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Aberration correction results in the IBM STEM instrument
ARTICLE IN PRESS
Ultramicroscopy 96 (2003) 239–249
Aberration correction results in the IBM STEM instrument P.E. Batson* IBM Research, Yorktown Heights, NY 10598, USA Received 27 January 2003; accepted 2 February 2003
Abstract Results from the installation of aberration correction in the IBM 120 kV STEM argue that a sub-angstrom probe size has been achieved. Results and the experimental methods used to obtain them are described here. Some postexperiment processing is necessary to demonstrate the probe size of about 0.078 nm. While the promise of aberration correction is demonstrated, we remain at the very threshold of practicality, given the very stringent stability requirements. r 2003 Elsevier B.V. All rights reserved. PACS: 07.78.+s; 61.16.Bg Keywords: Electron microscopy; Aberration correction; Quadrupole–octupole corrector; Scanning transmission electron microscopy
1. Introduction We are entering a new era in electron microscopy in which lens aberrations will no longer limit the ultimate probe size. Although the electron optical aberration problem was well understood from the first instruments [1], the first practical correction scheme was demonstrated only recently [2]. Since then, an explosion of capability in electronics, computation and optical design has redefined what optical capabilities are practical in a single instrument. I describe here results using the Nion aberration corrector in the Scanning Transmission Electron Microscope [3], achieving ( for the first an electron probe smaller than 1 A ( is 20 times time [4]. This performance, about 0.8 A, the electron wavelength at 120 keV energy, break*Tel.: +1-914-945-2782; fax: +1-914-945-2141. E-mail address: [email protected] (P.E. Batson).
ing a barrier which had been imposed by Cs in low voltage instruments. Atomic column imaging of semiconductor interfaces should be much easier now, using an acceleration voltage which is below the knock-on threshold for atomic displacement. The IBM instrument is a VG Microscopes HB501UX STEM, fitted with the Nion quadrupole–octupole aberration corrector [5]. This instrument has been modified in the past in the following ways: (1) a high resolution (60– 150 meV), Wien filter spectrometer has been added [6]; (2) the acceleration voltage has been increased to 120 kV to improve specimen penetration and the gun optics; (3) the objective lens strength has been increased about 10% to improve the postspecimen compression for better spectrometer operation; (4) the LN2 trapped diffusion pump has been replaced with a large ion pump; and (6) some simple computer control has been added to allow semi-automatic control of EELS acquisition
0304-3991/03/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0304-3991(03)00091-3
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to improve reproducibility [7]. The higher acceleration voltage and objective excitation delivered ( resolution using ADF imaging (Cs=1.2 mm 2.0 A at 120 kV). The corrector operation is described in detail elsewhere [5]. Briefly, it consists of a seven element system, four quadrupoles used to control the beam trajectory, and three octupoles used to adjust spherical aberration. The quadrupoles are adjusted to produce two orthogonal pencil beams, one in each of two octupoles, to allow the independent control of spherical aberration in the (x,y) plane. At the midplane of the corrector a round beam exists. The third octupole is placed here to correct four-fold distortions introduced by the other two octupoles. Finally, a round beam is produced at the exit of the corrector. To facilitate ideal operation of these seven elements, minor windings at each stage include dipoles, quadrupoles, sextupoles and octupoles to allow the control of parasitic aberrations. The corrector occupies a 15 cm long space originally used by the scan coils, which have been moved to within the bore of the objective lens. In this design, the beam cross over at the selected area aperture has been eliminated. This fact emphatically moves the dedicated STEM from a system which had retained some TEM characteristics (such as selected area diffraction) into a true small probe instrument, relying entirely on small probe diffraction for specimen crystallography and orientation determination. Although operation can be described using only the seven major lenses, addition of control of parasitic effects brings the total number of required windings to over 35. With these extra windings, it is necessary to use software to combine several windings to produce controls that specify pure dipole, quadrupole and octupole fields of specified orientation and position relative to the optic axis. The windings are all excited separately using 0.3 ppm stability, computer-controlled current supplies. The availability of this many controllable supplies in an affordable and manageable package is new to electron microscopy, and is largely a result of the explosion in capability that has become available in integrated electronics during the past 10 years.
2. Expected performance of the system Given the several changes made to the IBM system, it is useful to summarize the expected performance. In the uncorrected machine, for a spherical aberration coefficient, Cs=1.2 mm, and ( we expect to electron wavelength, l=0.034 A, achieve an ADF resolution [8]: ( at 120 kV; ð1Þ ds E0:43C 1=4 l3=4 ¼ 2:0 A s
( Si [2 2 0] consistent with the fact that the 1.92 A fringes have been imaged with this instrument. As discussed previously, in the Cs corrected system, we expect to be limited by the next higher aberration, C5, which we measure in this machine, for the lens excitations of these experiments, to be 1.6 cm. This aberration is introduced by the fact that the corrector is physically separate from the objective lens. We can therefore estimate a resolution limited by optics in this instrument [5] 1=6 ( at 120 kV; d5 E0:43C5 l5=6 ¼ 0:59 A
ð2Þ
a very exciting result. This measured value for C5 is about 5 better than expected, and so the probe resolution may be about 30% better than expected. It should be noted that a small error in camera length can result in a significant error in the measurement of C5. At this time, we are investigating possible reasons for this unexpected measurement. We then must add in quadrature several other contributions. We expect a source size contribution to be 1=2 I ( ds E 2 2 ¼ 0:320:5 A; ð3Þ p ba using a field emission source brightness, b=1.0– 3.0 109 A/Sr/cm2, a measured current, I=40 pA, and an illumination half angle, a=25 mR. Finally, we estimate a contribution from chromatic aberration, Cc=1.5 mm, by first calculating the focus spread caused by a spread in energy, DE=0.28 eV, nf ECc
nE ¼ 3:1 nm E0 ð1 þ E0 =m0 c2 Þ
ð4Þ
and where m0 is the electron rest mass. We then simulate the probe shape, as described below, ( for this spread in focus, obtaining dcE0.12 A.
