Monte Carlo electron-trajectory simulations in bright-field and dark-field STEM: Implications for tomography of thick biological sections

A Monte Carlo electron-trajectory calculation has been implemented to assess the optimal detector configuration for scanning transmission electron microscopy (STEM) tomography of thick biological sections. By modeling specimens containing 2 and 3 at% osmium in a carbon matrix, it was found that for 1-μm-thick samples the bright-field (BF) and annular dark-field (ADF) signals give similar contrast and signal-to-noise ratio provided the ADF inner angle and BF outer angle are chosen optimally. Spatial resolution in STEM imaging of thick sections is compromised by multiple elastic scattering which results in a spread of scattering angles and thus a spread in lateral distances of the electrons leaving the bottom surface. However, the simulations reveal that a large fraction of these multiply scattered electrons are excluded from the BF detector, which results in higher spatial resolution in BF than in high-angle ADF images for objects situated towards the bottom of the sample. The calculations imply that STEM electron tomography of thick sections should be performed using a BF rather than an ADF detector. This advantage was verified by recording simultaneous BF and high-angle ADF STEM tomographic tilt series from a stained 600-nm-thick section of C. elegans. It was found that loss of spatial resolution occurred markedly at the bottom surface of the specimen in the ADF STEM but significantly less in the BF STEM tomographic reconstruction. Our results indicate that it might be feasible to use BF STEM tomography to determine the 3D structure of whole eukaryotic microorganisms prepared by freeze-substitution, embedding, and sectioning.     

Thick specimens in the CEM and STEM. Resolution and image formation.

A theory of resolution and image formation is presented for thick amorphous specimens in transmission electron microscopes. Eight modes of operation are considered, four in the scanning transmission electron microscope (STEM) and four in the conventional electron microscope (CEM). A thick specimen is defined here as one in which the resolution of detail is limited by plural scattering of the electron beam. In practice this includes films on the order of a micron in thickness. An analytic theory of plural incoherent scattering is developed which is general with respect to material and beam voltage. The theory gives the distribution of elastically scattered electrons as a function of transverse coordinate and angles, and is directly applicable to optical systems. The theory applies to all thicknesses normally encountered, and includes thin specimens as well as thick specimens. Criteria are proposed for evaluation of the quality of microscope images, and the modulation transfer function is applied to determine some practical estimates of picture quality. The STEM is found to have distinct advantages over the CEM for thick specimens. For a carbon specimen one micron thick a STEM operating in bright field at 90 keV produces an image which is roughly equivalent to that of a CEM operating in bright field at 1 MeV. Improvement can be obtained in the CEM by filtering out eneryg-loss electrons which degrade resolution due to chromatic aberration. This results in a reduction in signal intensity and usable thickness, however.     

Contrast and resolution of scanning transmission electron microscope imaging modes

Image blurring due to delocalization of inelastic events was studied for scanning transmission electron microscopy (STEM) of unstained thin sections. The delocalization probability was obtained from the angular distribution of inelastic scattering, which was calculated from experimental electron loss spectra of organic samples. This probability was implemented in a Monte Carlo program to simulate the effects of multiple scattering and delocalization for STEM images collected by either the annular detector or the spectrometer, and images generated by a combination of these two signals. Depending on the illumination, the detector geometry and the energy-loss range selected for imaging the annular detector image is blurred by a non-negligible fraction of inelastically scattered electrons. Simultaneous acquisition of an inelastic image using a spectrometer allows the blurring to be reduced by calculation of either the ratio or the difference of the two darkfield signals. While inherent nonlinearities reduce the interpretability of ratio-contrast images, difference-contrast improves the visibility of details submerged in a diffuse background without introducing artifacts.     

