Progress and perspectives for atomic-resolution electron microscopy

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Ultramicroscopy 108 (2008) 159–166

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Progress and perspectives for atomic-resolution electron microscopy

David J. Smith�

Department of Physics, Arizona State University, Tempe, AZ 85287-1504, USA

This paper is dedicated to the memory of the late John M. Cowley

Abstract

The transmission electron microscope (TEM) has evolved into a highly sophisticated instrument that is ideally suited to the

characterization of advanced materials. Atomic-level information is routinely accessible using both fixed-beam and scanning TEMs.

This report briefly considers developments in the field of atomic-resolution electron microscopy. Recent activities include renewed

attention to on-line microscope control (‘autotuning’), and assessment and correction of aberrations. Aberration-corrected electron

microscopy has developed rapidly in several forms although more work needs to be done to identify standard imaging conditions and

to explore novel operating modes. Preparation of samples and image interpretation have also become more demanding. Ongoing

problems include discrepancies between measured and simulated image contrast, concerns about radiation damage, and inversion of

electron scattering.

r 2007 Elsevier B.V. All rights reserved.

Keywords: On-line microscope control; Aberration-corrected electron microscopy; Stobbs’ factor; Radiation damage

1. Introduction

The resolving power of the transmission electronmicroscope (TEM) has progressively improved throughthe years such that the latest instruments equipped withfield-emission electron guns (FEGs) can operate at close toor even beyond the one-Angstrom (0.1-nm) resolutionbarrier. Individual atomic columns can be resolved in manytypes of crystalline materials so that the TEM has becomean indispensable tool for characterizing defects in advancedand nanostructured materials. Review articles [1–4] andmost recent microscopy conference proceedings can beconsulted for examples of the many different applicationsof these powerful instruments. Our attention here isprimarily directed towards recent developments in instru-mentation and operation for atomic-resolution electronmicroscopy, especially detection and correction of lensaberrations, and topics for future attention. Backgroundmaterial relating to atomic-resolution imaging and defini-tions of resolution is first briefly discussed.

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2. Background

It is well known that image formation in the TEM occursin two stages [5]. First, incident electrons interact withatoms of the specimen, with both elastic and inelasticscattering processes taking place. The electrons that leavethe exit-surface of the specimen are then used to form thefinal enlarged image. Elastically scattered electrons con-tribute to the conventional bright-field, high-resolutionimage, while the inelastically scattered electrons can beused to provide compositional information using thetechnique of electron-energy-loss spectroscopy (EELS).Electrons scattered to very large angles are used inthe scanning TEM for high-angle annular-dark-field(HAADF) imaging—the so-called Z-contrast imagingmode [6]. Historically, image resolution has been restrictedby the unavoidable spherical aberration of the objectivelens, but aberration correction has been achieved in bothfixed-beam TEM [7] and scanning TEM [8].The transfer of electrons to the final viewing screen of the

fixed-beam TEM is dominated by the objective lens andcan be described in terms of its phase contrast transferfunction (TF), which is both specimen- and microscope-independent [9]. Because of the oscillatory nature of this

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ARTICLE IN PRESSD.J. Smith / Ultramicroscopy 108 (2008) 159–166160

function, electrons scattered to different angles experiencephase reversals, which will falsify image details. The lensdefocus must be accurately known since small focuschanges can also alter the image appearance. In practice,to maximize the transfer of information about the speci-men, high-resolution images should normally be recordedat the Scherzer defocus [10]. Envelope functions arecommonly used to represent the effects of focal spread(temporal coherence) and finite beam divergence (spatialcoherence), which cause the TF to be damped at largerscattering angles (i.e. higher resolution) [11,12]. Withlanthanum hexaboride as the electron source, little if anyspecimen information beyond the first TF zero crossover isusually available for almost any microscope and anyobjective lens. Additional, potentially useful details can,however, be extracted when a high-coherence FEG is usedas the electron source.

