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Spatially resolved diffractometry with atomic-column resolution
Ultramicroscopy 111 (2011) 1111–1116
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Spatially resolved diffractometry with atomic-column resolution Koji Kimoto a,n, Kazuo Ishizuka b a b
National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan HREM Research Inc., 14-48 Matsukazedai, Higashimatsuyama, Saitama 355-0055, Japan
a r t i c l e i n f o
abstract
Article history: Received 17 September 2010 Received in revised form 15 January 2011 Accepted 21 January 2011 Available online 1 February 2011
We demonstrate spatially resolved diffractometry in which diffraction patterns are acquired at twodimensional positions on a specimen using scanning transmission electron microscopy (STEM), resulting in four-dimensional data acquisition. A high spatial resolution of about 0.1 nm is achieved using a stabilized STEM instrument, a spherical aberration corrector and various post-acquisition data processings. We have found a few novel results in the radial and the azimuthal scattering angle dependences of atomic-column contrast in STEM images. Atomic columns are clearly observed in dark field images obtained using the excess Kikuchi band intensity even in small solid-angle detection. We also find that atomic-column contrasts in dark field images are shifted in the order of a few tens of picometers on changing the azimuthal scattering angle. This experimental result is approximately interpretable on the basis of the impact parameter in Rutherford scattering. Spatially resolved diffractometry provides fundamental knowledge related to various STEM techniques, such as annular dark field (ADF) and annular bright field (ABF) imaging, and it is expected to become an analytical platform for advanced STEM imaging. & 2011 Elsevier B.V. All rights reserved.
Keywords: Scanning transmission electron microscopy (STEM) Annular dark field (ADF) Annular bright field (ABF) Thermal diffuse scattering (TDS) Kikuchi band
1. Introduction Recent progress in the instrumentation of scanning transmission electron microscopy (STEM) has allowed us to acquire various signals from a specimen using a scanning incident probe [1]. One successful example of STEM-based methods is a combination with an analytical technique such as electron energy-loss spectroscopy (EELS) [2,3]. One-dimensional spectral intensity I(E) is acquired as a function of the probe position (x,y), resulting in three-dimensional (3D) data I(x,y,E) acquisition, i.e., spatially resolved spectroscopy. STEM primarily yields an electron diffraction pattern, which is a major subject for electron crystallography. Established STEM imaging techniques utilize the integrated intensities of diffraction patterns using low-angle circular and high-angle annular detectors to obtain bright field (BF) and annular dark field (ADF) images, respectively. Recently, high-angle ADF imaging is routinely applied because of its compositional sensitivity and intuitive interpretability [4]. Although we reported a few applications of crystal structure analyses based on ADF and BF imaging [5–7], these analyses do not fully utilize the information in the diffraction patterns. There have been several pioneering attempts to make use of more detailed information in diffraction patterns using segmented detectors, in which diffraction intensities were detected as a set of zero-dimensional signals [8–13]. A modern STEM system, however, allows us to record diffraction patterns as two-dimensional (2D) data by varying
n
Corresponding author. Tel.: +81 29 860 4402. E-mail address: [email protected] (K. Kimoto).
0304-3991/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2011.01.029
the probe position. In other words, four-dimensional (4D) data I(x,y,u,v) can be acquired, where (u,v) denotes a scattering vector in the diffraction pattern. This type of technique has been applied to a few materials using a nanometer-size incident probe [14]. In the present paper this 4D analytical technique is termed spatially resolved diffractometry. Here we report atomic-resolution spatially resolved diffractometry. The basic concept of this technique might not appear innovative; however, it substantially enhances STEM imaging capability. Spatially resolved diffractometry provides fundamental knowledge related to conventional STEM, including BF, ADF and annular bright field (ABF) imaging [15,16]. We propose variations of advanced STEM imaging based on spatially resolved diffractometry. We show the novel aspects of thermal diffuse scattering (TDS) that could not have been elucidated using the conventional techniques. 2. Methods We utilized a dedicated STEM instrument (Hitachi High-Technologies, HD-2300C) [17] equipped with a cold field-emission gun, a high-resolution pole piece, a digitized scanning system (Gatan, DigiScan), an energy filter (Gatan, GIF-Tridiem 863) [18] and a spherical aberration corrector (CEOS GmbH, CESCOR). The original commercial STEM system was modified to improve its mechanical and electrical stability. The acceleration voltage was 200 kV and the convergent semiangle was 27.5 mrad (except for Fig. 3b). The spatial resolution of the instrument was found to be about 0.1 nm using a conventional ADF image. The spherical aberration corrector is
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indispensable not only for high spatial resolution but also for the observation of BF disk without distortion. The phase shift due to the aberrations of the probe-forming system was found to be less than the p/4 limit up to 30 mrad using CEOS software; therefore, the aberrations did not affect the major features of BF disk. Spatially resolved diffraction patterns were acquired using a software (Gatan, STEM Diffraction-Imaging) and a charge-coupled-device (CCD) camera of the energy filter. An incident probe was scanned on 64 64 points with a 0.018 nm step, and the diffraction patterns were acquired as 128 128-pixel data up to 70 mrad (28 nm 1) in radial scattering angle. As a result, 4D data (64 64 128 128) was acquired. The exposure time for each diffraction pattern was 0.2 s and the total acquisition time was 32 min, including the time required for specimen drift correction. To realize high accuracy of the analyzed position, specimen drift was repeatedly corrected 256 times during the total acquisition, which substantially decreases throughput. Conventional ADF images were also observed using an actual annular detector whose inner angle was 80 mrad. Although the conventional ADF images were used for the drift correction during the experiment, all STEM images presented here were obtained from 4D data acquired by spatially resolved diffractometry. A (0 0 1) SrTiO3 specimen for the STEM observation was prepared by mechanical thinning and Ar ion milling. The specimen thickness at the analyzed area was estimated to be about 30 nm using the log-ratio method of EELS, assuming a mean free path of total inelastic scattering of 106 nm [19]. The 4D data was processed using the Gatan software and inhouse scripts [20] of DigitalMicrograph (Gatan). To perform an advanced investigation, we transformed the 4D data I(x,y,u,v) into processed 3D data, I(x,y,b) or I(x,y,f), where b and f denote the radial scattering angle and the azimuthal scattering angle, respectively.
