Electron holography surmounts resolution limit of electron microscopy

Interaction-Free Measurement with Electrons

Here, we experimentally demonstrate interaction-free measurements with electrons using a novel electron Mach-Zehnder interferometer. The flexible two-grating electron interferometer is constructed in a conventional transmission electron microscope and achieves high contrast in discrete output detectors, tunable alignment with independently movable beam splitters, and scanning capabilities for imaging. With this path-separated electron interferometer, which closely matches theoretical expectations, we demonstrate electron interaction-free measurements with an efficiency of 14±1%. Implementing this quantum protocol in electron imaging opens a path toward interaction-free electron microscopy.

Phase-shifting electron holography for accurate measurement of potential distributions in organic and inorganic semiconductors

Phase-shifting electron holography (PS-EH) is an interference transmission electron microscopy technique that accurately visualizes potential distributions in functional materials, such as semiconductors. In this paper, we briefly introduce the features of the PS-EH that overcome some of the issues facing the conventional EH based on Fourier transformation. Then, we present a high-precision PS-EH technique with multiple electron biprisms and a sample preparation technique using a cryo-focused-ion-beam, which are important techniques for the accurate phase measurement of semiconductors. We present several applications of PS-EH to demonstrate the potential in organic and inorganic semiconductors and then discuss the differences by comparing them with previous reports on the conventional EH. We show that in situ biasing PS-EH was able to observe not only electric potential distribution but also electric field and charge density at a GaAs p-n junction and clarify how local band structures, depletion layer widths and space charges changed depending on the biasing conditions. Moreover, the PS-EH clearly visualized the local potential distributions of two-dimensional electron gas layers formed at AlGaN/GaN interfaces with different Al compositions. We also report the results of our PS-EH application for organic electroluminescence multilayers and point out the significant potential changes in the layers. The proposed PS-EH enables more precise phase measurement compared to the conventional EH, and our findings introduced in this paper will contribute to the future research and development of high-performance semiconductor materials and devices.

Interference and interferometry in electron holography

This paper reviews the basics of electron holography as an introduction of the holography part of this special issue in Microscopy. We discuss the general principle of holography and interferometry regarding measurements and analyses of phase distributions, first using the optical holography. Next, we discuss physical phenomena peculiar to electron waves that cannot be realized by light waves and principles of electromagnetic field detection and observation methods. Furthermore, we discuss the interference optical systems of the electron waves and their features, and methods of reconstruction of the phase information from electron holograms, which are essential for realization of practical electron holography. We note that following this review application of electron holography will be discussed in detail in the papers of this special issue.

Quantitative measurement of nanoscale electrostatic potentials and charges using off-axis electron holography: Developments and opportunities

Off-axis electron holography has evolved into a powerful electron-microscopy-based technique for characterizing electromagnetic fields with nanometer-scale resolution. In this paper, we present a review of the application of off-axis electron holography to the quantitative measurement of electrostatic potentials and charge density distributions. We begin with a short overview of the theoretical and experimental basis of the technique. Practical aspects of phase imaging, sample preparation and microscope operation are outlined briefly. Applications of off-axis electron holography to a wide range of materials are then described in more detail. Finally, challenges and future opportunities for electron holography investigations of electrostatic fields and charge density distributions are presented.

Longevity in electron optics- Introduction to the Howie-Colliex-Lichte birthday issue

In 2019, Howie reaches the age of 85 and Colliex and Lichte, 75. Some moments in their scientific careers are evoked and their contributions to the theory of electron imaging, EELS and STEM and electron holography are recalled. Poetry, photography and music are not forgotten and nor are their families.

Digital holographic interferometry employing Fresnel transform reconstruction for the study of flow shear stabilized Z-pinch plasmas