Semianalytical treatment of beam broadening in crystals

Contrast and specimen resolution in electron micrographs of point defects, voids, aggregates, and precipitates in crystalline material are diminished by multiple scattering of the incident electrons within the crystalline top layer. For the scanning transmission electron microscope (STEM) the current density distribution inside the crystal has been calculated by employing the k · p perturbation expansion used in solid state physics. Neglecting inelastic scattering the solution of the electron wave function within the crystal can be expressed as a sum of Bloch waves. The excited Bloch waves are expanded in a power series of the angle of incidence, and only terms up to the second order inclusively are taken into account. This procedure permits the analytical integration over the illumination angles in STEM or the aperture angles in the case of a fixed-beam electron microscope (FBEM). Considering only the two strongest Bloch waves an approximate formula is obtained for the current density distribution within the crystal which is valid for light atoms and resolution limits larger than twice the lattice constant. In the case of heavy atoms the approximation for the current density is only valid in the region near the atoms. As the incident electrons channel along the atom rows beam broadening within the crystal is largely suppressed up to depths of about 1000 Å. The image contrast of an embedded scatterer resting on an atom row is strongly enhanced, whereas it is diminished when the scatterer is located midway among the atom rows. The proposed method makes possible a fast calculation of the electron wave propagating in crystalline material.     

Quantitative atomic resolution mapping using high-angle annular dark field scanning transmission electron microscopy

A model-based method is proposed to relatively quantify the chemical composition of atomic columns using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images. The method is based on a quantification of the total intensity of the scattered electrons for the individual atomic columns using statistical parameter estimation theory. In order to apply this theory, a model is required describing the image contrast of the HAADF STEM images. Therefore, a simple, effective incoherent model has been assumed which takes the probe intensity profile into account. The scattered intensities can then be estimated by fitting this model to an experimental HAADF STEM image. These estimates are used as a performance measure to distinguish between different atomic column types and to identify the nature of unknown columns with good accuracy and precision using statistical hypothesis testing. The reliability of the method is supported by means of simulated HAADF STEM images as well as a combination of experimental images and electron energy-loss spectra. It is experimentally shown that statistically meaningful information on the composition of individual columns can be obtained even if the difference in averaged atomic number Z is only 3. Using this method, quantitative mapping at atomic resolution using HAADF STEM images only has become possible without the need of simultaneously recorded electron energy loss spectra.     

Filtered dark-field and pure Z-contrast: two novel imaging modes in a Scanning Transmission Electron Microscope

For the investigation of biological objects with a Scanning Transmission Electron Microscope (STEM) the dark-field imaging mode is the one used most often. We will show, regarding calculations that we have done which took into account the finite angle of the illumination and multiple scattering processes, that the collected amount of inelastically scattered electrons with an annular dark-field detector is higher then normally expected. According to the above calculations, we designed a new detection system to enable us to acquire three different images (inelastic, filtered dark-field and filtered bright-field) simultaneously.     

Size determination of microscratches on silicon oxide wafer surface using scattered light

Scattered light intensity distributions from microscratches on a silicon oxide wafer surface are simulated and analyzed for the purpose of microscratch sizing using a boundary element method (BEM)-based electromagnetic scattering simulator. At normal incidence, the characteristic scattered light resulting from microscratches appears in two symmetric regions of scattering angles, namely, at high and low angles. The scattered light intensities at high and low angles show characteristic fluctuation according to the depth and width variations of microscratches. It is found that the size of a microscratch can be obtained from the scattered light intensities at these characteristic angles. We propose microscratch sizing map which uses the detected light intensities to size the microscratches. Once the map is created, quick and easy categorization of microscratch size can be realized by collating the detected intensities with the map. The major advantage of using the map is the ability to measure simultaneously not only microscratch width but also depth. Generally, the depth cannot be obtained from an imaging system. Several experiments demonstrate the feasibility of our scheme and their results are in very good agreement with the simulation results.     