3. Results and discussion 3.1. Experimental results and primitive survey Fig. 1a shows an ADF image constructed from the 4D data with inner and outer corresponding angles of 20 and 25 nm 1,
BG O
respectively. The contrast of this ADF image is similar to that of a conventional ADF image. Fig. 1b–e shows four diffraction patterns obtained on Sr (b), TiO (c) and O (d) atomic columns, and between atomic columns (BG) (e). Each diffraction pattern is obtained at each rectangle area, as shown by open squares in Fig. 1a. The diffraction intensities are dominated by the BF disk because of the small specimen thickness and the large convergence angle. Although the BF disks in the diffraction patterns taken on atomic columns (Fig. 1b–d) exhibit approximate 4 mm symmetry, the other BF disk (Fig. 1e) shows an asymmetric pattern. If we measure the BF intensity using an annular detector, this asymmetric intensity is approximately compensated, and accordingly the ABF image shows distinct contrasts only on atomic columns. Fig. 1 also shows the atomic site dependence of Kikuchi band (e.g., [21]). As shown in Fig. 1b–d, clear Kikuchi bands are observed only on the Sr and TiO atomic positions, and it indicates that the origin of Kikuchi bands is TDS localized on atomic sites. Thus, one can selectively visualize TDS by choosing excess Kikuchi band signals. Fig. 2 shows examples of such angular-selective dark field (DF) imaging. Fig. 2a–d shows DF images whose intensities are obtained from a very small solid angle (2 nm 1 in diameter) as shown by small open circles (i)–(iv) in Fig. 1b. Fig. 2a and c shows DF images of the excess Kikuchi bands, and Fig. 2b and d shows those slightly outside the excess Kikuchi bands. This result indicates important fundamental features of DF (or ADF) imaging. Firstly, atomic columns can be resolved despite the small detection solid angle of DF imaging. An annular detector for integrating the full azimuthal angle is not a prerequisite for resolving atomic columns, but a high-angle scattering is critical as demonstrated in the following Section 3.2. This result is a very important finding because it reveals the major origin of the incoherent feature in high-angle ADF imaging. Note that this feature of DF images is different from that of ABF images, because azimuthal averaging with appropriate radial scattering range [16] is indispensable to realize the incoherent imaging feature (e.g. thickness and defocus dependence) of ABF images. Secondly, the resolution of DF images is isotropic and basically independent of the azimuthal angle of the detector (its details will be discussed in Section 3.3). Thirdly, the DF images of the excess Kikuchi band exhibit high contrast compared with those
TiO
Sr
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10 nm-1
Sr
TiO
O
BG
Fig. 1. Experimental result of spatially resolved diffractometry with high spatial resolution. (a) ADF image constructed from 4D data, in which the corresponding inner and outer angles are 20 and 25 nm 1, respectively. (b)–(e) Diffraction patterns at Sr (b), TiO (c), O (d) atomic columns and at another point between atomic columns (e), whose positions are shown as open squares in (a). The contrast of the outer part in the diffraction patterns is enhanced to observe Kikuchi bands. The broken line in (b) shows the shadow edge of the conventional ADF detector and CCD detector. The small open circles in (b) show the detection area for the DF images shown in Fig. 2.
K. Kimoto, K. Ishizuka / Ultramicroscopy 111 (2011) 1111–1116
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Fig. 2. Angular-selective DF images (a)–(d) constructed from 4D data and their intensity profiles (e). These images are not ADF images but DF images obtained using a small detection solid angle. Note the atomic-column contrast in spite of the small detection solid angle, where the detector positions of the DF images (a), (b), (c) and (d) are denoted as small circles (i), (ii), (iii) and (iv) in Fig. 1b, respectively; (a) and (c) show images of the excess Kikuchi band, and (b) and (d) show images slightly outside the Kikuchi band. (e) DF intensity along the rectangle shown in (a). The DF image contrast is improved by selecting the excess Kikuchi band signal.
