Voxel dose-limited resolution for thick beam-sensitive specimens imaged in a TEM or STEM.

The resolution limit imposed by radiation damage is quantified in terms of a voxel dose-limited resolution (DLR), applicable to small features within a thick specimen. An analytical formula for this DLR is derived and applied to bright-field mass-thickness contrast from organic (polymer or biological) specimens of thickness between 400 nm and 20 µm. For a permissible dose of 330 MGy (typical of frozen-hydrated tissue), the TEM or STEM image resolution is determined by radiation damage rather than by lens aberrations or beam-broadening effects, which can be restricted by use of a small angle-limiting aperture. DLR is improved by a up to factor of 2 by increasing the primary-electron energy from 300 keV to 3 MeV, or by up to a factor of 3 by heavy-metal staining. For stained samples, a higher electron fluence allows better resolution but the improvement is modest because the voxel DLR is proportional to the 1/4 power of electron dose. The relevance of voxel and columnar DLR is discussed, for both thick and thin samples.

Transmission electron microscopy of thick polymer and biological specimens.

We explore the properties of elastic and inelastic scattering in a thick organic specimen, together with the mechanisms that provide contrast in a transmission electron microscope (TEM) and scanning-transmission electron microscope (STEM). Experimental data recorded from amorphous carbon are used to predict the bright-field image intensity, mass-thickness contrast and dose-limited resolution as a function of thickness, objective-aperture size, and primary-electron energy E0. Combining this information with estimates of chromatic aberration, objective-aperture diffraction and beam broadening in the specimen, we calculate the achievable TEM and STEM resolution to be around 4 nm at E0 = 300 keV (or below 3 nm at MeV energies) for a 10 µm-diameter objective aperture and 1 - 2 µm thickness of hydrated biological tissue. The 3 MeV resolution for a 10-µm tissue sample is probably closer to 10 nm. We also comment on the error involved in quadrature addition of resolution factors, when one or more of the point-spread functions are non-Gaussian.

Spatial resolution in secondary-electron microscopy.

We first review the significance of resolution and contrast in electron microscopy and the effect of the electron optics on these two quantities. We then outline the physics of the generation of secondary electrons (SEs) and their transport and emission from the surface of a specimen. Contrast and resolution are discussed for different kinds of SE imaging in scanning electron microscope (SEM) and scanning-transmission microscope instruments, with some emphasis on the observation of individual atoms and atomic columns in a thin specimen. The possibility of achieving atomic resolution from a bulk specimen at SEM energies is also considered.

Spatial resolution in transmission electron microscopy.

We review the practical factors that determine the spatial resolution of transmission electron microscopy (TEM) and scanning-transmission electron microscopy (STEM), then enumerate the advantages of representing resolution in terms of a point-spread function. PSFs are given for the major resolution-limiting factors: aperture diffraction, spherical and chromatic aberration, beam divergence, beam broadening, Coulomb delocalization, radiolysis damage and secondary-electron generation from adatoms or atoms in a matrix. We note various definitions of beam broadening, complications of describing this effect in very thin specimens, and ways of optimizing the resolution in bright-field STEM of thick samples. Beam spreading in amorphous and crystalline materials is compared by means of simulations. For beam-sensitive specimens, we emphasize the importance of dose-limited resolution (DLR) and briefly recognize efforts to overcome the fundamental resolution limits set by the wave and particle properties of electrons.

Evolution in X-ray analysis from micro to atomic scales in aberration-corrected scanning transmission electron microscopes.