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Therefore we have an expected probe size: 1=2 ( dtotal E d52 þ dc2 þ ds2 ¼ 0:6720:78 A;
ð5Þ
which matches closely the diffraction limited size ( using the 25 mR half-angle illumination of 0.68 A angle.
space coordinates ~ r : Writing the wavefunction as a function of k~ this way recognizes that the optics in the aberration corrected system are not required to have axial symmetry. For this work, then, we assume that w is not axially symmetric, and we use k~=(k,f) to write wðk; fÞ ¼ K0
3. Aberration characterization
6 M ¼ K0 D4
q w q2 kx2
q w qkx qky
q2 w qky qkx
q2 w q2 ky2
7 5 ;
X ðk=K0 Þðnþ1Þ X n
Measurement of axial aberrations is done by analysis of electron shadow images (Ronchigrams [9]) of a typical TEM resolution test sample consisting of 5–10 nm Au islands dispersed on a holey carbon film. In this technique, the local magnification is given by M=D/Df, where D is the working distance of the Ronchigram camera and Df is the probe defocus. The defocus is dependent on the phase shifts within the objective lens, so that [5,10] 2 2 31 2 ð6Þ
where wðk~Þ is the phase shift due to the aberrations, M is a matrix specifying how the local magnification depends on direction, and k~=K0 ¼ ðyx ; yy Þ defines the angle made by the electron trajectory relative to the optic axis at the sample. In this discussion, the incident wave vector, K0=2p/l, where l is the wavelength of the incident electrons. The aberration function in the uncorrected, axially symmetric system can be written as p 2 1 DE 2 Cs y Df Cc wðyÞ ¼ y ; l 2 Eð1 þ E=m0 c2 Þ ð7Þ where Cc is the chromatic aberration coefficient, DE/E is the fractional energy spread of the beam and we have included a relativistic correction. The probe wave function can then be written as [11] Z h i Cp ð~ r Þp exp iwðk~Þ ik~ ~ r dk~; ð8Þ aperture
where the probe is placed at the origin and the probe amplitude is given as a function of the real
241
ðn þ 1Þ
þ Cnmb sinðmfÞ ( m þ n odd; with mon þ 1:
½Cnma cosðmfÞ
m
ð9Þ
In this aberration numbering scheme, coefficients are identified by subscripts: the first giving the angular exponent of the aberration, the second its axial symmetry and the letter indicating the orientation of the axial symmetry. Thus the firstorder coefficient C1 defines defocus and C12a,b denotes astigmatism; coma becomes C21a,b and C3 identifies spherical aberration. In general, use of non-rotationally symmetric imaging elements will require that many terms be included in this description to adequately describe the system. Table 1 lists aberration coefficients measured during this work. As noted above, the ultimate resolution in this system is limited by C5 E 1.6 107 nm, introduced by the fact that the quadrupole/octupole correction plane does not coincide with the back focal plane of the objective lens. As discussed in another publication, the effect of this problem can be reduced by balancing it with lower-order aberrations which have the same axial variation—C1 and C3 in this case [5]. One way of doing this is, obviously, to measure C5 and calculate C3 to optimally oppose it—about C3 E15 mm for C5 E 1.6 107 nm. This is time consuming, however, and not necessarily successful, because the measurement uncertainty of C5 can be as large as 4 107 nm. However, if the measurement, and the fitting of coefficients, is limited to the third order, then we obtain an effective C3 which reflects a combination of both C3 and C5. We can then tune the system for C3 E 0 to obtain the best balance of C3 against C5. The same is true for C21 which balances against C41 but not for C12 against C32, because
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242 Table 1 Optical aberrations for this work Coefficient
Name
Measured (nm)
Error (nm)
Adjusted (nm)
No octupoles (nm)
C1 C12a C12b C21a C21b C23a C23b C3 C32a C32b C34a C34b C45a C45b
Defocus Astigmatism Astigmatism Coma Coma
1034 11.3 29.3 218 34.8 21.7 53.7 2062 23.0 4799 1233 506 — —
12 12 12 540 540 540 540 22 103 22 103 22 103 22 103 22 103 — —
2.5 0.3 1.3 50 60 As measured As measured As measured As measured As measured As measured As measured 4.0 104 6.0 104
40 0 0 0 0 7000 0 1.2 106 0 0 0 0 0 0
Spherical
Measured aberrations were obtained to third-order from the autotuning procedure. Defocus, astigmatism and coma were then adjusted for best images. The values in the last two columns are obtained to match the experimental Ronchigram images in Fig. 1.
both these coefficients are resolved to third order. Therefore, the method for setup of the small probe for these experiments was to tune up to third order using software to obtain nearly zero coefficients, minimizing C32. Then, focus, astigmatism and coma (C1, C12a,b and C21a,b) were adjusted by hand for the best image.
4. Analysis of the Ronchigram at focus We can predict the expected success of this setup method by comparing measured Ronchigram patterns, at best focus, with calculated patterns. The Ronchigram is essentially a shadow map of the specimen which reveals the local magnification, M, as a function of incident probe angle. Therefore, we may simulate this behavior by mapping a Ronchigram pixel into a specimen pixel by assuming (1) the specimen pixel distance from the origin is 1/|M|, and (2) the azimuthal angle is the same as that for the Ronchigram pixel. We take |M| as the sum in quadrature of the diagonal elements of the magnification matrix in Eq. (6). jMj ¼ h
K0 D ðq
2
w=qkx2 Þ2
þ ðq
2
w=qky2 Þ2
i1=2 :
ð10Þ
This simple approximation ignores the offdiagonal elements, which are responsible for the azimuthal rings of infinite magnification which are apparent at large defocus. However, it does reproduce the central area of constant phase, showing appropriate axial symmetries controlled by the various aberration coefficients. The ‘‘specimen’’ is constructed of random features having a range of spatial frequencies which are similar to the probe size. In the experiment, this is an amorphous carbon film. In Fig. 1a and b I show experimental Ronchigrams for the uncorrected and corrected system, using C3 =1.2 mm and C1 =40 nm. We find in Fig. 1c that the calculated pattern requires a large C23a=7000 nm to match the experimental threefold distortion. The calculated probe then has a strong three-fold astigmatism and an effective ( explaining the somewhat diameter of about 2.5 A, poorer than expected resolution for the uncorrected case reported in prior work [5]. It is a little sobering that the apparently minor distortion in the Ronchigram produces such a large degrada( tion of the probe size from the limiting value of 2 A for the uncorrected system. For the corrected case, we use the measured high-order coefficients (C23 and higher), with loworder coefficients adjusted for best probe size, as
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243
10 mR (a)
(b)
(c)
(d)
(e)
(f)
0.1 nm
Fig. 1. (a) Experimental Ronchigram for the uncorrected system, showing the roughly 20 mR diameter region of fixed phase shift used to produce the 0.25 nm probe. (b) Experimental measurement of the Ronchigram at focus in the corrected system. The uniform phase patch extends to a diameter of 50 mR. (c,d) Simulations using the adjusted aberration coefficients from Table 1. The three-fold shape in ( probe. The apparent multipole shape in (d) is a result of non-zero C45a,b. (e,f) (c) is due to C23a and results in the non-optimum 2.5 A The resulting probe shapes for these conditions.
