r t i c l e in f o
a b s t r a c t
Article history: Received 19 December 2008 Received in revised form 6 October 2009 Accepted 18 November 2009
We report a local crystal structure analysis with a high precision of several picometers on the basis of scanning transmission electron microscopy (STEM). Advanced annular dark-field (ADF) imaging has been demonstrated using software-based experimental and data-processing techniques, such as the improvement of signal-to-noise ratio, the reduction of image distortion, the quantification of experimental parameters (e.g., thickness and defocus) and the resolution enhancement by maximum-entropy deconvolution. The accuracy in the atom position measurement depends on the validity of the incoherent imaging approximation, in which an ADF image is described as the convolution between the incident probe profile and scattering objects. Although the qualitative interpretation of ADF image contrast is possible for a wide range of specimen thicknesses, the direct observation of a crystal structure with deep-sub-angstrom accuracy requires a thin specimen (e.g., 10 nm), as well as observation of the structure image by conventional high-resolution transmission electron microscopy. & 2009 Elsevier B.V. All rights reserved.
Keywords: Scanning transmission electron microscopy Crystal structure analysis Annular dark-field imaging
1. Introduction Conventional transmission electron microscopy (CTEM) and scanning transmission electron microscopy (STEM) are effective for analyzing a local crystal structure. In comparison with CTEM, annular dark-field (ADF) imaging in STEM has several advantages for material characterization. ADF imaging is considered to be incoherent imaging, in which the obtained image can be described as a convolution between the intensity profile of an incident probe and a compositionally sensitive object function [1,2], resulting in high compositional sensitivity and intuitive interpretability. The features of incoherent ADF imaging and coherent CTEM imaging are very different; the former is less dependent on optical parameters (e.g., defocus of the objective lens) and diffraction conditions (e.g., specimen thickness). ADF imaging is thus a promising method for local crystal structure analysis. The quantitative analysis of ADF images, however, has the following experimental difficulties. One is the quantum noise, i.e., a low signal-to-noise (SN) ratio, because it utilizes low-intensity high-angle scattering. The other is the marked image distortion due to specimen or/and incident probe drift. Although these drawbacks are reduced using a spherical aberration (Cs) corrector,
n
Corresponding author. Tel.: + 81 29 860 4402; fax: + 81 29 860 4700. E-mail address: [email protected] (K. Kimoto).
0304-3991/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2009.11.014
the inherent performance of ADF imaging has not yet been fully realized. In our previous works, we improved the energy resolution in electron energy-loss spectroscopy (EELS) using software-based techniques such as drift correction and deconvolution [3,4]. On the basis of these techniques for EELS, we also developed a STEM instrument and related software techniques [5–9] because the two methodologies are based on the same convolution model. Here, we report a comprehensive procedure for performing local crystal structure analysis using STEM. We present several software-based techniques for experiments and data processing, which are applicable for Cs-corrected STEM. We also point out the limitation of the proposed method, which is related to the validity of the incoherent imaging approximation of STEM–ADF.
2. Experimental We used a dedicated scanning transmission electron microscope (HD-2300C, Hitachi High-Technologies) equipped with cold field emission gun (CFEG) and DigiScan (Gatan) [7]. The accelerating voltage is 200 kV and the spherical aberration coefficient is 0.57 mm, resulting in the Scherzer incoherent resolution [2] of 0.13 nm. The microscope is highly stabilized, e.g., the specimen drift rate in this experiment is less than 0.3 nm/min. The probe current is 4.4 pA and the convergence semiangle is 15 mrad. The bright-field (BF) detector semiangle is 5 mrad. The ADF detector
ARTICLE IN PRESS K. Kimoto et al. / Ultramicroscopy 110 (2010) 778–782
inner angle is set to 36 mrad, which is relatively small compared to that for Cs-corrected STEM, to acquire sufficient ADF intensity. We confirmed that ADF images with an inner angle of 36 mrad show Z-contrasts [6,9]. The source size on the specimen is roughly estimated to be 0.03 nm assuming a CFEG virtual source size of 5 nm and a demagnification of 1/150; therefore the effect of the source size (e.g., as described in [10]) is not significant in comparison with the minimum probe size of this STEM. The BF and the ADF detector signals are measured using the DigiScan, whose background offsets are carefully calibrated. We have prepared experimental and data-processing software based on DigitalMicrograph (DM) script (Gatan). Examples of DM scripts are described elsewhere [3]. We observed a TmFeO3 single-crystal specimen. The crystal structure of TmFeO3 is gadolinium orthoferrite, GdFeO3 type [11], which has recently attracted much attention because of its magnetic properties [12,13]. GdFeO3 structure is considered to be a modified perovskite structure ABO3, in which the A-site position is substantially modulated. Its space group is Pnma: a =0.5571 nm, b= 0.7582 nm and c= 0.5249 nm. In this study we observe TmFeO3 along the [0 0 1] direction, which corresponds to the [1 1 0] direction of a primitive perovskite structure. The TEM specimen was prepared by mechanical thinning and low-voltage ion milling using the GentleMill (Technoorg LINDA). A multislice simulation program (xHREM, HREM Research, Inc.) was also used for quantitative analysis [14,15]. The abovementioned crystallographic parameters were used in the simulation. The Debye–Waller factor B of TmFeO3 has not been reported; therefore, we approximately used the B factor of GdFeO3, which has the same crystal structure and the most similar atomic number: B(Tm,Fe,O)= (0.19, 0.10, 0.77). Although the B factor is related to the ADF intensity, the major feature of the incident probe propagation, which is the main topic of this study, depends on elastic scattering; therefore, the approximate B parameter is applicable for the analysis of the atom position measurement.