X-ray analysis is one of the most robust approaches to extract quantitative information from various materials and is widely used in various fields ever since Raimond Castaing established procedures to analyze electron-induced X-ray signals for materials characterization '70 years ago'. The recent development of aberration-correction technology in a (scanning) transmission electron microscopes (S/TEMs) offers refined electron probes below the Å level, making atomic-resolution X-ray analysis possible. In addition, the latest silicon drift detectors allow complex detector arrangements and new configurational designs to maximize the collection efficiency of X-ray signals, which make it feasible to acquire X-ray signals from single atoms. In this review paper, recent progress and advantages related to S/TEM-based X-ray analysis will be discussed: (i) progress in quantification for materials characterization including the recent applications to light element analysis, (ii) progress in analytical spatial resolution for atomic-resolution analysis and (iii) progress in analytical sensitivity toward single-atom detection and analysis in materials. Both atomic-resolution analysis and single-atom analysis are evaluated theoretically through multislice-based calculation for electron propagation in oriented crystalline specimen in combination with X-ray spectrum simulation.

Direct measurement of the PSF for Coulomb delocalization - a reconsideration.

An interpretation of Coulomb delocalization, which limits the spatial resolution of inelastic TEM or STEM images, is given. We conclude that the corresponding point spread function cannot be measured as a broadening of a STEM probe.

Dose measurement in the TEM and STEM.

Practical aspects of dosimetry are considered, including the measurement of electron-beam current and current density. Complications that arise in the case of a focused probe or a STEM image are discussed and solutions proposed. Advantages of expressing the radiation dose in Grays are listed and a simple formula given for converting electron fluence to Gray units, based on a near constancy of the stopping power per atomic electron. Comparisons with stopping-power calculations and EELS measurements suggest that this formula is accurate to within 5%. Based on the stopping power formula, a new way of measuring the local mass-thickness of light-element specimens is proposed. The average energy loss per inelastic collision is shown to be higher than previous expectations.

Radiation damage to organic and inorganic specimens in the TEM.

Symptoms of radiation damage are reviewed, followed by a brief description of the three main damage mechanisms: knock-on displacement (predominant in electrically conducting specimens), ionization damage (radiolysis), and electrostatic charging effects in poorly conducting specimens. Measurements of characteristic dose and damage cross section are considered, together with direct and inverse dose-rate effects. Dose limited resolution is defined in terms of a characteristic dose and instrumental parameters. Damage control is discussed in terms of low-dose technique, choice of imaging mode, specimen temperature, specimen environment and TEM accelerating voltage. We examine the possibility of performing electron cryomicroscopy in STEM mode, with a judicious choice of probe current and probe diameter.

Characterization of single-atom catalysts by EELS and EDX spectroscopy.

Fitted with a field emission source, aberration-corrected optics and an energy-dispersive X-ray detector of large solid angle, a modern analytical TEM can generate a current density high enough to chemically identify a single metal atom within a fraction of a second, if the atom remains stationary within the electron probe. However, atom motion will occur if the atomic binding energy is too low, the specimen temperature too high, or the electron accelerating voltage above a certain threshold. We discuss such motion in terms of thermal diffusion, beam-induced sputtering and beam-assisted surface migration. Calculations based on a Rutherford-scattering approximation suggest that when atomic displacement is possible, it drastically reduces the analytical signal and signal/noise ratio. For certain elements, electron energy-loss spectroscopy (EELS) provides a higher detectability than energy-dispersive X-ray (EDX) but suffers from the same problem of atomic displacement.

Calculation, consequences and measurement of the point spread function for low-loss inelastic scattering.

We have previously derived an analytical formula for the point spread function (PSF) that describes the delocalization of low-loss inelastic scattering. Here, we modify the formula to take account variation of scattered-electron phase. The exponentially attenuated Lorentzian form is retained but its halfwidth at half maximum is chosen to provide better agreement with measurements of the median delocalization distance. For low energy losses, the 1/r2 tails of the PSF extend beyond the region of energy deposition, allowing a small-diameter electron probe to provide energy-loss data from relatively undamaged regions of a beam-sensitive specimen. Alternatively, a core-loss or elastic image can be recorded with less damage by sparse scanning, as in scanned moiré imaging. A procedure is proposed for directly measuring the PSF, using a TEM with aberration-corrected lenses and an energy-filtered imaging system.

Scattering delocalization and radiation damage in STEM-EELS.

