nature INSIGHT I REVIEW ARTICLES materials PUBLISHED ONLINE:24 MARCH 2009|DOI:10.1038/NMAT2406 Electron tomography and holography in materials science Paul A.Midgley1*and Rafal E.Dunin-Borkowski2* The rapid development of electron tomography,in particular the introduction of novel tomographic imaging modes,has led to the visualization and analysis of three-dimensional structural and chemical information from materials at the nanometre level. In addition,the phase information revealed in electron holograms allows electrostatic and magnetic potentials to be mapped quantitatively with high spatial resolution and,when combined with tomography,in three dimensions.Here we present an overview of the techniques of electron tomography and electron holography and demonstrate their capabilities with the aid of case studies that span materials science and the interface between the physical sciences and the life sciences. ver the past few years,transmission electron microscopy projection".The second paper showed how asymmetrical objects (TEM)has been revolutionized,not onlyby the introduction of can be reconstructed from a sufficient number of projections'.The new hardware such as field-emission electron guns,aberration third paper demonstrated how the signal-to-noise ratio could be correctors and monochromators,which are described elsewhere in improved by using an average re-projection calculated from a tilt this Insight edition2,but also by the development of new techniques, series of images.Three methods evolved:(1)electron crystallo- algorithms and software that take advantage of increased computa- graphy,in which diffraction patterns and/or high-resolution images tional speed and the ability to control and automate modern electron are recorded from biological systems,such as proteins,for which microscopes.Two techniques that have benefited from the intro- crystals can be grown;(2)single-particle analysis,in which images duction of digital image acquisition and the ability to record images of the same 'particle'(for example a virus)are recorded at differ- under different electron optical or specimen conditions are electron ent,often random,orientations;(3)electron tomography,in which tomography and electron holography.Electron tomography has been images of a single object are recorded about a tilt axis adopted rapidly by materials scientists as an important microscopy Although electron tomography was first applied in materials tool for the three-dimensional (3D)study of the morphologies and science in the late 1980s,its popularity has increased only in the chemical compositions of nanostructures,and electron holography last decade,with the introduction of novel tomographic imaging offers unique insights into the magnetic and electrostatic properties modes,automation of microscope control,new reconstruction of materials.For each technique,multiple images must be acquired algorithms and the increased speed and ease of the computation to reveal quantitative 3D,magnetic or electrical information,in com- involved.It is worth recalling,however,that electron tomography bination with automation and analysis software,resulting in the need is not the only 3D imaging mode available to the materials scientist. for challenging and often lengthy experiments. X-ray tomography is a routine tool in many laboratories,with desk- top instruments achieving a 3D resolution of a few micrometres. Electron tomography By using a synchrotron source,X-ray tomograms can be produced Although many forms of microscopy can be used to provide remark- with sub-100-nm resolution,and a 2D spatial resolution of~15 nm able images of materials across a range of length scales,the majority is possible using zone plates An X-ray approach based on'diffrac- of these techniques are used to record two-dimensional (2D)pro- tive imaging,which involves recording a tilt series of coherent dif- jections of 3D structures.However,the complexity of both natural fraction patterns and using phase-retrieval methods to reconstruct and artificial materials,such as device architectures in modern inte- real-space tomograms,allows a transverse resolution of-10 nm to grated circuits,highlights the need to develop tools and techniques be achieved.Scanning probe microscopy has been used by record- to explore the morphologies,compositions and physical proper- ing images of fresh surfaces revealed sequentially using a calibrated ties of materials in three dimensions.Such 3D imaging techniques chemical etch'.Atom probe tomography offers,in principle,atomic are encompassed by the field of tomography,which originates in a resolution in three dimensions's.Although recent developments 1917 paper on the projection of an object into a lower-dimensional have allowed problems with sample preparation and suitability to space3.Nearly 50 years later,tomographic X-ray scanning for 3D be overcome by using focused-ion-beam milling and laser-assisted medical imaging was proposed These ideas were picked up by staff field ionization,interpretation and the presence of artefacts remain at EMI,who built the first X-ray computed tomography scanner in a challenge. 1971 (ref.5).(It is often claimed that EMI were able to fund work The scanning electron microscope also provides an excellent on the computed tomography project only because of the enormous platform for 3D imaging at the 'mesoscale(20 nm to 20 um).To revenue generated by sales of the Beatles records in the 1960s.)Since achieve 3D imaging,new surfaces must be exposed in a sequential then the use and type of tomographic scanners for medical imaging and controlled fashion.Modern 'dual-beam'instruments,which have has proliferated. both electron optical and ion optical columns,enable a focused gal- The first examples of 3D reconstructions using TEM were pub- lium ion beam to mill thin slices sequentially and the electron beam lished in 1968 in three seminal papers.The first paper described the to image each exposed surface using secondary or backscattered determination of the structure of a biological macromolecule-the electrons.The in-plane resolution(typically ~5 nm)is finer than the helical symmetry of which allowed reconstruction from a single slice thickness(typically~100 nm),so the 3D resolution function is Department of Materials Science&Metallurgy,University of Cambridge,Pembroke Street,Cambridge CB2 3QZ,UK.Center for Electron Nanoscopy, Technical University of Denmark,DK-2800 Kongens Lyngby,Denmark."e-mail:pam33@cam.ac.uk;rdb@cen.dtu.dk. NATURE MATERIALS VOL 8|APRIL 2009 www.nature.com/naturematerials 271 2009 Macmillan Publishers Limited.All rights reserved
nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials 271 insight | review articles Published online: 24 march 2009 | doi: 10.1038/nmat2406 Over the past few years, transmission electron microscopy (TEM) has been revolutionized, not only by the introduction of new hardware such as field-emission electron guns, aberration correctors and monochromators, which are described elsewhere in this Insight edition1,2, but also by the development of new techniques, algorithms and software that take advantage of increased computational speed and the ability to control and automate modern electron microscopes. Two techniques that have benefited from the introduction of digital image acquisition and the ability to record images under different electron optical or specimen conditions are electron tomography and electron holography. Electron tomography has been adopted rapidly by materials scientists as an important microscopy tool for the three-dimensional (3D) study of the morphologies and chemical compositions of nanostructures, and electron holography offers unique insights into the magnetic and electrostatic properties of materials. For each technique, multiple images must be acquired to reveal quantitative 3D, magnetic or electrical information, in combination with automation and analysis software, resulting in the need for challenging and often lengthy experiments. electron tomography Although many forms of microscopy can be used to provide remarkable images of materials across a range of length scales, the majority of these techniques are used to record two-dimensional (2D) projections of 3D structures. However, the complexity of both natural and artificial materials, such as device architectures in modern integrated circuits, highlights the need to develop tools and techniques to explore the morphologies, compositions and physical properties of materials in three dimensions. Such 3D imaging techniques are encompassed by the field of tomography, which originates in a 1917 paper on the projection of an object into a lower-dimensional space3 . Nearly 50 years later, tomographic X-ray scanning for 3D medical imaging was proposed4 . These ideas were picked up by staff at EMI, who built the first X-ray computed tomography scanner in 1971 (ref. 5). (It is often claimed that EMI were able to fund work on the computed tomography project only because of the enormous revenue generated by sales of the Beatles records in the 1960s.) Since then the use and type of tomographic scanners for medical imaging has proliferated. The first examples of 3D reconstructions using TEM were published in 1968 in three seminal papers. The first paper described the determination of the structure of a biological macromolecule — the helical symmetry of which allowed reconstruction from a single electron tomography and holography in materials science Paul a. midgley1 * and rafal e. dunin-borkowski2 * The rapid development of electron tomography, in particular the introduction of novel tomographic imaging modes, has led to the visualization and analysis of three-dimensional structural and chemical information from materials at the nanometre level. In addition, the phase information revealed in electron holograms allows electrostatic and magnetic potentials to be mapped quantitatively with high spatial resolution and, when combined with tomography, in three dimensions. Here we present an overview of the techniques of electron tomography and electron holography and demonstrate their capabilities with the aid of case studies that span materials science and the interface between the physical sciences and the life sciences. projection6 . The second paper showed how asymmetrical objects can be reconstructed from a sufficient number of projections7 . The third paper demonstrated how the signal-to-noise ratio could be improved by using an average re-projection calculated from a tilt series of images8 . Three methods evolved: (1) electron crystallography, in which diffraction patterns and/or high-resolution images are recorded from biological systems, such as proteins, for which crystals can be grown9 ; (2) single-particle analysis, in which images of the same ‘particle’ (for example a virus) are recorded at different, often random, orientations10; (3) electron tomography, in which images of a single object are recorded about a tilt axis11. Although electron tomography was first applied in materials science in the late 1980s, its popularity has increased only in the last decade, with the introduction of novel tomographic imaging modes, automation of microscope control, new reconstruction algorithms and the increased speed and ease of the computation involved. It is worth recalling, however, that electron tomography is not the only 3D imaging mode available to the materials scientist. X-ray tomography is a routine tool in many laboratories, with desktop instruments achieving a 3D resolution of a few micrometres. By using a synchrotron source, X-ray tomograms can be produced with sub-100-nm resolution, and a 2D spatial resolution of ~15 nm is possible using zone plates12. An X-ray approach based on ‘diffractive imaging’, which involves recording a tilt series of coherent diffraction patterns and using phase-retrieval methods to reconstruct real-space tomograms, allows a transverse resolution of ~10 nm to be achieved13. Scanning probe microscopy has been used by recording images of fresh surfaces revealed sequentially using a calibrated chemical etch14. Atom probe tomography offers, in principle, atomic resolution in three dimensions15. Although recent developments have allowed problems with sample preparation and suitability to be overcome by using focused-ion-beam milling and laser-assisted field ionization, interpretation and the presence of artefacts remain a challenge. The scanning electron microscope also provides an excellent platform for 3D imaging at the ‘mesoscale’ (20 nm to 20 μm)16. To achieve 3D imaging, new surfaces must be exposed in a sequential and controlled fashion. Modern ‘dual-beam’ instruments, which have both electron optical and ion optical columns, enable a focused gallium ion beam to mill thin slices sequentially and the electron beam to image each exposed surface using secondary or backscattered electrons. The in-plane resolution (typically ~5 nm) is finer than the slice thickness (typically ~100 nm), so the 3D resolution function is 1 Department of Materials Science & Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK. 2 Center for Electron Nanoscopy, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark. *e-mail: pam33@cam.ac.uk; rdb@cen.dtu.dk. nmat_2406_APR09.indd 271 13/3/09 12:08:29 © 2009 Macmillan Publishers Limited. All rights reserved
