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Progress towards quantitative high-resolution electron microscopy
ultramicroscopy
Ultramicroscopy52 (1993) 591-601 North-Holland
Progress towards quantitative high-resolution electron microscopy D a v i d J. S m i t h Center for Solid State Science and Department of Physics and Astronomy, Arizona State University, Tempe, A Z 85287, USA
W.J. de R u i j t e r 1, M . R . M c C a r t n e y a n d J.K. Weiss Center for Solid State Science, Arizona State University, Tempe, A Z 85287, USA
Received 11 October 1993 Dedicated to Professor John M. Cowley on the occasion of his seventieth birthday
In recent years there has been a great upsurge of applications involvingquantitative high-resolution electron microscopy, in particular comparing experimental micrographswith image simulations for determination of defect structures. Emphasis has been given to the determination of experimental parameters, the utilization of slow-scan CCD cameras for digital recording and extraction of quantitative structural and chemical information. More attention to surface cleanliness is needed to improve signal quality and the possibility of electron irradiation damage should not be overlooked. Issues related to adoption of a reliability or R-factor are briefly discussed.
1. I n t r o d u c t i o n
The high-resolution electron microscope (HREM) is nowadays capable of routinely providing image information on the level of atomic dimensions [1,2]. In many types of inorganic materials, including semiconductors, metals and some ceramics, individual atomic columns can in principle be separately resolved in several low-index zone axes projections [3]. However, because of dynamical diffraction effects and the non-linear transfer characteristics of the objective lens, extracting reliable structural information about local irregularities on the same scale from recorded images may not be straightforward even when critical parameters such as the specimen thickness and the objective lens defocus are accurately known. Much progress has recently been made
i Present address: Macromolecular Structures Group, Department of Biochemistry and Biophysics, University of California at San Francisco, San Francisco, CA 94122, USA.
towards the quantification of high-resolution electron microscopy, including computer-controlled microscope operation, utilization of digital recording media and pattern recognition. In this paper, we provide a brief overview of (some of) the latest experimental efforts that have been directed towards the quantitative determination of atomic structure and chemistry. We consider some of the more important related experimental factors that limit the effectiveness of the H R E M in some areas of application, and we conclude with a discussion of the problems associated with adopting a reliability or R-factor for studies involving quantitative comparisons between experimental micrographs and simulated images [4].
2. D e t e r m i n a t i o n o f d e f e c t s t r u c t u r e s
The conventional "structure-image" resolution limit for H R E M is usually defined in terms of the first crossover of the objective lens transfer function (TF) at the optimum or extended Scherzer
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defocus [5]. Strictly speaking, TF theory only applies to weak phase objects but a knowledge of T F behavior is essential for understanding the focus dependence of high-resolution electron micrographs. Furthermore, depending upon the coherence, both spatial and temporal, of the incident illumination, it is recognised [6] that further transfer of potentially useful information occurs at higher resolution but with reversals of phase, necessitating T F deconvolution. Improvements in effective resolution can thus originate in one of two ways: either the first TF crossover can be extended to higher spatial frequencies as, for example, recently demonstrated by operation at 1.2 MeV [7], or else various types of image restoration techniques must be applied. Latest developments in electron holography [8] and focal-series reconstruction [9,10] enable partial compensation to be made for the prevailing imaging conditions as well as extraction of the complex phase and amplitude of the specimen exitsurface wavefunction out to the "information limit" of the particular H R E M [5,6]. The success of these methods is, however, dependent on quantitative image recording and processing. Historically, lattice resolution in the electron microscope was first demonstrated by Menter in 1956 [11], but it was not until some time later that the direct correlation between fringe images and projected crystal structure was properly established [12]. The positions of individual heavymetal atomic columns in large-unit-cell oxides were soon discriminated [13,14] leading to widespread application of the H R E M to the study of cation distributions in non-stoichiometric complex oxides [15] and minerals [16]. Even though the anion sub-lattice remained invisible, prior chemical and structural knowledge enabled reliable models for many novel materials and defects to be developed [17]. Image simulation programs primarily based upon the multislice algorithm were developed [18] and came into increasing use for justifying the structural interpretation of high-resolution electron micrographs [19]. However, very few attempts to place the comparisons of experimental micrographs and image simulations on a firm quantitative basis appear to have been made [4,20,21].
In large-unit-cell materials, the optimum defocus for directly interpretable images is usually easily recognized because of the highly characteristic image appearance, with the (well separated) positions of the heavy-metal cations appearing with black contrast. Focus recognition is complicated in the case of small-unit-cell materials by the recurrence of Fourier or self images of the crystal as the objective lens defocus is altered [22,23]. These periodic reversals of contrast, which continue to occur in thicker regions, force the microscopist to resort to alternative means for image focussing such as the appearance of the Fresnel fringe or amorphous material along the sample edge w h e n / i f available in the field of view. It is often considered helpful to have previously calculated a " m a p " or " t a b l e a u " of highresolution images of the perfect crystal lattice as functions of both thickness and defocus as an aid to identifying optimum imaging conditions, but the problems associated with the lack of unique-
Table 1 Examples of atomic-scale modelling of defect structures in small-unit-cell materials Material SnO 2 NiO ~-AI20 3 SrTiO3 Si Si, Ge Ge Ge Ge NiSi2/Si(lll) CoSi2/Si(lll) CdTe C (diamond) Nb Nb Mo AI AI AI AIN Pd/NiO Au
Defect (001) glide twin S5 (210) and X13 (320) tilt GB X11 (0111)/(0111) 35.2° tilt GB X5 (130)/[001] 36.8° tilt GB X13 (510)/[0011 GB Lomer edge dislocation X9 twin X5 (130)/[001] tilt GB X27 tilt GB 7-foldNi A-type 7-foldCo A-type; 7-fold/8-fold Co B-type 2 × 1, 3 × 1 (001) surface reconstruction {100} nitrogen platelet ~'5 (310)/[001] 36.9° tilt GB X25 (710)/[001] tilt GB ~41 (910)/[001]tilt GB X3 {112}incoherent twin X99 {557} (110) tilt GB XI 1 (113) and X9 (2.21) tilt GB Inversion domain boundary O-terminated (111) interface 2× 1 (110) surface reconstruction
Ref. [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41,42] [20] [43l [44] [45] [46] [47] [48] [49] [82]
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ness of thickness a n d / o r defocus still remain [24]. Recent work suggests that once the defocus is known, an analytical expression can be developed for determining the specimen thickness accurately [25]. Alternatively, the use of cross-correlation coefficients in Fourier space to determine both defocus and thickness automatically, and with high speed, once an initial tableau of images of the perfect crystal has been generated, appears to offer the prospect of almost real-time interactive microscopy [26]. It has also been suggested that the well known sensitivity of the high-resolution image to incident beam misalignment [27,28] could be obviated if necessary by applying symmetry restoration, but this clearly would not be applicable at aperiodic image features [26]. Use of the H R E M for the determination of defect structures in small-unit-cell materials has traditionally relied upon qualitative comparisons between experimental micrographs and image simulations, usually based upon a finite number of postulated structural models. A number of case studies are listed in table 1 [20,29-49,82] and fig. 1 shows two examples taken from a recent study of CdTe (001) surface reconstructions that occurred under ultrahigh-vacuum conditions at elevated temperatures [40]. The acceptability of a
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particular structural model is normally considered as being improved if an image "match" is obtained for two or more members of a throughfocal series (see, for example, refs. [20,29,33,38, 41,43,46-48]). It is important to appreciate, however, that in the typical through-focal series of high-resolution images, the apparent positions of closely spaced atomic columns at aperiodic features such as interfaces may vary by as much as 0.03 nm [50]. The temptation to assign image features, particularly intensity maxima and minima, to the exact positions of structural features should therefore be avoided. Indeed, the possibility of positioning errors arising from direct visual interpretation has been demonstrated in several studies by overlaying projected atomic column positions on the experimental a n d / o r simulated images [36,44,49]. Superposition [44] or subtraction [31] of these matching pairs of experimental and simulated images has also been used to assist in the refinement process. Recent work suggests that increased accuracy in the structure refinement should be obtainable by a process of iteration between the calculations and the experimental images using least-squares refinement methods [21,51]. This process is demonstrated in fig. 2 which shows an experimental micrograph of a
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mey are inaccessible to conventional bulk characterization methods. As a demonstration of this improvement for a material where the image resolution is limited by electron beam damage to ~ 3.0 A, fig. 3 compares the centroid map of perchlorocoronene as deduced from entropy maximization and likelihood estimation with the projected structure computed on the basis of singlecrystal, X-ray diffraction data [52]. o
Fig. 2. Comparison of optimum defocus image of naturally occurring TiO 2 (B) polymorph with simulations for: (a) initial structural model; and (b) distance-least-squares (DLS) improved model [51].