Annular electron energy-loss spectroscopy in the scanning transmission electron microscope

We study atomic-resolution annular electron energy-loss spectroscopy (AEELS) in scanning transmission electron microscopy (STEM) imaging with experiments and numerical simulations. In this technique the central part of the bright field disk is blocked by a beam stop, forming an annular entry aperture to the spectrometer. The EELS signal thus arises only from electrons scattered inelastically to angles defined by the aperture. It will be shown that this method is more robust than conventional EELS imaging to variations in specimen thickness and can also provide higher spatial resolution. This raises the possibility of lattice resolution imaging of lighter elements or ionization edges previously considered unsuitable for EELS imaging.     

Experimental investigation of phase contrast formed by inelastically scattered electrons

Phase contrast formed by inelastically scattered electrons in a crystal has been investigated using spatially resolved EELS, which enables simultaneous observation of lattice fringes formed by electrons of various energy losses. Lattice fringes produced by low-loss electrons overlap on an elastic TEM image like Fourier images. This means that the exit wave is preserved in low-loss scattering. Similar Fourier images occur for electrons suffering core-losses in the range 50-400 eV, which indicates delocalization and spatial coherence in those core-loss scattering events. The spatial coherence of inelastically scattered electrons is estimated from the focus dependence of energy-filtered lattice fringe contrast. Spatial coherence widths shorten with increasing energy-loss, and their energy-loss dependence is similar to diffraction errors derived from the characteristic angle for inelastic scattering.     

Quantitative analysis of image contrast in phase contrast STEM for low dose imaging

This work quantitatively evaluates the contrast in phase contrast images of thin vermiculite crystals recorded by TEM and aberration-corrected bright-field STEM. Specimen movement induced by electron irradiation remains a major problem limiting the phase contrast in TEM images of radiation-sensitive specimens. While spot scanning improves the contrast, it does not eliminate the problem. One possibility is to utilise aberration-corrected scanning transmission electron microscopy (STEM) with an Ångstrom-sized probe to illuminate the sample, and thus further reduce irradiation-induced specimen movement. Vermiculite is relatively radiation insensitive in TEM to electron fluences below 100,000 e⁻/Ų and this is likely to be similar for STEM although different damage mechanisms could occur. We compare the performance of a TEM with a thermally assisted field emission electron gun (FEG) and charge coupled device (CCD) image capture to the performance of STEMs with spherical aberration correction, cold field emission electron sources and photomultiplier tube image capture at a range of electron fluences and similar illumination areas. We show that the absolute contrast of the phase contrast images obtained by aberration-corrected STEM is better than that obtained by TEM. Although the STEM contrast is higher, the efficiency of collection of electrons in bright field STEM is still much less than that in bright field TEM (where for thin samples virtually all the electrons contribute to the image), and the SNR of equivalent STEM images is three times lower. This is better than expected, probably due to the absence of a frequency dependent modulation transfer function in the STEM detection system. With optimisation of the STEM bright field collection angles, the efficiency may approach that of bright field TEM, and if reductions in beam-induced specimen movement are found, STEM could surpass the overall performance of TEM.     

Prospects for 3D, nanometer-resolution imaging by confocal STEM

Confocal STEM is a new electron microscopy imaging mode. In a microscope with spherical aberration-corrected electron optics, it can produce three-dimensional (3D) images by optical sectioning. We have adapted the linear imaging theory of light confocal microscopy to confocal STEM and use it to suggest optimum imaging conditions for a confocal STEM limited by fifth-order spherical aberration. We predict that current or near-future microscopes will be able to produce 3D images with 1 nm vertical resolution and sub-Angstrom lateral resolution. Multislice simulations show that we will need to be cautious in interpreting these images, however, as they can be complicated by dynamical electron scattering.     

High resolution imaging properties of the stem

The effect of the finite size of the atom on the resolution of the STEM is investigated. When the probe size becomes comparable to the size of the atom, the quality of the image depends on the scattering properties of the atom as well as the distribution of electrons in the probe. A technique for calculating the image of a single atom is developed by expanding the scattering amplitude. This allows the image of an atom or its spatial frequency to be expanded into various components. The specific case of dark field contrast formed with elastically scattered electrons is considered. The coefficients of the components are evaluated for carbon and thorium using complex scattering amplitudes derived from relativistic Hartree-Fock-Slater wavefunctions. The coefficients are evaluated for a 100 keV microscope using an immersion type objective lens whose aperture is limited to 12 mrad by primary spherical aberration and a 100 keV microscope using the same objective lens in conjunction with a corrector lens for spherical aberration. Secondary spherical aberration limits the objective aperture of the corrected microscope to 30 mrad.     