REVIEW ARTICLES INSIGHT NATURE MATERIALS DOL:10.1038/NMAT2406 highly anisotropic.As the generation of characteristic X-rays by the the higher frequencies,suitably apodized to avoid enhancing electron beam allows elemental maps to be recorded in most scan- noise2.The second is an iterative scheme in which a reconstruc- ning electron microscopes,3D compositional information can be tion is re-projected along the original tilt series directions for com- obtained by recording sequential elemental maps.Crystallographic parison with the original recorded images25.A difference image is information can also be retrieved from electron-backscattered dif- formed at each of the tilt increments and a difference tomogram fraction patterns and a full 3D crystallographic analysis made from subsequently used to improve the reconstruction.An iterative a volume of~503 um3 in 24 h (refs 18,19). procedure follows until no further improvement is seen,typically after 20-40 iterations.This iterative approach is one of a number of Nanoscale tomography in TEM techniques that can be used to constrain the reconstruction to best For high-resolution (~13 nm)3D tomographic imaging in TEM, fit the information available.By imposing constraints,the number images are recorded every one or two degrees about a tilt axis,over of images required to achieve a high-fidelity reconstruction can be as large a specimen tilt range as possible (Fig.1a).Typically,the reduced considerably.This is the basis of 'discrete tomography.One ensemble of images is then 'back-projected'to form a 3D recon- implementation of this is the DART algorithm,which builds on the struction.The information required,and the type of specimen iterative reconstruction approach but adds extra constraints at each examined,often dictate which of the many imaging modes available iteration2.Specifically,the algorithm is told how many densities (or in the TEM is used. grey levels)should be present in the reconstruction.Often this prior It is important to understand the limitations of tomography in information is known.In the extreme limit,only one density may TEM and the artefacts that may arise.Early examples of electron be present in the object,so a binary solution is found-in this limit, tomography in materials science used bright-field techniques and if the signal-to-noise ratio is good then a handful of images may be approaches based on work in the biological sciences to study stained enough to produce a high-fidelity reconstruction even for complex polymer sections and the internal networks of block copolymers2. concave and convex structures?. Similarly,bright-field TEM was used to investigate the porosities When using conventional TEM samples and specimen holders, of zeolitic materials".In biological work and in non-crystalline a tilt may be reached beyond which the sample is too thick or shad- inorganic systems,the use of bright-field TEM is possible because owing occurs owing to the holder,grid or other parts of the speci- mass-thickness contrast satisfies the 'projection requirement'that men.This tilt maximum leads to a 'missing wedge'of information, the recorded signal should be a monotonic function of some physical as shown in Fig.1b.Such missing information can lead to artefacts, property22.If this requirement is not satisfied,then reconstruction and reconstructions can be elongated in the direction of the missing becomes complicated and conventional real-space back-projection wedge.The tilt range should therefore be as high as possible.Recent may fail. work has suggested that 75-80 should be sufficient to reduce arte- In general,the resolution of a reconstructed tomogram is gov- facts to a minimum and not lead to serious errors when measuring erned by the number of images in the tilt series and by the tilt range object sizes or shapes28.An alternative way of reducing the missing over which the series is recorded.In simple terms,the (Crowther) wedge is to record a second tilt series about an axis perpendicular resolution is equal to the angular increment of the tilt series multi- to the first-a 'dual-axis'series.In practice,the sample is usually plied by the size of the object2.Thus,as well as needing a fine rotated by 90 and a second tilt series recorded.This approach can angular increment,the resolution scales with the size of the object lead to a large improvement in the fidelity of the reconstruction2, studied.In practice,to limit beam damage and to keep acquisition as seen in Fig.2.There,dual-axis tomography has been combined times to a sensible level,images are recorded every 1-2.With accu- with iterative reconstruction to constrain the reconstruction to rate,often iterative,reconstruction techniques,the resolution is then best fit the images in both tilt series%.For samples for which high approximately 1/100 of the object diameter.Although real-space tilts lead to large projected thicknesses,recording a dual-axis series back-projection methods are used routinely for tomographic recon- with a smaller maximum tilt may be a better solution;for example, struction,it is useful to consider that each projection corresponds the fraction of missing information present in a dual-axis series to a central slice in Fourier space.By recording a tilt series about a recorded with +50 tilt(~20%)is approximately the same as that single axis,low-frequency information is sampled more finely than recorded in a single tilt series with +70 tilt.Ultrahigh-tilt holders higher frequency information.Thus,a simple back-projection,in are now commercially available,including those in which the use which all of the information from the ensemble of images is smeared of a needle-shaped sample allows 360 rotation within the pole- into 3D reconstruction space,leads to a blurred version of the origi- piece gap of the objective lens,eliminating missing-wedge arte- nal object.Two schemes exist to overcome this blurring.The first facts.Such specimens can be fabricated using a focused ion beam" is to use a ramp-like weighting filter in Fourier space to enhance Indeed,similar tips are fabricated for atom probe tomography Missing wedge ata points Missing wedge Figure 1 Electron tomography.a,Illustration of two-stage tomography process with (left)acquisition of an ensemble of images (projections)about a single tilt axis and(right)the back-projection of these images into 3D object space.b,Representation in Fourier space of the ensemble of projections, indicating the undersampling of high-spatial-frequency information and the missing wedge of information brought about by a restricted tilt range.0 is the tilt increment between successive images and a is the maximum tilt angle.(Adapted from ref.29.) 272 NATURE MATERIALS VOL 8 APRIL 2009|www.nature.com/naturematerials 2009 Macmillan Publishers Limited.All rights reserved
272 nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials review articles | insight NaTure maTerIals doi: 10.1038/nmat2406 highly anisotropic. As the generation of characteristic X-rays by the electron beam allows elemental maps to be recorded in most scanning electron microscopes, 3D compositional information can be obtained by recording sequential elemental maps17. Crystallographic information can also be retrieved from electron-backscattered diffraction patterns and a full 3D crystallographic analysis made from a volume of ~503 μm3 in 24 h (refs 18,19). nanoscale tomography in tem For high-resolution (~13 nm3 ) 3D tomographic imaging in TEM, images are recorded every one or two degrees about a tilt axis, over as large a specimen tilt range as possible (Fig. 1a). Typically, the ensemble of images is then ‘back-projected’ to form a 3D reconstruction. The information required, and the type of specimen examined, often dictate which of the many imaging modes available in the TEM is used. It is important to understand the limitations of tomography in TEM and the artefacts that may arise. Early examples of electron tomography in materials science used bright-field techniques and approaches based on work in the biological sciences to study stained polymer sections and the internal networks of block copolymers20. Similarly, bright-field TEM was used to investigate the porosities of zeolitic materials21. In biological work and in non-crystalline inorganic systems, the use of bright-field TEM is possible because mass-thickness contrast satisfies the ‘projection requirement’ that the recorded signal should be a monotonic function of some physical property22. If this requirement is not satisfied, then reconstruction becomes complicated and conventional real-space back-projection may fail. In general, the resolution of a reconstructed tomogram is governed by the number of images in the tilt series and by the tilt range over which the series is recorded. In simple terms, the (Crowther) resolution is equal to the angular increment of the tilt series multiplied by the size of the object23. Thus, as well as needing a fine angular increment, the resolution scales with the size of the object studied. In practice, to limit beam damage and to keep acquisition times to a sensible level, images are recorded every 1–2°. With accurate, often iterative, reconstruction techniques, the resolution is then approximately 1/100 of the object diameter. Although real-space back-projection methods are used routinely for tomographic reconstruction, it is useful to consider that each projection corresponds to a central slice in Fourier space. By recording a tilt series about a single axis, low-frequency information is sampled more finely than higher frequency information. Thus, a simple back-projection, in which all of the information from the ensemble of images is smeared into 3D reconstruction space, leads to a blurred version of the original object. Two schemes exist to overcome this blurring. The first is to use a ramp-like weighting filter in Fourier space to enhance the higher frequencies, suitably apodized to avoid enhancing noise24. The second is an iterative scheme in which a reconstruction is re-projected along the original tilt series directions for comparison with the original recorded images25. A difference image is formed at each of the tilt increments and a difference tomogram subsequently used to improve the reconstruction. An iterative procedure follows until no further improvement is seen, typically after 20–40 iterations. This iterative approach is one of a number of techniques that can be used to constrain the reconstruction to best fit the information available. By imposing constraints, the number of images required to achieve a high-fidelity reconstruction can be reduced considerably. This is the basis of ‘discrete tomography’. One implementation of this is the DART algorithm, which builds on the iterative reconstruction approach but adds extra constraints at each iteration26. Specifically, the algorithm is told how many densities (or grey levels) should be present in the reconstruction. Often this prior information is known. In the extreme limit, only one density may