The influence of relativistic energy losses on bandgap determination using valence EELS

Since monochromated transmission electron microscopes have become available, the determination of bandgaps and optical properties using electron energy loss spectrometry (EELS) has again attracted interest. The underlying idea is very simple: below the bandgap energy no transitions can contribute to the valence EELS signal. However, the bandgap cannot be directly read out from the recorded data. Therefore the optical properties cannot be determined correctly from the low loss using the Kramers-Kronig relations. We will discuss under which conditions relativistic effects may be suppressed. It is demonstrated that scanning TEM (STEM) geometry is not applicable for most bandgap measurements.     

Magnetic circular dichroism in EELS: towards 10 nm resolution

We describe a new experimental setup for the detection of magnetic circular dichroism with fast electrons (EMCD). As compared to earlier findings the signal is an order of magnitude higher, while the probed area could be significantly reduced, allowing a spatial resolution of better than 40 nm. A simplified analysis of the experimental results is based on the decomposition of the mixed dynamic form factor S(q-->,q-->('),E) into a real part related to the scalar product and an imaginary part related to the vector product of the scattering vectors q--> and q-->('). Following the recent detection of chiral electronic transitions in the electron microscope the present experiment is a crucial demonstration of the potential of EMCD for nanoscale investigations.     

Investigation of hole states near the Fermi level in Nb(1-)(x)Mg(x)B(2) by electron energy-loss spectroscopy and first-principles calculations

The fine structures of the electron energy-loss spectra (EELS) for the B-K edge have been examined in NbB(2) and superconducting Nb(0.75)Mg(0.25)B(2). The experimental results are analyzed based on the calculations of density functional theory (DFT) using the Wien2k code. The results of the EELS spectra and the angular decomposition of the density of states (DOS) reveal that both the B p(z) and B p(x)+p(y) states in NbB(2) have large weights at the Fermi energy due to intersheet covalent bonding with notable hybridization between the Nb 4d and B 2p states. This kind of hybridization also results in different core-hole behaviors for the B-K edge in two orthogonal crystallographic orientations. The best fit between experimental and theoretical data is achieved with consideration of the core-hole effect of the B 1s states, in particular for the q perpendicular c spectra. Analysis of the electronic structure of the Nb(1-)(x)Mg(x)B(2) superconductors suggests that confinement of the intersheet covalent bonding is likely to be favorable for the improvement of superconductivity in this kind of materials.     

Model-based quantification of EELS spectra: treating the effect of correlated noise

Correlated noise is generally present in experimentally recorded electron energy loss spectra due to a non-ideal electron detector. In this contribution we describe a method to experimentally measure the noise properties of the detector as well as the consequences it has for model-based quantification using maximum likelihood. The effect of the correlated noise on the maximum likelihood fitting results can be shown to be negligible for the estimated (co)variance of the parameters while an experimentally obtained scaling factor is required to correct the likelihood ratio test for the reduction of noise power with frequency. Both effects are derived theoretically under a set of approximations and tested for a range of signal-to-noise values using numerical experiments. Finally, an experimental example shows that the correction for correlated noise is essential and should always be included in the fitting procedure.     

The impact of surface and retardation losses on valence electron energy-loss spectroscopy

The inelastic scattering of fast electrons transmitting thin foils of silicon (Si), silicon nitride (Si(3)N(4)), gallium arsenide (GaAs), gallium nitride (GaN) and cadmium selenide (CdSe) was analyzed using dielectric theory. In particular, the impact of surface and bulk retardation losses on valence electron energy-loss spectroscopy (VEELS) was studied as a function of the foil thickness. It is shown that for the materials analyzed, surface and retardation losses can cause a systematic, thickness-dependent modulation of the dielectric volume losses, which can hamper the determination of the bulk dielectric data as well as the identification of band-gap and interband transition energies by VEELS. For Si and GaAs, where the dielectric function is strongly peaked with high absolute values, retardation losses lead to additional intensity maxima in the spectrum. For thin films of these materials (below approximately 100 nm), the additional intensity maxima are related to retardation effects due to the finite size of the sample leading to the excitation of guided light modes. For thicker films, exceeding about 200 nm, the intensity maxima are caused by bulk retardation losses, i.e., Cerenkov losses. Although thickness-dependent modulations were observed for Si(3)N(4), GaN and CdSe, the form of the dielectric functions and their lower maxima, means that for TEM samples < 100 nm thick, the band-gap energies of these materials can be accurately identified by VEELS. Guidelines are given that allow for forecasting the impact of surface and retardation losses on VEELS.     