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Fig. 3. Radial angular distributions at four different probe positions and STEM images taken at different radial scattering angles; (a) and (b) show experimental results obtained using a large convergence angle of 27.5 mrad and a small convergence angle of 11 mrad, respectively.
obtained from the outside of the band, as plotted in Fig. 2e. For example, the peak to background (PB) ratios of the upper profiles (i, iii) and the lower ones (vi, ii) are 2.0 and 1.5, respectively. Since TDS is localized on the atomic column, one can improve the PB ratio of DF images by setting the detector only on the excess Kikuchi bands. This imaging method will practically enhance the DF image contrast of a crystalline specimen because the scattering signal from an amorphous layer (e.g., a surface damaged layer or contamination) must have a homogeneous azimuthal distribution. 3.2. Radial distribution analysis Since the primary parameter in diffractometry is the radial scattering angle b, we calculate the rotationally averaged radial
scattering distribution I(b) of each diffraction pattern. As a result, 4D data I(x,y,u,v) is converted into 3D data I(x,y,b). Fig. 3a shows the radial angular distributions at four different probe positions: Sr, TiO, O and background (BG). At a high radial scattering angle, the atomic number dependence of the ADF signal is clearly observed in both intensity profiles and ADF images (insets). We also performed a similar experiment using a small convergence angle of 11 mrad (Fig. 3b). It is found that the absolute DF intensity is not always dependent on atomic number Z, particularly for a relatively low scattering angle (e.g., 20–30 mrad). Since high-Z atoms scatter electrons toward a high angle, their scattering distribution at a relatively low scattering angle appears to be absorbed. The inset STEM images show the contrast variation as a function of the radial scattering angle b. These STEM images are cross sections (x–y plane)
K. Kimoto, K. Ishizuka / Ultramicroscopy 111 (2011) 1111–1116
probe position. As a result, we obtain another 3D data IDF(x,y,f) whose dimensions are 64 64 252 and the minimum azimuthal step Df is 1.41. Fig. 5a–d shows examples of azimuthally resolved DF images, in which schematic quadrants of insets show each azimuthal angle range, i.e., annular-quadrant-detector observation. Open circles, which are placed at precisely the same position in Figs. 5a–d, clarify relative shifts in the four DF images. It is found that the positions of the bright spots in the DF images are shifted on changing the azimuthal angle, as shown by the white arrows in Fig. 5a–d. The direction of the peak shift is opposite to the detection direction. We have evaluated the azimuthal angle dependence in detail using the 3D data IDF(x,y,f), as shown in Fig. 5e, in which we plot the relative shifts of Sr (circles) and TiO (triangles) peaks in comparison with an ADF image (Fig. 1a). The relative shifts were measured using cross correlation [7,20]. Although the evaluation suffers poor SN ratio of the DF image, it is found that the bright spots of Sr and TiO sites are similarly rotated in a circular motion. Solid and dotted lines are curve fittings for the Sr and TiO sites assuming cosine and sine functions, respectively. The averaged rotational amplitudes of the Sr and TiO sites are found to be 20 and 16 pm, respectively. The difference in amplitude along the x- and y-axes is less than a few picometers (see Fig. 5e), indicating high reproducibility. The magnitudes of these shifts are not negligible compared with the probe size in recent advanced STEM instruments [11,22], the high precision achieved in our conventional STEM observation [7] or the spatial incoherence in a quantitative STEM simulation [23]. We find that the present experimental result is consistent with a classical view of charged-particle scattering, i.e., the Rutherford scattering of an electron by a nucleus. Fig. 6 shows a schematic of Rutherford scattering and the corresponding DF intensity profile. The DF intensity measured at a specific azimuthal angle (lower part of Fig. 6) has an off-centered peak in the STEM DF image (upper part of Fig. 6) in the classical particle viewpoint. The rotational displacement measured in Fig. 5 is consistent with this schematic, and the amplitude is considered to be an impact parameter. To our knowledge, this is the first measurement of the azimuthal dependence associated with DF image contrast.
normal to the b-axis of the 3D data I(x,y,b). A STEM image obtained at a scattering angle range of 5–10 nm 1 (Fig. 3a) has recently been recognized as an ABF image [16]. These variations of post-acquisition processing are advantageous in spatially resolved diffractometry. We observe the detailed probe position dependence of the radial distribution, e.g., I(x,b). In other words, the cross section along the b-axis (e.g., x–b plane) of the 3D data I(x,y,b) is observed (Fig. 4). Fig. 4a shows a BF image constructed from the 3D data—corresponding BF detection semiangle is 2.3 nm 1. We observe two cross sections (Fig. 4b and c) whose probe positions are shown as rectangles in Fig. 4a. The probe position dependence of the angular distribution is clarified by this procedure. The optimum BF detector range for enhancing the signal to noise (SN) ratio without contrast reduction can be estimated to be about 2 nm 1, as shown by a dotted line in Fig. 4c. Fig. 4d shows ABF and ADF intensity profiles whose corresponding detection angles (b0–b3) are indicated in Fig. 4b. The ABF image profile shows negative peaks on both Sr and O atomic columns as previously reported [15,16], although ADF images show peaks only on the Sr atomic columns. Due to the complicated angular dependence of BF intensity, it is estimated that the relationship between the darkness of an atomic column and its atomic number is rather dependent on the ABF detection angular range. The high scattering angle range is also informative; for example, we can observe the dependence of ADF image contrast on the radial scattering angle, as shown in Fig. 4d. A higher-angle ADF image has higher contrast.