3. Quantification novel, naturally occurring, polymorph of TiO 2 overlaid with simulated images that are based upon the original structural model and the improved version [51]. Approaches which combine image plane and diffraction pattern information, such as the maximum entropy method [52,53], have restricted applicability in that they are not usable for aperiodic features such as interfaces and dislocations and it is tacitly assumed that dynamical scattering effects are minimal [54,55]. Nevertheless, recent studies of oxides [54,56], minerals [57] and beamsensitive organic materials [52] have been reported which indicate that a substantial enhancement of structural resolution in perfect crystals beyond that available from the image alone can be achieved from regions that are so small that
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Fig. 3. (a) Centroid map of perchlorocoronene, C24C112,based upon entropy maximization methods applied to experimental micrograph and electron diffraction data; (b) image computed from single-crystal X-ray diffraction data [52].
An important preliminary step in quantifying the imaging and structure refinement process is the determination of several key instrumental and specimen parameters. These include the defocus and spherical aberration coefficient of the objective lens and the local specimen thickness. Experience shows that calculations based on the objective lens geometry are barely adequate for determining the first two of these parameters with any degree of accuracy and it is therefore necessary to resort to methods that utilize experimental micrographs [2]. In practice, determination of focal step sizes is rather straightforward to achieve for small-unit-cell materials, simply by referring to the Fourier oscillation period of the dominant lattice spacing and noting the corresponding changes of the lens controls. Absolute values of defocus are more difficult to obtain, particularly in the absence of Fresnel fringes or amorphous edge regions that preclude the use of optical diffraction techniques, and especially in the defocus range close to optimum where the broadband of the TF is relatively insensitive to small focal variations. Matching with experimental focal series to determine operating parameters has traditionally been achieved visually [58], but this subjective method suffers somewhat from insensitivity because the effects of thickness variations on the image contrast also need to be considered. Cross-correlation techniques that involve automatic comparisons of coefficients in Fourier space have recently been explored and appear very promising [26]. An alternative method, based on comparisons of experimental and simulated images, which utilizes an unconstrained, non-linear,
D.J. Smith et al. / Progress towards quantitative high-resolution electron microscopy
least-squares optimization process to determine defocus, thickness and beam tilt, has been reported to provide reasonable estimates for defoci close to the zero defocus setting [59]. Less attention has been given to C S determination since the appearance of high-resolution electron micrographs, at least those with detail within the interpretable resolution limit, is generally less sensitive to its absolute value. However, in order to utilize any further image information at higher spatial frequencies that might be available because of increased illumination coherence, for example provided by a field-emission electron source, traditional methods [2,60] are no longer adequate. Methods that use images recorded at several defoci and least-squares fitting based on the measurement of T F zeroes visible in optical diffractograms enable standard deviation values of better than 1% to be attained [61,62]. An accuracy in the estimated value of Cs approaching 1% has been achieved during implementation of a practical autoalignment procedure [63]. Further progress towards the experimental quantification of high-resolution electron microscopy is being realized in several other ways, including on-line computer-controlled operation of the microscope [64-67] and the utilization of slow-scan CCD cameras [67-70]. With the former, key parameters such as focal setting, astigmatism and incident beam alignment can be adjusted to an accuracy well beyond that achievable by an experienced microscopist. Original autotuning procedures relied on assessment of image variance (contrast) as the criterion for correction [65,66], which implied the availability of some amorphous material in the field of view or nearby, whereas the beam-induced-displacement (BID) method has been shown to work for crystalline materials [64]. The most recent method proposed, known as the automatic diffractogram analysis (ADA) method [67], again requires the presence of amorphous material for computation of diffractograms but it is less time-consuming than the variance method and probably less prone to error. Subsequent attempts at structure refinement after autotuning has taken place should in principle be simplified because artefactual details caused by inaccurate operator adjustment need
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not be accounted for with additional time-consuming calculations (although C~, defocus and thickness still need to be determined). Finally, it is interesting to note that, despite the increasing availability of user-friendly computer software, autotuning does not yet appear to have been adopted anywhere on a routine basis for the purposes of high-resolution electron microscopy applications. Digital image recording with slow-scan CCD cameras facilitates quantitative comparisons with calculated images. These cameras give excellent linearity over a wide dynamic range of the input signal intensity ( ~ 4 orders of magnitude), provided that bias correction and gain normalization procedures have been properly implemented [69]. Depending on the choice of electron detector and the electronic gain adjustment, a detection quantum efficiency (DQE) close to unity can be achieved for reasonable intensity levels. For example, DQEs of 0.99 for 100 keV electrons and 0.95 for 400 keV electrons have been reported for intensities of around 100 electrons per pixel using a single-crystal YAG scintillator [69]. However, it is important to realize that the same experimental set-up is unlikely to be optimal for recording electron diffraction pattern intensities or for low-dose imaging studies. The so-called modulation transfer function (MTF), which is a measure of the highest detectable spatial frequency, is always likely to be inferior for a CCD array relative to the photographic negative due to the limitation of finite pixel size of the CCD camera. It is therefore necessary to operate at higher electron-optical magnification with the camera, and the effective field of view will be less. Because of the positional stability of the imaging/detection system, geometric distortions introduced by the imaging lenses (and fiber-optic shear due to the camera [71]) can be compensated to the level where they are negligible, unlike conventional photographic recording where considerable off-line computer analysis is always likely to be required. This particular correction, demonstrated in fig. 4 for the Philips 400ST electron microscope in our laboratory, is absolutely essential in the process of making accurate phase measurements in off-axis electron holography
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[71,72]. Finally, it should be appreciated that, because of constraints imposed by the need to detect the high-frequency interference carrier signal, holographic reconstructions would benefit from CCD pixel arrays larger than 1024 × 1024 in size [73]. An inevitable handicap of electron microscopy studies, but one that is often not properly appreciated, is the fact that the final recorded micro-
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Fig. 4. Series of phase images recorded with slow-scan CCD camera: (a) GaAs crystal wedge without geometric distortion; (b) phase image of vacuum; (c) distortion-corrected phase image of GaAs crystal wedge. Equiphase contours of ~r/4 in a, c and ~r/8 in b [72].