The ZaP-HD flow Z-pinch project provides a platform to explore how shear flow stabilized Z-pinches could scale to high-energy-density plasma (plasma with pressures exceeding 1 Mbar) and fusion reactor conditions. The Z-pinch is a linear plasma confinement geometry in which the plasma carries axial electric current and is confined by its self-induced magnetic field. ZaP-HD generates shear stabilized, axisymmetric Z-pinches with stable lifetimes approaching 60 μs. The goal of the project is to increase the plasma density and temperature compared to the previous ZaP project by compressing the plasma to smaller radii (≈1 mm). Radial and axial plasma electron density structure is measured using digital holographic interferometry (DHI), which provides the necessary fine spatial resolution. ZaP-HD's DHI system uses a 2 ns Nd:YAG laser pulse with a second harmonic generator (λ = 532 nm) to produce holograms recorded by a Nikon D3200 digital camera. The holograms are numerically reconstructed with the Fresnel transform reconstruction method to obtain the phase shift caused by the interaction of the laser beam with the plasma. This provides a two-dimensional map of line-integrated electron density, which can be Abel inverted to determine the local number density. The DHI resolves line-integrated densities down to 3 × 10²⁰ m^-2 with spatial resolution near 10 μm. This paper presents the first application of Fresnel transform reconstruction as an analysis technique for a plasma diagnostic, and it analyzes the method's accuracy through study of synthetic data. It then presents an Abel inversion procedure that utilizes data on both sides of a Z-pinch local number density profile to maximize profile symmetry. Error estimation and Abel inversion are applied to the measured data.

Hybridization approach to in-line and off-axis (electron) holography for superior resolution and phase sensitivity

Holography--originally developed for correcting spherical aberration in transmission electron microscopes--is now used in a wide range of disciplines that involve the propagation of waves, including light optics, electron microscopy, acoustics and seismology. In electron microscopy, the two primary modes of holography are Gabor's original in-line setup and an off-axis approach that was developed subsequently. These two techniques are highly complementary, offering superior phase sensitivity at high and low spatial resolution, respectively. All previous investigations have focused on improving each method individually. Here, we show how the two approaches can be combined in a synergetic fashion to provide phase information with excellent sensitivity across all spatial frequencies, low noise and an efficient use of electron dose. The principle is also expected to be widely to applications of holography in light optics, X-ray optics, acoustics, ultra-sound, terahertz imaging, etc.

Dark-field electron holography for the measurement of geometric phase

The genesis, theoretical basis and practical application of the new electron holographic dark-field technique for mapping strain in nanostructures are presented. The development places geometric phase within a unified theoretical framework for phase measurements by electron holography. The total phase of the transmitted and diffracted beams is described as a sum of four contributions: crystalline, electrostatic, magnetic and geometric. Each contribution is outlined briefly and leads to the proposal to measure geometric phase by dark-field electron holography (DFEH). The experimental conditions, phase reconstruction and analysis are detailed for off-axis electron holography using examples from the field of semiconductors. A method for correcting for thickness variations will be proposed and demonstrated using the phase from the corresponding bright-field electron hologram.

Electron Holography of Ferromagnetic Nanoparticles Encapsulated in Three-Dimensional Arrays of Aligned Carbon Nanotubes

Closely-spaced ferromagnetic nanoparticles are of interest for applications that include data storage, magnetic imaging and drug delivery. Here, we use off-axis electron holography and micromagnetic simulations to study the magnetic properties of iron nanoparticles encapsulated in three-dimensional arrays of carbon nanotubes. The nanotubes constrain the shapes, sizes and separations of the nanoparticles, as well protecting them from oxidation. We record magnetic induction maps from individual particles that each contain a single magnetic domain. We also discuss the use of electron holography to assess magnetostatic interactions between adjacent particles.

Phase-shifting electron holography for atomic image reconstruction

Phase-shifting electron holography was used to reconstruct the object-wave function of high-spatial-frequency specimens of HgCdTe, and the requirements for precise measurements were investigated. Fresnel fringes due to the electrostatic biprism caused serious calculation errors during the phase-shifting reconstruction. Uniform interference fringes, obtained by adjusting the biprism voltage to cancel out the Fresnel fringes, were needed to minimize these errors. High-resolution holograms of a HgCdTe single crystal were recorded with coarse interference fringes and a high visibility of 65% and then used to reconstruct the atomic-scale object wave. Although the spatial resolution (0.25 nm) of the transmission electron microscope was worse than the separation (0.16 nm) between Hg (or Cd) and Te columns, the crystal polarity was determined from the aberration-corrected object wave.

Electron tomography and holography in materials science

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.