was done for the experimental setup of the best probe. In order to match the experimental Ronchigram obtained under these conditions, shown in Fig. 1b, we must include, also, a finite C45 which is not measured in the third-order measurement, and also not compensated by any of the low-order coefficients that are measured. This addition produces the characteristic five-fold
symmetry apparent in Figs. 1b and d. The resulting probe shape is shown in Fig. 1f, where we see that small three-fold astigmatism does still survive, but the calculated probe width has now ( Interestingly, the limiting probe dropped to 0.73 A. size is controlled by the higher-order coefficients, rather than the lower-order defocus, astigmatism and coma, which can be corrected by eye.
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5. Imaging results 5.1. Small Au islands ( Au islands on Preliminary imaging of 100 A amorphous carbon have yielded many images similar to that shown in Fig. 2. We see, in addition to the islands, a hierarchy of structures: areas with no apparent Au atoms, single atoms, clusters of 2– ( wide single layer rafts of Au 3 atoms, and 20–50 A atoms. Finally, the single atom contrast was high enough to follow of the motion of atoms under the electron beam: during dissolution of islands and during rapid reformation of islands from dilute groups of atoms. These results are promising but at the same time disappointing, because the images seldom contain spatial frequencies which are ( In Fig. 2 for instance, the highest below 1 A. ( It therespatial frequency corresponds to 1.17 A. fore appears that spatial frequencies in this case are limited by small crystal tilts. In a 5 nm diameter crystal, this tilt would need to be only
±1 (0.117nm) F IG.
10 mR in order to spread the apparent column ( In addition, since we are using a width to 0.5 A. 25 mR half-angle probe spread, we rely on crystal channelling to maintain the probe size for some finite distance into the crystal [12]. In fact, for a strong scatterer such as Au, we do not have a high expectation that this channelling would operate in a well-behaved fashion. 5.2. Ge30Si70 [1 1 0] Fig. 3a summarizes raw data for a relatively thick Ge30Si70 sample oriented for [1 1 0] channelling. The ‘‘dumbbell’’ structures are resolved so that the [0 0 4] spots are strong in the Fourier Transform in Fig. 3b. A puzzling result is that ( are spatial frequencies all the way out to 0.48 A % evident in the [2 2 0] direction, as well, in spite of ( aperture limitation. There are also the 0.68 A vertical streaking and satellite spots caused by apparent AC interference. We can remove some of this interference by masking the small satellite
2:
(0.123nm)±1
(0.144nm)±1
GB
<011> Projection 1 nm
( are visible. On the carbon surface are Fig. 2. Typical ADF image of a gold island on amorphous carbon. Lattice fringes to 1.17 A single layers of Au atoms, loosely arranged in apparently two-dimensional arrays having various structures.
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245
FIG.
(a)
1 nm (b)
(c)
1 nm (d)
0.048 nm
1 nm
( spots Fig. 3. Imaging results for the {1 1 0} projection of Ge30Si70: (a,b) Raw data, Fourier transform. The transform contains 0.48 A as well as many weak satellite spots and vertical streaks caused by AC interference in the image. (c) After removal of the AC-induced ( (d) The intensity removed by suppression of the satellite spots, amounting to about 1.5% of the total. satellite spots, filtered to 0.5 A.
spots that this interference produces, and replacing them with a background intensity having a ( gaussian filter is random phase. Finally, a 0.5 A applied to suppress non-physical spatial frequencies, producing the filtered image in Fig. 3c. The removed intensity amounts to 1.5% of the original intensity and is displayed in Fig. 3d. Images taken with the scans rotated by 90 reveals spatial frequencies in the [0 0 4] direction to the [0 0 6] ( while obscuring spots in the reflection (0.92 A), ( Therefore it [2 2% 0] direction beyond about 1.25 A. appears that about half of the AC interference results from ambient AC magnetic fields (oriented in the [0 0 4] direction in this example), and about
half is introduced by the scans. The filtered image also retains some long wavelength scan distortions, largely a result of non-linear response of the scan coils. Finally, some black level was used in obtaining this image, and this is suspected to produce a non-linear response near the minimum intensity. As discussed in another publication, this can produce the very high spatial frequencies observed in the [2 2% 0] direction [13]. In the [0 0 4] ( spots are easily visible, but direction, the 1.35 A quite a lot of the forbidden [0 0 2] spots are present, indicating that, on average, the ‘‘dumbbell’’ spacing or the spacing between ‘‘dumbbells’’ is not correct in this image.
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So this example also does not definitely define the attained spatial resolution. The known interferences, the non-linear intensity acquisition, and the scan distortions conspire to limit unambiguous physical information and add non-physical information, as well. We can go somewhat further in the analysis of this image by realizing that the scan distortions are slowly varying across the image, so that we should be able to pick out relatively undistorted, smaller regions. If several of these regions are then aligned through cross correlation and averaged, then some of the scan distortion can be suppressed. Fig. 4 summarizes this process. There, I show in Fig. 4a the original data, corrected for AC interference, but otherwise unfiltered, with square patches locating 20 smaller regions. These regions are picked for the best cross correlation match to each
FIG.
other. Fig. 4b shows the Fourier Transform of this ( spot indicated with a small image, with the 0.48 A arrow. Fig. 4c is a sum of the 20 regions, while (d) is the Fourier analysis of this sum. Several interesting results appear from this: (1) ( are elimispatial frequencies greater than 0.75 A nated in the averaged result, (2) the forbidden [0 0 2] spots are also suppressed, and (3) intensity ( and [2 2% 4] (1.10 A) ( type near the [3 3% 3] (1.04 A) spots are enhanced. Unfortunately, the ‘‘dumbbell’’ separation is still disappointing, with only about a 10% dip between the two spots. This is likely due to the AC interference discussed above. I conclude that scan distortions and AC interference are still the major limitations at this resolution level. But the persistence of the ( spots after the averaging process is en0.75 A couraging.