be present in the object, so a binary solution is found—in this limit, if the signal-to-noise ratio is good then a handful of images may be enough to produce a high-fidelity reconstruction even for complex concave and convex structures27. When using conventional TEM samples and specimen holders, a tilt may be reached beyond which the sample is too thick or shadowing occurs owing to the holder, grid or other parts of the specimen. This tilt maximum leads to a ‘missing wedge’ of information, as shown in Fig. 1b. Such missing information can lead to artefacts, and reconstructions can be elongated in the direction of the missing wedge. The tilt range should therefore be as high as possible. Recent work has suggested that 75–80° should be sufficient to reduce artefacts to a minimum and not lead to serious errors when measuring object sizes or shapes28. An alternative way of reducing the missing wedge is to record a second tilt series about an axis perpendicular to the first—a ‘dual-axis’ series. In practice, the sample is usually rotated by 90° and a second tilt series recorded. This approach can lead to a large improvement in the fidelity of the reconstruction29, as seen in Fig. 2. There, dual-axis tomography has been combined with iterative reconstruction to constrain the reconstruction to best fit the images in both tilt series30. For samples for which high tilts lead to large projected thicknesses, recording a dual-axis series with a smaller maximum tilt may be a better solution; for example, the fraction of missing information present in a dual-axis series recorded with ±50° tilt (~20%) is approximately the same as that recorded in a single tilt series with ±70° tilt. Ultrahigh-tilt holders are now commercially available, including those in which the use of a needle-shaped sample allows 360° rotation within the polepiece gap of the objective lens, eliminating missing-wedge artefacts. Such specimens can be fabricated using a focused ion beam31. Indeed, similar tips are fabricated for atom probe tomography a b Data points Missing wedge Missing wedge θ α Figure 1 | electron tomography. a, Illustration of two-stage tomography process with (left) acquisition of an ensemble of images (projections) about a single tilt axis and (right) the back-projection of these images into 3D object space. b, Representation in Fourier space of the ensemble of projections, indicating the undersampling of high-spatial-frequency information and the missing wedge of information brought about by a restricted tilt range. θ is the tilt increment between successive images and α is the maximum tilt angle. (Adapted from ref. 29.) nmat_2406_APR09.indd 272 13/3/09 12:08:30 © 2009 Macmillan Publishers Limited. All rights reserved
NATURE MATERIALS DOL:10.1038/NMAT2406 INSIGHT I REVIEW ARTICLES Tilt axis 2 Tilt axis 1 20nm Figure 3 Tomographic reconstruction of a heterogeneous catalyst. 100nm 100nm Surface-rendered representation of a tomographic reconstruction of a heterogeneous catalyst based on disordered mesoporous silica supporting bimetallic ruthenium-platinum nanoparticles.The surface has been colour- coded according to the Gaussian curvature of the surface,with blue regions delineating saddle points.The nanoparticles(red)appear to prefer to anchor themselves at the (blue)saddle points. atomic number.These properties make the STEM HAADF signal ideal for tomographic applications".The earliest example of STEM HAADF tomography was in the study of heterogeneous catalysts based on metallic nanoparticles distributed within highly porous siliceous and carbonaceous support structures".There the STEM HAADF signal was able to discriminate nanometre-sized particles 100nr 25 nm from the background support,whereas in bright-field TEM the contrast from the particles was very weak More recent work%on similar catalyst structures,as shown in Fig.3,has revealed the dis- Figure 2|Dual-axis electron tomography.a,Illustration showing how tribution of particles on and within a porous framework and the a dual-axis tilt series collapses a missing wedge into a missing pyramid fractal nature of the internal surface.Theoretical work has shown of information.b,c,d,e,Reconstructions of cadmium telluride tetrapods from a dual-axis tilt series,reconstructed individually (b,c)and then as that when two parallel chemical reactions are taking place on a a dual-axis series (d).The tetrapod shown boxed in d is magnified in e. fractal surface,the slower,often undesired,reaction can be sup- The arrows indicate regions where the missing wedge has had its greatest pressed.Figure 3 also shows that STEM tomography can be used to relate the distribution of particles to the underlying surface curva- effect on the individual reconstructions.Each leg'of each tetrapod is better ture,showing in this case the strong preference of the particles(red) reconstructed in the dual-axis reconstruction.(Adapted from ref.29.) for saddle-shaped anchor points(blue). The suppression of unwanted diffraction contrast in STEM and the same tip can be imaged using both techniques,to provide HAADF tomography has led to the study of faceting and crystal complementary information32. morphology.Figure 4 reveals the faceting of magnetite crystals that The TEM is a remarkably versatile instrument,and the strong make up the backbone'of one strain of magnetotactic bacteria27.38 interaction of the electron beam with the specimen leads to a host of Similar studies have now been completed on a number of nano- possible imaging modes that can be used,in principle,for electron crystals,especially in catalyst systems where different facets can tomography.Bright-field TEM,which is used so prevalently in bio- have different catalytic properties.STEM tomography has also been logical tomography,is not in general suited to the study of crystalline used to determine the real-space crystallography of mesoporous materials.Diffraction contrast and Fresnel fringes do not satisfy the structures".For example,in MCM-48 mesoporous silica,which has projection requirement and can lead to serious artefacts in recon- a double-gyroid form,electron diffraction and 2D high-resolution structions.The image signal seen in the scanning TEM(STEM), electron microscopy(HREM)studies had concluded that an addi- using high-angle annular dark-field(HAADF)imaging,offers an tional pore system was present in the system.STEM tomography excellent alternative.As described elsewhere in this Insight edition', was able to visualize this directly in three dimensions and confirm STEM HAADF imaging can be considered incoherent,almost com- the space group symmetry40. pletely eliminating diffraction and phase contrast.The contrast is In metallurgy,STEM tomography is especially useful for inves- then,to a good approximation,monotonic with thickness,and is tigating the morphologies and distributions of precipitates in steels also sensitive to changes in composition;for a typical geometry and alloys.Figure 5a shows an example of a surface-rendered recon- and material,it is approximately proportional to 2,where Z is the struction of germanium precipitates in an aluminium-germanium NATURE MATERIALS VOL 8|APRIL 2009 www.nature.com/naturematerials 273 2009 Macmillan Publishers Limited.All rights reserved
nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials 273 NaTure maTerIals doi: 10.1038/nmat2406 insight | review articles and the same tip can be imaged using both techniques, to provide complementary information32. The TEM is a remarkably versatile instrument, and the strong interaction of the electron beam with the specimen leads to a host of possible imaging modes that can be used, in principle, for electron tomography. Bright-field TEM, which is used so prevalently in biological tomography, is not in general suited to the study of crystalline materials. Diffraction contrast and Fresnel fringes do not satisfy the projection requirement and can lead to serious artefacts in reconstructions. The image signal seen in the scanning TEM (STEM), using high-angle annular dark-field (HAADF) imaging, offers an excellent alternative. As described elsewhere in this Insight edition1 , STEM HAADF imaging can be considered incoherent, almost completely eliminating diffraction and phase contrast. The contrast is then, to a good approximation, monotonic with thickness, and is also sensitive to changes in composition; for a typical geometry and material, it is approximately proportional to Z1.8, where Z is the atomic number. These properties make the STEM HAADF signal ideal for tomographic applications33. The earliest example of STEM HAADF tomography was in the study of heterogeneous catalysts based on metallic nanoparticles distributed within highly porous siliceous and carbonaceous support structures34. There the STEM HAADF signal was able to discriminate nanometre-sized particles from the background support, whereas in bright-field TEM the contrast from the particles was very weak35. More recent work36 on similar catalyst structures, as shown in Fig. 3, has revealed the distribution of particles on and within a porous framework and the fractal nature of the internal surface. Theoretical work has shown that when two parallel chemical reactions are taking place on a fractal surface, the slower, often undesired, reaction can be suppressed. Figure 3 also shows that STEM tomography can be used to relate the distribution of particles to the underlying surface curvature, showing in this case the strong preference of the particles (red) for saddle-shaped anchor points (blue). The suppression of unwanted diffraction contrast in STEM HAADF tomography has led to the study of faceting and crystal morphology. Figure 4 reveals the faceting of magnetite crystals that make up the ‘backbone’ of one strain of magnetotactic bacteria37,38. Similar studies have now been completed on a number of nanocrystals, especially in catalyst systems where different facets can have different catalytic properties. STEM tomography has also been used to determine the real-space crystallography of mesoporous structures39. For example, in MCM-48 mesoporous silica, which has a double-gyroid form, electron diffraction and 2D high-resolution electron microscopy (HREM) studies had concluded that an additional pore system was present in the system. STEM tomography was able to visualize this directly in three dimensions and confirm the space group symmetry40. In metallurgy, STEM tomography is especially useful for investigating the morphologies and distributions of precipitates in steels and alloys. Figure 5a shows an example of a surface-rendered reconstruction of germanium precipitates in an aluminium–germanium b a c d e 100 nm 100 nm 25 nm 100 nm Tilt axis 1 Tilt axis 2 20 nm Figure 3 | Tomographic reconstruction of a heterogeneous catalyst. Surface-rendered representation of a tomographic reconstruction of a heterogeneous catalyst based on disordered mesoporous silica supporting bimetallic ruthenium–platinum nanoparticles. The surface has been colourcoded according to the Gaussian curvature of the surface, with blue regions delineating saddle points. The nanoparticles (red) appear to prefer to anchor themselves at the (blue) saddle points. Figure 2 | Dual-axis electron tomography. a, Illustration showing how a dual-axis tilt series collapses a missing wedge into a missing pyramid of information. b, c, d, e, Reconstructions of cadmium telluride tetrapods from a dual-axis tilt series, reconstructed individually (b, c) and then as a dual-axis series (d). The tetrapod shown boxed in d is magnified in e. The arrows indicate regions where the missing wedge has had its greatest effect on the individual reconstructions. Each ‘leg’ of each tetrapod is better reconstructed in the dual-axis reconstruction. (Adapted from ref. 29.) nmat_2406_APR09.indd 273 13/3/09 12:08:31 © 2009 Macmillan Publishers Limited. All rights reserved