3. Procedure and experimental results 3.1. Outline of the procedure The proposed procedure consists of (i) experimental techniques and (ii) data-processing techniques. The former includes multiple fast acquisition and specimen drift tracking. The latter includes drift correction, the estimation of defocus and specimen thickness, resolution enhancement by deconvolution and a peak search. In the following section, we describe each technique in detail with a few experimental results.
3.2. Multiple fast acquisition with drift tracking STEM images with a high SN ratio are required for realizing high precision. To improve the SN ratio, we acquired many BF and ADF images (100 each) using a customized DM script. The dwell time and the number of pixels were 0.005 ms and 512 512 pixels, respectively. The total acquisition time for 200 images was 371 s. BF and ADF images are alternately acquired, i.e., quasisimultaneous acquisition is performed. The quasi-simultaneous acquisition of BF and ADF images is necessary in this study because of the following two reasons. First, the BF image is used for specimen thickness evaluation, which is described in Section 3.4. Second, we can estimate specimen drift using BF images even if the ADF images suffer poor SN ratio.
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If an instrument is not sufficiently stabilized, the specimen drift during multiple acquisition exceeds the original scanning area, resulting in an out-of-range failure. We measured the relative drifts of sequential STEM images by cross correlation during the acquisition, and the scanning area was shifted to counterbalance the measured drifts, i.e., drift tracking. The translational symmetry in crystals is problematic in the estimation of the relative shift because of the multiple peaks in the cross-correlation patterns of the crystallographic images. We have to optimize the experimental conditions (e.g., pixel size and dwell time) to keep the relative drift within half of the projected unit cell size. Otherwise, the data processing becomes translational averaging, which differs from local crystal structure analysis. It is, however, worth mentioning that the translation averaging is another effective software-based approach to analyze an average crystal structure with a high precision [16,17]. 3.3. Post-acquisition drift correction Since the drift tracking does not perfectly eliminate specimen drift, we perform post-acquisition drift correction. Relative drift is evaluated by the cross correlation between the first image and other images, because the subpixel shifts would be accumulated if we used the cross correlation of sequential STEM images. Since each specimen drift in BF and ADF images is evaluated individually, we can double-check the estimated specimen drifts by comparing them. We occasionally apply a convolution (e.g., 3 3 smoothing) before calculating the cross correlation for the noise reduction. Since the convoluted images are used only for drift measurement, the experimental data after the drift correction is still raw data. Fig. 1 shows BF and ADF images of TmFeO3 with the crystal structure model after post-acquisition drift correction. In the ADF image, Tm and Fe atomic columns are observed as bright and less bright dots, respectively. In the BF image, cation sites are not clearly observed owing to dynamical diffraction. Generally, it is difficult to find the corresponding atomic sites in conventional BF images; however, we can overlap the crystal structure because we simultaneously observed the ADF image. STEM images often suffer cyclic noise owing to stray electromagnetic fields at mains frequency and/or mechanical vibration of rotating equipment (e.g., turbo molecular pump). The amplitude of such noise in recent STEM scanning systems is smaller than the spatial resolution of the systems; however, the noise is often apparent in STEM images as fine stripes, and is also visible in the Fourier transform (FT) of the STEM image as duplicated spots far from the center of the FT pattern. The effect of the cyclic noise can be effectively reduced by this drift correction. This is also effective for reducing erroneous contrast changes owing to the instability of the probe current (e.g., the tip noise of a CFEG). A high SN ratio image is essential for distinguishing between atomic columns with a similar Z number, and also for detecting low-intensity objects in the image such as the signal of a dopant atom in matrix materials [9]. The precision in the measurement of peak positions in the ADF is improved; for example, we demonstrated the reduction of the standard deviation in interatomic distance measurement from 18 to 8 pm [8]. Using timeseries observation, we can also investigate damage to a specimen as a function of incident electron dose. 3.4. Defocus evaluation using ADF image The optical parameters and diffraction condition should be determined for precise analysis by STEM. In the case of BF imaging in CTEM, many parameters, such as defocus and specimen
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BF
ADF Fe Tm
Fe Tm
O
O
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Fig. 1. BF and ADF images of TmFeO3 specimen quasi-simultaneously observed from the same area. Post-acquisition drift correction has been performed; however, no data processing is applied. The crystal structure is overlapped, and the rectangle depicts the unit cell size. Observation of the [0 0 1] direction of TmFeO3 corresponds to that of the [1 1 0] direction of the primitive perovskite structure; Tm positions are modulated along the [1 0 0] or [ 1 0 0] direction. In the ADF image, bright dots correspond to cation atomic columns; however, in the BF image it is difficult to find the corresponding atom sites.