In the context of this report on progress in atomic-resolution electron microscopy, it is relevant here forclarification purposes to differentiate briefly between thevarious definitions of resolution. The TEM resolution isoften simply given by an expression of the form

d ¼ AC1=4s l3=4, (1)

where Cs is the spherical aberration coefficient of theobjective lens, l is the electron wavelength, and the con-stant A depends on the imaging conditions (i.e., coherent,partially coherent, or incoherent illumination). This re-solution limit involves the traditional compromise betweendiffraction, which varies inversely with the aperture angle,and spherical aberration, which varies with the cube of theangle. Improvements can only be realized by better lensdesign, by operation at higher electron energy, or byaberration correction using multipole elements [7,8,13].

There are several other more useful resolution limits incommon usage [14]:

(i)
The interpretable resolution, sometimes called thestructural resolution, is defined by the first zerocrossover of the TF at the optimum or Scherzerdefocus, and gives the widest possible band of spatialfrequencies without phase reversal [10]. Typical valuesrange from 2.5 to 1.2 A as electron energies areincreased from 100 keV to 1.0MeV. A first-zero TFcrossover of 1.05 A was achieved with the Stuttgartatomic-resolution microscope operating at 1.25MeV[15]. Practical factors such as size and cost, as well asincreased electron irradiation damage, are importantconstraints that negate any advantage of going tohigher electron energies to achieve even shorterelectron wavelengths.
(ii)
The instrumental resolution or information limit isdetermined by the envelope functions, with a value ofapproximately 15% [i.e., exp(�2)] often taken as theresolution cutoff [16]. This resolution limit extendswell beyond the interpretable resolution in recent200- or 300-keV FEG TEMs but the highly oscillatory
nature of the TF renders any very fine image detailuninterpretable. Note that such image interpretabilityis not an issue in the case of HAADF STEM imagingdue to the absence of TF oscillations [6]. Deconvolu-tion of the TF phase modulations can be readilyaccomplished by a posteriori image processing whenthe defocus and CS values are well known [17],enabling finer specimen features to be retrieved. Astriking early result of using a through-focal-serieswavefront restoration to improve image resolution wasthe imaging of individual columns of oxygen atoms forthe first time in a high-temperature ‘YBCO’ super-conductor [18]. In this particular application, thestructural resolution was only �2.4 A but the im-proved instrumental resolution extended the recoveredinformation out to �1.4 A. Wavefront reconstructionusing off-axis electron holography also enabled the fullinstrumental resolution to be utilized in studies ofsilicon ‘dumbbells’ [19].

(iii)
The term lattice-fringe resolution refers to the finestvisible lattice fringes for a crystalline material. Thesefringes result from the interference between two ormore diffracted beams but they do not usually provideany useful information about local atomic arrange-ments. Lattice-fringe spacings as fine as 0.489 A wereobtained with a 1-MeV FEG TEM [20]. This resolu-tion limit relates to overall instrumental stability andalso reflects freedom of the local environment fromadverse external factors such as noise, mechanicalvibrations, and stray magnetic fields. The lattice-fringeresolution was formerly regarded as an importantTEM figure of merit but the interpretable andinstrumental resolution limits are nowadays consid-ered as far more useful for practical purposes.
A common problem for microscopists interested inultrahigh resolution is to distinguish between lattice-fringeimaging and atomic-column imaging. Atomic-scale lattice-fringe images are nowadays relatively simple to obtain withmodern-day electron microscopes when elemental andcompound materials are examined in major low-indexprojections. However, only a very small subset of suchlattice images can be interpreted directly in terms of atomicarrangements. Materials with small unit cells have com-paratively few diffracted beams contributing to the finalimage, and perfect crystal regions will produce images withalmost identical appearance, referred to as Fourier- or self-

images, that recur periodically when the focus is changed[21,22]. The characteristic appearance of a crystal defect orthe thin amorphous strip along the sample edge will oftenbe indispensable for determining the prevailing defocus.And it is essential to have prior knowledge or calibration ofthe focal step size(s) of the instrument. Further complica-tions also arise in thicker crystals as intensity in thediffracted beams builds up. These beams can interfere toproduce very fine second-order fringes that have no directconnection to real specimen features, and such interference

ARTICLE IN PRESSD.J. Smith / Ultramicroscopy 108 (2008) 159–166 161

images should never be interpreted in terms of atomicpositions.