We discuss the delocalization of the inelastic scattering of 60-300keV electrons in a thin specimen, for energy losses below 50eV where the delocalization length exceeds atomic dimensions. Analytical expressions are derived for the point spread function (PSF) that describes the radial distribution of this scattering, based on its angular distribution and a dielectric representation of energy loss. We also compute a PSF for energy deposition, which is directly related to the radiolysis damage created by a small-diameter probe. These concepts are used to explain the damage kinetics, measured as a function of probe diameter, in various polymers. We also evaluate a "leapfrog" coarse-scanning procedure as a technique for energy-filtered imaging of a beam-sensitive specimen.

Vibrational-loss EELS and the avoidance of radiation damage.

We discuss vibrational-mode energy-loss spectroscopy using an aloof beam of electrons positioned a small distance b from the edge of a specimen in a probe-forming TEM or STEM equipped with a high-resolution monochromator. Due to the delocalization of inelastic scattering, a strong vibrational-loss signal can be recorded without causing significant damage to a beam-sensitive specimen. Calculations for b=20 nm suggest that damage is reduced by typically a factor of 1000 (relative to electrons of the same energy transmitted through the specimen) for the same signal strength and spatial resolution. About 50% of the vibrational-loss signal comes from material lying within a distance b of the edge of the specimen and extending over a length 2.5b parallel to the edge. Although energy-filtered imaging appears impossible in aloof mode, an undersampling STEM technique is proposed, taking advantage of scattering delocalization to obtain a vibrational-loss image that leaves most of the imaged area undamaged.

Validity of the dipole approximation in TEM-EELS studies.

Nondipole effects in electron energy-loss spectroscopy are evaluated in terms of deviation of the inelastic scattering from a Lorentzian angular distribution, which is assumed in established procedures for plural-scattering deconvolution, thickness measurement, and Kramers-Kronig analysis. The deviation appears to be small and may be outweighed by the effect of plural (elastic + inelastic) scattering, which is not removed by conventional deconvolution methods. In the core-loss region of the spectrum, non-Lorentzian behaviour stems from a reduction of the generalized oscillator strength from its optical value and (for energies far above an ionization threshold) formation of a Bethe-ridge angular distribution. At incident energies above 200 keV, retardation effects further distort the angular dependence, even for core losses just above threshold. With an on-axis collection aperture, non-dipole effects are masked by the rapid falloff of intensity with scattering angle, but they may become important for off-axis measurements. Near-edge fine structure is sensitive to nondipole effects but these can be minimized by use of an angle-limiting collection aperture.

Choice of operating voltage for a transmission electron microscope.

An accelerating voltage of 100-300kV remains a good choice for the majority of TEM or STEM specimens, avoiding the expense of high-voltage microscopy but providing the possibility of atomic resolution even in the absence of lens-aberration correction. For specimens thicker than a few tens of nm, the image intensity and scattering contrast are likely to be higher than at lower voltage, as is the visibility of ionization edges below 1000eV (as required for EELS elemental analysis). In thick (>100nm) specimens, higher voltage ensures less beam broadening and better spatial resolution for STEM imaging and EDX spectroscopy. Low-voltage (e.g. 30kV) TEM or STEM is attractive for a very thin (e.g. 10nm) specimen, as it provides higher scattering contrast and fewer problems for valence-excitation EELS. Specimens that are immune to radiolysis suffer knock-on damage at high current densities, and this form of radiation damage can be reduced or avoided by choosing a low accelerating voltage. Low-voltage STEM with an aberration-corrected objective lens (together with a high-angle dark-field detector and/or EELS) offers atomic resolution and elemental identification from very thin specimens. Conventional TEM can provide atomic resolution in low-voltage phase-contrast images but requires correction of chromatic aberration and preferably an electron-beam monochromator. Many non-conducting (e.g. organic) specimens damage easily by radiolysis and radiation damage then determines the TEM image resolution. For bright-field scattering contrast, low kV can provide slightly better dose-limited resolution if the specimen is very thin (a few nm) but considerably better resolution is possible from a thicker specimen, for which higher kV is required. Use of a phase plate in a conventional TEM offers the most dose-efficient way of achieving atomic resolution from beam-sensitive specimens.

