Review
David J. Smitha, 
Available online 15 July 2010.
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.
Article Outline
The resolving power of the transmission electron microscope (TEM) has progressively improved through the years such that the latest instruments equipped with field-emission electron guns (FEGs) can operate at close to or even beyond the one-Ångstrom (0.1-nm) resolution barrier. Individual atomic columns can be resolved in many types of crystalline materials so that the TEM has become an indispensable tool for characterizing defects in advanced and nanostructured materials. Review articles[1], [2], [3] and [4] and most recent microscopy conference proceedings can be consulted for examples of the many different applications of these powerful instruments. Our attention here is primarily directed towards recent developments in instrumentation and operation for atomic-resolution electron microscopy, especially detection and correction of lens aberrations, and topics for future attention. Background material relating to atomic-resolution imaging and definitions of resolution is first briefly discussed.
Background
It is well known that image formation in the TEM occurs in two stages5. First, incident electrons interact with atoms of the specimen, with both elastic and inelastic scattering processes taking place. The electrons that leave the exit-surface of the specimen are then used to form the final enlarged image. Elastically scattered electrons contribute to the conventional bright-field, high-resolution image, while the inelastically scattered electrons can be used to provide compositional information using the technique of electron-energy-loss spectroscopy (EELS). Electrons scattered to very large angles are used in the scanning TEM for high-angle annular-dark-field (HAADF) imaging – the so-called Z-contrast imaging mode6. Historically, image resolution has been restricted by the unavoidable spherical aberration of the objective lens, but aberration correction has been achieved in both fixed-beam TEM7 and scanning TEM8.
The transfer of electrons to the final viewing screen of the fixed-beam TEM is dominated by the objective lens and can be described in terms of its phase contrast transfer function (TF), which is both specimen- and microscope independent9. Because of the oscillatory nature of this function, electrons scattered to different angles experience phase reversals, which will falsify image details. The lens defocus must be accurately known since small focus changes can also alter the image appearance. In practice, to maximize the transfer of information about the specimen, high-resolution images should normally be recorded at the Scherzer defocus10. Envelope functions are commonly used to represent the effects of focal spread (temporal coherence) and finite beam divergence (spatial coherence), which cause the TF to be damped at larger scattering angles (i.e. higher resolution)[11] and [12]. With lanthanum hexaboride as the electron source, little if any specimen information beyond the first TF zero crossover is usually available for almost any microscope and any objective lens. Additional, potentially useful details can, however, be extracted when a high-coherence FEG is used as the electron source.
In the context of this report on progress in atomic-resolution electron microscopy, it is relevant here for clarification purposes to differentiate briefly between the various definitions of resolution. The TEM resolution is often simply given by an expression of the form
where Cs is the spherical aberration coefficient of the objective lens, l is the electron wavelength, and the constant A depends on the imaging conditions (i.e., coherent, partially coherent, or incoherent illumination). This resolution limit involves the traditional compromise between diffraction, which varies inversely with the aperture angle, and spherical aberration, which varies with the cube of the angle. Improvements can only be realized by better lens design, by operation at higher electron energy, or by aberration correction using multipole elements[7], [8] and [13].
There are several other more useful resolution limits in common usage14:
- (i) The interpretable resolution, sometimes called the structural resolution, is defined by the first zero crossover of the TF at the optimum or Scherzer defocus, and gives the widest possible band of spatial frequencies without phase reversal10. Typical values range from 2.5 to 1.2 Å as electron energies are increased from 100 keV to 1.0 MeV. A first-zero TF crossover of 1.05 Å was achieved with the Stuttgart atomic-resolution microscope operating at 1.25 MeV15. Practical factors such as size and cost, as well as increased electron irradiation damage, are important constraints that negate any advantage of going to higher electron energies to achieve even shorter electron wavelengths.