Finally, it is appropriate to recognize that the TEM hasbecome a complex instrument with an almost overwhelm-ing array of adjustable parameters. Fortunately, only asmall number need to be known with a high degree ofaccuracy, and on-line computer control, as discussedbelow, can also relieve some the burden of operation forthe non-expert microscopist. The accelerating voltage, theobjective-lens current and various corrector and alignmentpower supplies must be highly stable, typically to con-siderably better than one part per million, in order toachieve atomic-resolution imaging. Moreover, the objec-tive lens current should be kept fixed where possible sinceseveral adjustable parameters, such as the incident-beamtilt alignment and the objective lens astigmatism, are verysensitive to the exact current setting. Similar extremesensitivity to specimen height has also been reportedrecently in the case of aberration-corrected electronmicroscopy [23]. Focusing by readjustment of the sampleheight rather than by altering the current in the objective-lens windings, is therefore preferable, which of courseimplies continuous monitoring of the lens current with ahigh-precision ammeter.

3. Progress

3.1. Resolution milestones

The resolving power of the newly invented electronmicroscope easily surpassed the capabilities of the opticalmicroscope [24], but establishing a direct relationshipbetween lattice images and projected structure for large-unit-cell block oxides took many more years [25,26].Instrumentation eventually improved to the point whereinformation about atomic arrangements could be obtainedfor semiconductors, ceramics, and metals. Individualatomic columns were resolved in small gold particles [27],and high-voltage TEMs transcended the 2.0-A resolutionbarrier in the early 1980s [28,29]. Intermediate-voltagemicroscopes soon became available commercially thatcould also regularly attain this performance level [30–32].Instrumental resolutions closely approached 1.0 A in themid-1990s using the highly coherent illumination availablewith 300-kV FEG TEMs [33], and wavefront restorationenabled image interpretation at close to the same resolu-tion level using through-focal series reconstruction [18] andoff-axis electron holography [19]. Newer high-voltageTEMs, operating in the range of 1.0–1.5MV, closelyapproached the microscopists’ dream of 1.0-A structuralresolution without any phase reversals [15,34,35]. Directimage interpretation was then possible without needing anya posteriori image processing. Furthermore, informationtransfer beyond the first zero crossover of 1.05 A for the1.25-MeV instrument in Stuttgart was demonstrated [15].Sub-Angstrom electron microscopy with an instrumentalresolution of better than 0.9 A has since been achieved at

the turn of this century with a 300-keV FEG TEM usingexit-wave retrieval [36,37], and similar levels of instru-mental resolution were also obtained soon thereafter usingaberration-corrected HAADF imaging with scanningTEMs operating at 120 keV [38] and at 300 keV [39].

3.2. Detection and correction of aberrations

As microscope resolution limits improve, it becomesmore challenging for the operator to adjust focus and tocorrect the objective-lens astigmatism with sufficientaccuracy to ensure that image integrity is not compro-mised. Moreover, several higher-order aberrations, such asthree-fold astigmatism and axial coma, begin to play amore prominent role in the overall imaging process. Suchaberrations are difficult to detect and to quantify becausethey are not easily distinguished in high-resolution images(or the corresponding diffractograms) recorded with axialillumination [40]. On-line computer control, or ‘autotun-ing’, has thus become indispensable for microscopeadjustment and for obtaining high-quality micrographson a more routine basis. Automatic focusing and stigmat-ing routines were first initiated with the scanning electronmicroscope [41], and methods suitable for focusing,stigmating, and correction of incident-beam misalignmentin conventional fixed-beam TEM were also developed[42,43]. The emergence of the slow-scan CCD cameraprovided quantitative digital recording [44], and enabledimplementation of automated diffractogram analysis,which utilized tableaus of diffractograms computed fromthin amorphous materials [45]. Astigmatism correction andfocus adjustment to within a precision of 1 nm could beachieved, and the beam-tilt alignment was better than0.1mrad: such levels were well beyond the capabilities ofexperienced microscopists. Similar diffractogram tableausare nowadays essential for assessment of aberrations infixed-beam TEMs before implementing aberration correc-tion procedures [46].Spherical and chromatic aberration are unavoidable in