4:
(a)
(b) 1 nm
(c)
0.2 nm
(d)
Fig. 4. Summary of results for the {1 1 0} projection of Ge30Si70: (a,b) Unfiltered image, Fourier Transform. Patches used to generate ( spacings, eliminates the [0 0 2] panel (c) are indicated. (c,d) Averaged image, Fourier Transform. The transform retains 0.76 A ( spots which are present, but not very prominent in the original data. forbidden spots and enhance B1 A
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5.3. Single Au atoms In Fig. 5, I show three measurements of the apparent size of single Au atoms. In general, the single atoms are easy to distinguish on the carbon substrate, but to ensure that apparent spots of intensity are not noise related, I chose for measurement only those images that include four to six pixels having intensities which were greater
247
than three times the RMS spread of the background intensity. In most cases, three or more of these pixels are greater than that, with the peak being of order six times greater. To generate line ( wide scans for peak width measurements, 0.4 A strips across the atoms were summed. The obtained probe width measurements ranged from ( In one instance (top) effects of coma 0.7 to 0.85 A. on the probe shape were measurable. Fig. 6 shows
60
FIG. 5:
50
y±scan
0.08nm
40 30
Coma x−scan
20 10 0 −0.6
−0.4
−0.2
−0.0 0.2 Distance
0.4
0.6
45
0.07nm
40
y−scan
35 30 25 20 15 10 5 −0.6
−0.4
−0.2
−0.0 0.2 Distance
0.4
0.6
100 90 80 70 60 50 40
0.2 nm
30 −0.6
0.085nm separated by 0.28nm −0.4
−0.2
−0.0 0.2 Distance
0.4
0.6
Fig. 5. Atomic size analysis for two single Au atoms and a single-layer hexagonal cluster. The line scans are obtained from 2 pixel ( wide strips in the x and/or y direction as indicated. (0.4 A)
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248
Number of Measurements
12 10 8 6 4 2 0 0.00
0.02
0.04
0.06 0.08 0.10 0.12 Atom Diameter (nm)
0.14
0.16
Fig. 6. Histogram analysis for 46 atoms obtained from 13 images.
a histogram analysis for 46 atom images obtained from 13 images having varying magnifications. The required peak signal to noise was relaxed to 3 for this exercise. The result shows an average ( image width of 0.7870.15 A. In the image containing several atoms in the single layer hexagonal pattern (bottom), the near( This is consistent neighbor spacing is about 2.8 A. ( but is larger with the spacing in the bulk (2.88 A), than that for interacting pairs of atoms, observed in real time using a video camera on the microscope screen [4]. Au2 dimers in the gas are calculated to have an interatomic spacing of about ( while experiments have measured values as 2.6 A, ( [14]. Therefore, I speculate that an small as 2.47 A atomic dimer, in motion on the rough carbon surface, may not be observed lying flat, as on a smooth surface, but instead may be viewed obliquely, as is the case in the crystal where, for ( near-neighbor the [0 0 1] orientation, the 2.88 A ( We also note distance is far-shortened to 2.04 A. that the scale marker in Fig. 2 of Ref. [4] should ( rather than 1 A, ( but even with this read 1.5 A correction the Au atoms appear to approach much too closely. Further work on this is needed.
6. Discussion These results clearly represent an exciting advance over what has been possible previously
using a 100–120 kV instrument. Being able to image at the sub-angstrom level using a beam energy below the knock-on threshold for damage in silicon is especially exciting for the semiconductor field, where the quality of interfaces between silicon and radiation sensitive insulators is crucial to the successful operation of devices. Aberration correction technology now allows us to reproducibly set up the optics of the microscope using well understood procedures. Very small probe sizes can then be reliably produced, even at this low acceleration voltage. On the other hand, while the single atom measurements, which are consistent with the Ronchigram analysis, clearly demonstrate that ( images of crystals do the probe size is below 1 A, ( fringe not yet demonstrate clear examples of sub-A resolution, such as those recently obtained using a posteriori processing at 300 kV [15,16]. In addition, un-physically large spatial frequencies appear to be easily introduced by non-linearities in the acquisition of the scattering intensity and by scan interferences and distortion. Finally, the present system, which is a modification of a 20-year old optical column, clearly suffers from deficiencies related to both its age and to compromises made necessary by its pre-existing configuration. Therefore, routine use of aberration correction for materials analysis will require instruments built from the beginning with aberration correction as an integral part of the instrument. These instruments will require scan control and signal acquisition capabilities which are about an order of magnitude more accurate than the current systems. The success of aberration correction at this particular time is due to several reasons: (i) computation of non-rotationally symmetric electron optical parameters is now routinely possible, (ii) mechanical fabrication tolerances have advanced materially in the past 15 years, (iii) high stability electronic components have become available in the past 10 years, allowing the packaging of many, very high stability, computer controlled, power supplies in a small space, and (iv) our understanding of the available information in Ronchigram date now allows real-time measurement of aberration parameters.
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A particularly exciting possibility for the future is that multiple corrector systems will allow aberration control of both probe size and detector field of view, in a manner somewhat similar to confocal light microscopy. This will make possible a detailed control of the amplitude and phase of both the incident and scattered electron wave function, allowing specific specimen elastic and inelastic transitions to be accessed [17]. In sum, aberration correction truly marks a major shift away from the limited electron optics which have dominated the first 60 years of electron microscopy, and points the way towards a future where precise optical control will allow routine atomic level characterization of defects and interfaces within the bulk.
Acknowledgements I wish to acknowledge extensive collaboration with O.L. Krivanek and N. Dellby who are responsible for this corrector design and construction, and discussions with Z. Hu and J. Silcox.