Development of aberration-corrected electron microscopy

The successful correction of spherical aberration is an exciting and revolutionary development for the whole field of electron microscopy. Image interpretability can be extended out to sub-Angstrom levels, thereby creating many novel opportunities for materials characterization. Correction of lens aberrations involves either direct (online) hardware attachments in fixed-beam or scanning TEM or indirect (off-line) software processing using either off-axis electron holography or focal-series reconstruction. This review traces some of the important steps along the path to realizing aberration correction, including early attempts with hardware correctors, the development of online microscope control, and methods for accurate measurement of aberrations. Recent developments and some initial applications of aberration-corrected electron microscopy using these different approaches are surveyed. Finally, future prospects and problems are briefly discussed.

Progress and perspectives for atomic-resolution electron microscopy

The transmission electron microscope (TEM) has evolved into a highly sophisticated instrument that is ideally suited to the characterization of advanced materials. Atomic-level information is routinely accessible using both fixed-beam and scanning TEMs. This report briefly considers developments in the field of atomic-resolution electron microscopy. Recent activities include renewed attention to on-line microscope control ('autotuning'), and assessment and correction of aberrations. Aberration-corrected electron microscopy has developed rapidly in several forms although more work needs to be done to identify standard imaging conditions and to explore novel operating modes. Preparation of samples and image interpretation have also become more demanding. Ongoing problems include discrepancies between measured and simulated image contrast, concerns about radiation damage, and inversion of electron scattering.

Transmission electron microscope imaging of single-walled carbon nanotube interactions and mechanics on nitride grids

A method for analysing systems of isolated single-walled carbon nanotubes is of paramount importance if their structural characteristics are to be fully understood and utilized. Here we offer a simple technique for analysing such systems, with unprecedented contrast, using transmission electron microscope imaging of carbon nanotubes suspended over large holes in a silicon nitride grid. The nanotubes are grown directly on the viewing grids, using the chemical vapour deposition process, thus avoiding the use of chemicals or aggressive treatments. This method is simultaneously non-invasive, reusable, allows the analysis of multiple structures based on carbon nanotubes and is quickly implemented.

Measurement of crystal thickness and orientation from selected-area Fourier transformation of a high-resolution electron hologram

Precise knowledge of crystal thickness and orientation is critical for reliable interpretation of high-resolution transmission electron micrographs. In this paper, we propose a criterion of S(2)(T, u, v), which measures the crystal thickness by intensity matching of the selected-area Fourier transform of experimental holograms with the calculated electron diffraction pattern at a series of trial thicknesses (T) and crystal tilts (u, v). This criterion has been demonstrated successfully for local thickness determination from a simulated high-resolution image of a wedge-shaped YBa(2)Cu(3)O(7-delta) and from an experimental hologram of a Si crystal.

Diffractive electron imaging of nanoparticles on a substrate

The observation of the detailed atomic arrangement within nanostructures has previously required the use of an electron microscope for imaging. The development of diffractive (lensless) imaging in X-ray science and electron microscopy using ab initio phase retrieval provides a promising tool for nanostructural characterization. We show that it is possible experimentally to reconstruct the atomic-resolution complex image (exit-face wavefunction) of a small particle lying on a thin carbon substrate from its electron microdiffraction pattern alone. We use a modified iterative charge-flipping algorithm and an estimate of the complex substrate image is subtracted at each iteration. The diffraction pattern is recorded using a parallel beam with a diameter of approximately 50 nm, illuminating a gold nanoparticle of approximately 13.6 nm diameter. Prior knowledge of the boundary of the object is not required. The method has the advantage that the reconstructed exit-face wavefunction is free of the aberrations of the objective lens normally used in the microscope, whereas resolution is limited only by thermal vibration and noise.

A versatile double aberration-corrected, energy filtered HREM/STEM for materials science

A HREM/STEM incorporating aberration correctors in both the probe-forming and imaging lenses has been installed at Oxford University. This unique instrument is also equipped with an in-column energy-loss (Omega-type) filter, HAADF detectors above and beneath the filter, and an EDX system. Initial tests have shown it to be capable of approximately 0.1 nm resolution in both TEM and HAADF STEM imaging modes. Some examples of applications are finally presented.