3.3. Azimuthal distribution analysis of DF image Since the azimuthal scattering angle f is also an important diffraction parameter, we investigate the azimuthal angle dependence of the high-angle DF image contrast. In this study the DF intensity of each diffraction pattern within a radial scattering angle range from 21.4 to 24.5 nm 1 is integrated with varying azimuthal angle f (as shown by the inset of Fig. 5e), and then the azimuthal angle dependence of the DF intensity IDF(f) is evaluated at each
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Fig. 4. Variations of radial angular distribution analysis. (a) BF image, in which a corresponding BF detector angle is 2.3 nm 1. (b) and (c) Probe position dependences of the angular distribution, whose corresponding probe positions are shown in (a). In (b) and (c) brightness is proportional to the logarithm of its intensity. On the basis of this experimental result, the optimum range of the BF detector can be estimated as shown by the dotted line in (c). (d) Intensity profiles of STEM images at four scattering angles b0–b3 obtained using the result of (b). The site dependences of ABF and ADF contrasts are clearly observed.
K. Kimoto, K. Ishizuka / Ultramicroscopy 111 (2011) 1111–1116
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Fig. 5. Azimuthal scattering angle dependence of DF images whose radial integration range is from 21.4 to 24.5 nm 1. (a)–(d) Azimuthal integrated DF images whose detection range is schematically shown as each inset, i.e., annular-quadrant-detector observation. White arrows show the direction of relative shifts. (e) Detailed analysis of the relative displacements of Sr and TiO column peaks. Circles and triangles show experimental results and solid and broken lines indicate the curve fitting of the Sr and TiO atomic column contrasts, respectively. The insets in (e) are schematics of a diffraction pattern and a DF image. The rotational amplitudes of the Sr and TiO atomic columns are found to be 20 and 16 pm, respectively.
The impact parameter b of Rutherford scattering is given by the following equation [24]: b¼
e2 Z 1 1 þ cos b , 4pe0 mv2e sin b
ð1Þ
where e0 is the permittivity of space and e, ve and m denote the charge, mass and velocity of an electron, respectively. We calculated the impact parameters for Sr and Ti under the present experimental conditions, including the relativistic correction to the electron mass. The scattering angle b is set to 53 mrad, which corresponds to the radial angle from the center of the BF disk to the integration angle. The calculated impact parameters for 38Sr and 22Ti are 6 and 3.5 pm, respectively. The calculated values are not equal to the experimental values, but are also of picometer order, and the difference between the Sr and TiO sites is qualitatively consistent with their atomic numbers. Note that the minimum scattering angle b is rather small because of the large convergent angle, and therefore the maximum impact parameter becomes large. Consequently, the azimuthal dependence of the DF
image contrast can be approximately interpreted from the classical viewpoint of Rutherford scattering. Although Rutherford scattering is the simplest model of electron scattering, it is still usable for the qualitative interpretation of this experiment. There are lots of other physical factors to be considered, such as dynamical scattering effects and other inelastic scatterings. In the case of spherical aberration corrector, the depth of focus becomes short; e.g., it is estimated to be 6 nm in full width at half maximum. Therefore, even in the case of thick TEM specimen, focused incident electrons are scattered by the limited number of atoms, and the above-mentioned impact parameters might be increased by the plural scattering. This atomic-column image displacement is a fundamental issue in STEM imaging. The difference between each atomic site rotation is problematic in crystal structure analysis because it affects the observed structural symmetry. The present experimental result for SrTiO3, however, shows that both (Sr and TiO) atomic-column contrasts are similarly shifted. Since the impact parameter becomes large on using a low scattering angle, it is considered that the enlarged impact parameter in the case of a
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IDF Impact parameter
DF signal IDF b Probe position x
x
b electron
and the azimuthal scattering angle dependences, I(x,y,b) and I(x,y,f), respectively. Spatially resolved diffractometry allows us to perform various types of post-acquisition data processing, and it provides us fundamental knowledge related to existing STEM imaging techniques. We found that the atomic columns of DF images can be observed using a small solid angle, and the DF contrast can be improved by selecting the excess Kikuchi band or a large radial scattering angle. We also found that the bright dots of atomic columns in DF images are shifted on changing the azimuthal scattering angle of the DF detector. This can be approximately interpreted on the basis of Rutherford scattering. At present, spatially resolved diffractometry has a few technical difficulties, such as a long acquisition time owing to specimen drift correction and a relatively long dwell time for diffraction acquisition. This is, however, a similar situation to that during pioneering studies on spatially resolved spectroscopy in the 1980s [2,3]. The recent developments of high-sensitivity high-speed detectors (e.g., direct detection CMOS) and stabilized microscope columns are expected to increase the practicality of spatially resolved diffractometry, making it an analytical platform for state-of-the-art STEM imaging.
Acknowledgements We would like to express our thanks to Mr. Nakamura, Mr. Soda, Mr. Kato and Mr. Aizawa for improving our microscope performance, Dr. Wilbrink and Dr. Menon for advice about DigitalMicrograph and Dr. Suenaga and Dr. Freitag for invaluable discussion. We also thank Ms. Zhang and Ms. Ohwada for specimen preparation and Dr. Yoshimura and Dr. Matsui for discussion and support. This study is supported by the Nanotechnology Network of MEXT, KAKENHI and JST-CREST.
nucleus
References
DF detector
β Radial scattering angle on diffraction pattern Fig. 6. Schematic drawing of Rutherford scattering and corresponding DF intensity profile.
low scattering angle is not negligible in the further quantitative analysis.