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References [1] O. Scherzer, J. Appl. Phys. 20 (1949) 20. [2] M. Haider, S. Uhlemann, E. Schwan, H. Rose, B. Kabius, K. Urban, Nature 392 (1998) 768. [3] A.V. Crewe, M. Isaacson, D. Johnson, Rev. Sci. Instrum. 40 (1969) 241. [4] P.E. Batson, N. Dellby, O.L. Krivanek, Nature 418 (2002) 617. [5] N. Dellby, O.L. Krivanek, P.D. Nellist, P.E. Batson, A.R. Lupini, J. Electron Microsc. 50 (2001) 177. [6] P.E. Batson, Rev. Sci. Instrum. 57 (1986) 43. [7] P.E. Batson, G. Trafas, Ultramicroscopy 8 (1982) 293. [8] J. Silcox, P. Xu, R.F. Loane, Ultramicroscopy 47 (1992) 173. [9] V. Ronchi, Appl. Opt. 3 (1964) 437. [10] O.L. Krivanek, N. Dellby, A.R. Lupini, US Patent Application, unpublished. [11] E.J. Kirkland, Advanced Computing in Electron Microscopy, Plenum Press, New York, 1998. [12] R.F. Loane, E.J. Kirkland, J. Silcox, Acta. Crystallogr. A 44 (1988) 912. [13] Z. Yu, P.E. Batson, J. Silcox, Ultramicroscopy, submitted for publication. [14] R.B. Ross, W.C. Ermler, J. Phys. Chem. 89 (1985) 5202. [15] M.A. O’Keefe, C.J.D. Hetherington, Y.C. Wang, E.C. Nelson, J.H. Turner, C. Kisielowski, J.O. Malm, R. Mueller, J. Ringnalda, M. Pan, A. Thust, Ultramicroscopy 89 (2001) 215. [16] M.A. O’Keefe, L.F. Allard, 2002, private communication. [17] P.E. Batson, Phys. Rev. Lett. 70 (1993) 1822.
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Aberration correction results in the IBM STEM instrument P.E. Batson* IBM Research, Yorktown Heights, NY 10598, USA Received 27 January 2003; accepted 2 February 2003
Abstract Results from the installation of aberration correction in the IBM 120 kV STEM argue that a sub-angstrom probe size has been achieved. Results and the experimental methods used to obtain them are described here. Some postexperiment processing is necessary to demonstrate the probe size of about 0.078 nm. While the promise of aberration correction is demonstrated, we remain at the very threshold of practicality, given the very stringent stability requirements. r 2003 Elsevier B.V. All rights reserved. PACS: 07.78.+s; 61.16.Bg Keywords: Electron microscopy; Aberration correction; Quadrupole–octupole corrector; Scanning transmission electron microscopy
1. Introduction We are entering a new era in electron microscopy in which lens aberrations will no longer limit the ultimate probe size. Although the electron optical aberration problem was well understood from the first instruments [1], the first practical correction scheme was demonstrated only recently [2]. Since then, an explosion of capability in electronics, computation and optical design has redefined what optical capabilities are practical in a single instrument. I describe here results using the Nion aberration corrector in the Scanning Transmission Electron Microscope [3], achieving ( for the first an electron probe smaller than 1 A ( is 20 times time [4]. This performance, about 0.8 A, the electron wavelength at 120 keV energy, break*Tel.: +1-914-945-2782; fax: +1-914-945-2141. E-mail address: [email protected] (P.E. Batson).
ing a barrier which had been imposed by Cs in low voltage instruments. Atomic column imaging of semiconductor interfaces should be much easier now, using an acceleration voltage which is below the knock-on threshold for atomic displacement. The IBM instrument is a VG Microscopes HB501UX STEM, fitted with the Nion quadrupole–octupole aberration corrector [5]. This instrument has been modified in the past in the following ways: (1) a high resolution (60– 150 meV), Wien filter spectrometer has been added [6]; (2) the acceleration voltage has been increased to 120 kV to improve specimen penetration and the gun optics; (3) the objective lens strength has been increased about 10% to improve the postspecimen compression for better spectrometer operation; (4) the LN2 trapped diffusion pump has been replaced with a large ion pump; and (6) some simple computer control has been added to allow semi-automatic control of EELS acquisition
0304-3991/03/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0304-3991(03)00091-3
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to improve reproducibility [7]. The higher acceleration voltage and objective excitation delivered ( resolution using ADF imaging (Cs=1.2 mm 2.0 A at 120 kV). The corrector operation is described in detail elsewhere [5]. Briefly, it consists of a seven element system, four quadrupoles used to control the beam trajectory, and three octupoles used to adjust spherical aberration. The quadrupoles are adjusted to produce two orthogonal pencil beams, one in each of two octupoles, to allow the independent control of spherical aberration in the (x,y) plane. At the midplane of the corrector a round beam exists. The third octupole is placed here to correct four-fold distortions introduced by the other two octupoles. Finally, a round beam is produced at the exit of the corrector. To facilitate ideal operation of these seven elements, minor windings at each stage include dipoles, quadrupoles, sextupoles and octupoles to allow the control of parasitic aberrations. The corrector occupies a 15 cm long space originally used by the scan coils, which have been moved to within the bore of the objective lens. In this design, the beam cross over at the selected area aperture has been eliminated. This fact emphatically moves the dedicated STEM from a system which had retained some TEM characteristics (such as selected area diffraction) into a true small probe instrument, relying entirely on small probe diffraction for specimen crystallography and orientation determination. Although operation can be described using only the seven major lenses, addition of control of parasitic effects brings the total number of required windings to over 35. With these extra windings, it is necessary to use software to combine several windings to produce controls that specify pure dipole, quadrupole and octupole fields of specified orientation and position relative to the optic axis. The windings are all excited separately using 0.3 ppm stability, computer-controlled current supplies. The availability of this many controllable supplies in an affordable and manageable package is new to electron microscopy, and is largely a result of the explosion in capability that has become available in integrated electronics during the past 10 years.
2. Expected performance of the system Given the several changes made to the IBM system, it is useful to summarize the expected performance. In the uncorrected machine, for a spherical aberration coefficient, Cs=1.2 mm, and ( we expect to electron wavelength, l=0.034 A, achieve an ADF resolution [8]: ( at 120 kV; ð1Þ ds E0:43C 1=4 l3=4 ¼ 2:0 A s
( Si [2 2 0] consistent with the fact that the 1.92 A fringes have been imaged with this instrument. As discussed previously, in the Cs corrected system, we expect to be limited by the next higher aberration, C5, which we measure in this machine, for the lens excitations of these experiments, to be 1.6 cm. This aberration is introduced by the fact that the corrector is physically separate from the objective lens. We can therefore estimate a resolution limited by optics in this instrument [5] 1=6 ( at 120 kV; d5 E0:43C5 l5=6 ¼ 0:59 A
ð2Þ
a very exciting result. This measured value for C5 is about 5 better than expected, and so the probe resolution may be about 30% better than expected. It should be noted that a small error in camera length can result in a significant error in the measurement of C5. At this time, we are investigating possible reasons for this unexpected measurement. We then must add in quadrature several other contributions. We expect a source size contribution to be 1=2 I ( ds E 2 2 ¼ 0:320:5 A; ð3Þ p ba using a field emission source brightness, b=1.0– 3.0 109 A/Sr/cm2, a measured current, I=40 pA, and an illumination half angle, a=25 mR. Finally, we estimate a contribution from chromatic aberration, Cc=1.5 mm, by first calculating the focus spread caused by a spread in energy, DE=0.28 eV, nf ECc
nE ¼ 3:1 nm E0 ð1 þ E0 =m0 c2 Þ
ð4Þ
and where m0 is the electron rest mass. We then simulate the probe shape, as described below, ( for this spread in focus, obtaining dcE0.12 A.
