Artifacts in aberration-corrected ADF-STEM imaging

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Ultramicroscopy 96 (2003) 275–284

Artifacts in aberration-corrected ADF-STEM imaging Zhiheng Yua, Philip E. Batsonb, John Silcoxc,* a

Physics Department, Cornell University, 117 Clark Hall, Ithaca, NY 14850, USA b IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, USA c School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA Received 2 August 2002; accepted 27 October 2002

Abstract The introduction of an experimental black level may introduce unintended artifactual details into high-resolution annular dark field scanning transmission electron microscopy (ADF-STEM) lattice images. This article presents the multislice simulation results of such possible situations. Three simulated scanning transmission electron microscopy ( are scanned on the surface of a /1% 10S oriented Si/Ge crystal. The simulation (STEM) probes of sizes 0.8, 1.2 and 2.0 A results suggest that high-frequency artifact peaks will appear in the power spectra when an artificial black level clips the lowest (background) signal. The lowest signal in an ADF-STEM image decreases as the incident probe shrinks in size. Therefore, care must be taken when interpreting the resolution limit of the microscope from images taken with nonzero ( microscope. The simulation result is compared with an experimental black level setting, especially in case of sub-A image and they agree with each other. The analysis suggests that aberration corrected STEM provide sensitive low level detail. r 2003 Elsevier Science B.V. All rights reserved. ( probe; Black level; Artifact; Power Keywords: Scanning transmission electron microscopy (STEM); Annular dark field (ADF); Sub-A spectrum

1. Introduction The recent successful implementation of a spherical aberration (i.e., Cs or C3 ) corrector has demonstrated the achievement of an electron probe with a full-width at half-maximum height ( in annular dark field scanning that is less than 1 A transmission electron microscopy (ADF-STEM) images [1,2]. ADF-STEM high-resolution lattice *Corresponding author. Cornell University, 235 Clark Hall, Ithaca, NY 14850, USA. Tel.: +1-607-255-3332; fax: +1-607255-7658. E-mail address: [email protected] (J. Silcox).

images are formed by scanning an atomic scale focused probe over zone-axis oriented crystals and collecting the high-angle scattering with the ADF detector. Since the spatial resolution in ADFSTEM is determined by the probe size [3–5], this implies that the highest frequency observed in the power spectrum of a lattice image should be less than the reciprocal of the probe size. Thus, the power spectrum is often used to identify the resolution limit in the image (some examples can be found in Ref. [5]). The purpose of this paper is to note circumstances leading to the introduction of unintended artifactual detail into lattice images by the introduction of an experimental black level.

0304-3991/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-3991(03)00093-7

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For a uniform-thickness crystal, the highest ADF signal arises when the probe is located on the atomic column and the lowest (background) signal when the probe is located off the atomic column. When the STEM probe size is larger than or comparable to the spacing between neighboring atomic columns, the background signal is high. It is usually well above an experimentally introduced black level in some imaging systems. However, when the probe size shrinks significantly below the atomic spacing, higher order (but weak) Fourier components appear in the image. The background drops significantly. Should the intensity now be recorded with an experimentally introduced black level above the background level, clipping of the signal will occur and artifacts will be introduced in the power spectrum of the lattice images. A power spectrum of a recent micrograph caused some concern until it was realized that it was an example of this situation. Fig. 1 shows an

experimental lattice image and the associated power spectrum of a sample composed of 70% Si and 30% Ge obtained on the 120 kV IBM VG STEM equipped with a Cs corrector [5]. The FWHM size of the experimental probe was ( (the fifth-order estimated to be about 0.8 A aberration C5 ¼ 10 mm, the third-order aberration C3 ¼ 15 mm and objective aperture=25 mrad). As a result, high spatial frequency signals such as /5 5 1S peaks show up in the power spectrum. It also shows more striking and puzzling facts: even higher frequency signals are contained in the power spectrum due to the existence of the /7 7 1S and /8 8 0S peaks (and the /8 8 0S peaks ( which is far less correspond to a resolution of 0.5 A than the probe size) while the /6 6 0S peaks are absent. We speculated that a possible origin of this enigma is an experimentally introduced black level that arises from a DC offset necessarily introduced to cancel dark currents at the output of the photomultiplier and prior to the pre-amplifier chain. Fig. 2 shows an example of a black level setting clipping a signal and introducing artifacts to the recorded image. Since the DC offset is set experimentally an error can easily creep in if the image has unusual characteristics. We, therefore, have explored the possible effects of black level settings on ADF-STEM imaging with various probe sizes. This paper presents an account of