"Indirect" high-resolution transmission electron microscopy: aberration measurement and wavefunction reconstruction

Improvements in instrumentation and image processing techniques mean that methods involving reconstruction of focal or beam-tilt series of images are now realizing the promise they have long offered. This indirect approach recovers both the phase and the modulus of the specimen exit plane wave function and can extend the interpretable resolution. However, such reconstructions require the a posteriori determination of the objective lens aberrations, including the actual beam tilt, defocus, and twofold and threefold astigmatism. In this review, we outline the theory behind exit plane wavefunction reconstruction and describe methods for the accurate and automated determination of the required coefficients of the wave aberration function. Finally, recent applications of indirect reconstruction in the structural analysis of complex oxides are presented.

Influence of the elliptical illumination on acquisition and correction of coherent aberrations in high-resolution electron holography

In high-resolution off-axis electron holography, the interpretable lateral resolution is extended up to the information limit of the electron microscope by means of a correcting phase plate in Fourier space. A plane illuminating electron wave is generally assumed. However, in order to improve spatial coherence, which is essential for holography, the object under investigation is illuminated with an elliptically shaped electron source. This special illumination imposes a variation of beam directions over the field of view. Therefore, due to the interaction of beam tilt and coherent wave aberration, the effective aberrations vary over the field of view yielding a loss of isoplanicity. Consequently, in the past the aberrations were only corrected successfully for a small part of the field of view. However, a thorough analysis of the holographic imaging process shows that the imaging artifacts introduced by the elliptical illumination can be corrected under reconstruction by means of a phase curvature, which models the illuminating wave front. Applied in real space, this phase curvature is seamlessly incorporated into the correction process for coherent wave aberration resulting in an improvement of interpretable lateral resolution up to the information limit for the whole field of view.

Observation of magnetic multilayers by electron holography

Magnetic structures of Co/Cu multilayers in cross section are observed by two kinds of electron holography: a Fourier method and a phase-shifting method, which is introduced briefly. The Fourier method can easily reconstruct wave functions and is applied to many specimens, whereas the phase-shifting method requires longer time for processing, but has a higher spatial resolution that permits us to discuss fine structures. Magnetization vectors in Co layers aligning parallel and separating into two blocks with antiparallel alignment are observed. Magnetic blurring on the boundary between Co and Cu in the reconstructed phase images is larger than the estimated atomic roughness.

On the characterization of environmental nanoparticles

The presence and release of nanoparticles into the environment has important implications for human health and the environment. This article highlights and describes techniques that are effective in the characterization of anthropogenic and naturally occurring nanoparticles. Particle attributes like size, size distribution, shape, structure, microstructure, composition, and homogeneity are critically important to determining the potential impact of such materials on health and the environment. Many techniques yield data for a collection of nanoparticles; while others yield data for individual nanoparticles; and still others yield data showing the size, distribution of chemical species, and variations in structure and microstructure for a single nanoparticle. All are important in the context of environmental nanoparticles. Many of these techniques are complementary, and depending on the information required, the ideal characterization usually employs multiple techniques.

Structural characterization of atomically regulated nanocrystals formed within single-walled carbon nanotubes using electron microscopy

The structural chemistry of nanoscale materials encapsulated within single-walled carbon nanotubes (SWNTs) is reviewed. SWNTs form atomically thin channels within a restricted diameter range, and their internal van der Waals surfaces regulate the growth behavior of encapsulated crystals in a precise fashion, leading to atomically regulated growth. The structural properties of these systems are largely dictated by the structural chemistry of the bulk material, although significant deviations from bulk structures are often observed, with lower surface coordinations and substantial lattice distortions.

A new method for the determination of the wave aberration function for high resolution TEM 1. Measurement of the symmetric aberrations

A new method for the accurate determination of the symmetric coefficients of the wave aberration function has been developed. The relative defoci and displacements of images in a focus series are determined from an analysis of the phase correlation function between pairs of images, allowing the restoration of an image wave even when focus and specimen drift are present. Subsequently, the absolute coefficients of both defocus and 2-fold astigmatism are determined with a phase contrast index function. Overall this method allows a very accurate automated aberration determination even for largely crystalline samples with little amorphous contamination. Using experimental images of the complex oxide Nb16W18O94 we have demonstrated the new method and critically compared it with existing diffractogram based aberration determinations. A series of protocols for practical implementation is also given together with a detailed analysis of the accuracy achieved. Finally a focal series restoration of Nb16W18O94 with symmetric aberrations determined automatically using this method is presented.