REVIEW ARTICLES INSIGHT NATURE MATERIALS DOL:10.1038/NMAT2406 Membrane Crystallite 100nm 100nm 10i 10 0 001 110 End Centre 10 nm 10 nm Figure 4 Tomographic reconstruction of biogenic magnetite crystals Figure 5|3D reconstructions of precipitates and nanoparticles. Tomographic reconstruction of a magnetotactic bacterium(strain MV-1) a,Reconstruction obtained using STEM tomography of the distribution showing the internal backbone of magnetite crystals and the outer and morphology of germanium precipitates in an aluminium-germanium bacterial membrane.Slices taken from the end and centre of the boxed alloy.The colours differentiate the precipitate morphology:blue,platelets; magnetite crystal,and perpendicular to the axis of the backbone,are green,tetrahedra;orange,octahedra;yellow,rods;white,irregular shapes. shown in the lower part of the figure,illustrating the crystallography of The dotted lines indicate traces of {111}planes.(Adapted from ref.41.) the magnetite particles and the fidelity of the reconstruction.(Adapted b,Plasmon tomography of irregularly shaped silicon nanoparticles within a from ref.37). silica matrix.The white 'fog'is the reconstructed plasmon signal at 17 eV. (Reprinted from ref.52). alloy".The different shapes revealed by the reconstruction have been colour-coded and the dotted lines delineate the traces of {111} axes can sometime be avoided,and/or overly bright images can be planes in the aluminium-rich matrix.STEM tomography has been removed from the series without significant loss of tomographic applied to structures at the interface of materials science and life resolution or fidelity. science,such as carbon nanotubes in mammalian macrophages In STEM tomography,compositional information is determined and the self-assembly of ferritin in liver cells4.It has also been used indirectly through the 2 dependence of the signal.However,inelastic (in conjunction with the DART algorithm mentioned previously) signals,such as those detected using electron energy-loss spectro- to investigate the morphologies of catalyst particles in multiwalled scopy(EELS)and energy-dispersive X-ray spectroscopy(EDX),can nanotubes"and has been adopted by the semiconductor industry be used to map composition in two dimensions and,by extension, to investigate faults and voids in device structures and to determine in three dimensions.Energy-loss information can be recorded pixel the shapes of metal interconnects 5. by pixel as a sequence of spectra ('spectrum imaging)or by choos- For very thick samples and those with high mass density,STEM ing a particular energy loss(or a small width about that loss,typi- HAADF imaging is no longer suitable for tomographic applica- cally 5-10 eV)and forming an image using electrons that have lost tions as the signal may decrease as the sample thickness increases, only those energies.The latter approach,known as energy-filtered because proportionately more scattering occurs outside the outer TEM(EFTEM),can be extended to record images over an energy- edge of the annular detector.Schemes have been proposed that loss series,which by analogy with the EELS method is called image use incoherent bright-field imaging to overcome this problem. spectroscopy4 or EFTEM spectrum imaging.By choosing a par- In crystalline samples,STEM HAADF images are also affected by ticular energy loss,elemental maps can be recorded over a tilt series. channelling.At major zone axes,the STEM probe may propagate Examples of this approach have used plasmon lossess and core preferentially down atom cores,leading to stronger scattering to lossess,the latter being less prone to diffraction contrast but hav- large angles than at random'orientations.In the tilt series,such ing a weaker signal.3D compositional information can be extracted 274 NATURE MATERIALS VOL 8|APRIL 2009 www.nature.com/naturematerials 2009 Macmillan Publishers Limited.All rights reserved
274 nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials review articles | insight NaTure maTerIals doi: 10.1038/nmat2406 alloy41. The different shapes revealed by the reconstruction have been colour-coded and the dotted lines delineate the traces of {111} planes in the aluminium-rich matrix. STEM tomography has been applied to structures at the interface of materials science and life science, such as carbon nanotubes in mammalian macrophages42 and the self-assembly of ferritin in liver cells43. It has also been used (in conjunction with the DART algorithm mentioned previously) to investigate the morphologies of catalyst particles in multiwalled nanotubes44 and has been adopted by the semiconductor industry to investigate faults and voids in device structures and to determine the shapes of metal interconnects45. For very thick samples and those with high mass density, STEM HAADF imaging is no longer suitable for tomographic applications as the signal may decrease as the sample thickness increases, because proportionately more scattering occurs outside the outer edge of the annular detector. Schemes have been proposed that use incoherent bright-field imaging to overcome this problem46. In crystalline samples, STEM HAADF images are also affected by channelling. At major zone axes, the STEM probe may propagate preferentially down atom cores, leading to stronger scattering to large angles than at ‘random’ orientations. In the tilt series, such axes can sometime be avoided, and/or overly bright images can be removed from the series without significant loss of tomographic resolution or fidelity. In STEM tomography, compositional information is determined indirectly through the Z dependence of the signal. However, inelastic signals, such as those detected using electron energy-loss spectroscopy (EELS) and energy-dispersive X-ray spectroscopy (EDX), can be used to map composition in two dimensions and, by extension, in three dimensions. Energy-loss information can be recorded pixel by pixel as a sequence of spectra (‘spectrum imaging’47) or by choosing a particular energy loss (or a small width about that loss, typically 5–10 eV) and forming an image using electrons that have lost only those energies. The latter approach, known as energy-filtered TEM (EFTEM), can be extended to record images over an energyloss series, which by analogy with the EELS method is called image spectroscopy48,49 or EFTEM spectrum imaging. By choosing a particular energy loss, elemental maps can be recorded over a tilt series. Examples of this approach have used plasmon losses50 and core losses51, the latter being less prone to diffraction contrast but having a weaker signal. 3D compositional information can be extracted Figure 4 | Tomographic reconstruction of biogenic magnetite crystals. Tomographic reconstruction of a magnetotactic bacterium (strain MV-1) showing the internal backbone of magnetite crystals and the outer bacterial membrane. Slices taken from the end and centre of the boxed magnetite crystal, and perpendicular to the axis of the backbone, are shown in the lower part of the figure, illustrating the crystallography of the magnetite particles and the fidelity of the reconstruction. (Adapted from ref. 37). Figure 5 | 3D reconstructions of precipitates and nanoparticles. a, Reconstruction obtained using STEM tomography of the distribution and morphology of germanium precipitates in an aluminium–germanium alloy. The colours differentiate the precipitate morphology: blue, platelets; green, tetrahedra; orange, octahedra; yellow, rods; white, irregular shapes. The dotted lines indicate traces of {111} planes. (Adapted from ref. 41.) b, Plasmon tomography of irregularly shaped silicon nanoparticles within a silica matrix. The white ‘fog’ is the reconstructed plasmon signal at 17 eV. (Reprinted from ref. 52). QP 111 111 111 100 010 001 End 110 011 101 011 101 110 Centre 10 nm 100 nm Membrane Crystallite 100 nm 10 nm a b nmat_2406_APR09.indd 274 13/3/09 12:08:33 © 2009 Macmillan Publishers Limited. All rights reserved
NATURE MATERIALS DOL:10.1038/NMAT2406 INSIGHT I REVIEW ARTICLES from such EFTEM series,as illustrated in Fig.5b2.More recently, Electron holography image spectroscopy was extended to volume spectroscopy by Electron holography was originally proposedes as a means of recording a large energy series at every tilt angless.A low-loss series correcting for electron microscope lens aberrations,substantially of a nanocomposite composed of a multiwalled carbon nanotube before the advent of the laser and the use of holography in light encased in nylon was recorded every 3 eV over a wide range of tilts. optics.The technique is based on the formation of an interference The different plasmon excitation energies of the nylon(~22 eV)and pattern or 'hologram'in the TEM.Its development followed from the nanotube (~27 ev)enabled the two components of the com- earlier experiments in electron interferometry64-66,many of which posite to be distinguished.By reconstructing tomograms at indi- took place at the University of Tubingen,and relied on the develop- vidual energy losses,it was possible to identify a voxel or subvolume ment and availability of high-brightness electron sources.The tech- common to all of the energy-loss tomograms and,by plotting the nique overcomes the important limitation of most TEM imaging intensity of the voxel as a function of energy loss,to extract spec- modes,namely that only spatial distributions of image intensity are tral information from within the tomogram.In conventional EELS, recorded.All information about the phase shift of the high-energy spectral information is always projected through the structure,but electron wave that passes through the specimen is then lost now it is possible to extract spectral information from a subvolume By contrast,electron holography allows the phase shift of the without any projection artefact. electron wave to be recovered.As the phase shift is sensitive to local Early attempts to map chemical information using EDX were variations in magnetic and electrostatic potential,the technique complicated by the directionality and inefficiency of the sample- can be used to obtain quantitative information about magnetic detector geometry,by the need to tilt away from the detector and and electric fields in materials and devices with a spatial resolution by the consequent shadowing in half of the tilt seriess.Recent that can approach the nanometre scale.This capability is of great work has taken advantage of needle specimens,where shadowing is importance for the study of a wide variety of material properties. eliminated and the detector geometry is not such a problemss.EELS, such as the characterization of magnetic domain walls in spintronic EFTEM and EDX images are all prone to diffraction effects through devices?and the factors that affect the coercive fields of individual the coupling of elastic and inelastic signals.These can be mini- magnetic nanostructures8 mized by forming jump-ratio images or dividing elemental maps The original work described the reconstruction of an image by by low-loss (or zero-loss)images.However,care must be taken if illuminating an 'in-line'electron hologram with a parallel beam of such images are used for tomography as the resultant signal may not light and using a spherical-aberration-correcting plate and an astig- satisfy the projection requirement. matism corrector,but the image reconstructed in this way is dis- Electron tomography has also been developed to study crystal- turbed by a 'ghost'or 'conjugate'twin image.The mode of electron line defects,and especially dislocation networks,in three dimen- holography that is most often used for tackling problems in materials sions.By recording a tilt series of weak-beam dark-field images, science is instead the off-axis,or 'sideband,mode,which is available it was possible to reveal a dislocation network in a gallium nitride on many modern electron microscopes and has been applied to the epitaxial layers.However,to do so it is critical that the diffraction characterization of materials as diverse as quantum well structures, conditions do not change significantly as the tilt series is recorded magnetoresistive films,nanowires and semiconductor devices9 (a difficult practical task)and that extraneous contrast,such as The electron microscope geometry for the TEM mode of off-axis thickness fringe contrast,is minimized.Weak-beam dark-field electron holography is shown schematically in Fig.6a.A field- tomography has also been used to investigate secondary phases in