Crystal structure determination by direct inversion of dynamical microdiffraction patterns

The intensity at points where coherent convergent-beam transmission diffraction discs overlap is shown to be described by interference between elements of the same row but different columns of the dynamical scattering matrix for an axial orientation. These intensities are used as the basis for an exact, nonperturbative inversion of the multiple electron scattering problem, allowing crystal structure factors to be obtained directly from the intensities of multiply scattered Bragg beams. Eigenvectors of the structure matrix are obtained using coherent CBED patterns from many crystal orientations. Unique eigenvalues are obtained from these patterns recorded at two accelerating voltages. The inevitable variation in electron probe position at different crystal tilts is considered. The analysis applies to centrosymmetric crystals with anomalous absorption, to centrosymmetric projections of acentric crystals and to acentric crystals if the mean absorption potential only is included. The method would allow the direct synthesis of charge-density maps of unknown crystal structures at high resolution from multiple scattering data, using a scanning transmission electron microscope (STEM). The resolution of this map may be much higher than the first-order d -spacing; however, the STEM need only be capable of resolving this first-order spacing. Such a charge-density map provides fractional atomic coordinates and the identification of atomic species (as in X-ray crystallography) from microcrystalline samples and other multiphase inorganic materials for which large single crystals cannot be obtained or X-ray powder patterns obtained or analysed. In summary, we solve the inversion problem of quantum mechanics for the case of electron scattering from a periodic potential, described by the nonrelativistic Schrödinger equation, in which the scattering is given as a function of some parameter, and the potential sought.     

A simple procedure for evaluating effective scattering cross-sections in STEM

The quantitative interpretation of STEM images relies on a precise knowledge of the effective scattering cross-sections. To determine these cross-sections, it is necessary to take into account the finite angles of both the illuminating and the recorded beams. In the following a procedure is outlined by which at least two of the four integrations can be performed analytically. Single atom differential cross-sections require only a single numerical integration. Although the proposed method is rather simple, it does not seem to be commonly known.     

Spatially resolved diffractometry with atomic-column resolution

We demonstrate spatially resolved diffractometry in which diffraction patterns are acquired at two-dimensional positions on a specimen using scanning transmission electron microscopy (STEM), resulting in four-dimensional data acquisition. A high spatial resolution of about 0.1 nm is achieved using a stabilized STEM instrument, a spherical aberration corrector and various post-acquisition data processings. We have found a few novel results in the radial and the azimuthal scattering angle dependences of atomic-column contrast in STEM images. Atomic columns are clearly observed in dark field images obtained using the excess Kikuchi band intensity even in small solid-angle detection. We also find that atomic-column contrasts in dark field images are shifted in the order of a few tens of picometers on changing the azimuthal scattering angle. This experimental result is approximately interpretable on the basis of the impact parameter in Rutherford scattering. Spatially resolved diffractometry provides fundamental knowledge related to various STEM techniques, such as annular dark field (ADF) and annular bright field (ABF) imaging, and it is expected to become an analytical platform for advanced STEM imaging.     

Simulation of scanning transmission electron microscope images on desktop computers

Two independent strategies are presented for reducing the computation time of multislice simulations of scanning transmission electron microscope (STEM) images: (1) optimal probe sampling, and (2) the use of desktop graphics processing units. The first strategy is applicable to STEM images generated by elastic and/or inelastic scattering, and requires minimal effort for its implementation. Used together, these two strategies can reduce typical computation times from days to hours, allowing practical simulation of STEM images of general atomic structures on a desktop computer.     