4. Concluding remarks We have reported spatially resolved diffractometry with atomic-column resolution, in which diffraction patterns I(u,v) were acquired at 2D positions (x,y) on the specimen and then 4D data I(x,y,u,v) was analyzed. We demonstrated the effectiveness of data processing based on the 4D data, such as the radial
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Spatially resolved diffractometry with atomic-column resolution Koji Kimoto a,n, Kazuo Ishizuka b a b
National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan HREM Research Inc., 14-48 Matsukazedai, Higashimatsuyama, Saitama 355-0055, Japan
a r t i c l e i n f o
abstract
Article history: Received 17 September 2010 Received in revised form 15 January 2011 Accepted 21 January 2011 Available online 1 February 2011
We demonstrate spatially resolved diffractometry in which diffraction patterns are acquired at twodimensional positions on a specimen using scanning transmission electron microscopy (STEM), resulting in four-dimensional data acquisition. A high spatial resolution of about 0.1 nm is achieved using a stabilized STEM instrument, a spherical aberration corrector and various post-acquisition data processings. We have found a few novel results in the radial and the azimuthal scattering angle dependences of atomic-column contrast in STEM images. Atomic columns are clearly observed in dark field images obtained using the excess Kikuchi band intensity even in small solid-angle detection. We also find that atomic-column contrasts in dark field images are shifted in the order of a few tens of picometers on changing the azimuthal scattering angle. This experimental result is approximately interpretable on the basis of the impact parameter in Rutherford scattering. Spatially resolved diffractometry provides fundamental knowledge related to various STEM techniques, such as annular dark field (ADF) and annular bright field (ABF) imaging, and it is expected to become an analytical platform for advanced STEM imaging. & 2011 Elsevier B.V. All rights reserved.
Keywords: Scanning transmission electron microscopy (STEM) Annular dark field (ADF) Annular bright field (ABF) Thermal diffuse scattering (TDS) Kikuchi band
1. Introduction Recent progress in the instrumentation of scanning transmission electron microscopy (STEM) has allowed us to acquire various signals from a specimen using a scanning incident probe [1]. One successful example of STEM-based methods is a combination with an analytical technique such as electron energy-loss spectroscopy (EELS) [2,3]. One-dimensional spectral intensity I(E) is acquired as a function of the probe position (x,y), resulting in three-dimensional (3D) data I(x,y,E) acquisition, i.e., spatially resolved spectroscopy. STEM primarily yields an electron diffraction pattern, which is a major subject for electron crystallography. Established STEM imaging techniques utilize the integrated intensities of diffraction patterns using low-angle circular and high-angle annular detectors to obtain bright field (BF) and annular dark field (ADF) images, respectively. Recently, high-angle ADF imaging is routinely applied because of its compositional sensitivity and intuitive interpretability [4]. Although we reported a few applications of crystal structure analyses based on ADF and BF imaging [5–7], these analyses do not fully utilize the information in the diffraction patterns. There have been several pioneering attempts to make use of more detailed information in diffraction patterns using segmented detectors, in which diffraction intensities were detected as a set of zero-dimensional signals [8–13]. A modern STEM system, however, allows us to record diffraction patterns as two-dimensional (2D) data by varying
n
Corresponding author. Tel.: +81 29 860 4402. E-mail address: [email protected] (K. Kimoto).
0304-3991/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2011.01.029
the probe position. In other words, four-dimensional (4D) data I(x,y,u,v) can be acquired, where (u,v) denotes a scattering vector in the diffraction pattern. This type of technique has been applied to a few materials using a nanometer-size incident probe [14]. In the present paper this 4D analytical technique is termed spatially resolved diffractometry. Here we report atomic-resolution spatially resolved diffractometry. The basic concept of this technique might not appear innovative; however, it substantially enhances STEM imaging capability. Spatially resolved diffractometry provides fundamental knowledge related to conventional STEM, including BF, ADF and annular bright field (ABF) imaging [15,16]. We propose variations of advanced STEM imaging based on spatially resolved diffractometry. We show the novel aspects of thermal diffuse scattering (TDS) that could not have been elucidated using the conventional techniques. 2. Methods We utilized a dedicated STEM instrument (Hitachi High-Technologies, HD-2300C) [17] equipped with a cold field-emission gun, a high-resolution pole piece, a digitized scanning system (Gatan, DigiScan), an energy filter (Gatan, GIF-Tridiem 863) [18] and a spherical aberration corrector (CEOS GmbH, CESCOR). The original commercial STEM system was modified to improve its mechanical and electrical stability. The acceleration voltage was 200 kV and the convergent semiangle was 27.5 mrad (except for Fig. 3b). The spatial resolution of the instrument was found to be about 0.1 nm using a conventional ADF image. The spherical aberration corrector is
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indispensable not only for high spatial resolution but also for the observation of BF disk without distortion. The phase shift due to the aberrations of the probe-forming system was found to be less than the p/4 limit up to 30 mrad using CEOS software; therefore, the aberrations did not affect the major features of BF disk. Spatially resolved diffraction patterns were acquired using a software (Gatan, STEM Diffraction-Imaging) and a charge-coupled-device (CCD) camera of the energy filter. An incident probe was scanned on 64 64 points with a 0.018 nm step, and the diffraction patterns were acquired as 128 128-pixel data up to 70 mrad (28 nm 1) in radial scattering angle. As a result, 4D data (64 64 128 128) was acquired. The exposure time for each diffraction pattern was 0.2 s and the total acquisition time was 32 min, including the time required for specimen drift correction. To realize high accuracy of the analyzed position, specimen drift was repeatedly corrected 256 times during the total acquisition, which substantially decreases throughput. Conventional ADF images were also observed using an actual annular detector whose inner angle was 80 mrad. Although the conventional ADF images were used for the drift correction during the experiment, all STEM images presented here were obtained from 4D data acquired by spatially resolved diffractometry. A (0 0 1) SrTiO3 specimen for the STEM observation was prepared by mechanical thinning and Ar ion milling. The specimen thickness at the analyzed area was estimated to be about 30 nm using the log-ratio method of EELS, assuming a mean free path of total inelastic scattering of 106 nm [19]. The 4D data was processed using the Gatan software and inhouse scripts [20] of DigitalMicrograph (Gatan). To perform an advanced investigation, we transformed the 4D data I(x,y,u,v) into processed 3D data, I(x,y,b) or I(x,y,f), where b and f denote the radial scattering angle and the azimuthal scattering angle, respectively.