Phase recovery and lensless imaging by iterative methods in optical, X-ray and electron diffraction

Thomas Young's quantitative analysis of interference effects provided the confidence needed to revive the wave theory of light, and firmly established the concept of phase in optics. Phase plays a similarly fundamental role in matter-wave interferometry, for which the field-emission electron microscope provides ideal instrumentation. The wave-particle duality is vividly demonstrated by experimental 'Young's fringes' using coherent electron beams under conditions in which the flight time is less than the time between particle emission. A brief historical review is given of electron interferometry and holography, including the Aharonov-Bohm effect and the electron Sagnac interferometer. The simultaneous development of phase-contrast imaging at subnanometre spatial resolution has greatly deepened our understanding of atomic processes in biology, materials science and condensed-matter physics, while electron holography has become a routine tool for the mapping of electrostatic and magnetic fields in materials on a nanometre scale. The encoding of phase information in scattered farfield intensities is discussed, and non-interferometric, non-crystallographic methods for phase retrieval are reviewed in relationship to electron holography. Examples of phase measurement and diffraction-limited imaging using the hybrid input-output iterative algorithm are given, including simulations for soft X-ray imaging, and new experimental results for coherent electron and visible-light scattering. Image reconstruction is demonstrated from experimental electron and visible-light Fraunhofer diffraction patterns. The prospects this provides for lensless imaging using particles for which no lenses exist (such as neutrons, condensates, coherent atom beams and X-rays) are discussed. These new interactions can be expected to provide new information, perhaps, for example, in biology, with the advantage of less damage to samples.

Electron holography of field-emitting carbon nanotubes

Electron holography performed in situ inside a high resolution transmission electron microscope has been used to determine the magnitude and spatial distribution of the electric field surrounding individual field-emitting carbon nanotubes. The electric field (and hence the associated field emission current) is concentrated precisely at the tips of the nanotubes and not at other nanotube defects such as sidewall imperfections. The electric field magnitude and distribution are stable in time, even in cases where the nanotube field emission current exhibits extensive temporal fluctuations.

Atomic structure holography using thermal neutrons

The idea of atomic-resolution holography has its roots in the X-ray work of Bragg and in Gabor's electron interference microscope. Gabor's lensless microscope was not realized in his time, but over the past twelve years there has been a steady increase in the number of reports on atomic-resolution holography. All of this work involves the use of electrons or hard X-rays to produce the hologram. Neutrons are often unique among scattering probes in their interaction with materials: for example, the relative visibility of hydrogen and its isotopes is a great advantage in the study of polymers and biologically relevant materials. Recent work proposed that atomic-resolution holography could be achieved with thermal neutrons. Here we use monochromatic thermal neutrons, adopting the inside-source concept of Szöke, to image planes of oxygen atoms located above and below a single hydrogen atom in the oxide mineral simpsonite.

Imaging columns of the light elements carbon, nitrogen and oxygen with sub Angstrom resolution

It is reported that lattice imaging with a 300 kV field emission microscope in combination with numerical reconstruction procedures can be used to reach an interpretable resolution of about 80 pm for the first time. A retrieval of the electron exit wave from focal series allows for the resolution of single atomic columns of the light elements carbon, nitrogen, and oxygen at a projected nearest neighbor spacing down to 85 pm. Lens aberrations are corrected on-line during the experiment and by hardware such that resulting image distortions are below 80 pm. Consequently, the imaging can be aberration-free to this extent. The resolution enhancement results from increased electrical and mechanical stability of the instrument coupled with a low spherical aberration coefficient of 0.595 + 0.005 mm.

Structure determination at the atomic level from dynamical electron diffraction data under systematic row conditions

We discuss a method to obtain structural information on crystals at the atomic level in high-resolution transmission electron microscopy from dynamical diffraction data under systematic row conditions. Working at a fixed incident energy and within an N-beam approximation, data is required at a well defined set of N incident beam orientations to determine the scattering matrix, one orientation for each column in the matrix. At each orientation the corresponding column of the scattering-matrix is obtained by Fourier transformation of the exit surface wave function. Thus, in addition to each exit surface image, we must recover the phase of the wave function for that orientation in the image plane. We show that retrieval of the phase using algorithms based on conservation of flux, which assume continuity of the phase, can yield incorrect solutions for the phase. This is because singularities can occur in the phase of the wave field at points where the intensity is zero, which can lead to edge dislocations in the phase. We demonstrate, using a model example, how these edge dislocations arise. We will show that phase retrieval from a through focal series of measurements or using the Gerchberg-Saxton algorithm (starting from measurements of an image and the corresponding diffraction pattern), correctly retrieves the phase and hence the exit surface wave function for all the orientations required to obtain the scattering-matrix. The dynamical (multiple) scattering can then be inverted to uniquely obtain the projected potential.