Input Signal

Black Level Fig. 1. An experimental lattice image of /1% 1 0S Si/Ge crystal obtained on the IBM VG STEM equipped with a Cs corrector and its power spectrum. The FWHM size of the experimental ( (C5 ¼ 10 mm, probe is estimated to be about 0.8 A C3 ¼ 15 mm and objective aperture=25 mrad). Note the presence of the /7 7 1S and /8 8 0S peaks and the absence of the /6 6 0S peaks in the power spectrum. The large thick circle of radius 50 mrad indicates the expected resolution limit for the ( probe which is twice the objective aperture size (for 0.8 A details, see the Section 4 and the Refs. [26–28]). The small thin ( probe. circle corresponds to the 1.2 A

Recorded Signal

Fig. 2. An example of a black level setting clipping the signal and introducing artifacts to the recorded image.

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multislice simulations of ADF-STEM imaging with an artificially introduced black level for three different STEM probes. Comparison with an experimental image emphasizes the subtleties emerging in those images available via aberration-corrected ADF-STEM.

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where the contribution of chromatic aberration is included in the effective defocus Dfeff : When C5 ¼ 0; optimizing Eq. (1) reduces to the well-known Scherzer condition [6,7]. Given a constant positive C5 of the order of millimeters, C3 in micrometers and Dfeff in angstroms as in normal experimental units, wðyÞ stays close to zero over a certain angular region as shown in Fig. 3(a). Choice of the objective aperture is thus a compromise. A large objective aperture gives a smaller probe but a bigger value of wðyÞ near the edge of the objective aperture results in a large tail on the probe, as shown in Fig. 3(b). As reported earlier, it is necessary and beneficial to minimize the probe tails [1]. Therefore, we choose C3 ; Dfeff and objective aperture to keep wðyÞ close to zero (absolute value less than 0.1p) over the objective aperture region. As a result, for C5 ¼ 10 mm and ( l ¼ 0:0334 A we choose C3 ¼ 15 mm, ( and a 25 mrad objective aperture Dfeff ¼ 28 A to obtain a STEM probe with the FWHM size of ( as shown in Fig. 4. Similarly, a STEM probe 0.8 A ( is generated with with the FWHM size of 1.2 A ( and a 14.3 mrad obC3 ¼ 15 mm, Dfeff ¼ 6 A jective aperture. An optimized probe with FWHM ( is also shown in Fig. 4 for the case size of 2.0 A C5 ¼ 0 mm generated following the conventional procedure [7].

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The primary effect of adding an aberration corrector to the system is to provide an additional controlled parameter (i.e., the third-order spherical aberration term, C3 ) to the electron wave forming the probe. In the presence of C3 and C5 ; the aberration function becomes
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3. Multislice simulation Multislice simulation is an important theoretical approach for calculating the evolution of an electron beam inside a sample [8–14]. It divides the sample into many thin layers, calculates the scattering of the incident electron beam by each layer and then propagates the scattered electron beam to the next layer. Kirkland [7] presents and discusses the computer codes realizing multislice simulation that have been successfully used to match the simulated CBED patterns with the experimental ones [15,16]. The ADF intensity for a sample with certain thickness collected by a detector can be calculated by integrating the CBED pattern formed by the exit electron beam over the detector dimension. We divide the

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Fig. 4. (a) Aberration functions and (b) intensity profiles of three simulated STEM probes with FWHM sizes of 0.8, 1.2 and ( 2.0 A, respectively. The parameters are: V ¼ 120 kV, ( for C5 ¼ 10 mm, C3 ¼ 15 mm, a ¼ 25 mrad and Df ¼ 28 A ( probe, V ¼ 120 kV, C5 ¼ 10 mm, C3 ¼ 15 mm, the 0.8 A ( for the 1.2 A ( probe, a ¼ 14:3 mrad and Df ¼ 6 A V ¼ 100 kV, C5 ¼ 0 mm, C3 ¼ 1300 mm, a ¼ 8:9 mrad and ( for the 2.0 A ( probe. Df ¼ 566 A

procedure used to simulate the effect of black level on ADF imaging into the following two steps. 3.1. Step 1: line scan of ADF-STEM intensity Since the specimen in the experiment is a mixture of 70% Si (Z ¼ 14) and 30% Ge (Z ¼ 32), in the simulation we modeled the specimen with an average Z ¼ 14  0:7 þ 32  0:3E19 ( similar to that and a lattice constant of a ¼ 5:43 A   of silicon. The optical axis is parallel to the 1% 10 zone axis of the specimen and a projected unit cell along this direction is shown in Fig. 5. The unit cell was replicated five times in the x direction and