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Therefore we have an expected probe size: 1=2 ( dtotal E d52 þ dc2 þ ds2 ¼ 0:6720:78 A;
ð5Þ
which matches closely the diffraction limited size ( using the 25 mR half-angle illumination of 0.68 A angle.
space coordinates ~ r : Writing the wavefunction as a function of k~ this way recognizes that the optics in the aberration corrected system are not required to have axial symmetry. For this work, then, we assume that w is not axially symmetric, and we use k~=(k,f) to write wðk; fÞ ¼ K0
3. Aberration characterization
6 M ¼ K0 D4
q w q2 kx2
q w qkx qky
q2 w qky qkx
q2 w q2 ky2
7 5 ;
X ðk=K0 Þðnþ1Þ X n
Measurement of axial aberrations is done by analysis of electron shadow images (Ronchigrams [9]) of a typical TEM resolution test sample consisting of 5–10 nm Au islands dispersed on a holey carbon film. In this technique, the local magnification is given by M=D/Df, where D is the working distance of the Ronchigram camera and Df is the probe defocus. The defocus is dependent on the phase shifts within the objective lens, so that [5,10] 2 2 31 2 ð6Þ
where wðk~Þ is the phase shift due to the aberrations, M is a matrix specifying how the local magnification depends on direction, and k~=K0 ¼ ðyx ; yy Þ defines the angle made by the electron trajectory relative to the optic axis at the sample. In this discussion, the incident wave vector, K0=2p/l, where l is the wavelength of the incident electrons. The aberration function in the uncorrected, axially symmetric system can be written as p 2 1 DE 2 Cs y Df Cc wðyÞ ¼ y ; l 2 Eð1 þ E=m0 c2 Þ ð7Þ where Cc is the chromatic aberration coefficient, DE/E is the fractional energy spread of the beam and we have included a relativistic correction. The probe wave function can then be written as [11] Z h i Cp ð~ r Þp exp iwðk~Þ ik~ ~ r dk~; ð8Þ aperture
where the probe is placed at the origin and the probe amplitude is given as a function of the real
241
ðn þ 1Þ
þ Cnmb sinðmfÞ ( m þ n odd; with mon þ 1:
½Cnma cosðmfÞ
m
ð9Þ
In this aberration numbering scheme, coefficients are identified by subscripts: the first giving the angular exponent of the aberration, the second its axial symmetry and the letter indicating the orientation of the axial symmetry. Thus the firstorder coefficient C1 defines defocus and C12a,b denotes astigmatism; coma becomes C21a,b and C3 identifies spherical aberration. In general, use of non-rotationally symmetric imaging elements will require that many terms be included in this description to adequately describe the system. Table 1 lists aberration coefficients measured during this work. As noted above, the ultimate resolution in this system is limited by C5 E 1.6 107 nm, introduced by the fact that the quadrupole/octupole correction plane does not coincide with the back focal plane of the objective lens. As discussed in another publication, the effect of this problem can be reduced by balancing it with lower-order aberrations which have the same axial variation—C1 and C3 in this case [5]. One way of doing this is, obviously, to measure C5 and calculate C3 to optimally oppose it—about C3 E15 mm for C5 E 1.6 107 nm. This is time consuming, however, and not necessarily successful, because the measurement uncertainty of C5 can be as large as 4 107 nm. However, if the measurement, and the fitting of coefficients, is limited to the third order, then we obtain an effective C3 which reflects a combination of both C3 and C5. We can then tune the system for C3 E 0 to obtain the best balance of C3 against C5. The same is true for C21 which balances against C41 but not for C12 against C32, because
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242 Table 1 Optical aberrations for this work Coefficient
Name
Measured (nm)
Error (nm)
Adjusted (nm)
No octupoles (nm)
C1 C12a C12b C21a C21b C23a C23b C3 C32a C32b C34a C34b C45a C45b
Defocus Astigmatism Astigmatism Coma Coma
1034 11.3 29.3 218 34.8 21.7 53.7 2062 23.0 4799 1233 506 — —
12 12 12 540 540 540 540 22 103 22 103 22 103 22 103 22 103 — —
2.5 0.3 1.3 50 60 As measured As measured As measured As measured As measured As measured As measured 4.0 104 6.0 104
40 0 0 0 0 7000 0 1.2 106 0 0 0 0 0 0
Spherical
Measured aberrations were obtained to third-order from the autotuning procedure. Defocus, astigmatism and coma were then adjusted for best images. The values in the last two columns are obtained to match the experimental Ronchigram images in Fig. 1.
both these coefficients are resolved to third order. Therefore, the method for setup of the small probe for these experiments was to tune up to third order using software to obtain nearly zero coefficients, minimizing C32. Then, focus, astigmatism and coma (C1, C12a,b and C21a,b) were adjusted by hand for the best image.