3. Results and discussion 3.1. Experimental results and primitive survey Fig. 1a shows an ADF image constructed from the 4D data with inner and outer corresponding angles of 20 and 25 nm 1,
BG O
respectively. The contrast of this ADF image is similar to that of a conventional ADF image. Fig. 1b–e shows four diffraction patterns obtained on Sr (b), TiO (c) and O (d) atomic columns, and between atomic columns (BG) (e). Each diffraction pattern is obtained at each rectangle area, as shown by open squares in Fig. 1a. The diffraction intensities are dominated by the BF disk because of the small specimen thickness and the large convergence angle. Although the BF disks in the diffraction patterns taken on atomic columns (Fig. 1b–d) exhibit approximate 4 mm symmetry, the other BF disk (Fig. 1e) shows an asymmetric pattern. If we measure the BF intensity using an annular detector, this asymmetric intensity is approximately compensated, and accordingly the ABF image shows distinct contrasts only on atomic columns. Fig. 1 also shows the atomic site dependence of Kikuchi band (e.g., [21]). As shown in Fig. 1b–d, clear Kikuchi bands are observed only on the Sr and TiO atomic positions, and it indicates that the origin of Kikuchi bands is TDS localized on atomic sites. Thus, one can selectively visualize TDS by choosing excess Kikuchi band signals. Fig. 2 shows examples of such angular-selective dark field (DF) imaging. Fig. 2a–d shows DF images whose intensities are obtained from a very small solid angle (2 nm 1 in diameter) as shown by small open circles (i)–(iv) in Fig. 1b. Fig. 2a and c shows DF images of the excess Kikuchi bands, and Fig. 2b and d shows those slightly outside the excess Kikuchi bands. This result indicates important fundamental features of DF (or ADF) imaging. Firstly, atomic columns can be resolved despite the small detection solid angle of DF imaging. An annular detector for integrating the full azimuthal angle is not a prerequisite for resolving atomic columns, but a high-angle scattering is critical as demonstrated in the following Section 3.2. This result is a very important finding because it reveals the major origin of the incoherent feature in high-angle ADF imaging. Note that this feature of DF images is different from that of ABF images, because azimuthal averaging with appropriate radial scattering range [16] is indispensable to realize the incoherent imaging feature (e.g. thickness and defocus dependence) of ABF images. Secondly, the resolution of DF images is isotropic and basically independent of the azimuthal angle of the detector (its details will be discussed in Section 3.3). Thirdly, the DF images of the excess Kikuchi band exhibit high contrast compared with those
TiO
Sr
0.39 nm
10 nm-1
Sr
TiO
O
BG
Fig. 1. Experimental result of spatially resolved diffractometry with high spatial resolution. (a) ADF image constructed from 4D data, in which the corresponding inner and outer angles are 20 and 25 nm 1, respectively. (b)–(e) Diffraction patterns at Sr (b), TiO (c), O (d) atomic columns and at another point between atomic columns (e), whose positions are shown as open squares in (a). The contrast of the outer part in the diffraction patterns is enhanced to observe Kikuchi bands. The broken line in (b) shows the shadow edge of the conventional ADF detector and CCD detector. The small open circles in (b) show the detection area for the DF images shown in Fig. 2.
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Sr
Position in reconstructed STEM images
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0
Fig. 2. Angular-selective DF images (a)–(d) constructed from 4D data and their intensity profiles (e). These images are not ADF images but DF images obtained using a small detection solid angle. Note the atomic-column contrast in spite of the small detection solid angle, where the detector positions of the DF images (a), (b), (c) and (d) are denoted as small circles (i), (ii), (iii) and (iv) in Fig. 1b, respectively; (a) and (c) show images of the excess Kikuchi band, and (b) and (d) show images slightly outside the Kikuchi band. (e) DF intensity along the rectangle shown in (a). The DF image contrast is improved by selecting the excess Kikuchi band signal.
Scattering angle (mrad)
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10 15 Scattering angle (nm-1)
20
5-10 nm-1 10-15 nm-1 15-20 nm-1
0
5 10 15 Scattering angle (nm-1)
TiO O 20
Fig. 3. Radial angular distributions at four different probe positions and STEM images taken at different radial scattering angles; (a) and (b) show experimental results obtained using a large convergence angle of 27.5 mrad and a small convergence angle of 11 mrad, respectively.