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thickness, should be simultaneously determined through iterative data analyses. In this study, we estimate the defocus of the objective lens using an ADF image, because the ADF image contrast is less sensitive to specimen thickness. Under the incoherent imaging approximation, an ADF image is a convolution between a scattering object and the intensity profile of the incident probe, which depends on the defocus. We select an appropriate defocus that can reproduce the experimental ADF image contrast based on the incoherent imaging approximation. Fig. 2 shows an example of the defocus evaluation. Figs. 2(a–c) show simulated incident probes with various amount of defocuses of (a) 50 nm, (b) 40 nm and (c) 30 nm (the underfocus is negative), near an optimum defocus (Csl)1/2 of 38 nm. The full-width at half-maximum (FWHM) of the underfocused probe (Fig. 2(a)) becomes slightly small; however, intense side bands appear (white arrows), resulting in highfrequency enhancement and low-frequency suppression in the contrast transfer function. Assuming these incident probe profiles (Figs. 2(a and b)), the experimental ADF image (Fig. 1) is deconvoluted using the maximum-entropy (ME) algorithm (DeConvHAADF, HREM Research, Inc.) [18]. In the deconvolution software, the iterative procedure was stopped when the difference between the original and an estimated result becomes constant. As a result, the present high SN ratio STEM images can be deconvoluted without significant artifacts such as noise enhancement. Figs. 2(d–f) show the deconvoluted images obtained using the incident probes of Figs. 2(a–c), respectively. These deconvoluted results are almost identical; however, as shown in Figs. 2(g–i), the residuals depend on the defocus of each probe profile, where the residual is the difference between the experimental ADF image and the convolution of each probe profile and each deconvoluted image. The unit of the residual intensity is the ratio (%) to the mean intensity of the original image. The residuals suggest the suitability of the incident probe profile. Fig. 2j shows the root mean square (RMS) of the residuals for different defocuses of the incident probe. It is concluded that a defocus of 40 nm is the most suitable for describing the experimental ADF image. The FT patterns of the residuals, Figs. 2(g) and 2(i), show higher and lower frequencies, respectively (see the black arrows in the insets). This is consistent with the frequency dependence of the contrast transfer function, and it supports that the estimated focus is not a local minimum.
g i
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Defocus of incident probe for deconvolution (nm) Fig. 2. Example of the defocus evaluation using experimental ADF image and ME deconvolution. Figs. 2(a–c) show simulated incident probes at a defocus of 50, 40 and 30 nm, respectively. Figs. 2(d–f) show deconvoluted ADF images using the incident probes of Figs. 2(a–c), respectively. Figs. 2(g–i) show the residuals, which is the differences between the experimental ADF image and the convolution between the deconvoluted image and each incident probe. The insets in Figs. 2(g–i) show their FTs. Fig. 2(j) shows the defocus dependence of the root mean square of the residuals. The incident probe with 40 nm defocus reproduces the experimental profile well under the incoherent imaging approximation.
ARTICLE IN PRESS
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K. Kimoto et al. / Ultramicroscopy 110 (2010) 778–782
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Specimen thickness in simulation (nm) Fig. 3. Thickness evaluation using experimental and simulated BF images. The cross correlation and relative shift between the experimental and simulated images are plotted as a function of the thickness in the simulation. The most probable thickness is found to be 33 nm (white arrow). The second highest peak is at 4.7 nm (black arrows); however, it exhibits a lateral shift, suggesting that this thickness is not correct.
3.5. Thickness evaluation using BF image BF image contrasts depend on various optical parameters and diffraction conditions. If the optical parameters are known, the parameter most closely associated with the BF image contrast is the specimen thickness. We estimate the specimen thickness by comparing an experimental BF image with the simulated images. We calculated the cross correlation between the experimental BF image and simulated BF images varying the specimen thickness. As shown in Fig. 3, we estimate a specimen thickness of 33 nm from the maximum of the cross correlation. Since the ADF image is simultaneously acquired, the contrast reversal in BF images due to dynamical diffraction is easily recognized. For example, the second highest peak (black arrows in Fig. 3) shows the lateral shift between the calculated and the experimental images, even though the experimental BF image is aligned with the expected position in advance using the position of the ADF image. This means that the second maximum is a misinterpretation, and thus, this method is robust.
3.6. Atom position evaluation using deconvoluted ADF image The deconvoluted ADF image includes high-frequency information, e.g., the FT of Fig. 2e shows 50 pm spots. Although this value does not corresponds to the resolution regulated by the Rayleigh’s criterion, it allows us to measure each atom position with high precision. As a result of the resolution enhancement by the ME deconvolution, a simple peak search algorithm is sufficient to evaluate the maximum position in the ADF image. Fig. 4 shows an example of the peak search by the DM scripts. The 192 circles in the figure denote the positions of maximums, and their diameters denote the peak heights in the deconvoluted ADF image. The white rectangle shows the unit cell. The inset in dashed rectangle shows a portion of the deconvoluted ADF image. Using this method of analysis, we can discuss the local lattice distortion. In the present study, we analyzed a single crystal; therefore, the detected atom positions should have translational symmetry. We estimate the accuracy of this method by observing the scattering of the atom positions, based on the translational symmetry. Fig. 5 shows the evaluated atom positions (dots) and projected crystal structure, in which small circles, large solid circles and dotted circles denote Fe, Tm and O, respectively.
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Fig. 4. Evaluated atom positions of Tm and Fe overlapped on the ADF image. Open circles denote the positions of maximums, which are measured after maximumentropy deconvolution. The diameters of the circles denote the peak heights in the deconvoluted ADF image. The white rectangle shows the unit cell. The inset in dashed rectangle shows a portion of the deconvoluted ADF image.
The standard deviation of all the measured atom positions is about 5 pm for all the crystallographic sites, indicating very high precision. All Fe atom positions are successfully evaluated with very high precision compared with the Scherzer resolution of the STEM instrument. There is, however, systematic deviation from the known crystal structure, e.g., the Tm site is shifted toward oxygen atomic columns (see arrows in Fig. 5). We investigate this systematic deviation in the following section. The precision of this method is sufficiently high to analyze the local crystal structure, because it is smaller than the variation of the ionic radius. Note that the 5-pm-order distortion in the crystal corresponds to about 1% strain. The present high precision is essential for local crystal structure study, for example, the local distortion near grain boundaries or defects in a crystal.