graph represents an intensity distribution that is lacking in phase information. Inversion of the imaging process to retrieve the complex exitsurface wavefunction should significantly enhance the prospects of eventually determining the structure of unknown defects, and recent developments in this direction have been particularly encouraging [9,10]. Moreover, because of the enhanced coherence of the incident illumination afforded by field-emission electron sources, due to greater source brightness and reduced energy spread, it becomes worthwhile to deconvolute the oscillatory effects of the T F and thereby also improve the effective structural resolution. Appropriate algorithms have been developed for extracting the complex image wavefunction from a focal series of images, and a further transform is then used in compensating for the aberrations of the imaging lens in order to recover the exitsurface wavefunction. We have recently applied one of these methods, the so-called paraboloid method [9], to reconstruction of a focal series of images of amorphous carbon. Fig. 5a compares diffractograms of the amplitude and phase of the image wavefunction and, as expected for a thin phase object, the zeroes in the amplitude diffractogram coincide with the passbands of the phase diffractogram. For comparison, fig. 5b shows the diffractogram from the phase of the exit-surface wavefunction: the absence of zeroes confirms that the spherical aberration and defocus of the objective lens have been successfully corrected. In conclusion, it is worth reiterating that it was the ready availability of digitally recorded images with a CCD camera that ultimately enabled us to readily and reliably extract the phase and amplitude of the exit-surface wavefunction from the focal series of images. Techniques for resolution improvement based either upon electron holography or focal series restoration should likewise become routinely viable, given a properly adjusted slow-scan CCD camera. In addition to structure determination from high-resolution electron micrographs, considerable attention has recently been given to the determination of compositional variations on the basis of local changes in image contrast [74-80]. This line of work was triggered by the realization
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Fig. 5. Image and exit-surface wavefunction reconstruction of amorphous carbon: (a) comparison diffractogram of image amplitude (left) and phase (right); (b) diffractogram of phase of exit-surface wavefunction.
that there are important groups of materials, such as the A1As/GaAs heterostructures, having subsets of reflections that are "chemically sensitive" [74]. A classic example is the (200) reflection in GaAs which is a structure-factor-difference reflection with an amplitude that remains very low o even for crystal thicknesses in excess of 200 A, unlike the lattice-matched material AlAs where this reflection is comparatively strong, although oscillatory, over wide thickness ranges [81]. By appropriate choices of thickness and defocus, high-resolution images of high contrast are formed that are, in effect, compositionally sensitive. Furthermore, a vector pattern recognition algorithm has been developed, based on lattice averaging to eliminate noise, that facilitates the quantification of local composition on the unit-cell scale [75]. Confidence levels of 60% and 90%, respectively, for recognition of single-atom and double-atom substitution in individual atomic columns at AlAs/GaAs heterojunctions have been reported [75]. The same pattern recognition approach has also been applied successfully to ordering at y/y' interfaces in Ni3Al intermetallic alloys [78]. A novel three-step algorithm has recently been developed for application to strained heterostructures of SixGel_ . alloys [79]. For this system, "chemical imaging" in the sense of reflections with structure-factor differences, is not applicable, but comprehensive analysis of electron scattering behavior, aided by confirmatory experimental measurements, establishes that
layer compositions can be determined at least semi-quantitatively to within _+10% by appropriate choice of operating conditions.
4. Experimental concerns
There are several practical factors not discussed above that affect the reliability or reproducibility of the ongoing efforts to quantify highresolution imaging. These include the presence of amorphous surface overlayers, the occurrence of multiple and inelastic scattering, and the likelihood of electron irradiation damage to the sample during examination. The nature of these effects differ but they all have the same net result of blurring out image detail and thus they could be considered as contributing "noise" to the imaging process. Moreover, it should not be forgotten that electron noise associated with image recording represents a fundamental limitation on information recording. It has been shown, for example, that attaining the greatest accuracy in locating atomic column positions is more a question of statistical definition rather than resolution per se [82]. Irrespective of the particular method used for thinning, most specimens prepared for electron microscopy are covered with an amorphous overlayer. Since the final recorded image is formed by electron transmission through the entire sample, it must be expected that the appearance of the
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object will be affected by the overlayer. This expectation has been substantiated by image simulation [83], as well as being immediately apparent from a comparison of simulated images and experimental micrographs published in the papers listed in table 1. Image-averaging techniques are clearly inapplicable to any aperiodic defects that are of primary interest, although the obvious advantages in terms of improving signal statistics have been demonstrated [84]. Careful attention must therefore be given to sample preparation methods to overcome the unwanted deleterious effect of the surface layer on the recorded image. Measurements of signal-to-noise ratios for S i ( l l l ) lattice images have been used to evaluate the efficacy of different thinning methods: it was also emphasized that reduction, or even elimination, of the surface-generated noise should result in significant improvements in image quantification
cause atomic displacements in materials as high as copper ( Z = 29) in the Periodic Table, and atoms at lattice defects, being less tightly bound, are even more susceptible to displacement [90]. Observation at the very high magnifications that are needed to statistically resolve fine structural detail implies high beam current densities: as the resolution is improved, the electron dose must be further increased (the required specimen current is proportional to the square of the magnification for equivalent signal-to-noise ratio), in turn increasing the damage rate. Electron microscopists must be continually alert to the possibility that, because of beam damage, the defect configuration apparently recorded in their high-resolution electron micrographs may no longer be truly representative of their original defect of interest, especially with respect to relating image contrast levels to the original microstructure.
[85]. The extent of inelastic scattering and its implications in H R E M structural studies seem, to a large extent, to have been deliberately overlooked or ignored. The problem is that it is not at all obvious just how the angular and energy spread of electrons inelastically scattered from the local vicinity of defects could be determined nor how this information could be easily incorporated into image simulations. One suggestion for partially overcoming this difficulty [86], which has yet to be evaluated quantitatively although the possibility has been demonstrated qualitatively [87], is to utilize an electron-energy-imaging filter to form high-resolution images only with electrons that have not lost energy traversing the specimen. Alternatively, it should be appreciated that the complex wavefunction reconstructed from an off-axis electron hologram is also energy-filtered [88]. Retrieval of the object structure in the face of multiple scattering still, however, appears to remain problematical except under special channeling circumstances [89]. Structure determinations based on high-resolution images necessarily remain restricted to the thinnest specimen regions, and the proximity to the specimen surfaces could then result in structural changes. Electron irradiation effects are inescapable. Electron energies of 400 keV are sufficient to
5. Perspective and outlook The quest for quantitative high-resolution electron microscopy with improved levels of resolution is driven by many factors, not just scientific curiosity. For example, fundamental insights into many physical and chemical processes would be provided by better knowledge of atomic structure and chemical composition, leading in turn to important scientific and technological applications. One such case is illustrated in fig. 6 which shows an example of an oxygen-containing inversion domain boundary that is found in aluminum nitride after sintering. At present levels of resolution (fig. 6a), individual atomic columns of the AIN dimer pairs in the bulk crystal, and oxygen atomic columns along the defect, are not resolved [48]. Image simulations based upon the currently favored structural model indicate that discrimination of all separate columns would become possible with an improvement in resolution to 1.0 A (fig. 6b). Many other interesting and worthwhile examples could be described but most readers should be able to provide adequate justification for their own particular choice(s). Inherent to resolution improvement is the fact that microscope operation becomes more de-
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Fig. 6. (a) Experimental high-resolution electron micrograph of oxygen-containing inversion domain boundary (IDB) defect in AIN (arrowed), recorded at 400 keV with JEM-4000EX [48]; (b) simulated image for 1.0 ,~ resolution. Separate AI (darker) and N (lighter) atomic columns resolved in perfect crystal, and O atomic columns (arrowed) resolved at IDB.