obtained from the outside of the band, as plotted in Fig. 2e. For example, the peak to background (PB) ratios of the upper profiles (i, iii) and the lower ones (vi, ii) are 2.0 and 1.5, respectively. Since TDS is localized on the atomic column, one can improve the PB ratio of DF images by setting the detector only on the excess Kikuchi bands. This imaging method will practically enhance the DF image contrast of a crystalline specimen because the scattering signal from an amorphous layer (e.g., a surface damaged layer or contamination) must have a homogeneous azimuthal distribution. 3.2. Radial distribution analysis Since the primary parameter in diffractometry is the radial scattering angle b, we calculate the rotationally averaged radial
scattering distribution I(b) of each diffraction pattern. As a result, 4D data I(x,y,u,v) is converted into 3D data I(x,y,b). Fig. 3a shows the radial angular distributions at four different probe positions: Sr, TiO, O and background (BG). At a high radial scattering angle, the atomic number dependence of the ADF signal is clearly observed in both intensity profiles and ADF images (insets). We also performed a similar experiment using a small convergence angle of 11 mrad (Fig. 3b). It is found that the absolute DF intensity is not always dependent on atomic number Z, particularly for a relatively low scattering angle (e.g., 20–30 mrad). Since high-Z atoms scatter electrons toward a high angle, their scattering distribution at a relatively low scattering angle appears to be absorbed. The inset STEM images show the contrast variation as a function of the radial scattering angle b. These STEM images are cross sections (x–y plane)
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probe position. As a result, we obtain another 3D data IDF(x,y,f) whose dimensions are 64 64 252 and the minimum azimuthal step Df is 1.41. Fig. 5a–d shows examples of azimuthally resolved DF images, in which schematic quadrants of insets show each azimuthal angle range, i.e., annular-quadrant-detector observation. Open circles, which are placed at precisely the same position in Figs. 5a–d, clarify relative shifts in the four DF images. It is found that the positions of the bright spots in the DF images are shifted on changing the azimuthal angle, as shown by the white arrows in Fig. 5a–d. The direction of the peak shift is opposite to the detection direction. We have evaluated the azimuthal angle dependence in detail using the 3D data IDF(x,y,f), as shown in Fig. 5e, in which we plot the relative shifts of Sr (circles) and TiO (triangles) peaks in comparison with an ADF image (Fig. 1a). The relative shifts were measured using cross correlation [7,20]. Although the evaluation suffers poor SN ratio of the DF image, it is found that the bright spots of Sr and TiO sites are similarly rotated in a circular motion. Solid and dotted lines are curve fittings for the Sr and TiO sites assuming cosine and sine functions, respectively. The averaged rotational amplitudes of the Sr and TiO sites are found to be 20 and 16 pm, respectively. The difference in amplitude along the x- and y-axes is less than a few picometers (see Fig. 5e), indicating high reproducibility. The magnitudes of these shifts are not negligible compared with the probe size in recent advanced STEM instruments [11,22], the high precision achieved in our conventional STEM observation [7] or the spatial incoherence in a quantitative STEM simulation [23]. We find that the present experimental result is consistent with a classical view of charged-particle scattering, i.e., the Rutherford scattering of an electron by a nucleus. Fig. 6 shows a schematic of Rutherford scattering and the corresponding DF intensity profile. The DF intensity measured at a specific azimuthal angle (lower part of Fig. 6) has an off-centered peak in the STEM DF image (upper part of Fig. 6) in the classical particle viewpoint. The rotational displacement measured in Fig. 5 is consistent with this schematic, and the amplitude is considered to be an impact parameter. To our knowledge, this is the first measurement of the azimuthal dependence associated with DF image contrast.
normal to the b-axis of the 3D data I(x,y,b). A STEM image obtained at a scattering angle range of 5–10 nm 1 (Fig. 3a) has recently been recognized as an ABF image [16]. These variations of post-acquisition processing are advantageous in spatially resolved diffractometry. We observe the detailed probe position dependence of the radial distribution, e.g., I(x,b). In other words, the cross section along the b-axis (e.g., x–b plane) of the 3D data I(x,y,b) is observed (Fig. 4). Fig. 4a shows a BF image constructed from the 3D data—corresponding BF detection semiangle is 2.3 nm 1. We observe two cross sections (Fig. 4b and c) whose probe positions are shown as rectangles in Fig. 4a. The probe position dependence of the angular distribution is clarified by this procedure. The optimum BF detector range for enhancing the signal to noise (SN) ratio without contrast reduction can be estimated to be about 2 nm 1, as shown by a dotted line in Fig. 4c. Fig. 4d shows ABF and ADF intensity profiles whose corresponding detection angles (b0–b3) are indicated in Fig. 4b. The ABF image profile shows negative peaks on both Sr and O atomic columns as previously reported [15,16], although ADF images show peaks only on the Sr atomic columns. Due to the complicated angular dependence of BF intensity, it is estimated that the relationship between the darkness of an atomic column and its atomic number is rather dependent on the ABF detection angular range. The high scattering angle range is also informative; for example, we can observe the dependence of ADF image contrast on the radial scattering angle, as shown in Fig. 4d. A higher-angle ADF image has higher contrast.
3.3. Azimuthal distribution analysis of DF image Since the azimuthal scattering angle f is also an important diffraction parameter, we investigate the azimuthal angle dependence of the high-angle DF image contrast. In this study the DF intensity of each diffraction pattern within a radial scattering angle range from 21.4 to 24.5 nm 1 is integrated with varying azimuthal angle f (as shown by the inset of Fig. 5e), and then the azimuthal angle dependence of the DF intensity IDF(f) is evaluated at each
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10 20 Scattering angle (nm-1)
Fig. 4. Variations of radial angular distribution analysis. (a) BF image, in which a corresponding BF detector angle is 2.3 nm 1. (b) and (c) Probe position dependences of the angular distribution, whose corresponding probe positions are shown in (a). In (b) and (c) brightness is proportional to the logarithm of its intensity. On the basis of this experimental result, the optimum range of the BF detector can be estimated as shown by the dotted line in (c). (d) Intensity profiles of STEM images at four scattering angles b0–b3 obtained using the result of (b). The site dependences of ABF and ADF contrasts are clearly observed.