4. Limitation of this method The above procedure allows us to measure atom positions with high precision. The source of the systematic deviation from actual atom positions is the dynamical diffraction effect, i.e., incoherent imaging approximation is not always valid at deep-sub-angstrom accuracy. Here we calculate ADF images, and the peak positions of Tm and Fe columns are plotted as a function of the specimen thickness. Fig. 6 shows the thickness dependence of the observed atom positions obtained by the multislice program. Fe
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peak positions in an ADF image correspond to the actual projected positions for a thickness of less than 10 nm, which is considered to be the upper limit of thickness that can be used to analyze atomic arrangements with deep-sub-angstrom accuracy. Although no straightforward criterion of applicable thickness has been found, we could estimate the applicable thickness range from the multislice simulation as shown in Fig. 6.
Tm Fe
5. Summary
O
Fig. 5. Tm and Fe atom positions are re-plotted assuming translational symmetry, in which 24 dots from 4 6 unit cells are evaluated. Fe atom positions are acquired with a high accuracy of about 5 pm. Tm atom positions are also evaluated, however, they are shifted toward the oxygen atom columns, as shown by arrows.
We have demonstrated crystal structure analysis using STEM. We measured a crystal structure with a high precision of several picometers. Several technical problems in conventional electron microscopy have been solved using software-based techniques such as for drift correction and deconvolution. The limitation of this method originates from the validity of the incoherent imaging approximation. To realize ADF structure imaging, weak scattering object approximation should be applied in the same way as in high-resolution transmission electron microscopy. However, under appropriate experimental conditions, the quantitative method is applicable to local crystal structure analysis.
Acknowledgements We thank Drs. Wilbrink, Zhang, Tsuruta, Nakamura, Aizawa, Soda, Kato and Isakozawa for their cooperation in developing the STEM system and experiments. We also thank Prof. Kimura for TmFeO3 specimen and Prof. Browning for invaluable suggestion about 2dx. This work was partially supported by JST-CREST, the Nanotechnology Support Project by MEXT, Japan, and a Grant-inAid for Scientific Research from the Japan Society for the Promotion of Science.
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Fig. 6. Peak positions of cations in the simulated ADF image for various specimen thicknesses. Fe atom position can be precisely evaluated by the calculation for the entire thickness range. In contrast, the bright spot near the Tm atomic column is shifted toward adjacent oxygen atomic columns with increase in specimen thickness. The shift at a thickness of 30 nm is 54 pm, which is of the same order as that observed in the experiment.
atom positions are constant even for a thickness of 100 nm. It is found that Tm atom position appears to be shifted in the oxygen column direction, e.g., by 54 pm at a thickness of 33 nm, which is in the same direction and of the same order as the observed shifts. The oxygen atomic potential is not large and the oxygen atomic columns do not show the clear contrast; nevertheless, the oxygen atomic columns have a substantial effect on the accuracy of crystal structure analysis. This dynamical diffraction effect on the atom position is highly dependent on the atomic arrangement near the atomic columns. We have reported a similar crystal structure (A-site ordered double perovskite structure), in which the observed shift is less than 10 pm [8]. In both cases, the
References [1] S.J. Pennycook, D.E. Jesson, Ultramicroscopy 37 (1991) 14. [2] S.J. Pennycook, P.D. Nellist, Z-contrast scanning transmission electron microscopy, in: D.G. Rickerby, G. Valdre, U. Valdre (Eds.), Impact of Electron and Scanning Probe Microscopy on Materials Science, Kluwer Academic Publishers, London, 1999, p. 161. [3] K. Kimoto, Y. Matsui, J. Microsc. 208 (2002) 224. [4] K. Kimoto, K. Ishizuka, et al., J. Electron. Microsc. 52 (2003) 299. [5] K. Kimoto, K. Ishizuka et al., in: Proceedings of the IMC16, Sapporo, 2006, p. 609. [6] K. Kimoto, T. Asaka, et al., Nature 450 (2007) 702. [7] K. Kimoto, K. Nakamura, et al., J. Electron. Microsc. 56 (2007) 17. [8] M. Saito, K. Kimoto, et al., J. Electron. Microsc. 58 (2009) 131. [9] K. Kimoto, R.-J. Xie, et al., Appl. Phys. Lett. 94 (2009) 041908 (3 pages). [10] J.M. LeBeau, S.D. Findlay, et al., Phys. Rev. Lett. 100 (2008) 4. [11] P. Coppens, M. Eibschu¨tz, Acta Crystallogr. 19 (1965) 524. [12] A. Bombik, B. Les´niewska, et al., J. Magn. Magn. Mater. 214 (2000) 243. [13] A.V. Kimel, A. Kirilyuk, et al., Nature 429 (2004) 850. [14] K. Ishizuka, Ultramicroscopy 90 (2002) 71. [15] K. Ishizuka, J. Electron. Microsc. 50 (2001) 291. [16] D. Neiner, N.L. Okamoto, et al., J. Am. Chem. Soc. 129 (2007) 13857. [17] Q.M. Ramasse, N.L. Okamoto et al., in: Proceedings of the Microscopy and Microanalysis, Albuquerque, NM, 2008, p. 270. [18] K. Ishizuka, E. Abe, in: Proceedings of 13th European Microscopy Congress (EMC2004), Antwerp, 2004, p. 117.