(i1) The instrumental resolution or information limit is determined by the envelope functions, with a value of approximately 15% [i.e., exp(–2)] often taken as the resolution cutoff16. This resolution limit extends well beyond the interpretable resolution in recent 200- or 300-keV FEG TEMs but the highly oscillatory nature of the TF renders any very fine image detail uninterpretable. Note that such image interpretability is not an issue in the case of HAADF STEM imaging due to the absence of TF oscillations6. Deconvolution of the TF phase modulations can be readily accomplished by a posteriori image processing when the defocus and CS values are well known17, enabling finer specimen features to be retrieved. A striking early result of using a through-focal-series wavefront restoration to improve image resolution was the imaging of individual columns of oxygen atoms for the first time in a high-temperature ‘YBCO’ superconductor18. In this particular application, the structural resolution was only
2.4 Å but the improved instrumental resolution extended the recovered information out to 1.4 Å. Wavefront reconstruction using off-axis electron holography also enabled the full instrumental resolution to be utilized in studies of silicon ‘dumbbells’19.
(iii) The term lattice-fringe resolution refers to the finest visible lattice fringes for a crystalline material. These fringes result from the interference between two or more diffracted beams but they do not usually provide any useful information about local atomic arrangements. Lattice-fringe spacings as fine as 0.489 Å were obtained with a 1-MeV FEG TEM20. This resolution limit relates to overall instrumental stability and also reflects freedom of the local environment from adverse external factors such as noise, mechanical vibrations, and stray magnetic fields. The lattice-fringe resolution was formerly regarded as an important TEM figure of merit but the interpretable and instrumental resolution limits are nowadays considered as far more useful for practical purposes.
A common problem for microscopists interested in ultrahigh resolution is to distinguish between lattice-fringe imaging and atomic-column imaging. Atomic-scale lattice-fringe images are nowadays relatively simple to obtain with modern-day electron microscopes when elemental and compound materials are examined in major low-index projections. However, only a very small subset of such lattice images can be interpreted directly in terms of atomic arrangements. Materials with small unit cells have comparatively few diffracted beams contributing to the final image, and perfect crystal regions will produce images with almost identical appearance, referred to as Fourier- or self images, that recur periodically when the focus is changed[21] and [22]. The characteristic appearance of a crystal defect or the thin amorphous strip along the sample edge will often be indispensable for determining the prevailing defocus. And it is essential to have prior knowledge or calibration of the focal step size(s) of the instrument. Further complications also arise in thicker crystals as intensity in the diffracted beams builds up. These beams can interfere to produce very fine second-order fringes that have no direct connection to real specimen features, and such interference images should never be interpreted in terms of atomic positions.
Finally, it is appropriate to recognize that the TEM has become a complex instrument with an almost overwhelming array of adjustable parameters. Fortunately, only a small number need to be known with a high degree of accuracy, and on-line computer control, as discussed below, can also relieve some the burden of operation for the non-expert microscopist. The accelerating voltage, the objective-lens current and various corrector and alignment power supplies must be highly stable, typically to considerably better than one part per million, in order to achieve atomic-resolution imaging. Moreover, the objective lens current should be kept fixed where possible since several adjustable parameters, such as the incident-beam tilt alignment and the objective lens astigmatism, are very sensitive to the exact current setting. Similar extreme sensitivity to specimen height has also been reported recently in the case of aberration-corrected electron microscopy23. Focusing by readjustment of the sample height rather than by altering the current in the objectivelens windings, is therefore preferable, which of course implies continuous monitoring of the lens current with a high-precision ammeter.