eight times in the y direction to form a super cell of (  30.72 A ( and it is represented by 27.15 A 512  512 pixels. Preliminary calculations with different setups suggest that these are good choices for this calculation. A STEM probe can be put anywhere on top of the super cell and the multislice technique is used to calculate the exit beam after a certain thickness. The ADF intensity is obtained by integrating over the ADF detector range (40–200 mrad in all the simulations) and normalized by rescaling the incident probe intensity to one. Thus, ideally a two-dimensional simulated ADF image can be obtained by putting the incident probe on every pixel of the super cell, propagating it through the whole thickness and then integrating the CBED to get the ADF intensity for each pixel. Unfortunately, this will take weeks or perhaps even months of computing time with a computer with 450 MHz CPU (the computer we used for this simulation has dual processors of 450 MHz each ( thick sample and and 512 MB RAM) for a 600 A 512  512 incident probe positions. Instead, a one-dimensional line scan can be simulated by stepping the incident probe along a specific line over one or two unit cells and calculating the resultant ADF intensity at each probe position over that line. Specifically, line scans along the x direction (/0 0 1S) and the y direction (/1 1 0S) were carried out for each

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3.2. Step 2: FFT of the ADF line scan intensity and introduction of a black level Power spectra of real space lattice images have been widely used to analyze microscope performance [5, 17–19]. We carried out a one-dimensional fast Fourier transform (FFT) of the realspace line scan intensity. The intensity profiles in Fig. 6 were first extended 32 times to increase the real space dimension and therefore increase the reciprocal space resolution. A Tukey window was then applied to the extended data to make the Fourier peaks in reciprocal space symmetric and sharp [21,22]. And finally an FFT of the modulated data was carried out. Fig. 8 shows the FFT of the data in Fig. 6 with the Fourier peaks indexed. The peaks labeled as /X X 1S with X ¼ 1; 3 and 5 represent the one-dimensional components of the corresponding peaks in two-dimensional reciprocal space projected on the y-axis.

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of the three probes. The dimension of the line scan extended over two unit cells with the STEM probe located in turn on every pixel along the line. Fig. 6 shows the calculated ADF intensity profiles of the line scan in the y direction for a ( thick specimen for the three STEM probes. 600 A ( probe is just a The line scan profile of the 2.0 A constant plus a simple cosine wave, determined by the resolution as discussed by earlier papers for ( probe and the 0.8 A ( InP studies [17–19]. The 1.2 A probe add much more detail, reflecting the higher resolutions. The inset magnifies the lowest intensity region and reveals a small peak half way between two atomic columns in the y direction for the two smaller probes. This small peak probably arises from the tails of the probe sitting on the nearest atomic column, as previously suggested as the explanation for the observed off-column bright spots due to subsidiary peaks (tails) of the incident probe [20]. Note that the background signals for ( probe and the 0.8 A ( probe are much the 1.2 A ( lower than that for the 2.0 A probe. The line scan profiles along the x direction are shown in Fig. 7, ( suggesting that both the 0.8 and the 1.2 A ( probes resolve the dumbbells while the 2.0 A probe does not.

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The highest resolvable frequencies are /1 1 1S, ( /3 3 1S and /5 5 1S for the 2.0, 1.2 and 0.8 A probes, respectively. An artificial black level can be introduced as follows: ( Id ¼

I0  b when I0 > b; 0 otherwise;

ð2Þ

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where I0 is the true (input) intensity of the exit electron beam reaching the detector, b is the black level introduced experimentally by the imaging system and Id is the resultant recorded (output) intensity by the imaging system. After the black level was applied to the original data, the FFT was repeated to examine the effects of a detector black level. As an example, Fig. 9 shows the comparison between the FFT for the y direction line scan ( probe with two different intensity for the 0.8 A

black level settings, indicating artifactual highfrequency peaks can result from a black level. By changing the black level systematically and finding the FFT of the corresponding Id ; we obtained the changes of various Fourier peaks as a function of the respective black levels for the y direction line ( probe, as shown in Fig. 10. scan with the 0.8 A ( Fig. 11 shows the same plots for the 1.2 and 2.0 A probes. These plots suggest that when the black level is high enough, there will be higher-frequency artifacts in the power spectra for all three probes.