manding in terms of the sensitivities required for selection a n d / o r adjustment of focus, astigmatism and incident beam alignment. Improved resolution also implies reduced depth of field, and hence thinner regions will be required for imaging unless ways can be found to overcome, or at least alleviate, the problems of multiple and inelastic scattering. Further gains would accrue, however, from the opportunity to characterize defects such as grain boundaries and interfaces over the wider range of crystal projections that would become accessible to imaging. Furthermore, as the resolution is improved, the locations of atomic columns should still be determined to ~ 5% of the resolution limit using focal-series restoration methods [50]. An ability to locate relative atomic column positions to ~ 0.05 would be highly useful for comparisons with structures predicted from theoretical modelling calculations. The potential of combined imaging/ diffraction studies for periodic crystals of small dimensions is largely untapped in the material
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science field, although appropriate interactive programs for this purpose are already available [55]. A major, unresolved problem in quantitative H R E M , attracting considerable recent discussion, is the issue of uniqueness or "goodness of fit" between experimental micrographs and image simulations based on structural models. Mechanical problems such as adjusting relative magnification and ensuring image registration are easily handled by computer processing routines, but photographic recording is a non-linear process and intensity scaling is somewhat arbitrary. Digital recording with a slow-scan CCD camera is obviously a preferable starting point. Originally [4], several different parameters were discussed as a basis for comparison of images but none of them appear to be satisfactory in practice because of their dependence on defocus. Later work based upon a non-linear, least-squares optimization approach [21] aimed to minimize residuals that were calculated by comparing experimental and simulated grain boundary images using 20 atomic positions as free parameters. A final contour plot overlaid on the experimental image verified the convergence of the refinement. However, despite this particular success, it is in general unclear how a quantitative measure can be assigned to the reliability of any defect determination made using high-resolution electron microscopy. For example, no specific defocu~ can be prescribed that universally maximizes image sensitivity to atomic arrangements at defects in all materials. How many atoms (and at what maximum distance from a defect) should be included in the R-factor calculation? Similarly, a comparison of diffracted beam intensities in reciprocal space, whilst suitable for one-dimensional line scans in convergent beam diffraction patterns from perfect crystals [91], would be inapplicable for an aperiodic defect. We propose that defocus and other microscope parameters should be removed as variables in the optimization process by referring instead to the complex exit-surface wavefunction of the sample, even though this is still affected by multiple and inelastic scattering. With computer-controlled microscope operation, quantitative CCD recording and sufficient corn-
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p u t i n g p o w e r , e x t r a c t i o n o f this w a v e f u n c t i o n f o r comparison with image simulations should bec o m e m o r e s t r a i g h t f o r w a r d in f u t u r e . In conclusion, state-of-the-art high-resolution electron microscopy increasingly involves quantification of atomic structure and chemical composition. Recent experimental developments and s u c c e s s f u l a p p l i c a t i o n to a w i d e v a r i e t y o f struct u r a l d e f e c t s in m a n y m a t e r i a l s a u g u r w e l l f o r future studies.
Acknowledgements O u r e x p e r i m e n t a l w o r k w a s c o n d u c t e d at t h e Center for High Resolution Electron Microscopy at A r i z o n a S t a t e U n i v e r s i t y s u p p o r t e d by N S F Grants DMR-89-15584 and DMR-91-15680. D.J.S. gratefully acknowledges discussions with Drs. U. Dahmen and M.A. O'Keefe.
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[18] P.A. Goodman and A.F. Moodie, Acta Cryst. A 30 (1974) 280. [19] P.R. Self and M.A. O'Keefe, in: High-Resolution Transmission Electron Microscopy, Eds. P.R. Buseck, L. Eyring and J.M. Cowley (Oxford University Press, New York, 1988) ch. 8. [20] W.E. King and G.H. Campbell, in: Atomic Scale Imaging of Surfaces and Interfaces, Eds. D. Biegelsen, D.J. Smith and S.-Y. Tong, MRS Symp. Proc. 295 (Materials Research Society, Pittsburgh, 1993) p. 83. [21] W.E. King and B.S. Lamver, in: Microbeam Analysis 1991, Ed. D.G. Howitt (San Francisco Press, San Francisco, 1991) p.217. [22] J.M. Cowley and A.F. Moodie, Proc. Phys. Soc. (London) B 70 (1957) 486. [23] S. Iijima and M.A. O'Keefe, J. Microscopy 117 (1979) 347. [24] M.A. O'Keefe, U. Dahmen and C.J.D. Hetherington, MRS Symp. Proc. 159 (Materials Research Society, Pittsburgh, 1990) p. 453. [25] T. Geipel and M. Hohenstein, Ultramicroscopy 45 (1992) 167. [26] A.. Thust and K. Urban, Ultramicroscopy 45 (1992) 23. [27] F. Zemlin, K. Weiss, P. Schiske, W. Kunath and K.-H. Herrmann, Ultramicroscopy 3 (1978) 49. [28] D.J. Smith, W.O. Saxton, M.A. O'Keefe, G.J. Wood and W.M. Stobbs, Ultramicroscopy 11 (1983) 263. [29] D.J. Smith, L.A. Bursill and G.J. Wood, J. Solid State Chem. 50 (1983) 51. [30] K.L. Merkle and D.J. Smith, Ultramicroscopy 22 (1987) 57. [31] T. Hoche, P.R. Kenway, H.-J. Kleebe and M. Ruhle, in: Atomic Scale Imaging of Surfaces and Interfaces, Eds. D. Biegelsen, D.J. Smith and S.-Y. Tong, MRS Symp. Proc. 295 (Materials Research Society, Pittsburgh, 1993) p. 103. [32] V. Ravikumar and V.P. Dravid, in: Atomic Scale Imaging of Surfaces and Interfaces, Eds. D. Biegelsen, D.J. Smith and S.-Y. Tong, MRS Symp. Proc. 295 (Materials Research Society, Pittsburgh, 1993) p. 115. [33] M.J. Kim, R.W. Carpenter, Y.L. Chen and G.H. Schwuttke, Ultramicroscopy 40 (1992) 258. [34] A. Bourret, J. Desseaux and A. Renault, Phil. Mag. A. 45 (1982) 1. [35] C. D'Anterroches and A.. Bourret, Phil. Mag. A 49 (1984) 783. [36] A.. Bourret, J.L. Rouviere and J.M. Penisson, Acta Cryst. A. 44 (1988) 838. [37] S. McKernan and C.B. Carter, in: Atomic Scale Imaging of Surfaces and Interfaces, Eds. D. Biegelsen, D.J. Smith and S.-Y. Tong, MRS Symp. Proc. 295 (Materials Research Society, Pittsburgh, 1993) p. 173. [38] D. Cherns, J.C.H. Spence, G.R.A.nstis and J.L. Hutchison, Phil. Mag. A. 46 (1982) 849. [39] A. Catana, P.E. Schmid, P. Lu and D.J. Smith, Phil. Mag. A 66 (1992) 933. [40] P. Lu and D.J. Smith, Surf. Sci. 254 (1991) 119.
D.J. Smith et al. / Progress towards quantitative high-resolution electron microscopy [41] J.C. Barry, L.A. Bursill and J.L. Hutchison, Phil. Mag. A 51 (1985) 15. [42] J.C. Barry, Phil. Mag. A 64 (1991) 111. [43] G.H. Campbell, W.L. Wien, W.E. King, S.M. Foiles and M. Ruhle, Ultramicroscopy 51 (1993) 247. [44] J.M. Penisson, T. Nowicki and M. Biscondi, Phil. Mag. A 58 (1988) 947. [45] D.L. Medlin, M.J. Mills, W.M. Stobbs, M.S. Daw and F. Cosandey, in: Atomic Scale Imaging of Surfaces and Interfaces, Eds. D. Biegelsen, D.J. Smith and S.-Y. Tong, MRS Symp. Proc. 295 (Materials Research Society, Pittsburgh, 1993) p. 91. [46] U. Dahmen, C.J.D. Hetherington, M.A. O'Keefe, K.H. Westmacott, M.J. Mills, M.S. Daw and V. Vitek, Phil. Mag. Lett. 62 (1990) 327. [47] M.J. Mills, M.S. Daw, G.J. Thomas and F. Cosandey, Ultramicroscopy 40 (1992) 247. [48] M.R. McCartney, R.A. Youngman and R.G. Teller, UItramicroscopy 40 (1992) 291. [49] M.I. Buckett, J.P. Shaffer and K.L. Merkle, in: Atomic Scale Imaging of Surfaces and Interfaces, Eds. D. Biegelsen, D.J. Smith and S.-Y. Tong, MRS Symp. Proc. 295 (Materials Research Society, Pittsburgh, 1993) p. 109. [50] W.O. Saxton and D.J. Smith, Ultramicroscopy 18 (1985) 39. [51] J.F. Banfield, D.R. Veblen and D.J. Smith, Am. Mineral. 76 (1991) 343. [52] W. Dong, T. Baird, J.R. Fryer, C.J. Gilmore, D.D. MacNicol, G. Bricogne, D.J. Smith, M.A. O'Keefe and S. Hovm611er, Nature 355 (1992) 605. [53] J.J. Hu and F.H. Li, Ultramicroscopy 35 (1991) 339. [54] S. Hovm611er, A. Sjogren, G. Farrants, M. Sundberg and B.-O. Marinder, Nature 311 (1984) 238. [55] S. Hovm/511er, Microsc. Microanal. Microstruct. 1 (1990) 423. [56] J.J. n u , F.H. Li and H.F. Fan, Ultramicroscopy 41 (1992) 387. [57] K.H. Downing, H. Meisheng, H.-R. Wenk and M.A. O'Keefe, Nature 348 (1990) 525. [58] A.R. Wilson, A.E. Spargo and D.J. Smith, Optik 61 (1982) 63. [59] W.E. King and G.H. Campbell, Ultramicroscopy 51 (1993) 128. [60] O.L. Krivanek, Optik 45 (1976) 97. [61] A.R. Glanvill, A.F. Moodie, H.J. Whitfield and I.J. Wilson, Aust. J. Phys. 39 (1985) 71. [62] W.M.J. Coene and T.J. Denteneer, Ultramicroscopy 38 (1991) 225. [63] A.J. Koster and A.F. de Jong, Ultramicroscopy 38 (1991) 235. [64] A.J. Koster and W.J. de Ruijter, Ultramicroscopy 40 (1992) 89. [65] W.O. Saxton, D.J. Smith and S.J. Erasmus, J. Microscopy 130 (1983) 187.