4. Analysis of the Ronchigram at focus We can predict the expected success of this setup method by comparing measured Ronchigram patterns, at best focus, with calculated patterns. The Ronchigram is essentially a shadow map of the specimen which reveals the local magnification, M, as a function of incident probe angle. Therefore, we may simulate this behavior by mapping a Ronchigram pixel into a specimen pixel by assuming (1) the specimen pixel distance from the origin is 1/|M|, and (2) the azimuthal angle is the same as that for the Ronchigram pixel. We take |M| as the sum in quadrature of the diagonal elements of the magnification matrix in Eq. (6). jMj ¼ h
K0 D ðq
2
w=qkx2 Þ2
þ ðq
2
w=qky2 Þ2
i1=2 :
ð10Þ
This simple approximation ignores the offdiagonal elements, which are responsible for the azimuthal rings of infinite magnification which are apparent at large defocus. However, it does reproduce the central area of constant phase, showing appropriate axial symmetries controlled by the various aberration coefficients. The ‘‘specimen’’ is constructed of random features having a range of spatial frequencies which are similar to the probe size. In the experiment, this is an amorphous carbon film. In Fig. 1a and b I show experimental Ronchigrams for the uncorrected and corrected system, using C3 =1.2 mm and C1 =40 nm. We find in Fig. 1c that the calculated pattern requires a large C23a=7000 nm to match the experimental threefold distortion. The calculated probe then has a strong three-fold astigmatism and an effective ( explaining the somewhat diameter of about 2.5 A, poorer than expected resolution for the uncorrected case reported in prior work [5]. It is a little sobering that the apparently minor distortion in the Ronchigram produces such a large degrada( tion of the probe size from the limiting value of 2 A for the uncorrected system. For the corrected case, we use the measured high-order coefficients (C23 and higher), with loworder coefficients adjusted for best probe size, as
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243
10 mR (a)
(b)
(c)
(d)
(e)
(f)
0.1 nm
Fig. 1. (a) Experimental Ronchigram for the uncorrected system, showing the roughly 20 mR diameter region of fixed phase shift used to produce the 0.25 nm probe. (b) Experimental measurement of the Ronchigram at focus in the corrected system. The uniform phase patch extends to a diameter of 50 mR. (c,d) Simulations using the adjusted aberration coefficients from Table 1. The three-fold shape in ( probe. The apparent multipole shape in (d) is a result of non-zero C45a,b. (e,f) (c) is due to C23a and results in the non-optimum 2.5 A The resulting probe shapes for these conditions.
was done for the experimental setup of the best probe. In order to match the experimental Ronchigram obtained under these conditions, shown in Fig. 1b, we must include, also, a finite C45 which is not measured in the third-order measurement, and also not compensated by any of the low-order coefficients that are measured. This addition produces the characteristic five-fold
symmetry apparent in Figs. 1b and d. The resulting probe shape is shown in Fig. 1f, where we see that small three-fold astigmatism does still survive, but the calculated probe width has now ( Interestingly, the limiting probe dropped to 0.73 A. size is controlled by the higher-order coefficients, rather than the lower-order defocus, astigmatism and coma, which can be corrected by eye.
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5. Imaging results 5.1. Small Au islands ( Au islands on Preliminary imaging of 100 A amorphous carbon have yielded many images similar to that shown in Fig. 2. We see, in addition to the islands, a hierarchy of structures: areas with no apparent Au atoms, single atoms, clusters of 2– ( wide single layer rafts of Au 3 atoms, and 20–50 A atoms. Finally, the single atom contrast was high enough to follow of the motion of atoms under the electron beam: during dissolution of islands and during rapid reformation of islands from dilute groups of atoms. These results are promising but at the same time disappointing, because the images seldom contain spatial frequencies which are ( In Fig. 2 for instance, the highest below 1 A. ( It therespatial frequency corresponds to 1.17 A. fore appears that spatial frequencies in this case are limited by small crystal tilts. In a 5 nm diameter crystal, this tilt would need to be only
±1 (0.117nm) F IG.
10 mR in order to spread the apparent column ( In addition, since we are using a width to 0.5 A. 25 mR half-angle probe spread, we rely on crystal channelling to maintain the probe size for some finite distance into the crystal [12]. In fact, for a strong scatterer such as Au, we do not have a high expectation that this channelling would operate in a well-behaved fashion. 5.2. Ge30Si70 [1 1 0] Fig. 3a summarizes raw data for a relatively thick Ge30Si70 sample oriented for [1 1 0] channelling. The ‘‘dumbbell’’ structures are resolved so that the [0 0 4] spots are strong in the Fourier Transform in Fig. 3b. A puzzling result is that ( are spatial frequencies all the way out to 0.48 A % evident in the [2 2 0] direction, as well, in spite of ( aperture limitation. There are also the 0.68 A vertical streaking and satellite spots caused by apparent AC interference. We can remove some of this interference by masking the small satellite
2:
(0.123nm)±1
(0.144nm)±1
GB
<011> Projection 1 nm
( are visible. On the carbon surface are Fig. 2. Typical ADF image of a gold island on amorphous carbon. Lattice fringes to 1.17 A single layers of Au atoms, loosely arranged in apparently two-dimensional arrays having various structures.
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245
FIG.
(a)
1 nm (b)
(c)
1 nm (d)
0.048 nm
1 nm
( spots Fig. 3. Imaging results for the {1 1 0} projection of Ge30Si70: (a,b) Raw data, Fourier transform. The transform contains 0.48 A as well as many weak satellite spots and vertical streaks caused by AC interference in the image. (c) After removal of the AC-induced ( (d) The intensity removed by suppression of the satellite spots, amounting to about 1.5% of the total. satellite spots, filtered to 0.5 A.
spots that this interference produces, and replacing them with a background intensity having a ( gaussian filter is random phase. Finally, a 0.5 A applied to suppress non-physical spatial frequencies, producing the filtered image in Fig. 3c. The removed intensity amounts to 1.5% of the original intensity and is displayed in Fig. 3d. Images taken with the scans rotated by 90 reveals spatial frequencies in the [0 0 4] direction to the [0 0 6] ( while obscuring spots in the reflection (0.92 A), ( Therefore it [2 2% 0] direction beyond about 1.25 A. appears that about half of the AC interference results from ambient AC magnetic fields (oriented in the [0 0 4] direction in this example), and about
half is introduced by the scans. The filtered image also retains some long wavelength scan distortions, largely a result of non-linear response of the scan coils. Finally, some black level was used in obtaining this image, and this is suspected to produce a non-linear response near the minimum intensity. As discussed in another publication, this can produce the very high spatial frequencies observed in the [2 2% 0] direction [13]. In the [0 0 4] ( spots are easily visible, but direction, the 1.35 A quite a lot of the forbidden [0 0 2] spots are present, indicating that, on average, the ‘‘dumbbell’’ spacing or the spacing between ‘‘dumbbells’’ is not correct in this image.