emission electron gun is used to provide a highly coherent source of metallic alloys where ordered phases grow from the matrix.In con- electrons.In reality,the source is never perfectly coherent,but the junction with EFTEM tomography,the shapes and compositions of degree of coherence must be such that an interference fringe pattern y'precipitates were determined in a nickel-aluminium-titanium of sufficient quality can be recorded within a reasonable acquisition superalloys.The practical difficulties of weak-beam dark-field time,during which specimen and/or beam drift must be negligible. tomography led to the development of a STEM analogue using a Although electron holograms have historically been recorded on low-angle annular dark-field imaging mode in which a number of photographic film,digital acquisition using charge-coupled-device dark-field beams contribute to the image.The advantages of this cameras is now common practice.To acquire an off-axis electron method for dislocation tomography are that the image is less sensi- hologram,the specimen is positioned so that it covers approxi- tive to changes in diffraction conditions,the image is effectively a mately half the field of view.A voltage is then applied to an elec- sum of many dark-field images,which tends to average out thick- trostatic 'biprism',which is usually located in place of one of ness contrast but enhance (albeit slightly blur)dislocation contrast, the conventional selected-area apertures in the microscope.The and data collection is easily automatedss biprism is analogous to a glass prism in light optics,but takes the As well as being able to map morphology and composition,it form of a fine(<1-um diameter)wire that is often made from gold- is also possible to map physical properties in three dimensions coated quartz.The voltage applied to the biprism acts to tilt a'ref- using a combination of electron holography,which is sensitive to erence'electron wave that passes through vacuum with respect to changes in electrostatic potentials and magnetic fields,and electron the electron wave that passes through the specimen.The two waves tomography.Such 3D potential and field mapping will be discussed are allowed to overlap and interfere.If the electron source is suf- below.A future goal is to be able to visualize atoms in three dimen- ficiently coherent then,in addition to a bright-field image of the sions.True atomic-resolution tomography may become possible specimen,an interference fringe pattern is formed on the detector either using new aberration-corrected instruments39.40 in combi- in the overlap region.Just as in a textbook 'double-slit experiment; nation with the discrete constraint that the object is composed of electrons are emitted one by one from the field-emission electron atoms,or by using an aberration-corrected STEM to reduce the gun in the microscope.After being deflected by the biprism,they depth of field and recording a series of 'confocal'images to build reach the detector and are detected individually as particles.When a up a 3D atomic lattice.Suggestions have been made to combine the large number of electrons has accumulated,their wave-like proper- confocal approach with a limited tilt series and use iterative con- ties become apparent and an interference fringe pattern is built up. straints and discrete tomography algorithms to build up a best-fit The amplitude and the phase shift of the electron wave that 3D lattice.Electron diffractive imaging,analogous to the synchro- leaves the specimen are recorded in the intensities and the posi- tron X-ray technique,may also be able to help in the quest for 3D tions of the interference fringes in the hologram,respectively. lattice imaging. The phase shift is sensitive to the in-plane component of the NATURE MATERIALS|VOL 8|APRIL 2009 www.nature.com/naturematerials 275 2009 Macmillan Publishers Limited.All rights reserved
nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials 275 NaTure maTerIals doi: 10.1038/nmat2406 insight | review articles from such EFTEM series, as illustrated in Fig. 5b52. More recently, image spectroscopy was extended to volume spectroscopy by recording a large energy series at every tilt angle53. A low-loss series of a nanocomposite composed of a multiwalled carbon nanotube encased in nylon was recorded every 3 eV over a wide range of tilts. The different plasmon excitation energies of the nylon (~22 eV) and the nanotube (~27 eV) enabled the two components of the composite to be distinguished. By reconstructing tomograms at individual energy losses, it was possible to identify a voxel or subvolume common to all of the energy-loss tomograms and, by plotting the intensity of the voxel as a function of energy loss, to extract spectral information from within the tomogram. In conventional EELS, spectral information is always projected through the structure, but now it is possible to extract spectral information from a subvolume without any projection artefact. Early attempts to map chemical information using EDX were complicated by the directionality and inefficiency of the sample– detector geometry, by the need to tilt away from the detector and by the consequent shadowing in half of the tilt series54. Recent work has taken advantage of needle specimens, where shadowing is eliminated and the detector geometry is not such a problem55. EELS, EFTEM and EDX images are all prone to diffraction effects through the coupling of elastic and inelastic signals. These can be minimized by forming jump-ratio images or dividing elemental maps by low-loss (or zero-loss) images. However, care must be taken if such images are used for tomography as the resultant signal may not satisfy the projection requirement. Electron tomography has also been developed to study crystalline defects, and especially dislocation networks, in three dimensions. By recording a tilt series of weak-beam dark-field images, it was possible to reveal a dislocation network in a gallium nitride epitaxial layer56. However, to do so it is critical that the diffraction conditions do not change significantly as the tilt series is recorded (a difficult practical task) and that extraneous contrast, such as thickness fringe contrast, is minimized. Weak-beam dark-field tomography has also been used to investigate secondary phases in metallic alloys where ordered phases grow from the matrix. In conjunction with EFTEM tomography, the shapes and compositions of γ′ precipitates were determined in a nickel–aluminium–titanium superalloy57. The practical difficulties of weak-beam dark-field tomography led to the development of a STEM analogue using a low-angle annular dark-field imaging mode in which a number of dark-field beams contribute to the image. The advantages of this method for dislocation tomography are that the image is less sensitive to changes in diffraction conditions, the image is effectively a sum of many dark-field images, which tends to average out thickness contrast but enhance (albeit slightly blur) dislocation contrast, and data collection is easily automated58. As well as being able to map morphology and composition, it is also possible to map physical properties in three dimensions using a combination of electron holography, which is sensitive to changes in electrostatic potentials and magnetic fields, and electron tomography. Such 3D potential and field mapping will be discussed below. A future goal is to be able to visualize atoms in three dimensions. True atomic-resolution tomography may become possible either using new aberration-corrected instruments59,60 in combination with the discrete constraint that the object is composed of atoms, or by using an aberration-corrected STEM to reduce the depth of field and recording a series of ‘confocal’ images to build up a 3D atomic lattice. Suggestions have been made to combine the confocal approach with a limited tilt series and use iterative constraints and discrete tomography algorithms to build up a best-fit 3D lattice. Electron diffractive imaging61, analogous to the synchrotron X-ray technique, may also be able to help in the quest for 3D lattice imaging. electron holography Electron holography62 was originally proposed63 as a means of correcting for electron microscope lens aberrations, substantially before the advent of the laser and the use of holography in light optics. The technique is based on the formation of an interference pattern or ‘hologram’ in the TEM. Its development followed from earlier experiments in electron interferometry64–66, many of which took place at the University of Tübingen, and relied on the development and availability of high-brightness electron sources. The technique overcomes the important limitation of most TEM imaging modes, namely that only spatial distributions of image intensity are recorded. All information about the phase shift of the high-energy electron wave that passes through the specimen is then lost. By contrast, electron holography allows the phase shift of the electron wave to be recovered. As the phase shift is sensitive to local variations in magnetic and electrostatic potential, the technique can be used to obtain quantitative information about magnetic and electric fields in materials and devices with a spatial resolution that can approach the nanometre scale. This capability is of great importance for the study of a wide variety of material properties, such as the characterization of magnetic domain walls in spintronic devices67 and the factors that affect the coercive fields of individual magnetic nanostructures68. The original work63 described the reconstruction of an image by illuminating an ‘in-line’ electron hologram with a parallel beam of light and using a spherical-aberration-correcting plate and an astigmatism corrector, but the image reconstructed in this way is disturbed by a ‘ghost’ or ‘conjugate’ twin image. The mode of electron holography that is most often used for tackling problems in materials science is instead the off-axis, or ‘sideband’, mode, which is available on many modern electron microscopes and has been applied to the characterization of materials as diverse as quantum well structures, magnetoresistive films, nanowires and semiconductor devices69. The electron microscope geometry for the TEM mode of off-axis electron holography is shown schematically in Fig. 6a. A fieldemission electron gun is used to provide a highly coherent source of electrons. In reality, the source is never perfectly coherent, but the degree of coherence must be such that an interference fringe pattern of sufficient quality can be recorded within a reasonable acquisition time, during which specimen and/or beam drift must be negligible. Although electron holograms have historically been recorded on photographic film, digital acquisition using charge-coupled-device cameras is now common practice. To acquire an off-axis electron hologram, the specimen is positioned so that it covers approximately half the field of view. A voltage is then applied to an electrostatic ‘biprism’70, which is usually located in place of one of the conventional selected-area apertures in the microscope. The biprism is analogous to a glass prism in light optics, but takes the form of a fine (<1-μm diameter) wire that is often made from goldcoated quartz. The voltage applied to the biprism acts to tilt a ‘reference’ electron wave that passes through vacuum with respect to the electron wave that passes through the specimen. The two waves are allowed to overlap and interfere. If the electron source is sufficiently coherent then, in addition to a bright-field image of the specimen, an interference fringe pattern is formed on the detector in the overlap region. Just as in a textbook ‘double-slit experiment’, electrons are emitted one by one from the field-emission electron gun in the microscope. After being deflected by the biprism, they reach the detector and are detected individually as particles. When a large number of electrons has accumulated, their wave-like properties become apparent and an interference fringe pattern is built up. The amplitude and the phase shift of the electron wave that leaves the specimen are recorded in the intensities and the positions of the interference fringes in the hologram, respectively. The phase shift is sensitive to the in-plane component of the nmat_2406_APR09.indd 275 13/3/09 12:08:33 © 2009 Macmillan Publishers Limited. All rights reserved