Contents lists available at ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
Local crystal structure analysis with several picometer precision using scanning transmission electron microscopy Koji Kimoto a,n, Toru Asaka b, Xiuzhen Yu a, Takuro Nagai a, Yoshio Matsui a, Kazuo Ishizuka c,a a
National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan Japanese Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta, Nagoya 456-8587, Japan c HREM Research, Inc., 14-48 Matsukazedai, Higashimatsuyama, Saitama 355-0055, Japan b
a r t i c l e in f o
a b s t r a c t
Article history: Received 19 December 2008 Received in revised form 6 October 2009 Accepted 18 November 2009
We report a local crystal structure analysis with a high precision of several picometers on the basis of scanning transmission electron microscopy (STEM). Advanced annular dark-field (ADF) imaging has been demonstrated using software-based experimental and data-processing techniques, such as the improvement of signal-to-noise ratio, the reduction of image distortion, the quantification of experimental parameters (e.g., thickness and defocus) and the resolution enhancement by maximum-entropy deconvolution. The accuracy in the atom position measurement depends on the validity of the incoherent imaging approximation, in which an ADF image is described as the convolution between the incident probe profile and scattering objects. Although the qualitative interpretation of ADF image contrast is possible for a wide range of specimen thicknesses, the direct observation of a crystal structure with deep-sub-angstrom accuracy requires a thin specimen (e.g., 10 nm), as well as observation of the structure image by conventional high-resolution transmission electron microscopy. & 2009 Elsevier B.V. All rights reserved.
Keywords: Scanning transmission electron microscopy Crystal structure analysis Annular dark-field imaging
1. Introduction Conventional transmission electron microscopy (CTEM) and scanning transmission electron microscopy (STEM) are effective for analyzing a local crystal structure. In comparison with CTEM, annular dark-field (ADF) imaging in STEM has several advantages for material characterization. ADF imaging is considered to be incoherent imaging, in which the obtained image can be described as a convolution between the intensity profile of an incident probe and a compositionally sensitive object function [1,2], resulting in high compositional sensitivity and intuitive interpretability. The features of incoherent ADF imaging and coherent CTEM imaging are very different; the former is less dependent on optical parameters (e.g., defocus of the objective lens) and diffraction conditions (e.g., specimen thickness). ADF imaging is thus a promising method for local crystal structure analysis. The quantitative analysis of ADF images, however, has the following experimental difficulties. One is the quantum noise, i.e., a low signal-to-noise (SN) ratio, because it utilizes low-intensity high-angle scattering. The other is the marked image distortion due to specimen or/and incident probe drift. Although these drawbacks are reduced using a spherical aberration (Cs) corrector,
n
Corresponding author. Tel.: + 81 29 860 4402; fax: + 81 29 860 4700. E-mail address: [email protected] (K. Kimoto).
0304-3991/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2009.11.014
the inherent performance of ADF imaging has not yet been fully realized. In our previous works, we improved the energy resolution in electron energy-loss spectroscopy (EELS) using software-based techniques such as drift correction and deconvolution [3,4]. On the basis of these techniques for EELS, we also developed a STEM instrument and related software techniques [5–9] because the two methodologies are based on the same convolution model. Here, we report a comprehensive procedure for performing local crystal structure analysis using STEM. We present several software-based techniques for experiments and data processing, which are applicable for Cs-corrected STEM. We also point out the limitation of the proposed method, which is related to the validity of the incoherent imaging approximation of STEM–ADF.
2. Experimental We used a dedicated scanning transmission electron microscope (HD-2300C, Hitachi High-Technologies) equipped with cold field emission gun (CFEG) and DigiScan (Gatan) [7]. The accelerating voltage is 200 kV and the spherical aberration coefficient is 0.57 mm, resulting in the Scherzer incoherent resolution [2] of 0.13 nm. The microscope is highly stabilized, e.g., the specimen drift rate in this experiment is less than 0.3 nm/min. The probe current is 4.4 pA and the convergence semiangle is 15 mrad. The bright-field (BF) detector semiangle is 5 mrad. The ADF detector
ARTICLE IN PRESS K. Kimoto et al. / Ultramicroscopy 110 (2010) 778–782
inner angle is set to 36 mrad, which is relatively small compared to that for Cs-corrected STEM, to acquire sufficient ADF intensity. We confirmed that ADF images with an inner angle of 36 mrad show Z-contrasts [6,9]. The source size on the specimen is roughly estimated to be 0.03 nm assuming a CFEG virtual source size of 5 nm and a demagnification of 1/150; therefore the effect of the source size (e.g., as described in [10]) is not significant in comparison with the minimum probe size of this STEM. The BF and the ADF detector signals are measured using the DigiScan, whose background offsets are carefully calibrated. We have prepared experimental and data-processing software based on DigitalMicrograph (DM) script (Gatan). Examples of DM scripts are described elsewhere [3]. We observed a TmFeO3 single-crystal specimen. The crystal structure of TmFeO3 is gadolinium orthoferrite, GdFeO3 type [11], which has recently attracted much attention because of its magnetic properties [12,13]. GdFeO3 structure is considered to be a modified perovskite structure ABO3, in which the A-site position is substantially modulated. Its space group is Pnma: a =0.5571 nm, b= 0.7582 nm and c= 0.5249 nm. In this study we observe TmFeO3 along the [0 0 1] direction, which corresponds to the [1 1 0] direction of a primitive perovskite structure. The TEM specimen was prepared by mechanical thinning and low-voltage ion milling using the GentleMill (Technoorg LINDA). A multislice simulation program (xHREM, HREM Research, Inc.) was also used for quantitative analysis [14,15]. The abovementioned crystallographic parameters were used in the simulation. The Debye–Waller factor B of TmFeO3 has not been reported; therefore, we approximately used the B factor of GdFeO3, which has the same crystal structure and the most similar atomic number: B(Tm,Fe,O)= (0.19, 0.10, 0.77). Although the B factor is related to the ADF intensity, the major feature of the incident probe propagation, which is the main topic of this study, depends on elastic scattering; therefore, the approximate B parameter is applicable for the analysis of the atom position measurement.