Accuracy and precision in model based EELS quantification

We present results on model based quantification of electron energy loss spectra (EELS), focusing on the factors that influence accuracy and precision in determining chemical concentrations. Several sources of systematical errors are investigated. The spectrometer entrance aperture determines the collection angle, and the effects of its position with respect to the transmitted beam are investigated, taking into account the diffraction by the crystal structure. The effect of the orientation of the sample is tested experimentally and theoretically on SrTiO3, and finally, a simulated experiment on c-BN at different thicknesses confirms the superior results of the model based method with respect to the conventional method. A test on a set of experimental reference compounds is presented, showing that remarkably good accuracy can be obtained. Recommendations are given to achieve high accuracy and precision in practice.     

Prospects for analyzing the electronic properties in nanoscale systems by VEELS

Valence electron energy-loss spectroscopy in the scanning transmission electron microscope can provide detailed information on the electronic structure of individual nanostructures. By employing the latest advances in electron optical devices, such as a probe aberration corrector and an electron monochromator, the probe size, spectroscopic resolution, probe current and primary electron energy can be varied over a large range. This flexibility is particularly important for nanostructures where each of these variables needs to be carefully counterbalanced in order to collect spectroscopic data without altering the integrity of the sample. Here the implementation of valence electron energy-loss spectroscopy to the study of nanostructures is discussed, with particular mention to the theoretical understanding of each of the contributions to the overall spectrum.     

Volcano structure in atomic resolution core-loss images

A feature commonly present in simulations of atomic resolution electron energy loss spectroscopy images in the scanning transmission electron microscope is the volcano or donut structure. In the past this has been understood in terms of a geometrical perspective using a dipole approximation. It is shown that the dipole approximation for core-loss spectroscopy begins to break down as the probe forming aperture semi-angle increases, necessitating the inclusion of higher order terms for a quantitative understanding of volcano formation. Using such simulations we further investigate the mechanisms behind the formation of such structures in the single atom case and extend this to the case of crystals. The cubic SrTiO3 crystal is used as a test case to show the effects of nonlocality, probe channelling and absorption in producing the volcano structure in crystal images.     

Imaging Si nanoparticles embedded in SiO(2) layers by (S)TEM-EELS

Fabrication of systems in which Si nanoparticles are embedded in a thin silica layer is today mature for non-volatile memory and opto-electronics applications. The control of the different parameters (position, size and density) of the nanoparticles population is a key point to optimize the properties of such systems. A review of dedicated transmission electron microscopy (TEM) methods, which can be used to measure these parameters, is presented with an emphasis on those relying on electron energy-loss spectroscopy (EELS). Defocused bright-field imaging can be used in order to determine topographic information of a whole assembly of nanoparticles, but it is not efficient for looking at individual nanoparticles. High-resolution electron imaging or dark-field imaging can be of help in the case of crystalline particles but they always provide underestimated values of the nanocrystals population. EELS imaging in the low-energy-loss domain around the Si plasmon peak, which gives rise to strong signals, is the only way to visualize all Si nanoparticles within a silica film and to perform reliable size and density measurements. Two complementary types of experiments are investigated and discussed more extensively: direct imaging with a transmission electron microscope equipped with an imaging filter (EFTEM) and indirect imaging from spectrum-imaging data acquired with a scanning transmission electron microscope equipped with a spectrometer (STEM-PEELS). The direct image (EFTEM) and indirect set of spectra (STEM-PEELS) are processed in order to deliver images where the contribution of the silica matrix is minimized. The contrast of the resulting images can be enhanced with adapted numerical filters for further morphometric analysis. The two methods give equivalent results, with an easier access for EFTEM and the possibility of a more detailed study of the EELS signatures in the case of STEM-PEELS. Irradiation damage in such systems is also discussed.     