rotationally symmetric electron lenses [47,48]. Sphericalaberration (and defocus) introduces artefactual imageinformation via TF oscillations at higher scattering angle,especially for FEG TEMs, while chromatic aberration willeventually cause loss of higher-resolution detail via thedamping effect of the temporal-coherence envelope func-tion. Early attempts to correct CS (and CC) using multipoleelements failed, mostly because of insufficient electricalstability, and poor mechanical alignment [48], and partlybecause mechanical and electrical adjustments became toocomplex and interconnected for an un-aided operator [49].Breakthroughs in hardware correction of spherical aberra-tion have occurred in recent years [7,8]. A double-hexapoleCS-corrector system enabled the interpretable resolution of�2.4 A of a 200-keV FEG TEM to be extended to �1.3 A[46], while a corrector system based on multiple quad-rupole–octopole elements enabled probe sizes of less than1.0 A to be achieved with a 100-keV scanning TEM [23].


Both of these CS-correction approaches are com-pletely reliant for success on fully automated measurementof lens aberrations and precise feedback under computercontrol to the numerous corrector and deflector powersupplies.

Chromatic aberration does not impact the interpretableresolution, and its exact value need not be known since theeffect of the temporal coherence envelope can be con-veniently represented by an effective focal spread, whichcan be estimated empirically [12]. Nevertheless, reductionor correction of chromatic aberration is still desirable sincethe temporal coherence envelope will eventually limit theinstrumental resolution. Correction of CC has beenaccomplished in a low-voltage scanning electron micro-scope [50], but no significant success for electron withhigher energies has so far been reported. Alternatively,chromatic effects could be reduced by installing a mono-chromator immediately following the electron gun. Calcu-lations for an early design suggested that the energy spreadcould in principle be reduced to about 0.1 eV [51].However, the reduced beam current associated with theuse of such a monochromator [52] might then beconsidered as a drawback, at least for microanalyticalapplications. A more optimistic recent paper stressed theneed to optimize the choices of beam diameter, beamcurrent, and energy width, depending on the specificmaterials problem [53]. An information limit of betterthan 1.0 A with aberration correction has recently beenreported for fixed-beam imaging with a 200-keV FEGTEM equipped with a monochromator [54].

3.3. Aberration-corrected electron microscopy

Correction or elimination of spherical aberration bywhatever means possible enables image interpretability tobe extended out as far as the information limit, asdetermined either by the coherence envelope(s) or byincoherent effects such as local noise, mechanical vibra-tions, or external fields. CS-correction can be achieved off-line by reconstruction of exit-surface wavefunctions [17,18]or by reconstruction of off-axis electron holograms [19], oron-line using hardware corrector systems for either fixed-beam TEM [7] or scanning TEM [8]. All of these methodsare being actively pursued in many laboratories worldwide:attempting to provide an up-to-date summary of applica-tions is thus an unrealistic task. The following representa-tive examples of these techniques have been chosen more toillustrate the largely untapped potential of aberration-corrected electron microscopy as a unique tool forinvestigating the atomic-scale microstructure of manydifferent types of materials.

In principle, only a relatively small number of images isrequired for exit-wave retrieval although the individualdefocus values must be accurately known [17]; in practice,the prevailing method is based upon combining equidistantimages from an extensive focal series, which shouldincidentally also provide a much improved signal-to-noise

ratio in the final reconstructed wavefunction [18]. An earlystudy of an abrupt GaAs/AlAs interface and a GaAs edgedislocation combined experimental results and simulationsto validate the reconstruction algorithm [55]. The atomicstructure of novel Mg5Si6 precipitates observed in acommercial Al–Mg–Si alloy were determined [56], andatomic-column displacements across a S3 {1 1 1} twinboundary in BaTiO3 perovskite were measured with anaccuracy of �0.2 A [57]. Oxygen atomic columns in theboundary plane were also visualized in this latter study.The atomic ‘dumbbell’ structure of carbon atoms in [1 1 0]-oriented diamond was resolved for the first time [37], andimaging of individual carbon, nitrogen, and oxygen atomiccolumns with sub-Angstrom resolution was clearly demon-strated [38].Electron holography was originally proposed as a means