3. Procedure and experimental results 3.1. Outline of the procedure The proposed procedure consists of (i) experimental techniques and (ii) data-processing techniques. The former includes multiple fast acquisition and specimen drift tracking. The latter includes drift correction, the estimation of defocus and specimen thickness, resolution enhancement by deconvolution and a peak search. In the following section, we describe each technique in detail with a few experimental results.
3.2. Multiple fast acquisition with drift tracking STEM images with a high SN ratio are required for realizing high precision. To improve the SN ratio, we acquired many BF and ADF images (100 each) using a customized DM script. The dwell time and the number of pixels were 0.005 ms and 512 512 pixels, respectively. The total acquisition time for 200 images was 371 s. BF and ADF images are alternately acquired, i.e., quasisimultaneous acquisition is performed. The quasi-simultaneous acquisition of BF and ADF images is necessary in this study because of the following two reasons. First, the BF image is used for specimen thickness evaluation, which is described in Section 3.4. Second, we can estimate specimen drift using BF images even if the ADF images suffer poor SN ratio.
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If an instrument is not sufficiently stabilized, the specimen drift during multiple acquisition exceeds the original scanning area, resulting in an out-of-range failure. We measured the relative drifts of sequential STEM images by cross correlation during the acquisition, and the scanning area was shifted to counterbalance the measured drifts, i.e., drift tracking. The translational symmetry in crystals is problematic in the estimation of the relative shift because of the multiple peaks in the cross-correlation patterns of the crystallographic images. We have to optimize the experimental conditions (e.g., pixel size and dwell time) to keep the relative drift within half of the projected unit cell size. Otherwise, the data processing becomes translational averaging, which differs from local crystal structure analysis. It is, however, worth mentioning that the translation averaging is another effective software-based approach to analyze an average crystal structure with a high precision [16,17]. 3.3. Post-acquisition drift correction Since the drift tracking does not perfectly eliminate specimen drift, we perform post-acquisition drift correction. Relative drift is evaluated by the cross correlation between the first image and other images, because the subpixel shifts would be accumulated if we used the cross correlation of sequential STEM images. Since each specimen drift in BF and ADF images is evaluated individually, we can double-check the estimated specimen drifts by comparing them. We occasionally apply a convolution (e.g., 3 3 smoothing) before calculating the cross correlation for the noise reduction. Since the convoluted images are used only for drift measurement, the experimental data after the drift correction is still raw data. Fig. 1 shows BF and ADF images of TmFeO3 with the crystal structure model after post-acquisition drift correction. In the ADF image, Tm and Fe atomic columns are observed as bright and less bright dots, respectively. In the BF image, cation sites are not clearly observed owing to dynamical diffraction. Generally, it is difficult to find the corresponding atomic sites in conventional BF images; however, we can overlap the crystal structure because we simultaneously observed the ADF image. STEM images often suffer cyclic noise owing to stray electromagnetic fields at mains frequency and/or mechanical vibration of rotating equipment (e.g., turbo molecular pump). The amplitude of such noise in recent STEM scanning systems is smaller than the spatial resolution of the systems; however, the noise is often apparent in STEM images as fine stripes, and is also visible in the Fourier transform (FT) of the STEM image as duplicated spots far from the center of the FT pattern. The effect of the cyclic noise can be effectively reduced by this drift correction. This is also effective for reducing erroneous contrast changes owing to the instability of the probe current (e.g., the tip noise of a CFEG). A high SN ratio image is essential for distinguishing between atomic columns with a similar Z number, and also for detecting low-intensity objects in the image such as the signal of a dopant atom in matrix materials [9]. The precision in the measurement of peak positions in the ADF is improved; for example, we demonstrated the reduction of the standard deviation in interatomic distance measurement from 18 to 8 pm [8]. Using timeseries observation, we can also investigate damage to a specimen as a function of incident electron dose. 3.4. Defocus evaluation using ADF image The optical parameters and diffraction condition should be determined for precise analysis by STEM. In the case of BF imaging in CTEM, many parameters, such as defocus and specimen
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Fig. 1. BF and ADF images of TmFeO3 specimen quasi-simultaneously observed from the same area. Post-acquisition drift correction has been performed; however, no data processing is applied. The crystal structure is overlapped, and the rectangle depicts the unit cell size. Observation of the [0 0 1] direction of TmFeO3 corresponds to that of the [1 1 0] direction of the primitive perovskite structure; Tm positions are modulated along the [1 0 0] or [ 1 0 0] direction. In the ADF image, bright dots correspond to cation atomic columns; however, in the BF image it is difficult to find the corresponding atom sites.