Prospects for vibrational-mode EELS with high spatial resolution.

Taking advantage of previous measurements by Geiger and co-workers, we discuss the possibilities and problems of measuring vibrational modes of energy loss in a transmission electron microscope fitted with a monochromator and a high-resolution energy-loss spectrometer. The tail of the zero-loss peak is seen to be a major limitation, rather than its full-width at half-maximum. Because of the low oscillator strengths and small cross-sections involved, radiation damage will limit the spatial resolution if this technique is applied to organic specimens. Delocalization of the inelastic scattering may also be a limitation, if a dipole description of the scattering process is valid.

Beam-induced motion of adatoms in the transmission electron microscope.

Equations governing the elastic scattering of electrons are applied to the knock-on displacement of atoms along a substrate, yielding analytical expressions for the surface-translation energy, threshold incident energy, and displacement rate. For a surface perpendicular to the incident beam, scattering angles around 90° contribute most to the kinetic energy of surface atoms. Tilting the specimen lowers the threshold incident energy for displacement and leads to anisotropy in the atomic motion but has little effect on the directionally-averaged displacement rate. The rate of beam-induced adatom motion is predicted to exceed that of room-temperature thermal motion when the surface-diffusion energy is greater than about 0.5 eV.

Control of radiation damage in the TEM.

The problem of electron-beam damage in the transmission electron microscope is reviewed, with an emphasis on radiolysis processes in soft materials and organic specimens. Factors that determine the dose-limited resolution are identified for three different operational modes: bright-field scattering-contrast, phase-contrast and dark-field microscopy. Methods of reducing radiation damage are discussed, including low-dose techniques, cooling or encapsulating the specimen, and the choice of imaging mode, incident-beam diameter and incident-electron energy. Further experiments are suggested as a means of obtaining a better understanding and control of electron-beam damage.

Image simulation for atomic resolution secondary electron image.

It has been demonstrated recently that an atomic resolution secondary electron (SE) image can be achieved with a scanning transmission electron microscope (STEM) equipped with a probe-aberration corrector. Its high sensitivity to the surface structure provides a powerful tool to simultaneously study both surface and bulk structure in the STEM, in the combination with the annular dark field (ADF) image. To quantitatively explain the atomic resolution SE image and retrieve surface-structure information, an image simulation is required. Here, we develop a method to simultaneously calculate, for the first time, the atomic resolution SE and ADF-STEM images, based on the multislice method with a frozen-phonon approximation. An object function for secondary electrons, derived from the inelastic scattering, is used to calculate the intensity distribution of the secondary electrons emitted from each slice. The simulations show that the SE image contrast is sensitive to the surface structure and the electron inelastic mean free path, but insensitive to specimen thickness when the thickness is more than 5 nm. The simulated SE images for SrTiO(3) crystal show good agreement with the experimental observations.

Mechanisms of radiation damage in beam-sensitive specimens, for TEM accelerating voltages between 10 and 300 kV.

Ionization damage (radiolysis) and knock-on displacement are compared in terms of scattering cross section and stopping power, for thin organic specimens exposed to the electrons in a TEM. Based on stopping power, which includes secondary processes, radiolysis is found to be predominant for all incident energies (10-300 keV), even in materials containing hydrogen. For conducting inorganic specimens, knock-on displacement is the only damage mechanism but an electron dose exceeding 1000 C cm(-2) is usually required. Ways of experimentally determining the damage mechanism (with a view to minimizing damage) are discussed.

TEM-EELS: a personal perspective.

The development of electron energy-loss spectroscopy in a transmission electron microscope (TEM-EELS) is illustrated through personal anecdote, highlighting some of the basic principles, instrumentation and personalities involved. The current state of the art is reviewed, together with some challenges for the future.