to offset the resolution limitations imposed by sphericalaberration [58]. However, the potential of the technique forresolution improvement after hologram reconstruction wasnot convincingly demonstrated until the characteristicatomic ‘dumbbell’ structure was resolved in both phaseand amplitude images for a [1 1 0]-oriented Si crystalobserved using the off-axis geometry [19]. Note that theapplication of a suitable phase plate during the hologramreconstruction process was essential in accounting forcoherent lens aberrations prevailing at the time of holo-gram recording. Later holography studies of a wedge-shaped GaAs crystal showed that both Ga and As atomiccolumns could be separately identified in the reconstructedphase image over certain thickness ranges, thereby allowingthe crystal polarity to be uniquely determined [59]. Initialobservations of a non-periodic GaAs/AlAs multilayershowed that crystal thicknesses could be accuratelydetermined by measuring the phase shifts for individualAl, Ga, and As atomic columns relative to vacuum, whilethe specific number of Au atoms in separate atomiccolumns of a thin Au foil could be identified from phasemeasurements [60].Hardware correctors for fixed-beam TEMs, based on the

double hexapole plus transfer lenses concept [7,46], havealready become commercially available from severalmanufacturers. Initial applications mostly concentratedon verifying resolution improvements [46,61], but thesuppression of delocalization artifacts at Si/CoSi2 inter-faces was an important early result [61,62]. Atomic stepsand defects at SiO2/Si(1 0 0) interfaces, again without imagedelocalization caused by the coherent FEG illumination,were also reported [63]. Another interesting observationwas that negative spherical aberration combined withoverfocus imaging significantly improved the visibility ofatomic columns of oxygen located in close proximity tostrongly scattering metal atoms in SrTiO3 and YBa2Cu3O7

specimens [64]. Oxygen concentrations at twin boundariesin BaTiO3 were later quantified using this approach [65].The advantages of combining negative CS imaging withexit-wave retrieval were demonstrated in studies ofsemiconductor defects and heterostructures [66].


The possibility of sub-Angstrom probe diameters com-bined with greatly increased incidence angles has stimu-lated great interest in aberration-corrected probes foratomic-scale microanalysis [67]. Of more relevance here isthe potential for enhanced resolution in aberration-corrected HAADF imaging which has so far been realizedusing corrector systems retrofitted to various scanningTEMs operating at different electron energies (see, forexample, Refs. [8,38,39,67,68]). Early observations in-cluded the obligatory atomic-resolution Si(1 1 0) ‘dumbbell’images, and individual Au atoms coexisting with single-atomic-layer ‘rafts’ were observed [38,69]. Imaging andspectroscopic identification of single La atoms within aCaTiO3 matrix was reported [70], and 3-D tomographicimaging of individual Hf atoms within a semiconductordevice was achieved using an approach that combined ahighly convergent, short-focal-depth, incident probe with athrough-focal image series [71]. Applications of aberration-corrected HAADF imaging to supported metal catalystshave been reported [72], and further examples from thefields of catalysts, ceramics and complex oxides aredescribed in a recent review article [68].

4. Perspectives

Aberration-corrected electron microscopy in its severalforms has pushed microscope resolution limits up to andbeyond the 1-A barrier, attracting much attention andopening up new opportunities for atomic-resolutionimaging, but also leaving behind some nagging issuesand raising some additional challenges that need tobe addressed.

4.1. Extra benefits

Compensation of the spherical aberration of theobjective lens means that image detail should becomeinterpretable out to the information limit of the particularmicroscope without the necessity for unscrambling any TFoscillations. The problem of image delocalization, whichoriginates from the very high spatial coherence of the field-emission electron gun [73], is markedly reduced so thatimages of discontinuities such as surfaces and interfacesrecorded with FEG TEMs are no longer blurred [46,62].Moreover, under aberration-corrected imaging conditionswith much reduced axial coma, incident-beam tilts of up toseveral millirads can be tolerated, which allows for moresensitive alignment of the incident beam direction with thedesired crystallographic orientation of the specimen thannormally obtainable by mechanical tilting [74]. A furtherbenefit of reducing other lens aberrations on-line with ahardware corrector system is that off-line reconstructionmethods should become more straightforward, since thesomewhat empirical process of identifying the aberrationphase plate needed for reconstruction [55,59] is greatlysimplified. Initial results [66] of using this combinedapproach for exit-wave retrieval were mentioned above.