Progress
Resolution milestones
The resolving power of the newly invented electron microscope easily surpassed the capabilities of the optical microscope24, but establishing a direct relationship between lattice images and projected structure for large-unit-cell block oxides took many more years[25] and [26]. Instrumentation eventually improved to the point where information about atomic arrangements could be obtained for semiconductors, ceramics, and metals. Individual atomic columns were resolved in small gold particles27, and high-voltage TEMs transcended the 2.0-Å resolution barrier in the early 1980s[28] and [29]. Intermediate-voltage microscopes soon became available commercially that could also regularly attain this performance level[30], [31] and [32]. Instrumental resolutions closely approached 1.0 Å in the mid-1990s using the highly coherent illumination available with 300-kV FEG TEMs33, and wavefront restoration enabled image interpretation at close to the same resolution level using through-focal series reconstruction18 and off-axis electron holography19. Newer high-voltage TEMs, operating in the range of 1.0–1.5 MV, closely approached the microscopists' dream of 1.0-Å structural resolution without any phase reversals[15], [34] and [35]. Direct image interpretation was then possible without needing any a posteriori image processing. Furthermore, information transfer beyond the first zero crossover of 1.05Å for the 1.25-MeV instrument in Stuttgart was demonstrated15. Sub-Ångstrom electron microscopy with an instrumental resolution of better than 0.9 Å has since been achieved at the turn of this century with a 300-keV FEG TEM using exit-wave retrieval[36] and [37], and similar levels of instrumental resolution were also obtained soon thereafter using aberration-corrected HAADF imaging with scanning TEMs operating at 120 keV38 and at 300 keV39.
Detection and correction of aberrations
As microscope resolution limits improve, it becomes more challenging for the operator to adjust focus and to correct the objective-lens astigmatism with sufficient accuracy to ensure that image integrity is not compromised. Moreover, several higher-order aberrations, such as three-fold astigmatism and axial coma, begin to play a more prominent role in the overall imaging process. Such aberrations are difficult to detect and to quantify because they are not easily distinguished in high-resolution images (or the corresponding diffractograms) recorded with axial illumination40. On-line computer control, or ‘autotuning’, has thus become indispensable for microscope adjustment and for obtaining high-quality micrographs on a more routine basis. Automatic focusing and stigmating routines were first initiated with the scanning electron microscope41, and methods suitable for focusing, stigmating, and correction of incident-beam misalignment in conventional fixed-beam TEM were also developed[42] and [43]. The emergence of the slow-scan CCD camera provided quantitative digital recording44, and enabled implementation of automated diffractogram analysis, which utilized tableaus of diffractograms computed from thin amorphous materials45. Astigmatism correction and focus adjustment to within a precision of 1 nm could be achieved, and the beam-tilt alignment was better than 0.1 mrad: such levels were well beyond the capabilities of experienced microscopists. Similar diffractogram tableaus are nowadays essential for assessment of aberrations in fixed-beam TEMs before implementing aberration correction procedures46.
Spherical and chromatic aberration are unavoidable in rotationally symmetric electron lenses[47] and [48]. Spherical aberration (and defocus) introduces artefactual image information via TF oscillations at higher scattering angle, especially for FEG TEMs, while chromatic aberration will eventually cause loss of higher-resolution detail via the damping effect of the temporal-coherence envelope function. Early attempts to correct CS (and CC) using multipole elements failed, mostly because of insufficient electrical stability, and poor mechanical alignment48, and partly because mechanical and electrical adjustments became too complex and interconnected for an un-aided operator49. Breakthroughs in hardware correction of spherical aberration have occurred in recent years[7] and [8]. A double-hexapole CS-corrector system enabled the interpretable resolution of 2.4 Å of a 200-keV FEG TEM to be extended to 1.3 Å46, while a corrector system based on multiple quadrupole–octopole elements enabled probe sizes of less than 1.0 Å to be achieved with a 100-keV scanning TEM23. Both of these CS-correction approaches are completely reliant for success on fully automated measurement of lens aberrations and precise feedback under computer control to the numerous corrector and deflector power supplies.