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[66] D.J. Smith, A. Higgs and P. Perkes, in: Proc. 45th Annual EMSA Meeting, Baltimore, Ed. G.W. Bailey (San Francisco Press, San Francisco, 1987) p. 67. [67] O.L. Krivanek and P.E. Mooney, Ultramicroscopy 49 (1993) 95. [68] I. Daberwow, K.-H. Herrmann, L.B. Liu and W.D. Rau, Ultramicroscopy 38 (1991) 215. [69] W.J. de Ruijter and J.K. Weiss, Rev. Sci. Instr. 63 (1992) 4314. [70] S. Kujawa and D. Krahl, Ultramicroscopy 46 (1992) 395. [71] W.J. de Ruijter and J.K. Weiss, Ultramicroscopy 50 (1993) 269. [72] M. Gajdardziska-Josifovska, W.J. de Ruijter, M.R. McCartney, D.J. Smith, J.K. Weiss and J.M. Zuo, Ultramicroscopy 50 (1993) 285. [73] H. Lichte, Ultramicroscopy 51 (1993) 15. [74] A. Ourmazd, F.H. Baumann, M. Bode and Y. Kim, Ultramicroscopy 34 (1990) 237. [75] A. Ourmazd, D.W. Taylor, M. Bode and Y. Kim, Science 246 (1989) 1571. [76] F.H. Baumann, M. Bode, Y. Kim and A. Ourmazd, Ultramicroscopy 47 (1992) 167. [77] P. Rez, Ultramicroscopy 41 (1992) 115. [78] J.M. Penisson, F.H. Baumann, M. Bode and A. Ourmazd, Phil. Mag. Lett. 64 (1991) 239. [79] D. Stenkamp and W. J~iger, Ultramicroscopy 50 (1993) 269. [80] C.J. Jia, A. Thust, G. Jakob and K. Urban, Ultramicroscopy 49 (1993) 330. [81] H. Ichinose, Y. Ishida and H. Sakaki, JEOL News 26E (1988) 8. [82] L.D. Marks, Surface Sci. 139 (1983) 281. [83] R. Kilaas and R. Gronsky, Ultramicroscopy 16 (1985) 193. [84] S. Paciornik, R. Kilaas and R. Gronsky, Ultramicroscopy 50 (1993) 255. [85] J.M. Gibson and M.L. McDonald, MRS Symp. Proc. 82 (Materials Research Society, Pittsburgh, 1987) p. 109. [86] W.M. Stobbs and W.O. Saxton, J. Microscopy 151 (1988) 88. [87] A.J. Gubbens and O.L. Krivanek, Ultramicroscopy 51 (1993) 146. [88] M.R. McCartney and M. Gajdardziska, Ultramicroscopy 53 (1994) in press. [89] D. Van Dyck, in: Proc. 12th Int. Congr. on Electron Microscopy, Seattle (San Francisco Press, San Francisco, 1990) Vol. 1, p. 26. [90] L.W. Hobbs, in: Quantitative Electron Microscopy, Eds. J.N. Chapman and A.J. Craven (SUSSP Publications, Edinburgh, 1984) ch. 11. [91] J.M. Zuo and J.C.H. Spence, Ultramicroscopy 35 (1991) 185.
Ultramicroscopy52 (1993) 591-601 North-Holland
Progress towards quantitative high-resolution electron microscopy D a v i d J. S m i t h Center for Solid State Science and Department of Physics and Astronomy, Arizona State University, Tempe, A Z 85287, USA
W.J. de R u i j t e r 1, M . R . M c C a r t n e y a n d J.K. Weiss Center for Solid State Science, Arizona State University, Tempe, A Z 85287, USA
Received 11 October 1993 Dedicated to Professor John M. Cowley on the occasion of his seventieth birthday
In recent years there has been a great upsurge of applications involvingquantitative high-resolution electron microscopy, in particular comparing experimental micrographswith image simulations for determination of defect structures. Emphasis has been given to the determination of experimental parameters, the utilization of slow-scan CCD cameras for digital recording and extraction of quantitative structural and chemical information. More attention to surface cleanliness is needed to improve signal quality and the possibility of electron irradiation damage should not be overlooked. Issues related to adoption of a reliability or R-factor are briefly discussed.
1. I n t r o d u c t i o n
The high-resolution electron microscope (HREM) is nowadays capable of routinely providing image information on the level of atomic dimensions [1,2]. In many types of inorganic materials, including semiconductors, metals and some ceramics, individual atomic columns can in principle be separately resolved in several low-index zone axes projections [3]. However, because of dynamical diffraction effects and the non-linear transfer characteristics of the objective lens, extracting reliable structural information about local irregularities on the same scale from recorded images may not be straightforward even when critical parameters such as the specimen thickness and the objective lens defocus are accurately known. Much progress has recently been made
i Present address: Macromolecular Structures Group, Department of Biochemistry and Biophysics, University of California at San Francisco, San Francisco, CA 94122, USA.
towards the quantification of high-resolution electron microscopy, including computer-controlled microscope operation, utilization of digital recording media and pattern recognition. In this paper, we provide a brief overview of (some of) the latest experimental efforts that have been directed towards the quantitative determination of atomic structure and chemistry. We consider some of the more important related experimental factors that limit the effectiveness of the H R E M in some areas of application, and we conclude with a discussion of the problems associated with adopting a reliability or R-factor for studies involving quantitative comparisons between experimental micrographs and simulated images [4].