REVIEW ARTICLES INSIGHT NATURE MATERIALS DOL:10.1038/NMAT2406 beyond the point resolution of the microscope)"and to measure -FEG variations in specimen thickness and mean inner potential,here we concentrate on the 'medium-resolution'application of the tech- Vacuum Specimen nique to characterize longer-range electromagnetic fields.For stud- reference wave wave ies of magnetic materials,a Lorentz lens(a high-strength mini-lens) allows the microscope to be operated at high magnification with the Magnetic conventional objective lens switched off and the specimen either crystals in magnetic-field-free conditions or in a chosen externally applied magnetic field.The typical field of view of such measurements is between a few hundred nanometres and a few micrometres,and Lorentz lens the spatial resolution of the recorded electrostatic or magnetic fields can approach or exceed 5 nm. Holography applications The practical application of electron holography to the character- ization of magnetic materials was pioneered by a research group at the Hitachi Advanced Research Laboratory in Japan2.Their work included studies of magnetic fields in fine particles,recorded mediaz,flux vortices in superconductors747s and,most notably, Biprism the experimental verification of the Aharonov-Bohm effect and the confirmation of the physical reality of magnetic vector poten- tials"6.In each of these studies,the strength and direction of the Hologram local projected in-plane magnetic induction were obtained by dis- playing contours that had been generated from the magnetic con- tribution to the recorded electron holographic phase shift using a laser bench.A phase difference of 2nt between any two contours corresponded to an enclosed magnetic flux of 4n x 10-is Wb.More recently,off-axis electron holography has been used to characterize magnetic states in nanostructures that are less than 100 nm in size77 The application of electron holography to the study of magnetic nanocrystals of this size is challenging both because of a fundamen- tal signal-to-noise limit and because the magnetic signal must be separated from unwanted contributions to the recorded phase shift from local variations in specimen thickness and composition.This separation can be achieved more reliably from electron holographic phase images than from images recorded using differential phase- contrast imaging in the STEM or the Fresnel or Foucault modes of Lorentz electron microscopy.Digital acquisition and analysis of electron holograms and sophisticated image analysis software are then essential. Figure 6b and Fig.6c illustrate the use of electron holography to image magnetostatic interactions between closely spaced nano- particles of polycrystalline cobalt that each have diameters of -20 nm.A ring of six cobalt particles has a diameter of less than Figure 6|Electron holography of magnetic nanoparticle rings. 100 nm,with the constituent crystals each acting as single-domain a,Illustration of the application of a voltage to an electron biprism located magnets at room temperature.Such nanoscale rings are of interest close to a conjugate image plane in a field-emission electron gun(FEG)TEM, for magnetic recording and storage applications because they can to overlap a vacuum reference electron wave with the electron wave that support bistable flux-closed magnetic states.Representative mag- has passed through a region of the specimen to form an off-axis electron netic induction maps recorded using off-axis electron holography hologram.Variations in the spacing and direction of the recorded holographic are shown in Fig.6b,c in the form of phase contours,colours and interference fringes contain information about the projected magnetic flux arrows's.The handedness of the magnetic domain structures in the density inside and surrounding the crystals.The experimental electron rings is clear.A statistical sampling of magnetic states from such hologram shown in the figure was acquired from five 20-nm-diameter cobalt images indicates an approximately 50:50 mixture of clockwise and nanocrystals.The spacing of the holographic interference fringes is 3 nm. anticlockwise ground-state configurations,to which the rings relax b,c,Magnetic phase contours (x128 amplification;0.049 rad spacing) after exposure to a saturating out-of-plane magnetic field.In each formed from the magnetic contribution to the phase shift measured from case,the magnetic induction is essentially confined within the two different cobalt nanoparticle rings.Each image was acquired with the annular ensemble. specimen in magnetic-field-free conditions.The outlines of the nanoparticles Closely spaced magnetic nanocrystals that are found in nature are marked in white,and the direction of the measured magnetic induction is are often more perfect in their sizes,shapes and arrangements indicated using arrows and according to the colour wheel shown (red,right; than their synthetic counterparts.As a result,they can be used yellow,down;green,left;blue,up).(Adapted from ref.77.) as model systems to study the effect of particle size,morphology, crystallography and spacing on magnetic microstructure.Figure 7a magnetic induction and the electrostatic potential in the specimen. and Fig.7b show chemical maps of a crystalline,naturally occur- Although the technique can be used to record phase informa-ring magnetite-ulvospinel (Fe,O,-Fe,TiO,)mineral,which tion at atomic resolution(to improve the interpretable resolution exsolved during slow cooling over geological timescales to yield an 276 NATURE MATERIALS VOL 8|APRIL 2009 www.nature.com/naturematerials 2009 Macmillan Publishers Limited.All rights reserved
276 nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials review articles | insight NaTure maTerIals doi: 10.1038/nmat2406 magnetic induction and the electrostatic potential in the specimen. Although the technique can be used to record phase information at atomic resolution (to improve the interpretable resolution beyond the point resolution of the microscope)71 and to measure variations in specimen thickness and mean inner potential, here we concentrate on the ‘medium-resolution’ application of the technique to characterize longer-range electromagnetic fields. For studies of magnetic materials, a Lorentz lens (a high-strength mini-lens) allows the microscope to be operated at high magnification with the conventional objective lens switched off and the specimen either in magnetic-field-free conditions or in a chosen externally applied magnetic field. The typical field of view of such measurements is between a few hundred nanometres and a few micrometres, and the spatial resolution of the recorded electrostatic or magnetic fields can approach or exceed 5 nm. holography applications The practical application of electron holography to the characterization of magnetic materials was pioneered by a research group at the Hitachi Advanced Research Laboratory in Japan72. Their work included studies of magnetic fields in fine particles, recorded media73, flux vortices in superconductors74,75 and, most notably, the experimental verification of the Aharonov–Bohm effect and the confirmation of the physical reality of magnetic vector potentials76. In each of these studies, the strength and direction of the local projected in-plane magnetic induction were obtained by displaying contours that had been generated from the magnetic contribution to the recorded electron holographic phase shift using a laser bench. A phase difference of 2π between any two contours corresponded to an enclosed magnetic flux of 4π × 10−15 Wb. More recently, off-axis electron holography has been used to characterize magnetic states in nanostructures that are less than 100 nm in size77. The application of electron holography to the study of magnetic nanocrystals of this size is challenging both because of a fundamental signal-to-noise limit and because the magnetic signal must be separated from unwanted contributions to the recorded phase shift from local variations in specimen thickness and composition. This separation can be achieved more reliably from electron holographic phase images than from images recorded using differential phasecontrast imaging in the STEM or the Fresnel or Foucault modes of Lorentz electron microscopy. Digital acquisition and analysis of electron holograms and sophisticated image analysis software are then essential. Figure 6b and Fig. 6c illustrate the use of electron holography to image magnetostatic interactions between closely spaced nanoparticles of polycrystalline cobalt that each have diameters of ~20 nm. A ring of six cobalt particles has a diameter of less than 100 nm, with the constituent crystals each acting as single-domain magnets at room temperature. Such nanoscale rings are of interest for magnetic recording and storage applications because they can support bistable flux-closed magnetic states. Representative magnetic induction maps recorded using off-axis electron holography are shown in Fig. 6b, c in the form of phase contours, colours and arrows78. The handedness of the magnetic domain structures in the rings is clear. A statistical sampling of magnetic states from such images indicates an approximately 50:50 mixture of clockwise and anticlockwise ground-state configurations, to which the rings relax after exposure to a saturating out-of-plane magnetic field. In each case, the magnetic induction is essentially confined within the annular ensemble. Closely spaced magnetic nanocrystals that are found in nature are often more perfect in their sizes, shapes and arrangements than their synthetic counterparts. As a result, they can be used as model systems to study the effect of particle size, morphology, crystallography and spacing on magnetic microstructure. Figure 7a and Fig. 7b show chemical maps of a crystalline, naturally occurring magnetite–ulvöspinel (Fe3O4–Fe2TiO4) mineral, which exsolved during slow cooling over geological timescales to yield an FEG Specimen wave Magnetic crystals Lorentz lens Biprism Hologram Vacuum reference wave 20 nm 20 nm a b c Figure 6 | electron holography of magnetic nanoparticle rings. a, Illustration of the application of a voltage to an electron biprism located close to a conjugate image plane in a field-emission electron gun (FEG) TEM, to overlap a vacuum reference electron wave with the electron wave that has passed through a region of the specimen to form an off-axis electron hologram. Variations in the spacing and direction of the recorded holographic interference fringes contain information about the projected magnetic flux density inside and surrounding the crystals. The experimental electron hologram shown in the figure was acquired from five 20-nm-diameter cobalt nanocrystals. The spacing of the holographic interference fringes is 3 nm. b, c, Magnetic phase contours (×128 amplification; 0.049 rad spacing) formed from the magnetic contribution to the phase shift measured from two different cobalt nanoparticle rings. Each image was acquired with the specimen in magnetic-field-free conditions. The outlines of the nanoparticles are marked in white, and the direction of the measured magnetic induction is indicated using arrows and according to the colour wheel shown (red, right; yellow, down; green, left; blue, up). (Adapted from ref. 77.) nmat_2406_APR09.indd 276 13/3/09 12:08:34 © 2009 Macmillan Publishers Limited. All rights reserved