K. Kimoto, K. Ishizuka / Ultramicroscopy 111 (2011) 1111–1116
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x DF image
along y-axis 15 pm
0
20 pm
-50 0
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100 150 200 250 Azimuthal angle of DF detection, (degree)
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Fig. 5. Azimuthal scattering angle dependence of DF images whose radial integration range is from 21.4 to 24.5 nm 1. (a)–(d) Azimuthal integrated DF images whose detection range is schematically shown as each inset, i.e., annular-quadrant-detector observation. White arrows show the direction of relative shifts. (e) Detailed analysis of the relative displacements of Sr and TiO column peaks. Circles and triangles show experimental results and solid and broken lines indicate the curve fitting of the Sr and TiO atomic column contrasts, respectively. The insets in (e) are schematics of a diffraction pattern and a DF image. The rotational amplitudes of the Sr and TiO atomic columns are found to be 20 and 16 pm, respectively.
The impact parameter b of Rutherford scattering is given by the following equation [24]: b¼
e2 Z 1 1 þ cos b , 4pe0 mv2e sin b
ð1Þ
where e0 is the permittivity of space and e, ve and m denote the charge, mass and velocity of an electron, respectively. We calculated the impact parameters for Sr and Ti under the present experimental conditions, including the relativistic correction to the electron mass. The scattering angle b is set to 53 mrad, which corresponds to the radial angle from the center of the BF disk to the integration angle. The calculated impact parameters for 38Sr and 22Ti are 6 and 3.5 pm, respectively. The calculated values are not equal to the experimental values, but are also of picometer order, and the difference between the Sr and TiO sites is qualitatively consistent with their atomic numbers. Note that the minimum scattering angle b is rather small because of the large convergent angle, and therefore the maximum impact parameter becomes large. Consequently, the azimuthal dependence of the DF
image contrast can be approximately interpreted from the classical viewpoint of Rutherford scattering. Although Rutherford scattering is the simplest model of electron scattering, it is still usable for the qualitative interpretation of this experiment. There are lots of other physical factors to be considered, such as dynamical scattering effects and other inelastic scatterings. In the case of spherical aberration corrector, the depth of focus becomes short; e.g., it is estimated to be 6 nm in full width at half maximum. Therefore, even in the case of thick TEM specimen, focused incident electrons are scattered by the limited number of atoms, and the above-mentioned impact parameters might be increased by the plural scattering. This atomic-column image displacement is a fundamental issue in STEM imaging. The difference between each atomic site rotation is problematic in crystal structure analysis because it affects the observed structural symmetry. The present experimental result for SrTiO3, however, shows that both (Sr and TiO) atomic-column contrasts are similarly shifted. Since the impact parameter becomes large on using a low scattering angle, it is considered that the enlarged impact parameter in the case of a
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IDF Impact parameter
DF signal IDF b Probe position x
x
b electron
and the azimuthal scattering angle dependences, I(x,y,b) and I(x,y,f), respectively. Spatially resolved diffractometry allows us to perform various types of post-acquisition data processing, and it provides us fundamental knowledge related to existing STEM imaging techniques. We found that the atomic columns of DF images can be observed using a small solid angle, and the DF contrast can be improved by selecting the excess Kikuchi band or a large radial scattering angle. We also found that the bright dots of atomic columns in DF images are shifted on changing the azimuthal scattering angle of the DF detector. This can be approximately interpreted on the basis of Rutherford scattering. At present, spatially resolved diffractometry has a few technical difficulties, such as a long acquisition time owing to specimen drift correction and a relatively long dwell time for diffraction acquisition. This is, however, a similar situation to that during pioneering studies on spatially resolved spectroscopy in the 1980s [2,3]. The recent developments of high-sensitivity high-speed detectors (e.g., direct detection CMOS) and stabilized microscope columns are expected to increase the practicality of spatially resolved diffractometry, making it an analytical platform for state-of-the-art STEM imaging.
Acknowledgements We would like to express our thanks to Mr. Nakamura, Mr. Soda, Mr. Kato and Mr. Aizawa for improving our microscope performance, Dr. Wilbrink and Dr. Menon for advice about DigitalMicrograph and Dr. Suenaga and Dr. Freitag for invaluable discussion. We also thank Ms. Zhang and Ms. Ohwada for specimen preparation and Dr. Yoshimura and Dr. Matsui for discussion and support. This study is supported by the Nanotechnology Network of MEXT, KAKENHI and JST-CREST.
nucleus
References
DF detector
β Radial scattering angle on diffraction pattern Fig. 6. Schematic drawing of Rutherford scattering and corresponding DF intensity profile.
low scattering angle is not negligible in the further quantitative analysis.
4. Concluding remarks We have reported spatially resolved diffractometry with atomic-column resolution, in which diffraction patterns I(u,v) were acquired at 2D positions (x,y) on the specimen and then 4D data I(x,y,u,v) was analyzed. We demonstrated the effectiveness of data processing based on the 4D data, such as the radial
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