2. D e t e r m i n a t i o n o f d e f e c t s t r u c t u r e s
The conventional "structure-image" resolution limit for H R E M is usually defined in terms of the first crossover of the objective lens transfer function (TF) at the optimum or extended Scherzer
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defocus [5]. Strictly speaking, TF theory only applies to weak phase objects but a knowledge of T F behavior is essential for understanding the focus dependence of high-resolution electron micrographs. Furthermore, depending upon the coherence, both spatial and temporal, of the incident illumination, it is recognised [6] that further transfer of potentially useful information occurs at higher resolution but with reversals of phase, necessitating T F deconvolution. Improvements in effective resolution can thus originate in one of two ways: either the first TF crossover can be extended to higher spatial frequencies as, for example, recently demonstrated by operation at 1.2 MeV [7], or else various types of image restoration techniques must be applied. Latest developments in electron holography [8] and focal-series reconstruction [9,10] enable partial compensation to be made for the prevailing imaging conditions as well as extraction of the complex phase and amplitude of the specimen exitsurface wavefunction out to the "information limit" of the particular H R E M [5,6]. The success of these methods is, however, dependent on quantitative image recording and processing. Historically, lattice resolution in the electron microscope was first demonstrated by Menter in 1956 [11], but it was not until some time later that the direct correlation between fringe images and projected crystal structure was properly established [12]. The positions of individual heavymetal atomic columns in large-unit-cell oxides were soon discriminated [13,14] leading to widespread application of the H R E M to the study of cation distributions in non-stoichiometric complex oxides [15] and minerals [16]. Even though the anion sub-lattice remained invisible, prior chemical and structural knowledge enabled reliable models for many novel materials and defects to be developed [17]. Image simulation programs primarily based upon the multislice algorithm were developed [18] and came into increasing use for justifying the structural interpretation of high-resolution electron micrographs [19]. However, very few attempts to place the comparisons of experimental micrographs and image simulations on a firm quantitative basis appear to have been made [4,20,21].
In large-unit-cell materials, the optimum defocus for directly interpretable images is usually easily recognized because of the highly characteristic image appearance, with the (well separated) positions of the heavy-metal cations appearing with black contrast. Focus recognition is complicated in the case of small-unit-cell materials by the recurrence of Fourier or self images of the crystal as the objective lens defocus is altered [22,23]. These periodic reversals of contrast, which continue to occur in thicker regions, force the microscopist to resort to alternative means for image focussing such as the appearance of the Fresnel fringe or amorphous material along the sample edge w h e n / i f available in the field of view. It is often considered helpful to have previously calculated a " m a p " or " t a b l e a u " of highresolution images of the perfect crystal lattice as functions of both thickness and defocus as an aid to identifying optimum imaging conditions, but the problems associated with the lack of unique-
Table 1 Examples of atomic-scale modelling of defect structures in small-unit-cell materials Material SnO 2 NiO ~-AI20 3 SrTiO3 Si Si, Ge Ge Ge Ge NiSi2/Si(lll) CoSi2/Si(lll) CdTe C (diamond) Nb Nb Mo AI AI AI AIN Pd/NiO Au
Defect (001) glide twin S5 (210) and X13 (320) tilt GB X11 (0111)/(0111) 35.2° tilt GB X5 (130)/[001] 36.8° tilt GB X13 (510)/[0011 GB Lomer edge dislocation X9 twin X5 (130)/[001] tilt GB X27 tilt GB 7-foldNi A-type 7-foldCo A-type; 7-fold/8-fold Co B-type 2 × 1, 3 × 1 (001) surface reconstruction {100} nitrogen platelet ~'5 (310)/[001] 36.9° tilt GB X25 (710)/[001] tilt GB ~41 (910)/[001]tilt GB X3 {112}incoherent twin X99 {557} (110) tilt GB XI 1 (113) and X9 (2.21) tilt GB Inversion domain boundary O-terminated (111) interface 2× 1 (110) surface reconstruction
Ref. [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41,42] [20] [43l [44] [45] [46] [47] [48] [49] [82]
D.J. Smith et al. / Progress towards quantitative high-resolution electron microscopy
ness of thickness a n d / o r defocus still remain [24]. Recent work suggests that once the defocus is known, an analytical expression can be developed for determining the specimen thickness accurately [25]. Alternatively, the use of cross-correlation coefficients in Fourier space to determine both defocus and thickness automatically, and with high speed, once an initial tableau of images of the perfect crystal has been generated, appears to offer the prospect of almost real-time interactive microscopy [26]. It has also been suggested that the well known sensitivity of the high-resolution image to incident beam misalignment [27,28] could be obviated if necessary by applying symmetry restoration, but this clearly would not be applicable at aperiodic image features [26]. Use of the H R E M for the determination of defect structures in small-unit-cell materials has traditionally relied upon qualitative comparisons between experimental micrographs and image simulations, usually based upon a finite number of postulated structural models. A number of case studies are listed in table 1 [20,29-49,82] and fig. 1 shows two examples taken from a recent study of CdTe (001) surface reconstructions that occurred under ultrahigh-vacuum conditions at elevated temperatures [40]. The acceptability of a
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particular structural model is normally considered as being improved if an image "match" is obtained for two or more members of a throughfocal series (see, for example, refs. [20,29,33,38, 41,43,46-48]). It is important to appreciate, however, that in the typical through-focal series of high-resolution images, the apparent positions of closely spaced atomic columns at aperiodic features such as interfaces may vary by as much as 0.03 nm [50]. The temptation to assign image features, particularly intensity maxima and minima, to the exact positions of structural features should therefore be avoided. Indeed, the possibility of positioning errors arising from direct visual interpretation has been demonstrated in several studies by overlaying projected atomic column positions on the experimental a n d / o r simulated images [36,44,49]. Superposition [44] or subtraction [31] of these matching pairs of experimental and simulated images has also been used to assist in the refinement process. Recent work suggests that increased accuracy in the structure refinement should be obtainable by a process of iteration between the calculations and the experimental images using least-squares refinement methods [21,51]. This process is demonstrated in fig. 2 which shows an experimental micrograph of a
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Fig. 1. (a) Profile image showing ( 2 x 1) reconstruction of CdTe (001) surface recorded in [1101 projection at specimen temperature of 140°C; (b) (3 x 1) reconstruction at 240°C; (c) schematic model for (a); (d) schematic model for (b) [40].
594
D.J. Smith et al. / Progress towards quantitative high-resolution electron microscopy
mey are inaccessible to conventional bulk characterization methods. As a demonstration of this improvement for a material where the image resolution is limited by electron beam damage to ~ 3.0 A, fig. 3 compares the centroid map of perchlorocoronene as deduced from entropy maximization and likelihood estimation with the projected structure computed on the basis of singlecrystal, X-ray diffraction data [52]. o
Fig. 2. Comparison of optimum defocus image of naturally occurring TiO 2 (B) polymorph with simulations for: (a) initial structural model; and (b) distance-least-squares (DLS) improved model [51].
3. Quantification novel, naturally occurring, polymorph of TiO 2 overlaid with simulated images that are based upon the original structural model and the improved version [51]. Approaches which combine image plane and diffraction pattern information, such as the maximum entropy method [52,53], have restricted applicability in that they are not usable for aperiodic features such as interfaces and dislocations and it is tacitly assumed that dynamical scattering effects are minimal [54,55]. Nevertheless, recent studies of oxides [54,56], minerals [57] and beamsensitive organic materials [52] have been reported which indicate that a substantial enhancement of structural resolution in perfect crystals beyond that available from the image alone can be achieved from regions that are so small that
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Fig. 3. (a) Centroid map of perchlorocoronene, C24C112,based upon entropy maximization methods applied to experimental micrograph and electron diffraction data; (b) image computed from single-crystal X-ray diffraction data [52].