The added advantage for applications involving off-axiselectron holography in terms of a factor of four improve-ments in phase detection limits has just been reported [75].The flexibility of treating the spherical aberration as a

variable parameter opens up some intriguing possibilities.Mention has already been made of using a small negativeCS value with a slightly overfocus imaging condition toselectively image weakly scattering atomic columns such asoxygen [64,65]. Adjustment of CS to exactly zero meansthat the phase-contrast transfer function vanishes at zerodefocus, leading to purely amplitude-contrast imaging.Simulations for Ge(1 1 0) as a function of thickness underthese conditions indicate that atomic-resolution imagingwill occur as a result of diffraction channeling [74]. Furtherwork is clearly needed to investigate the full range ofparameter space and to establish some useful recommen-dations about standard imaging conditions if at allpossible.

4.2. Assessment and corrections of higher-order aberrations

Experience with assessment and correction of aberra-tions, and the corresponding achievement of improvedresolution limits has led to refined autotuning procedures.With the probe corrector, aberration coefficients up to fifthorder can be rapidly measured using a refined analysisprocedure [23], which is based on changes in appearance offar-field shadow images termed Ronchigrams [76]. Insimilar fashion for the hexapole corrector system with thefixed-beam TEM, all axial aberrations up to fifth order arealso determined, in this case by reference to a diffracto-gram tableau [61]. Moreover, the initial successes withvarious CS-correction projects has led to proposals forimproved corrector designs that should actually be able tocorrect for all aberrations up to fifth order. One suchproposal for a probe corrector is based on a refinedquadrupole–octopole system, and has stated the ambitioustarget of achieving a probe size of 0.5 A at 200-kVoperating voltage [77]. A second proposal for a probecorrector is based on optimizing the double hexapolecorrector, with a gun monochromator to halve the energywidth, and calculations also suggest that a probe size of0.5 A might just be possible at either 200 or 300 kV [78]. Inboth cases, meeting the additional stringent requirementsfor instrument and stage stability, and high voltage andpower supply stabilities, as well as accurate measurementand correction of all ‘parasitic’ aberrations, will surely be adifficult task.

4.3. Challenges

There are a host of inter-related challenges for theelectron microscopist seeking to take advantage of theatomic-resolution imaging capabilities of contemporarymicroscopes. Sample preparation alone presents severalproblems. On the one hand, clean sample surfaces arehighly recommended so that background noise originating


from the surface oxide or contamination layer does notdegrade image quality. This cleanliness is especiallyimportant when attempting to image single dopant atoms(or other impurities) within a host matrix [79]. Conversely,the absence of any amorphous material in the region ofinterest makes normal focusing and stigmating difficult toachieve, and the procedures for assessment and correctionof aberrations based on Ronchigrams or diffractogram tilttableaus are inapplicable. Higher-resolution imaging placesmore stringent demands on local crystal tilt and thinnercrystals are generally required, but these regions are morelikely to be susceptible to local bending. Suitable strategiesfor overcoming these conflicting requirements continue tobe a topic of ongoing discussion.

Image interpretation in the ‘aberration-free’ era providesadditional problems. Image appearance at ultrahigh-resolution levels becomes much more sensitive to changesin specimen thickness and/or lens defocus as resolutionlimits improve, while the additional parameter spaceintroduced by varying the CS value, as mentioned above,adds to the confusion. These issues are well representedand described in a recent study of a simple Si(1 1 0) wedge-shaped sample [80], where image simulations were essentialfor explaining the rapid variations in image contrast acrossthe highly restricted (o20 nm) field of view. Such simula-tions are likely to become an integral and indispensablepart of future atomic-resolution studies.