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thickness, should be simultaneously determined through iterative data analyses. In this study, we estimate the defocus of the objective lens using an ADF image, because the ADF image contrast is less sensitive to specimen thickness. Under the incoherent imaging approximation, an ADF image is a convolution between a scattering object and the intensity profile of the incident probe, which depends on the defocus. We select an appropriate defocus that can reproduce the experimental ADF image contrast based on the incoherent imaging approximation. Fig. 2 shows an example of the defocus evaluation. Figs. 2(a–c) show simulated incident probes with various amount of defocuses of (a) 50 nm, (b) 40 nm and (c) 30 nm (the underfocus is negative), near an optimum defocus (Csl)1/2 of 38 nm. The full-width at half-maximum (FWHM) of the underfocused probe (Fig. 2(a)) becomes slightly small; however, intense side bands appear (white arrows), resulting in highfrequency enhancement and low-frequency suppression in the contrast transfer function. Assuming these incident probe profiles (Figs. 2(a and b)), the experimental ADF image (Fig. 1) is deconvoluted using the maximum-entropy (ME) algorithm (DeConvHAADF, HREM Research, Inc.) [18]. In the deconvolution software, the iterative procedure was stopped when the difference between the original and an estimated result becomes constant. As a result, the present high SN ratio STEM images can be deconvoluted without significant artifacts such as noise enhancement. Figs. 2(d–f) show the deconvoluted images obtained using the incident probes of Figs. 2(a–c), respectively. These deconvoluted results are almost identical; however, as shown in Figs. 2(g–i), the residuals depend on the defocus of each probe profile, where the residual is the difference between the experimental ADF image and the convolution of each probe profile and each deconvoluted image. The unit of the residual intensity is the ratio (%) to the mean intensity of the original image. The residuals suggest the suitability of the incident probe profile. Fig. 2j shows the root mean square (RMS) of the residuals for different defocuses of the incident probe. It is concluded that a defocus of 40 nm is the most suitable for describing the experimental ADF image. The FT patterns of the residuals, Figs. 2(g) and 2(i), show higher and lower frequencies, respectively (see the black arrows in the insets). This is consistent with the frequency dependence of the contrast transfer function, and it supports that the estimated focus is not a local minimum.
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Defocus of incident probe for deconvolution (nm) Fig. 2. Example of the defocus evaluation using experimental ADF image and ME deconvolution. Figs. 2(a–c) show simulated incident probes at a defocus of 50, 40 and 30 nm, respectively. Figs. 2(d–f) show deconvoluted ADF images using the incident probes of Figs. 2(a–c), respectively. Figs. 2(g–i) show the residuals, which is the differences between the experimental ADF image and the convolution between the deconvoluted image and each incident probe. The insets in Figs. 2(g–i) show their FTs. Fig. 2(j) shows the defocus dependence of the root mean square of the residuals. The incident probe with 40 nm defocus reproduces the experimental profile well under the incoherent imaging approximation.
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Specimen thickness in simulation (nm) Fig. 3. Thickness evaluation using experimental and simulated BF images. The cross correlation and relative shift between the experimental and simulated images are plotted as a function of the thickness in the simulation. The most probable thickness is found to be 33 nm (white arrow). The second highest peak is at 4.7 nm (black arrows); however, it exhibits a lateral shift, suggesting that this thickness is not correct.
3.5. Thickness evaluation using BF image BF image contrasts depend on various optical parameters and diffraction conditions. If the optical parameters are known, the parameter most closely associated with the BF image contrast is the specimen thickness. We estimate the specimen thickness by comparing an experimental BF image with the simulated images. We calculated the cross correlation between the experimental BF image and simulated BF images varying the specimen thickness. As shown in Fig. 3, we estimate a specimen thickness of 33 nm from the maximum of the cross correlation. Since the ADF image is simultaneously acquired, the contrast reversal in BF images due to dynamical diffraction is easily recognized. For example, the second highest peak (black arrows in Fig. 3) shows the lateral shift between the calculated and the experimental images, even though the experimental BF image is aligned with the expected position in advance using the position of the ADF image. This means that the second maximum is a misinterpretation, and thus, this method is robust.
3.6. Atom position evaluation using deconvoluted ADF image The deconvoluted ADF image includes high-frequency information, e.g., the FT of Fig. 2e shows 50 pm spots. Although this value does not corresponds to the resolution regulated by the Rayleigh’s criterion, it allows us to measure each atom position with high precision. As a result of the resolution enhancement by the ME deconvolution, a simple peak search algorithm is sufficient to evaluate the maximum position in the ADF image. Fig. 4 shows an example of the peak search by the DM scripts. The 192 circles in the figure denote the positions of maximums, and their diameters denote the peak heights in the deconvoluted ADF image. The white rectangle shows the unit cell. The inset in dashed rectangle shows a portion of the deconvoluted ADF image. Using this method of analysis, we can discuss the local lattice distortion. In the present study, we analyzed a single crystal; therefore, the detected atom positions should have translational symmetry. We estimate the accuracy of this method by observing the scattering of the atom positions, based on the translational symmetry. Fig. 5 shows the evaluated atom positions (dots) and projected crystal structure, in which small circles, large solid circles and dotted circles denote Fe, Tm and O, respectively.
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Fig. 4. Evaluated atom positions of Tm and Fe overlapped on the ADF image. Open circles denote the positions of maximums, which are measured after maximumentropy deconvolution. The diameters of the circles denote the peak heights in the deconvoluted ADF image. The white rectangle shows the unit cell. The inset in dashed rectangle shows a portion of the deconvoluted ADF image.
The standard deviation of all the measured atom positions is about 5 pm for all the crystallographic sites, indicating very high precision. All Fe atom positions are successfully evaluated with very high precision compared with the Scherzer resolution of the STEM instrument. There is, however, systematic deviation from the known crystal structure, e.g., the Tm site is shifted toward oxygen atomic columns (see arrows in Fig. 5). We investigate this systematic deviation in the following section. The precision of this method is sufficiently high to analyze the local crystal structure, because it is smaller than the variation of the ionic radius. Note that the 5-pm-order distortion in the crystal corresponds to about 1% strain. The present high precision is essential for local crystal structure study, for example, the local distortion near grain boundaries or defects in a crystal.