An important preliminary step in quantifying the imaging and structure refinement process is the determination of several key instrumental and specimen parameters. These include the defocus and spherical aberration coefficient of the objective lens and the local specimen thickness. Experience shows that calculations based on the objective lens geometry are barely adequate for determining the first two of these parameters with any degree of accuracy and it is therefore necessary to resort to methods that utilize experimental micrographs [2]. In practice, determination of focal step sizes is rather straightforward to achieve for small-unit-cell materials, simply by referring to the Fourier oscillation period of the dominant lattice spacing and noting the corresponding changes of the lens controls. Absolute values of defocus are more difficult to obtain, particularly in the absence of Fresnel fringes or amorphous edge regions that preclude the use of optical diffraction techniques, and especially in the defocus range close to optimum where the broadband of the TF is relatively insensitive to small focal variations. Matching with experimental focal series to determine operating parameters has traditionally been achieved visually [58], but this subjective method suffers somewhat from insensitivity because the effects of thickness variations on the image contrast also need to be considered. Cross-correlation techniques that involve automatic comparisons of coefficients in Fourier space have recently been explored and appear very promising [26]. An alternative method, based on comparisons of experimental and simulated images, which utilizes an unconstrained, non-linear,
D.J. Smith et al. / Progress towards quantitative high-resolution electron microscopy
least-squares optimization process to determine defocus, thickness and beam tilt, has been reported to provide reasonable estimates for defoci close to the zero defocus setting [59]. Less attention has been given to C S determination since the appearance of high-resolution electron micrographs, at least those with detail within the interpretable resolution limit, is generally less sensitive to its absolute value. However, in order to utilize any further image information at higher spatial frequencies that might be available because of increased illumination coherence, for example provided by a field-emission electron source, traditional methods [2,60] are no longer adequate. Methods that use images recorded at several defoci and least-squares fitting based on the measurement of T F zeroes visible in optical diffractograms enable standard deviation values of better than 1% to be attained [61,62]. An accuracy in the estimated value of Cs approaching 1% has been achieved during implementation of a practical autoalignment procedure [63]. Further progress towards the experimental quantification of high-resolution electron microscopy is being realized in several other ways, including on-line computer-controlled operation of the microscope [64-67] and the utilization of slow-scan CCD cameras [67-70]. With the former, key parameters such as focal setting, astigmatism and incident beam alignment can be adjusted to an accuracy well beyond that achievable by an experienced microscopist. Original autotuning procedures relied on assessment of image variance (contrast) as the criterion for correction [65,66], which implied the availability of some amorphous material in the field of view or nearby, whereas the beam-induced-displacement (BID) method has been shown to work for crystalline materials [64]. The most recent method proposed, known as the automatic diffractogram analysis (ADA) method [67], again requires the presence of amorphous material for computation of diffractograms but it is less time-consuming than the variance method and probably less prone to error. Subsequent attempts at structure refinement after autotuning has taken place should in principle be simplified because artefactual details caused by inaccurate operator adjustment need
595
not be accounted for with additional time-consuming calculations (although C~, defocus and thickness still need to be determined). Finally, it is interesting to note that, despite the increasing availability of user-friendly computer software, autotuning does not yet appear to have been adopted anywhere on a routine basis for the purposes of high-resolution electron microscopy applications. Digital image recording with slow-scan CCD cameras facilitates quantitative comparisons with calculated images. These cameras give excellent linearity over a wide dynamic range of the input signal intensity ( ~ 4 orders of magnitude), provided that bias correction and gain normalization procedures have been properly implemented [69]. Depending on the choice of electron detector and the electronic gain adjustment, a detection quantum efficiency (DQE) close to unity can be achieved for reasonable intensity levels. For example, DQEs of 0.99 for 100 keV electrons and 0.95 for 400 keV electrons have been reported for intensities of around 100 electrons per pixel using a single-crystal YAG scintillator [69]. However, it is important to realize that the same experimental set-up is unlikely to be optimal for recording electron diffraction pattern intensities or for low-dose imaging studies. The so-called modulation transfer function (MTF), which is a measure of the highest detectable spatial frequency, is always likely to be inferior for a CCD array relative to the photographic negative due to the limitation of finite pixel size of the CCD camera. It is therefore necessary to operate at higher electron-optical magnification with the camera, and the effective field of view will be less. Because of the positional stability of the imaging/detection system, geometric distortions introduced by the imaging lenses (and fiber-optic shear due to the camera [71]) can be compensated to the level where they are negligible, unlike conventional photographic recording where considerable off-line computer analysis is always likely to be required. This particular correction, demonstrated in fig. 4 for the Philips 400ST electron microscope in our laboratory, is absolutely essential in the process of making accurate phase measurements in off-axis electron holography
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D.J. Smith et al. / Progress towards quantitatil,e high-resolution electron microscopy
[71,72]. Finally, it should be appreciated that, because of constraints imposed by the need to detect the high-frequency interference carrier signal, holographic reconstructions would benefit from CCD pixel arrays larger than 1024 × 1024 in size [73]. An inevitable handicap of electron microscopy studies, but one that is often not properly appreciated, is the fact that the final recorded micro-
a
b
C
Fig. 4. Series of phase images recorded with slow-scan CCD camera: (a) GaAs crystal wedge without geometric distortion; (b) phase image of vacuum; (c) distortion-corrected phase image of GaAs crystal wedge. Equiphase contours of ~r/4 in a, c and ~r/8 in b [72].
graph represents an intensity distribution that is lacking in phase information. Inversion of the imaging process to retrieve the complex exitsurface wavefunction should significantly enhance the prospects of eventually determining the structure of unknown defects, and recent developments in this direction have been particularly encouraging [9,10]. Moreover, because of the enhanced coherence of the incident illumination afforded by field-emission electron sources, due to greater source brightness and reduced energy spread, it becomes worthwhile to deconvolute the oscillatory effects of the T F and thereby also improve the effective structural resolution. Appropriate algorithms have been developed for extracting the complex image wavefunction from a focal series of images, and a further transform is then used in compensating for the aberrations of the imaging lens in order to recover the exitsurface wavefunction. We have recently applied one of these methods, the so-called paraboloid method [9], to reconstruction of a focal series of images of amorphous carbon. Fig. 5a compares diffractograms of the amplitude and phase of the image wavefunction and, as expected for a thin phase object, the zeroes in the amplitude diffractogram coincide with the passbands of the phase diffractogram. For comparison, fig. 5b shows the diffractogram from the phase of the exit-surface wavefunction: the absence of zeroes confirms that the spherical aberration and defocus of the objective lens have been successfully corrected. In conclusion, it is worth reiterating that it was the ready availability of digitally recorded images with a CCD camera that ultimately enabled us to readily and reliably extract the phase and amplitude of the exit-surface wavefunction from the focal series of images. Techniques for resolution improvement based either upon electron holography or focal series restoration should likewise become routinely viable, given a properly adjusted slow-scan CCD camera. In addition to structure determination from high-resolution electron micrographs, considerable attention has recently been given to the determination of compositional variations on the basis of local changes in image contrast [74-80]. This line of work was triggered by the realization
D.J. Smith et al. / Progress towards quantitative high-resolution electron microscopy
597
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• ~2%,
Fig. 5. Image and exit-surface wavefunction reconstruction of amorphous carbon: (a) comparison diffractogram of image amplitude (left) and phase (right); (b) diffractogram of phase of exit-surface wavefunction.
that there are important groups of materials, such as the A1As/GaAs heterostructures, having subsets of reflections that are "chemically sensitive" [74]. A classic example is the (200) reflection in GaAs which is a structure-factor-difference reflection with an amplitude that remains very low o even for crystal thicknesses in excess of 200 A, unlike the lattice-matched material AlAs where this reflection is comparatively strong, although oscillatory, over wide thickness ranges [81]. By appropriate choices of thickness and defocus, high-resolution images of high contrast are formed that are, in effect, compositionally sensitive. Furthermore, a vector pattern recognition algorithm has been developed, based on lattice averaging to eliminate noise, that facilitates the quantification of local composition on the unit-cell scale [75]. Confidence levels of 60% and 90%, respectively, for recognition of single-atom and double-atom substitution in individual atomic columns at AlAs/GaAs heterojunctions have been reported [75]. The same pattern recognition approach has also been applied successfully to ordering at y/y' interfaces in Ni3Al intermetallic alloys [78]. A novel three-step algorithm has recently been developed for application to strained heterostructures of SixGel_ . alloys [79]. For this system, "chemical imaging" in the sense of reflections with structure-factor differences, is not applicable, but comprehensive analysis of electron scattering behavior, aided by confirmatory experimental measurements, establishes that
layer compositions can be determined at least semi-quantitatively to within _+10% by appropriate choice of operating conditions.