Correction of aberration for a high-resolution electron hologram by means of the amplitude contrast criterion of image wave

In order to further improve the resolution for a high-resolution electron hologram, the aberration working on the hologram must be corrected. Since it is rather difficult to precisely control aberration coefficients in the experimental stage, we proposed an amplitude contrast D criterion of imaging wave to determine the working aberration from the hologram itself. In the determination or correction of the aberration, we assume a symmetrical aberration function is parameterized only by a spherical aberration coefficient and a defocus value. First, D is calculated from a holographically reconstructed imaging wave of YBa(2)Cu(3)O(7-x) for each combination of these parameters. The working aberration on the imaging wave is determined from the combination of the parameters by noting the maximum or minimum D of the imaging wave at some specifically chosen thickness regions. The theoretical validity for the D criterion is then proved with three-beam dynamical diffraction formula. Finally, the 'experimental' examination for the D criterion is successfully performed on the reconstructed image wave for the Sigma=9 interface structure of a wedge-shaped silicon sample.

Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy

We discuss phase retrieval and the correction of images for aberrations, in particular defocus and spherical aberration, in high-resolution transmission electron microscopy. Non-interferometric phase retrieval requires at least two intensity measurements in different planes. Vortices in the phase may occur in the image plane or the other planes involved in the phase retrieval. We discuss the performance of various methods of phase retrieval in that case. After retrieval of the phase, the aberrations can be corrected in the Fraunhofer diffraction space (the wave function in the diffraction space is related to that in the image space by a Fourier transform). The aberration-corrected image is obtained from the aberration-corrected wave function in the diffraction plane by inverse Fourier transformation.

Atomic string holography

A new diffraction-channeling effect has been discovered, in which Kikuchi or channeling line patterns formed by high energy electrons, neutrons, and positrons are shown to break up into a series of annular disks if the crystal thickness traversed by the beam is small. The disks may be interpreted as Gabor in-line holograms of strings of atoms projected along the beam path. For electrons or positrons the patterns may be detected with little background by detecting characteristic x-ray emission from a thin film as a function of the diffraction conditions of a collimated, ionizing, high energy beam. Uses of the effect for structure determination and atomic-resolution lensless imaging are suggested.

An accurate analytical approach to electron crystallography

A much more accurate analytical expression of dynamical electron diffraction than the phase object approximation (POA) formula has been derived in this paper which decreases the restriction of sample thickness up to almost one order of magnitude compared to POA theory. The importance of the new expression is twofold. First, a sample with such a thickness that new expression remains valid can be prepared experimentally. Second, the new expression reveals a clear and straightforward relationship between the wave function and crystal potential. In the expression, the effect of dynamical diffraction on wave function can be simply attributed to two factors TP(D) = (sin(lambda pi zg2))/(4pi2g2) and TA(D) = [1 - cos(lambda pi zg2)]/4pi2g2. Compared to the effect of transfer functions of an electron microscope on wave function, we found that TP(d) and TA(d) play the same role as transfer function but are independent of the instrument. For this reason, we here call the former as "extrinsic transfer functions" and the latter as "intrinsic" ones. In principle, one should correct not only extrinsic transfer functions but also intrinsic ones if one desires to achieve higher resolution.

Impact of column bending in high-resolution transmission electron microscopy on the strain evaluation of GaAs/InAs/GaAs heterostructures

The accuracy of strain profiles obtained by a quantitative analysis of lattice fringe spacings from high-resolution micrographs is discussed. Focusing on highly lattice mismatched GaAs/InAs/GaAs heterostructures the local strain distribution of the layers is calculated by finite element simulations to determine the atom positions in elastically relaxed transmission electron microscopy specimens. By analysing simulated images a significant decoupling between the layer structure and the contrast pattern motifs is found for relevant imaging conditions, which may result in an incorrect determination of strain profiles and layer compositions when examining experimental micrographs.