NATURE MATERIALS DOL:10.1038/NMAT2406 INSIGHT I REVIEW ARTICLES intergrowth of ferrimagnetic magnetite-rich regions separated by non-magnetic ulvospinel-rich lamellae.The remanent magnetiza- tion in such rocks is used by geophysicists to map the motions of continents and ocean beds resulting from the dynamics of plate tectonics.As an example of the application of electron holography to rock magnetism,Fig.7c,d shows two remanent magnetic states recorded from the same region of the specimen.The induction maps show that individual blocks'of magnetite contain primarily single-domain magnetic states,which have lower energies than vortex states in the presence of strong interactions with neighbour- ing magnetic crystals.They also reveal the magnetostatic inter- action fields between them.Magnetic superstates,in which clusters 2250e 2250e of magnetite blocks act collectively to form vortex and multidomain states that have zero net magnetization,are also visible.The images Afte After illustrate the complexity of the magnetic structure in this system saturating saturating Electron holography has considerable potential for measuring both remanent magnetizations and magnetization reversal mechanisms in rocks,and for understanding mineral magnetism at the nano- metre scale. 200nm Similar magnetic interactions are observed in nature in magnetotactic bacteria,which contain single or multiple chains of ferrimagnetic magnetite (Fe,O)or greigite (FeS)crystals that are typically between 35 and 120 nm in size.In this size range,the crystals are uniformly magnetized single magnetic domains at room 200nm temperature.The arrangement of the crystals in linear chains results in a magnetic moment that orients the bacteria parallel to the geo- magnetic field in an aquatic environment.A magnetic induction map recorded from a single helical bacterial cell containing a chain of equi-dimensional magnetite crystals is shown in Fig.7es.The magnetic phase contours are parallel to each other in the crystals and follow the chain axis.Unlike the more complicated magnetic arrangements seen in Fig.7c,d,the magnetic moment in the linear bacterial chain is maximized,and its remanent magnetic state is almost equal to its saturated state.Although a single chain would appear to be ideal for magnetotaxis,a number of strains of bacteria possess either disorganized multiple arrangements of crystals or Figure 7 Magnetic induction maps of geological and biogenic magnetic large crystals(up to 200 nm in length)that would each be expected particles.a,b,Three-window background-subtracted elemental maps to contain several magnetic domains if they were isolated. acquired from a naturally occurring titanomagnetite sample with a Gatan For a fuller understanding of nanoparticle interactions and imaging filter using the iron L edge (a)and the titanium L edge (b). magnetic response,systematic studies of both continuous ferro- Brighter contrast indicates higher concentrations of iron and titanium in magnetic films4 and lithographically patterned ferromagnetic (a)and (b),respectively.c,d,Magnetic phase contours from the same nanostructures have been carried out using electron holography for region,measured using electron holography.Each image was acquired different film thicknesses and element sizes,thicknesses and shapes, with the specimen in magnetic-field-free conditions.The outlines of illustrating switching variability in nominally identical structuress magnetite-rich regions are marked in white,and the direction of the and prompting consideration of modified shapes such as rings, measured magnetic induction is indicated using arrows and according to slotted disks and slotted rings for applications the colour wheel shown (red,right;yellow,down;green,left;blue,up). The development of electron holography for the characteriza- The image in c was acquired after applying a large(>10,000 Oe)field tion ofelectrostatic fields in materials has a long history,most nota- towards the top left,then the indicated (225 Oe)field towards the bottom bly at the University of Bologna.Although it has been used to right,after which the external magnetic field was removed for hologram characterize the electric fields of microtips,electrically biased car- acquisition.The image in d was acquired after applying identical fields in bon nanotubes"0 and electroceramics,perhaps the most important the opposite directions.(Adapted from ref.77.)e,Contours of 0.064-rad potential application of electron holography in materials science spacing formed from the magnetic contribution to the holographic phase and technology is the prospect that the technique can fulfil the shift acquired from a single bacterial cell (inset)of Magnetospirillum requirement of the semiconductor industry to provide quantitative magnetotacticum strain MS-1,imaged in magnetic-field-free conditions information about electrostatic potentials in doped semiconductors The contours,which spread out at the ends of the chain,are overlaid onto (and in ferroelectric materials")with nanometre spatial resolution. the contribution of the mean inner potential to the phase shift,to allow Figure 8a illustrates the geometry of a semiconductor p-n junc- the positions of the crystals to be correlated with the magnetic contours. tion in a thin TEM sample.The true junction potential(Fig.8b)is (Adapted from ref.81.) assumed to lie within specimen thickness,t which is smaller than the total specimen thickness,t,as a result of the presence of speci- respectively.Similar phase images are now used routinely to charac- men surfaces that are altered electrically as a result of the presence terize electrostatic potentials at source and drain regions in transis- of surface states and specimen preparation for electron microscopy. tors23,and techniques have been developed to measure electrostatic A representative phase image recorded from a silicon p-n junction potentials in reverse-biased semiconductor devices prepared for using electron holography is shown in Fig.8c;p-type and n-type TEM examination using focused-ion-beam milling.However, regions are delineated clearly as areas of darker and lighter contrast, questions still remain about aspects of the interpretation of such NATURE MATERIALS|VOL 8|APRIL 2009 www.nature.com/naturematerials 277 2009 Macmillan Publishers Limited.All rights reserved
nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials 277 NaTure maTerIals doi: 10.1038/nmat2406 insight | review articles intergrowth of ferrimagnetic magnetite-rich regions separated by non-magnetic ulvöspinel-rich lamellae. The remanent magnetization in such rocks is used by geophysicists to map the motions of continents and ocean beds resulting from the dynamics of plate tectonics. As an example of the application of electron holography to rock magnetism, Fig. 7c, d shows two remanent magnetic states recorded from the same region of the specimen. The induction maps show that individual ‘blocks’ of magnetite contain primarily single-domain magnetic states, which have lower energies than vortex states in the presence of strong interactions with neighbouring magnetic crystals79,80. They also reveal the magnetostatic interaction fields between them. Magnetic superstates, in which clusters of magnetite blocks act collectively to form vortex and multidomain states that have zero net magnetization, are also visible. The images illustrate the complexity of the magnetic structure in this system. Electron holography has considerable potential for measuring both remanent magnetizations and magnetization reversal mechanisms in rocks, and for understanding mineral magnetism at the nanometre scale. Similar magnetic interactions are observed in nature in magnetotactic bacteria, which contain single or multiple chains of ferrimagnetic magnetite (Fe3O4) or greigite (Fe3S4) crystals that are typically between 35 and 120 nm in size. In this size range, the crystals are uniformly magnetized single magnetic domains at room temperature. The arrangement of the crystals in linear chains results in a magnetic moment that orients the bacteria parallel to the geomagnetic field in an aquatic environment. A magnetic induction map recorded from a single helical bacterial cell containing a chain of equi-dimensional magnetite crystals is shown in Fig. 7e81. The magnetic phase contours are parallel to each other in the crystals and follow the chain axis. Unlike the more complicated magnetic arrangements seen in Fig. 7c, d, the magnetic moment in the linear bacterial chain is maximized, and its remanent magnetic state is almost equal to its saturated state. Although a single chain would appear to be ideal for magnetotaxis, a number of strains of bacteria possess either disorganized multiple arrangements of crystals82 or large crystals (up to 200 nm in length) that would each be expected to contain several magnetic domains if they were isolated. For a fuller understanding of nanoparticle interactions and magnetic response, systematic studies of both continuous ferromagnetic films83,84 and lithographically patterned ferromagnetic nanostructures have been carried out using electron holography for different film thicknesses and element sizes, thicknesses and shapes, illustrating switching variability in nominally identical structures85 and prompting consideration of modified shapes such as rings, slotted disks and slotted rings for applications86. The development of electron holography for the characterization of electrostatic fields in materials has a long history, most notably at the University of Bologna87,88. Although it has been used to characterize the electric fields of microtips89, electrically biased carbon nanotubes90 and electroceramics, perhaps the most important potential application of electron holography in materials science and technology is the prospect that the technique can fulfil the requirement of the semiconductor industry to provide quantitative information about electrostatic potentials in doped semiconductors (and in ferroelectric materials91) with nanometre spatial resolution. Figure 8a illustrates the geometry of a semiconductor p–n junction in a thin TEM sample. The true junction potential (Fig. 8b) is assumed to lie within specimen thickness, tel, which is smaller than the total specimen thickness, t, as a result of the presence of specimen surfaces that are altered electrically as a result of the presence of surface states and specimen preparation for electron microscopy. A representative phase image recorded from a silicon p–n junction using electron holography is shown in Fig. 8c; p-type and n-type regions are delineated clearly as areas of darker and lighter contrast, respectively. Similar phase images are now used routinely to characterize electrostatic potentials at source and drain regions in transistors92,93, and techniques have been developed to measure electrostatic potentials in reverse-biased semiconductor devices prepared for TEM examination using focused-ion-beam milling94. However, questions still remain about aspects of the interpretation of such a e b c d 225 Oe After saturating 225 Oe After saturating 200 nm 200 nm Figure 7 | magnetic induction maps of geological and biogenic magnetic particles. a, b, Three-window background-subtracted elemental maps acquired from a naturally occurring titanomagnetite sample with a Gatan imaging filter using the iron L edge (a) and the titanium L edge (b). Brighter contrast indicates higher concentrations of iron and titanium in (a) and (b), respectively. c, d, Magnetic phase contours from the same region, measured using electron holography. Each image was acquired with the specimen in magnetic-field-free conditions. The outlines of magnetite-rich regions are marked in white, and the direction of the measured magnetic induction is indicated using arrows and according to the colour wheel shown (red, right; yellow, down; green, left; blue, up). The image in c was acquired after applying a large (>10,000 Oe) field towards the top left, then the indicated (225 Oe) field towards the bottom right, after which the external magnetic field was removed for hologram acquisition. The image in d was acquired after applying identical fields in the opposite directions. (Adapted from ref. 77.) e, Contours of 0.064-rad spacing formed from the magnetic contribution to the holographic phase shift acquired from a single bacterial cell (inset) of Magnetospirillum magnetotacticum strain MS-1, imaged in magnetic-field-free conditions. The contours, which spread out at the ends of the chain, are overlaid onto the contribution of the mean inner potential to the phase shift, to allow the positions of the crystals to be correlated with the magnetic contours. (Adapted from ref. 81.) nmat_2406_APR09.indd 277 13/3/09 12:08:35 © 2009 Macmillan Publishers Limited. All rights reserved