4.4. Ongoing problems

The excitement associated with achieving sub-Angstromelectron microscopy has deflected attention from severalfundamental questions that remain unanswered or un-resolved, and should receive attention from the electronmicroscopy community.

The first relates to the significant disagreements betweencontrast levels of simulated and experimental micrographs[81]. In early qualitative studies involving photographicfilm, absolute intensity was not easily measured and thecontrast of image simulations was simply scaled to matchexperimental micrographs. Quantitative studies using slow-scan CCD cameras showed major contrast differences [81],typically by about a factor of three [82], although a recent,very thorough investigation using a cleaved Si samplefound a focus-dependent mismatch factor of �1.5–2.3 [83].Contributions from surface contamination and inelasticscattering did not adequately account for the contrastdifferences [84], which led to further efforts to identify thecause of what is nowadays termed the Stobbs’ factor [85].Thermal diffuse scattering was at least partly implicated byexperiments combining energy-filtered imaging with off-axis electron holography [86].

Specimen-beam interactions are ever-present in electronmicroscopy, so that sample morphology is always liable tobe permanently altered during imaging, and especiallyduring microanalysis [87]. For example, bulk displacementswill occur in Si and Al at electron energies of less than

300 keV, and the energy required for surface sputtering orinterface diffusion is considerably less than in the bulk.Higher magnifications mean higher current densities, whichmean much higher damage rates because the currentdensity increases with the square of the magnification.The imaging magnification and the current density shouldobviously be kept as low as practicable, and periodicchecks for signs of structural change should be made sothat erroneous results can be discounted [88]. Structuralchange due to the intense focused probe is far more likelyto occur during atomic-scale microanalysis, especially forsituations involving oxides and/or interfaces. This possibi-lity should always be carefully monitored by routinelyrecording, and publishing in special cases for credibilitypurposes, before-and-after micrographs of the regionanalyzed.Finally, brief mention needs to be made of the basic and

unresolved problem of inverting crystal scattering toretrieve the crystal potential. The exit-surface wavefunctionitself can be reliably retrieved using several reconstructionmethods, and simple Fourier inversion permits the crystalpotential to be extracted for very thin samples when thekinematical or weak phase object approximations are valid.An iterative method was proposed based on inversion ofthe multislice algorithm [89], but further work is needed toextend thickness limits in the case of non-periodicwavefields [90]. A simulated annealing algorithm was usedfor a GaAs zincblende crystal, enabling successful recon-struction for a thickness of 5.6 nm but not for a thicknessof 11.2 nm [91]. Inversion of crystal scattering hasotherwise received little attention over many years. Overall,it appears that the uniqueness of the inversion process forunknown structures remains unresolved because of thelikelihood of multiple solutions to the inverse scatteringproblem for samples of finite thickness.

5. Final outlook

This paper has provided an overview of atomic-resolu-tion electron microscopy, with the specific objective ofhighlighting areas of ongoing research and development.The atomic-resolution electron microscope permits theatomic structure of interfaces and defects to be determinedroutinely, reliably and with very high positional accuracy,thus potentially allowing improved insights into thephysical behavior of many types of materials. Furtherexperience with microscope operation and familiarity withemerging imaging modes should lead to many novelapplications. Tomographic imaging at the atomic scaleand in situ environmental electron microscopy are antici-pated to be areas of concentrated activity. Experts in themicroscopy field should find time to assist their colleagueswho are more interested in materials properties, withcapitalizing on the exciting possibilities. Meanwhile,further developments in assessment and correction ofhigher-order aberrations can be expected. Operatingconditions for aberration-corrected imaging need to be


further explored and optimized. Improved microscopecontrol with digital recording and processing should permit(almost) real-time structure refinement but many chal-lenges remain. Sample preparation and intuitive imageinterpretation are no longer straightforward. The differ-ences between simulated and experimental contrast levelsneed to be fully explained. These issues will undoubtedlyreceive much attention over the forthcoming years.

Acknowledgment

I am pleased to acknowledge my gratitude to the lateJohn M. Cowley for his invaluable support and encourage-ment over several decades.

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