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So this example also does not definitely define the attained spatial resolution. The known interferences, the non-linear intensity acquisition, and the scan distortions conspire to limit unambiguous physical information and add non-physical information, as well. We can go somewhat further in the analysis of this image by realizing that the scan distortions are slowly varying across the image, so that we should be able to pick out relatively undistorted, smaller regions. If several of these regions are then aligned through cross correlation and averaged, then some of the scan distortion can be suppressed. Fig. 4 summarizes this process. There, I show in Fig. 4a the original data, corrected for AC interference, but otherwise unfiltered, with square patches locating 20 smaller regions. These regions are picked for the best cross correlation match to each
FIG.
other. Fig. 4b shows the Fourier Transform of this ( spot indicated with a small image, with the 0.48 A arrow. Fig. 4c is a sum of the 20 regions, while (d) is the Fourier analysis of this sum. Several interesting results appear from this: (1) ( are elimispatial frequencies greater than 0.75 A nated in the averaged result, (2) the forbidden [0 0 2] spots are also suppressed, and (3) intensity ( and [2 2% 4] (1.10 A) ( type near the [3 3% 3] (1.04 A) spots are enhanced. Unfortunately, the ‘‘dumbbell’’ separation is still disappointing, with only about a 10% dip between the two spots. This is likely due to the AC interference discussed above. I conclude that scan distortions and AC interference are still the major limitations at this resolution level. But the persistence of the ( spots after the averaging process is en0.75 A couraging.
4:
(a)
(b) 1 nm
(c)
0.2 nm
(d)
Fig. 4. Summary of results for the {1 1 0} projection of Ge30Si70: (a,b) Unfiltered image, Fourier Transform. Patches used to generate ( spacings, eliminates the [0 0 2] panel (c) are indicated. (c,d) Averaged image, Fourier Transform. The transform retains 0.76 A ( spots which are present, but not very prominent in the original data. forbidden spots and enhance B1 A
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5.3. Single Au atoms In Fig. 5, I show three measurements of the apparent size of single Au atoms. In general, the single atoms are easy to distinguish on the carbon substrate, but to ensure that apparent spots of intensity are not noise related, I chose for measurement only those images that include four to six pixels having intensities which were greater
247
than three times the RMS spread of the background intensity. In most cases, three or more of these pixels are greater than that, with the peak being of order six times greater. To generate line ( wide scans for peak width measurements, 0.4 A strips across the atoms were summed. The obtained probe width measurements ranged from ( In one instance (top) effects of coma 0.7 to 0.85 A. on the probe shape were measurable. Fig. 6 shows
60
FIG. 5:
50
y±scan
0.08nm
40 30
Coma x−scan
20 10 0 −0.6
−0.4
−0.2
−0.0 0.2 Distance
0.4
0.6
45
0.07nm
40
y−scan
35 30 25 20 15 10 5 −0.6
−0.4
−0.2
−0.0 0.2 Distance
0.4
0.6
100 90 80 70 60 50 40
0.2 nm
30 −0.6
0.085nm separated by 0.28nm −0.4
−0.2
−0.0 0.2 Distance
0.4
0.6
Fig. 5. Atomic size analysis for two single Au atoms and a single-layer hexagonal cluster. The line scans are obtained from 2 pixel ( wide strips in the x and/or y direction as indicated. (0.4 A)
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248
Number of Measurements
12 10 8 6 4 2 0 0.00
0.02
0.04
0.06 0.08 0.10 0.12 Atom Diameter (nm)
0.14
0.16
Fig. 6. Histogram analysis for 46 atoms obtained from 13 images.
a histogram analysis for 46 atom images obtained from 13 images having varying magnifications. The required peak signal to noise was relaxed to 3 for this exercise. The result shows an average ( image width of 0.7870.15 A. In the image containing several atoms in the single layer hexagonal pattern (bottom), the near( This is consistent neighbor spacing is about 2.8 A. ( but is larger with the spacing in the bulk (2.88 A), than that for interacting pairs of atoms, observed in real time using a video camera on the microscope screen [4]. Au2 dimers in the gas are calculated to have an interatomic spacing of about ( while experiments have measured values as 2.6 A, ( [14]. Therefore, I speculate that an small as 2.47 A atomic dimer, in motion on the rough carbon surface, may not be observed lying flat, as on a smooth surface, but instead may be viewed obliquely, as is the case in the crystal where, for ( near-neighbor the [0 0 1] orientation, the 2.88 A ( We also note distance is far-shortened to 2.04 A. that the scale marker in Fig. 2 of Ref. [4] should ( rather than 1 A, ( but even with this read 1.5 A correction the Au atoms appear to approach much too closely. Further work on this is needed.
6. Discussion These results clearly represent an exciting advance over what has been possible previously
using a 100–120 kV instrument. Being able to image at the sub-angstrom level using a beam energy below the knock-on threshold for damage in silicon is especially exciting for the semiconductor field, where the quality of interfaces between silicon and radiation sensitive insulators is crucial to the successful operation of devices. Aberration correction technology now allows us to reproducibly set up the optics of the microscope using well understood procedures. Very small probe sizes can then be reliably produced, even at this low acceleration voltage. On the other hand, while the single atom measurements, which are consistent with the Ronchigram analysis, clearly demonstrate that ( images of crystals do the probe size is below 1 A, ( fringe not yet demonstrate clear examples of sub-A resolution, such as those recently obtained using a posteriori processing at 300 kV [15,16]. In addition, un-physically large spatial frequencies appear to be easily introduced by non-linearities in the acquisition of the scattering intensity and by scan interferences and distortion. Finally, the present system, which is a modification of a 20-year old optical column, clearly suffers from deficiencies related to both its age and to compromises made necessary by its pre-existing configuration. Therefore, routine use of aberration correction for materials analysis will require instruments built from the beginning with aberration correction as an integral part of the instrument. These instruments will require scan control and signal acquisition capabilities which are about an order of magnitude more accurate than the current systems. The success of aberration correction at this particular time is due to several reasons: (i) computation of non-rotationally symmetric electron optical parameters is now routinely possible, (ii) mechanical fabrication tolerances have advanced materially in the past 15 years, (iii) high stability electronic components have become available in the past 10 years, allowing the packaging of many, very high stability, computer controlled, power supplies in a small space, and (iv) our understanding of the available information in Ronchigram date now allows real-time measurement of aberration parameters.
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A particularly exciting possibility for the future is that multiple corrector systems will allow aberration control of both probe size and detector field of view, in a manner somewhat similar to confocal light microscopy. This will make possible a detailed control of the amplitude and phase of both the incident and scattered electron wave function, allowing specific specimen elastic and inelastic transitions to be accessed [17]. In sum, aberration correction truly marks a major shift away from the limited electron optics which have dominated the first 60 years of electron microscopy, and points the way towards a future where precise optical control will allow routine atomic level characterization of defects and interfaces within the bulk.
Acknowledgements I wish to acknowledge extensive collaboration with O.L. Krivanek and N. Dellby who are responsible for this corrector design and construction, and discussions with Z. Hu and J. Silcox.
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