Chromatic aberration does not impact the interpretable resolution, and its exact value need not be known since the effect of the temporal coherence envelope can be conveniently represented by an effective focal spread, which can be estimated empirically12. Nevertheless, reduction or correction of chromatic aberration is still desirable since the temporal coherence envelope will eventually limit the instrumental resolution. Correction of CC has been accomplished in a low-voltage scanning electron microscope50, but no significant success for electron with higher energies has so far been reported. Alternatively, chromatic effects could be reduced by installing a monochromator immediately following the electron gun. Calculations for an early design suggested that the energy spread could in principle be reduced to about 0.1 eV51. However, the reduced beam current associated with the use of such a monochromator52 might then be considered as a drawback, at least for microanalytical applications. A more optimistic recent paper stressed the need to optimize the choices of beam diameter, beam current, and energy width, depending on the specific materials problem53. An information limit of better than 1.0 Å with aberration correction has recently been reported for fixed-beam imaging with a 200-keV FEG TEM equipped with a monochromator54.
Aberration-corrected electron microscopy
Correction or elimination of spherical aberration by whatever means possible enables image interpretability to be extended out as far as the information limit, as determined either by the coherence envelope(s) or by incoherent effects such as local noise, mechanical vibrations, or external fields. CS-correction can be achieved offline by reconstruction of exit-surface wavefunctions[17] and [18] or by reconstruction of off-axis electron holograms19, or on-line using hardware corrector systems for either fixed beam TEM7 or scanning TEM8. All of these methods are being actively pursued in many laboratories worldwide: attempting to provide an up-to-date summary of applications is thus an unrealistic task. The following representative examples of these techniques have been chosen more to illustrate the largely untapped potential of aberration corrected electron microscopy as a unique tool for investigating the atomic-scale microstructure of many different types of materials.
In principle, only a relatively small number of images is required for exit-wave retrieval although the individual defocus values must be accurately known17; in practice, the prevailing method is based upon combining equidistant images from an extensive focal series, which should incidentally also provide a much improved signal-to-noise ratio in the final reconstructed wavefunction18. An early study of an abrupt GaAs/AlAs interface and a GaAs edge dislocation combined experimental results and simulations to validate the reconstruction algorithm55. The atomic structure of novel Mg5Si6 precipitates observed in a commercial Al–Mg–Si alloy were determined56, and atomic-column displacements across a ∑3 {1 1 1} twin boundary in BaTiO3 perovskite were measured with an accuracy of 0.2 Å57. Oxygen atomic columns in the boundary 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 time37, and imaging of individual carbon, nitrogen, and oxygen atomic columns with sub-Ångstrom resolution was clearly demonstrated38.
Electron holography was originally proposed as a means to offset the resolution limitations imposed by spherical aberration58. However, the potential of the technique for resolution improvement after hologram reconstruction was not convincingly demonstrated until the characteristic atomic ‘dumbbell’ structure was resolved in both phase and amplitude images for a [1 1 0]-oriented Si crystal observed using the off-axis geometry19. Note that the application of a suitable phase plate during the hologram reconstruction process was essential in accounting for coherent lens aberrations prevailing at the time of hologram recording. Later holography studies of a wedgeshaped GaAs crystal showed that both Ga and As atomic columns could be separately identified in the reconstructed phase image over certain thickness ranges, thereby allowing the crystal polarity to be uniquely determined59. Initial observations of a non-periodic GaAs/AlAs multilayer showed that crystal thicknesses could be accurately determined by measuring the phase shifts for individual Al, Ga, and As atomic columns relative to vacuum, while the specific number of Au atoms in separate atomic columns of a thin Au foil could be identified from phase measurements60.
Hardware correctors for fixed-beam TEMs, based on the double hexapole plus transfer lenses concept[7] and [46], have already become commercially available from several manufacturers. Initial applications mostly concentrated on verifying resolution improvements[46] and [61], but the suppression of delocalization artifacts at Si/CoSi2 interfaces was an important early result[61] and [62]. Atomic steps and defects at SiO2/Si(1 0 0) interfaces, again without image delocalization caused by the coherent FEG illumination, were also reported63. Another interesting observation was that negative spherical aberration combined with overfocus imaging significantly improved the visibility of atomic columns of oxygen located in close proximity to strongly scattering metal atoms in SrTiO3 and YBa2Cu3O7 specimens64. Oxygen concentrations at twin boundaries in BaTiO3 were later quantified using this approach65. The advantages of combining negative CS imaging with exit-wave retrieval were demonstrated in studies of semiconductor defects and heterostructures66.