4. Discussion 4.1. Image calculations The results reported above indicate that an identifiable, distinct background becomes evident

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between the atom columns as the probe size nears ( (Figs. 6 and 7). This differs from the case at 1A ( where the signal is a sum of a few cosine waves 2A superimposed on a constant signal level. The atom column peak narrows and the peak intensity grows as the probe width is reduced. We conclude that the atom column image is still dominated by the instrument optics whereas the background is now controlled by the sample properties. ADF-STEM imaging is a complex nonlinear process and the interpretation is not necessarily trivial. However, a linear approximation to the ADF images can be made based on the incoherent imaging model (for example, see Ref. [17]) that gives: Sk ðtÞ ¼ HðkÞFk ðtÞ;

ð3Þ

where HðkÞ is the ADF-STEM contrast transfer function (CTF) [4,17,23–26]. It is the Fourier transform of the intensity profile of the incident probe and is determined only by the electron optical conditions of the microscope. Fk ðtÞ is the specimen object function in reciprocal space independent of the instrument. For an ideal microscope with an infinitely high resolution (the probe is a delta function), the CTF is unity for all spatial frequencies. As a result the specimen object function Fk ðtÞ for any spatial frequency k is conveyed by the resultant image and can be found from the corresponding power spectra. In the presence of a finite resolution limit, kr those frequencies higher than this value are not detected by the microscope. In an earlier paper [17] addressing a situation very similar to the present case, (zone axis imaging of (1 0 0) InP) the CTF was found to be completely consistent with simulations. Comparison of the CTF predictions with experiment were also in substantial agreement once effects such as chromatic aberration, astigmatism and so forth were taken into account. Thus we can take the CTF to be a good predictor of zone axis imaging. ( Fig. 12 shows the CTF for the 2.0, 1.2 and 0.8 A probes, respectively. These curves exhibit an increasing cutoff frequency, kr and also increase for non-zero k as the probes get smaller. Hð0Þ ¼ 1

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for all three probes (i.e. the CTF is always unity at zero spatial frequency) since Hð0Þ is just a normalized spatial integration of the probe. All frequencies in the object above kr contribute nothing to the image. Fig. 12 also shows that, as the probes get smaller, the number and intensity of the non-zero k spacings increase. Thus, the electron probability in the atom columns grows relative to that in the background as the resolution improves. 4.2. Resolution and the effects of black level settings The smaller probes reveal more detailed features of the specimen as illustrated by Figs. 6 and 7. Power spectra obtained by Fourier transforming the real space lattice images have been widely used and are believed to be an indication of the resolution [5,17–19]. Fig. 8 confirms this by showing the high frequency limit is approximately ( the reciprocal of the probe sizes (for the 0.8 A probe the high frequency limit in Fig. 8 is ( 1 which is very close to the reciprocal of B1.3 A ( Fig. 8 also agrees with another wellthe 0.8 A). known criterion applicable to ADF-STEM. The highest detectable spatial frequency is slightly less than twice the size of the objective aperture [26–28] (see Fig. 1). (In fact the /5 5 1S and the /6 6 0S spots are respectively, 44 mrad and 52 mrad, from the origin in reciprocal space according to Bragg’s law and the objective aperture is 25 mrad for the ( probe.) 0.8 A Fig. 8 is for the ideal case when the black level setting is zero. In reality, some imaging systems record images with small positive black level settings. When the black level settings are lower than the background intensities in the ADF image, the resultant power spectra are similar to those with a zero black level setting and no high frequency artifacts are introduced. These are illustrated by the high-frequency (artifact) Fourier peaks in Figs. 10 and 11 that stay essentially zero for black level settings lower than the background signal. As soon as the black level becomes bigger than the background intensity in the ADF images, high frequency artifacts are introduced, as shown by Figs. 9–11. Now the power