4. Experimental concerns
There are several practical factors not discussed above that affect the reliability or reproducibility of the ongoing efforts to quantify highresolution imaging. These include the presence of amorphous surface overlayers, the occurrence of multiple and inelastic scattering, and the likelihood of electron irradiation damage to the sample during examination. The nature of these effects differ but they all have the same net result of blurring out image detail and thus they could be considered as contributing "noise" to the imaging process. Moreover, it should not be forgotten that electron noise associated with image recording represents a fundamental limitation on information recording. It has been shown, for example, that attaining the greatest accuracy in locating atomic column positions is more a question of statistical definition rather than resolution per se [82]. Irrespective of the particular method used for thinning, most specimens prepared for electron microscopy are covered with an amorphous overlayer. Since the final recorded image is formed by electron transmission through the entire sample, it must be expected that the appearance of the
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object will be affected by the overlayer. This expectation has been substantiated by image simulation [83], as well as being immediately apparent from a comparison of simulated images and experimental micrographs published in the papers listed in table 1. Image-averaging techniques are clearly inapplicable to any aperiodic defects that are of primary interest, although the obvious advantages in terms of improving signal statistics have been demonstrated [84]. Careful attention must therefore be given to sample preparation methods to overcome the unwanted deleterious effect of the surface layer on the recorded image. Measurements of signal-to-noise ratios for S i ( l l l ) lattice images have been used to evaluate the efficacy of different thinning methods: it was also emphasized that reduction, or even elimination, of the surface-generated noise should result in significant improvements in image quantification
cause atomic displacements in materials as high as copper ( Z = 29) in the Periodic Table, and atoms at lattice defects, being less tightly bound, are even more susceptible to displacement [90]. Observation at the very high magnifications that are needed to statistically resolve fine structural detail implies high beam current densities: as the resolution is improved, the electron dose must be further increased (the required specimen current is proportional to the square of the magnification for equivalent signal-to-noise ratio), in turn increasing the damage rate. Electron microscopists must be continually alert to the possibility that, because of beam damage, the defect configuration apparently recorded in their high-resolution electron micrographs may no longer be truly representative of their original defect of interest, especially with respect to relating image contrast levels to the original microstructure.
[85]. The extent of inelastic scattering and its implications in H R E M structural studies seem, to a large extent, to have been deliberately overlooked or ignored. The problem is that it is not at all obvious just how the angular and energy spread of electrons inelastically scattered from the local vicinity of defects could be determined nor how this information could be easily incorporated into image simulations. One suggestion for partially overcoming this difficulty [86], which has yet to be evaluated quantitatively although the possibility has been demonstrated qualitatively [87], is to utilize an electron-energy-imaging filter to form high-resolution images only with electrons that have not lost energy traversing the specimen. Alternatively, it should be appreciated that the complex wavefunction reconstructed from an off-axis electron hologram is also energy-filtered [88]. Retrieval of the object structure in the face of multiple scattering still, however, appears to remain problematical except under special channeling circumstances [89]. Structure determinations based on high-resolution images necessarily remain restricted to the thinnest specimen regions, and the proximity to the specimen surfaces could then result in structural changes. Electron irradiation effects are inescapable. Electron energies of 400 keV are sufficient to
5. Perspective and outlook The quest for quantitative high-resolution electron microscopy with improved levels of resolution is driven by many factors, not just scientific curiosity. For example, fundamental insights into many physical and chemical processes would be provided by better knowledge of atomic structure and chemical composition, leading in turn to important scientific and technological applications. One such case is illustrated in fig. 6 which shows an example of an oxygen-containing inversion domain boundary that is found in aluminum nitride after sintering. At present levels of resolution (fig. 6a), individual atomic columns of the AIN dimer pairs in the bulk crystal, and oxygen atomic columns along the defect, are not resolved [48]. Image simulations based upon the currently favored structural model indicate that discrimination of all separate columns would become possible with an improvement in resolution to 1.0 A (fig. 6b). Many other interesting and worthwhile examples could be described but most readers should be able to provide adequate justification for their own particular choice(s). Inherent to resolution improvement is the fact that microscope operation becomes more de-
D.J. Smith et aL / Progress towards quantitative high-resolution electron microscopy
Fig. 6. (a) Experimental high-resolution electron micrograph of oxygen-containing inversion domain boundary (IDB) defect in AIN (arrowed), recorded at 400 keV with JEM-4000EX [48]; (b) simulated image for 1.0 ,~ resolution. Separate AI (darker) and N (lighter) atomic columns resolved in perfect crystal, and O atomic columns (arrowed) resolved at IDB.
manding in terms of the sensitivities required for selection a n d / o r adjustment of focus, astigmatism and incident beam alignment. Improved resolution also implies reduced depth of field, and hence thinner regions will be required for imaging unless ways can be found to overcome, or at least alleviate, the problems of multiple and inelastic scattering. Further gains would accrue, however, from the opportunity to characterize defects such as grain boundaries and interfaces over the wider range of crystal projections that would become accessible to imaging. Furthermore, as the resolution is improved, the locations of atomic columns should still be determined to ~ 5% of the resolution limit using focal-series restoration methods [50]. An ability to locate relative atomic column positions to ~ 0.05 would be highly useful for comparisons with structures predicted from theoretical modelling calculations. The potential of combined imaging/ diffraction studies for periodic crystals of small dimensions is largely untapped in the material
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science field, although appropriate interactive programs for this purpose are already available [55]. A major, unresolved problem in quantitative H R E M , attracting considerable recent discussion, is the issue of uniqueness or "goodness of fit" between experimental micrographs and image simulations based on structural models. Mechanical problems such as adjusting relative magnification and ensuring image registration are easily handled by computer processing routines, but photographic recording is a non-linear process and intensity scaling is somewhat arbitrary. Digital recording with a slow-scan CCD camera is obviously a preferable starting point. Originally [4], several different parameters were discussed as a basis for comparison of images but none of them appear to be satisfactory in practice because of their dependence on defocus. Later work based upon a non-linear, least-squares optimization approach [21] aimed to minimize residuals that were calculated by comparing experimental and simulated grain boundary images using 20 atomic positions as free parameters. A final contour plot overlaid on the experimental image verified the convergence of the refinement. However, despite this particular success, it is in general unclear how a quantitative measure can be assigned to the reliability of any defect determination made using high-resolution electron microscopy. For example, no specific defocu~ can be prescribed that universally maximizes image sensitivity to atomic arrangements at defects in all materials. How many atoms (and at what maximum distance from a defect) should be included in the R-factor calculation? Similarly, a comparison of diffracted beam intensities in reciprocal space, whilst suitable for one-dimensional line scans in convergent beam diffraction patterns from perfect crystals [91], would be inapplicable for an aperiodic defect. We propose that defocus and other microscope parameters should be removed as variables in the optimization process by referring instead to the complex exit-surface wavefunction of the sample, even though this is still affected by multiple and inelastic scattering. With computer-controlled microscope operation, quantitative CCD recording and sufficient corn-
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p u t i n g p o w e r , e x t r a c t i o n o f this w a v e f u n c t i o n f o r comparison with image simulations should bec o m e m o r e s t r a i g h t f o r w a r d in f u t u r e . In conclusion, state-of-the-art high-resolution electron microscopy increasingly involves quantification of atomic structure and chemical composition. Recent experimental developments and s u c c e s s f u l a p p l i c a t i o n to a w i d e v a r i e t y o f struct u r a l d e f e c t s in m a n y m a t e r i a l s a u g u r w e l l f o r future studies.
Acknowledgements O u r e x p e r i m e n t a l w o r k w a s c o n d u c t e d at t h e Center for High Resolution Electron Microscopy at A r i z o n a S t a t e U n i v e r s i t y s u p p o r t e d by N S F Grants DMR-89-15584 and DMR-91-15680. D.J.S. gratefully acknowledges discussions with Drs. U. Dahmen and M.A. O'Keefe.
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