The possibility of sub-Ångstrom probe diameters combined with greatly increased incidence angles has stimulated great interest in aberration-corrected probes for atomic-scale microanalysis67. Of more relevance here is the potential for enhanced resolution in aberrationcorrected HAADF imaging which has so far been realized using corrector systems retrofitted to various scanning TEMs operating at different electron energies (see, for example[8], [38], [39], [67] and [68]). Early observations included the obligatory atomic-resolution Si(1 1 0) ‘dumbbell’ images, and individual Au atoms coexisting with singleatomic-layer ‘rafts’ were observed[38] and [69]. Imaging and spectroscopic identification of single La atoms within a CaTiO3 matrix was reported70, and 3-D tomographic imaging of individual Hf atoms within a semiconductor device was achieved using an approach that combined a highly convergent, short-focal-depth, incident probe with a through-focal image series71. Applications of aberration-corrected HAADF imaging to supported metal catalysts have been reported72, and further examples from the fields of catalysts, ceramics and complex oxides are described in a recent review article68.
Perspectives
Aberration-corrected electron microscopy in its several forms has pushed microscope resolution limits up to and beyond the 1-Å barrier, attracting much attention and opening up new opportunities for atomic-resolution imaging, but also leaving behind some nagging issues and raising some additional challenges that need to be addressed.
Extra benefits
Compensation of the spherical aberration of the objective lens means that image detail should become interpretable out to the information limit of the particular microscope without the necessity for unscrambling any TF oscillations. The problem of image delocalization, which originates from the very high spatial coherence of the fieldemission electron gun73, is markedly reduced so that images of discontinuities such as surfaces and interfaces recorded with FEG TEMs are no longer blurred[46] and [62]. Moreover, under aberration-corrected imaging conditions with much reduced axial coma, incident-beam tilts of up to several millirads can be tolerated, which allows for more sensitive alignment of the incident beam direction with the desired crystallographic orientation of the specimen than normally obtainable by mechanical tilting74. A further benefit of reducing other lens aberrations on-line with a hardware corrector system is that off-line reconstruction methods should become more straightforward, since the somewhat empirical process of identifying the aberration phase plate needed for reconstruction[55] and [59] is greatly simplified. Initial results66 of using this combined approach for exit-wave retrieval were mentioned above. The added advantage for applications involving off-axis electron holography in terms of a factor of four improvements in phase detection limits has just been reported75.
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 negative CS value with a slightly overfocus imaging condition to selectively image weakly scattering atomic columns such as oxygen[64] and [65]. Adjustment of CS to exactly zero means that the phase-contrast transfer function vanishes at zero defocus, leading to purely amplitude-contrast imaging. Simulations for Ge(1 1 0) as a function of thickness under these conditions indicate that atomic-resolution imaging will occur as a result of diffraction channeling74. Further work is clearly needed to investigate the full range of parameter space and to establish some useful recommendations about standard imaging conditions if at all possible.
Assessment and corrections of higher-order aberrations
Experience with assessment and correction of aberrations, and the corresponding achievement of improved resolution limits has led to refined autotuning procedures. With the probe corrector, aberration coefficients up to fifth order can be rapidly measured using a refined analysis procedure23, which is based on changes in appearance of far-field shadow images termed Ronchigrams76. In similar fashion for the hexapole corrector system with the fixed-beam TEM, all axial aberrations up to fifth order are also determined, in this case by reference to a diffractogram tableau61. Moreover, the initial successes with various CS<