Quantitative STEM mass measurement of biological macromolecules in a 300 kV TEM

For almost four decades, the scanning transmission electron microscope (STEM) has made significant contributions to structural biology by providing accurate determinations of the molecular masses of large protein assemblies that have arbitrary shapes and sizes. Nevertheless, STEM mass mapping has been implemented in very few laboratories, most of which have employed cold field‐emission gun (FEG) electron sources operating at acceleration voltages of 100 kV and lower. Here we show that a 300 kV commercial transmission electron microscope (TEM) equipped with a thermally assisted Shottky FEG can also provide accurate STEM mass measurements. Using the recently published database of elastic‐scattering cross sections from the National Institute of Standards and Technology, we show that the measured absolute mass values for tobacco mosaic virus and limpet hemocyanin didecamers agree with the known values to within better than 10%. Applying the established approach, whereby tobacco mosaic virus is added to a specimen as a calibration standard, we find that the measured molecular weight of the hemocyanin assemblies agrees with the known value to within 3%. This accuracy is achievable although only a very small fraction (∼0.002) of the incident probe current of 300 kV electrons is scattered onto the annular dark‐field STEM detector. FEG TEMs operating at intermediate voltages (200–400 kV) are becoming common tools for determining the structure of frozen hydrated protein assemblies. The ability to perform mass determination with the same instrument can provide important complementary information about the numbers of subunits comprising the protein assemblies whose structure is being studied.     

Phosphorus detection in vitrified bacteria by cryo‐STEM annular dark‐field analysis

Bacterial cells often contain dense granules. Among these, polyphosphate bodies (PPBs) store inorganic phosphate for a variety of essential functions. Identification of PPBs has until now been accomplished by analytical methods that required drying or chemically fixing the cells. These methods entail large electron doses that are incompatible with low‐dose imaging of cryogenic specimens. We show here that Scanning Transmission Electron Microscopy (STEM) of fully hydrated, intact, vitrified bacteria provides a simple means for mapping of phosphorus‐containing dense granules based on quantitative sensitivity of the electron scattering to atomic number. A coarse resolution of the scattering angles distinguishes phosphorus from the abundant lighter atoms: carbon, nitrogen and oxygen. The theoretical basis is similar to Z contrast of materials science. EDX provides a positive identification of phosphorus, but importantly, the method need not involve a more severe electron dose than that required for imaging. The approach should prove useful in general for mapping of heavy elements in cryopreserved specimens when the element identity is known from the biological context.     

光学粉尘浓度测量仪响应特性曲线的计算与分析

根据 Mie散射理论计算了 5种光学粉尘浓度测量仪的光散射响应特性曲线 ,对照呼吸性粉尘在人体呼吸道中的沉降效率曲线 ,对这些光学粉尘浓度测量仪的响应特性进行了分析。得出的结论是 :采用近前向型光散射结构、多波长照明光源和大孔径散射光收集系统的光学粉尘浓度测量仪 ,其响应特性曲线更接近于人体对呼吸性粉尘的采集效率     

Detection of hydrogen by electron Rutherford backscattering

A novel method for detection of hydrogen by an electron beam in extremely thin samples is described. Elastically scattered electrons impinging with 20-30 keV on a thin formvar film were detected at a scattering angle near 45 degrees. In these large momentum transfer elastic collisions a clear separation of the signal of hydrogen and heavier elements was found. By changing the momentum transfer we can verify that the hydrogen signal is not due to inelastic energy loss contributions. The width of the hydrogen elastic peak is much larger than the elastic peaks due to heavy elements (carbon and oxygen). The ratio of the hydrogen elastic peak and the main elastic peak is smaller than expected by 30-50% depending on the energy of the impinging electron. This could be due to electronic excitations directly coupled to the elastic collision. The stability of the formvar film under electron radiation was studied. A reduction in thickness of the film with increasing fluence, as well as the preferential depletion of hydrogen, was found. Possible improvements of the experimental configuration for this type of experiments are discussed.