spectra are quite different from the original ones with higher frequency peaks showing up well beyond the resolution limits. This jeopardizes the ability to use power spectra as indications of the resolution. Another interesting point evident in Fig. 9 is that the /6 6 0S peak is more than 20 times lower than the /7 7 1S or /8 8 0S peak. This explains the experimental observation of the presence of the /7 7 1S and /8 8 0S peaks and the absence of the /6 6 0S peak in Fig. 1. The power spectrum seen in Fig. 1 also shows a high eccentricity of B3, i.e., the pattern extends much further along the y direction than in the x direction. Two circles corresponding to the resolu( probe sizes are tion limits of 0.8 and 1.2 A projected onto that power spectrum. One possible explanation for this is a small 60 cycle additional deflection on the x-scan corresponding to approxi( degradation of the resolution. An mately 0.5 A additional possible factor is the shape of the dumbbell in the image (see Appendix A). Our calculations suggest that this latter term is no more than a ratio of B2 and thus cannot account for the full value of this artifact. To illustrate this, Fig. 13 shows the simulated power spectra in the x direction for the 0.8 and ( probes in the presence of black level settings 1.2 A at the same value as that in Fig. 9 (the y direction ( probe, higher power spectra). For the 0.8 A frequency spots beyond /0 0 4S such as /1 1 5S and /1 1 7S should show up no matter whether a ( probe, black level is present or not. For the 1.2 A the maximum frequency detected is the /0 0 4S peak for a black level setting of 0.032(2). From Fig. 7 one can see this black level setting is lower ( probe so than the background signal for the 1.2 A no artifactual higher frequency peaks show up in the power spectrum. This is consistent with the experimental observation that in the x direction the power spectrum stops at /004S spots (see Fig. 1). ( probe is The background signal for the 2.0 A ( probe and the much higher than that for the 0.8 A ( probe. Thus, images with a 2.0 A ( probe 1.2 A tolerate higher black levels than images ( probes. A black level formed with 0.8 and 1.2 A ( level could be setting tolerated at a 2.0 A

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( level. In comparison with dangerous at a 0.8 A the effects in the reciprocal space, the effects of black level settings in real space are not as obvious nor as remarkable. Fig. 14 shows the real space data corresponding to the power spectra shown in Fig. 9. Apart from the vertical shift, it is difficult to distinguish the two curves by simple inspection. This is because the dominant features in real space are the strong on-column peaks and the small black level settings may only affect the lower off-column signals. However, the lower offcolumn signals may contain important information about the specimen and the probe and the slight modifications may introduce artifacts in the power spectra.

Artifacts will be introduced into an image when an experimental black level setting is big enough to clip the signal. Caution is necessary. For the ADFSTEM case, the lowest (background) signal decreases as the incident probe shrinks in size. ( scale, As the STEM probe advances into the sub-A the incident probe will produce a very low background signal which may be easily lower than the black level settings (if they exist) and thus introduce high-frequency artifacts in the data. If readily available during image recording, a histogram of image intensities might ensure accurate black level settings. The modification due to black level may be hardly noticeable in the real space lattice images since only the weakest signals in the images are modified. The changes in the Fourier space can be very significant with high-frequency spots well beyond the resolution limit showing up, which may lead to incorrect interpretations. In the example reviewed here, it is clear that the experimental image recorded on the IBM instrument lost some detail as a result of applying a relatively minor black level setting. This suggests that very low intensity signals (the small peaks

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between the on-column signals in Fig. 6) can be actually recorded by that instrument.

Acknowledgements This work was supported by the Cornell Center for Materials Research (CCMR), a Materials Research Science and Engineering Center of the National Science Foundation (DMR-0079992). Special thanks to K.A. Mkhoyan and R.R. Vanfleet for reading the manuscript and giving helpful comments and suggestions. Z.Y. would like to thank E.J. Kirkland for valuable discussions of black levels in STEM. Appendix A. The effect of the dumbbell shape function The ADF image of (1 1 0) Si/Ge crystal (such as the one in Fig. 1) can be treated as a dumbbell shape object repeated periodically over space. According to the definition of convolution, the image Iðx; yÞ is just a convolution between a dumbbell shape function Dðx; yÞ with one underlying two-dimensional Bravais lattice Lðx; yÞ (each atom dumbbell is represented by a lattice point). Iðx; yÞ ¼ Dðx; yÞ#Lðx; yÞ:

ðA:1Þ

Therefore, the power spectrum FIðkx ; ky Þ (the Fourier transform of the image) is a product of the Fourier transform of the underlying lattice FLðkx ; ky Þ with that of the dumbbell shape function FDðkx ; ky Þ: FIðkx ; ky Þ ¼ FDðkx ; ky ÞFLðkx ; ky Þ:

ðA:2Þ

Suppose in the real space Dðx; yÞ has size ax in the x direction and ay in the y direction, then in reciprocal space, the dimension of FDðkx ; ky Þis 1=ax in the x direction and 1=ay in the y direction. From the simulation results in Figs. 6 and 7, ( for the dumbbell shape ax ¼ 3:4 and ay ¼ 1:8 A ( probe at function in the image formed by the 0.8 A the value of 0.032. This gives an aspect ratio (the size in the y direction divided by that in the x direction) of roughly 2 in the reciprocal space.

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