4. Limitation of this method The above procedure allows us to measure atom positions with high precision. The source of the systematic deviation from actual atom positions is the dynamical diffraction effect, i.e., incoherent imaging approximation is not always valid at deep-sub-angstrom accuracy. Here we calculate ADF images, and the peak positions of Tm and Fe columns are plotted as a function of the specimen thickness. Fig. 6 shows the thickness dependence of the observed atom positions obtained by the multislice program. Fe
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peak positions in an ADF image correspond to the actual projected positions for a thickness of less than 10 nm, which is considered to be the upper limit of thickness that can be used to analyze atomic arrangements with deep-sub-angstrom accuracy. Although no straightforward criterion of applicable thickness has been found, we could estimate the applicable thickness range from the multislice simulation as shown in Fig. 6.
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Fig. 5. Tm and Fe atom positions are re-plotted assuming translational symmetry, in which 24 dots from 4 6 unit cells are evaluated. Fe atom positions are acquired with a high accuracy of about 5 pm. Tm atom positions are also evaluated, however, they are shifted toward the oxygen atom columns, as shown by arrows.
We have demonstrated crystal structure analysis using STEM. We measured a crystal structure with a high precision of several picometers. Several technical problems in conventional electron microscopy have been solved using software-based techniques such as for drift correction and deconvolution. The limitation of this method originates from the validity of the incoherent imaging approximation. To realize ADF structure imaging, weak scattering object approximation should be applied in the same way as in high-resolution transmission electron microscopy. However, under appropriate experimental conditions, the quantitative method is applicable to local crystal structure analysis.
Acknowledgements We thank Drs. Wilbrink, Zhang, Tsuruta, Nakamura, Aizawa, Soda, Kato and Isakozawa for their cooperation in developing the STEM system and experiments. We also thank Prof. Kimura for TmFeO3 specimen and Prof. Browning for invaluable suggestion about 2dx. This work was partially supported by JST-CREST, the Nanotechnology Support Project by MEXT, Japan, and a Grant-inAid for Scientific Research from the Japan Society for the Promotion of Science.
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Fig. 6. Peak positions of cations in the simulated ADF image for various specimen thicknesses. Fe atom position can be precisely evaluated by the calculation for the entire thickness range. In contrast, the bright spot near the Tm atomic column is shifted toward adjacent oxygen atomic columns with increase in specimen thickness. The shift at a thickness of 30 nm is 54 pm, which is of the same order as that observed in the experiment.
atom positions are constant even for a thickness of 100 nm. It is found that Tm atom position appears to be shifted in the oxygen column direction, e.g., by 54 pm at a thickness of 33 nm, which is in the same direction and of the same order as the observed shifts. The oxygen atomic potential is not large and the oxygen atomic columns do not show the clear contrast; nevertheless, the oxygen atomic columns have a substantial effect on the accuracy of crystal structure analysis. This dynamical diffraction effect on the atom position is highly dependent on the atomic arrangement near the atomic columns. We have reported a similar crystal structure (A-site ordered double perovskite structure), in which the observed shift is less than 10 pm [8]. In both cases, the
References [1] S.J. Pennycook, D.E. Jesson, Ultramicroscopy 37 (1991) 14. [2] S.J. Pennycook, P.D. Nellist, Z-contrast scanning transmission electron microscopy, in: D.G. Rickerby, G. Valdre, U. Valdre (Eds.), Impact of Electron and Scanning Probe Microscopy on Materials Science, Kluwer Academic Publishers, London, 1999, p. 161. [3] K. Kimoto, Y. Matsui, J. Microsc. 208 (2002) 224. [4] K. Kimoto, K. Ishizuka, et al., J. Electron. Microsc. 52 (2003) 299. [5] K. Kimoto, K. Ishizuka et al., in: Proceedings of the IMC16, Sapporo, 2006, p. 609. [6] K. Kimoto, T. Asaka, et al., Nature 450 (2007) 702. [7] K. Kimoto, K. Nakamura, et al., J. Electron. Microsc. 56 (2007) 17. [8] M. Saito, K. Kimoto, et al., J. Electron. Microsc. 58 (2009) 131. [9] K. Kimoto, R.-J. Xie, et al., Appl. Phys. Lett. 94 (2009) 041908 (3 pages). [10] J.M. LeBeau, S.D. Findlay, et al., Phys. Rev. Lett. 100 (2008) 4. [11] P. Coppens, M. Eibschu¨tz, Acta Crystallogr. 19 (1965) 524. [12] A. Bombik, B. Les´niewska, et al., J. Magn. Magn. Mater. 214 (2000) 243. [13] A.V. Kimel, A. Kirilyuk, et al., Nature 429 (2004) 850. [14] K. Ishizuka, Ultramicroscopy 90 (2002) 71. [15] K. Ishizuka, J. Electron. Microsc. 50 (2001) 291. [16] D. Neiner, N.L. Okamoto, et al., J. Am. Chem. Soc. 129 (2007) 13857. [17] Q.M. Ramasse, N.L. Okamoto et al., in: Proceedings of the Microscopy and Microanalysis, Albuquerque, NM, 2008, p. 270. [18] K. Ishizuka, E. Abe, in: Proceedings of 13th European Microscopy Congress (EMC2004), Antwerp, 2004, p. 117.