REVIEW ARTICLES INSIGHT NATURE MATERIALS DOL:10.1038/NMAT2406 images,and approaches such as in situ annealing of specimens in the TEM"and simulations of the effect of the presence of the speci- men surfaces"and the high-energy electron beam on the electrical properties of the specimen are being studied.An interesting vari- ant of off-axis electron holography,which can be used to provide 2D information about strain distributions in semiconductors,has recently been developed.This approach involves using the electro- W,depletion width static biprism to form a dark-field electron hologram by interfering with each other diffracted electrons that have been scattered in strained and unstrained regions of the specimen'00. b Potential,V(x) Electron holographic tomography A particularly exciting prospect is the combination of electron holography with electron tomography to characterize electrostatic and magnetic fields inside nanostructured materials with nano- metre spatial resolution in three dimensions,rather than simply in projection,by acquiring ultrahigh-tilt series of electron holo- grams.Both the electrostatic phase shift and the magnetic phase gradient recorded using electron holography satisfy the projection requirement for electron tomographic reconstruction.Figure 8d shows the extremely promising result of an experiment performed to characterize the 3D electrostatic potential of a semiconductor p-n junction in a thin TEM specimen examined under an applied reverse bias,in which the effect of the surfaces of the thin specimen on the internal potential has been measured in three dimensions0 The prospect of characterizing magnetic vector fields inside nano- crystals in three dimensions by combining electron tomography with electron holography is also of great interest This approach has previously been used to image magnetic fringing fields outside 25m materials in three dimensions,by acquiring two ultrahigh-tilt series 25 nm of differential phase-contrast images or electron holograms about orthogonal specimen tilt axes'04.Although the theory underlying such measurements is well establisheds,their application to the 280nm characterization of magnetic fields inside nanostructured materi- als is complicated by the fact that the (often dominant)contribu- tion of the mean inner potential to the measured phase shift must be removed at each sample tilt angle.Four tilt series of holograms may then be required.In addition,the need to acquire electron holograms at high specimen tilt angles about two axes imposes 1,000nm additional requirements on the specimen geometry. y Concluding remarks Electron tomographic acquisition and reconstruction,coupled Crystalline but electrically ■n-type silicon with the remarkably large number of imaging modes available damaged silicon in the electron microscope,ensures that a diversity of 3D struc- Amorphous surface layers ■p-type silicon tural and chemical information can be obtained from a variety of materials.There is great scope to develop the technique further as a Figure 8|Electron holographic tomography.a,Diagram showing the cross reliable method for quantitative measurements of the physical and sectional geometry of a TEM specimen of uniform thickness that contains a chemical properties of nanoscale structures in three dimensions, symmetrical semiconductor p-n junction.The thickness of the 'electrically to move towards genuine 3D nanometrology.Off-axis electron active'specimen is denoted by to The layers at the top and bottom surfaces of holography provides quantitative information about electrostatic the specimen represent electrically passivated or depleted layers,the physical and magnetic fields in materials,as well as allowing fundamental and electrical nature of which is affected by TEM specimen preparation. studies of the physics of electromagnetic fields in nanoscale struc- b,Diagram showing the electrostatic potential profile across the p-n junction. tures.Considerable further work is possible to develop,optimize The built-in voltage is denoted by V,and W is the width of the depletion and automate the technique,including the measurement of weak region over which the potential changes.The sign convention for the potential fields(towards detecting single magnetic spins),the development of is consistent with the mean inner potential of the specimen being positive approaches for improving its time resolution(for studying chemical relative to vacuum.c,Representative phase image reconstructed from an reactions,biological samples and beam-sensitive materials such as off-axis electron hologram of a silicon p-n junction sample.The sample edge zeolites)and overcoming the effects of specimen preparation and is at the lower right of the image,and no attempt has been made to remove electron irradiation on measurements of electrostatic fields. phase 'wraps'lying along this edge.The sign convention for the potential As well as individually providing unique high-spatial-resolution is as in b.d,Tomographic reconstruction of the electrostatic potential in a information,electron tomography and electron holography can focused-ion-beam-milled specimen containing an electrically biased silicon be combined with other capabilities available in modern elec- p-n junction.Contours spaced every 0.2 V have been superimposed onto the tron microscopes,including aberration-corrected imaging,in situ reconstructed tomogram.(Adapted from refs 95 and 101.) environmental cells and the ability to examine working devices 278 NATURE MATERIALS VOL 8|APRIL 2009 www.nature.com/naturematerials 2009 Macmillan Publishers Limited.All rights reserved
278 nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials review articles | insight NaTure maTerIals doi: 10.1038/nmat2406 images95,96, and approaches such as in situ annealing of specimens in the TEM97 and simulations of the effect of the presence of the specimen surfaces98 and the high-energy electron beam99 on the electrical properties of the specimen are being studied. An interesting variant of off-axis electron holography, which can be used to provide 2D information about strain distributions in semiconductors, has recently been developed. This approach involves using the electrostatic biprism to form a dark-field electron hologram by interfering with each other diffracted electrons that have been scattered in strained and unstrained regions of the specimen100. electron holographic tomography A particularly exciting prospect is the combination of electron holography with electron tomography to characterize electrostatic and magnetic fields inside nanostructured materials with nanometre spatial resolution in three dimensions, rather than simply in projection, by acquiring ultrahigh-tilt series of electron holograms. Both the electrostatic phase shift and the magnetic phase gradient recorded using electron holography satisfy the projection requirement for electron tomographic reconstruction. Figure 8d shows the extremely promising result of an experiment performed to characterize the 3D electrostatic potential of a semiconductor p–n junction in a thin TEM specimen examined under an applied reverse bias, in which the effect of the surfaces of the thin specimen on the internal potential has been measured in three dimensions101. The prospect of characterizing magnetic vector fields inside nanocrystals in three dimensions by combining electron tomography with electron holography is also of great interest102,103. This approach has previously been used to image magnetic fringing fields outside materials in three dimensions, by acquiring two ultrahigh-tilt series of differential phase-contrast images or electron holograms about orthogonal specimen tilt axes104. Although the theory underlying such measurements is well established105, their application to the characterization of magnetic fields inside nanostructured materials is complicated by the fact that the (often dominant) contribution of the mean inner potential to the measured phase shift must be removed at each sample tilt angle. Four tilt series of holograms may then be required. In addition, the need to acquire electron holograms at high specimen tilt angles about two axes imposes additional requirements on the specimen geometry. concluding remarks Electron tomographic acquisition and reconstruction, coupled with the remarkably large number of imaging modes available in the electron microscope, ensures that a diversity of 3D structural and chemical information can be obtained from a variety of materials. There is great scope to develop the technique further as a reliable method for quantitative measurements of the physical and chemical properties of nanoscale structures in three dimensions, to move towards genuine 3D nanometrology. Off-axis electron holography provides quantitative information about electrostatic and magnetic fields in materials, as well as allowing fundamental studies of the physics of electromagnetic fields in nanoscale structures. Considerable further work is possible to develop, optimize and automate the technique, including the measurement of weak fields (towards detecting single magnetic spins), the development of approaches for improving its time resolution (for studying chemical reactions, biological samples and beam-sensitive materials such as zeolites) and overcoming the effects of specimen preparation and electron irradiation on measurements of electrostatic fields. As well as individually providing unique high-spatial-resolution information, electron tomography and electron holography can be combined with other capabilities available in modern electron microscopes, including aberration-corrected imaging, in situ environmental cells and the ability to examine working devices e– tel Vbi Potential, V(x) W, depletion width x p n p n 200 nm 25 nm 25 nm 25 nm 25 nm 280 nm 1,000 nm z x y Crystalline but electrically damaged silicon Amorphous surface layers n-type silicon p-type silicon a b c d Figure 8 | electron holographic tomography. a, Diagram showing the crosssectional geometry of a TEM specimen of uniform thickness that contains a symmetrical semiconductor p–n junction. The thickness of the ‘electrically active’ specimen is denoted by tel. The layers at the top and bottom surfaces of the specimen represent electrically passivated or depleted layers, the physical and electrical nature of which is affected by TEM specimen preparation. b, Diagram showing the electrostatic potential profile across the p–n junction. The built-in voltage is denoted by Vbi and W is the width of the depletion region over which the potential changes. The sign convention for the potential is consistent with the mean inner potential of the specimen being positive relative to vacuum. c, Representative phase image reconstructed from an off-axis electron hologram of a silicon p–n junction sample. The sample edge is at the lower right of the image, and no attempt has been made to remove phase ‘wraps’ lying along this edge. The sign convention for the potential is as in b. d, Tomographic reconstruction of the electrostatic potential in a focused-ion-beam-milled specimen containing an electrically biased silicon p–n junction. Contours spaced every 0.2 V have been superimposed onto the reconstructed tomogram. (Adapted from refs 95 and 101.) nmat_2406_APR09.indd 278 13/3/09 12:08:35 © 2009 Macmillan Publishers Limited. All rights reserved
NATURE MATERIALS DOL:10.1038/NMAT2406 INSIGHT I REVIEW ARTICLES under applied bias or during mechanical deformation.Although 30.Tong,I.R..Arslan,I.Midgley,P.A.A novel dual-axis iterative algorithm for the need to acquire multiple images still limits their application to electron tomography.J.Struct.Biol.153,55-63(2006). truly dynamic studies,advances in both techniques are leading to 31.Koguchi,M.et al.Three-dimensional STEM for observing nanostructures the development of a true laboratory in the electron microscope. I.Electron Microsc.50,235-241 (2001). 32.Arslan,I,Marquis,E.A.,Homer,M.,Hekmaty,M.A.Bartelt,N.C. 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