Mapping of valence energy losses via energy-filtered annular dark-field scanning transmission electron microscopy

The advent of electron monochromators has opened new perspectives on electron energy-loss spectroscopy at low energy losses, including phenomena such as surface plasmon resonances or electron transitions from the valence to the conduction band. In this paper, we report first results making use of the combination of an energy filter and a post-filter annular dark-field detector. This instrumental design allows us to obtain energy-filtered (i.e. inelastic) annular dark-field images in scanning transmission electron microscopy of the 2-dimensional semiconductor band-gap distribution of a GaN/Al₄₅Ga₅₅N structure and of surface plasmon resonances of silver nanoprisms. In comparison to other approaches, the technique is less prone to inelastic delocalization and relativistic artefacts. The mixed contribution of elastic and inelastic contrast is discussed.     

On some contrast reversals in SEM: application to metal/insulator systems

Contrast changes of SEM images with experimental conditions (beam energy, angle of detection, etc.) are analyzed by combining physical arguments based on secondary electron emission (SEE) to instrumental arguments involving detection. Possible occurrences of contrast reversals are explored to illustrate these changes in a striking manner. Deduced from SEE yield data, simulated SEM images show a material contrast reversal for a Pt/quartz specimen, a result partly supported by real images of a Cr/quartz integrated circuit. A shift of reversal energy with the detector's position is deduced from a difference in secondary electrons (SE) angular distributions between metals and insulators. Similarly, changes of topographic contrast with detection conditions, specimen composition and angle of tilt are investigated and a possible contrast reversal is again indicated. Finally, it is shown how charging contrast deduced from the expected evolution of SEE yield during irradiation is amplified by in-lens detection: a point illustrated by a contrast reversal of images of SiC particles. The main application concerns a proper interpretation of SEM images that is essential in the investigation of devices obtained from lithographic processes. The discussion on material contrast outlines the difficulty in generalizing the present analysis based on published data and experimental strategies based on implementing specific attachments in the SEM or on biasing the specimen holder are suggested.     

Response analysis for identifying the origin of photo-modulated current contrasts in scanning tunneling microscopic imaging semiconductor surfaces

Inhomogeneities in semiconductor solids can be imaged by two-dimensional mapping of the amplitude of periodically modulated tip current in scanning tunneling microscopy that is induced by illumination of semiconductor samples with a chopped light. It has been shown that it is possible to distinguish between plural origins of the photo-modulated current by analyzing the response properties of the current signal. A judicial choice of the modulation frequency is important for the required contrasts to be obtained.     

A systematic approach to choosing parameters for modelling fine structure in electron energy-loss spectroscopy

A potential methodology is presented for the systematic prediction of EELS edges using DFT, suitable for codes that calculate ELNES for a specific atom in a unit cell. The method begins with the selection of a unit cell, chosen as the smallest cell that still provides a physically valid representation of the bulk material. Within this small cell, a single electron core–hole is included in the atom for which the EELS ionisation edge is to be calculated. The basis-set size and k-point mesh of the DFT calculation are converged specifically against the predicted EELS result. Subsequently, the cell size is increased until the theoretical core–holes no longer interfere. At this point one can then modify the exact core–hole approximation. This methodology was applied to the new EELS module of the CASTEP pseudopotential DFT code, as well as the all-electron code Wien2k. Aluminium K edges were investigated for various aluminium metal systems. It was observed that as the cell size was increased the predicted EELS result became less sensitive to the exact core–hole approximation used. It was noted however that due to high screening in metals a ground state single cell calculation is often acceptable. The semiconductor aluminium nitride (wurtzite form) was also investigated. It was observed that for both Wien2k and CASTEP, with careful convergence of the key DFT code parameters, single cell ground state calculations gave a reasonable agreement with experiment, contrary to what might be expected for a semiconductor with a large band gap. This was particularly true of the Wien2k result. Given the greater computational effort required for supercell calculations, these results are likely to form the beginnings of a detailed investigation into accepted methods of ELNES predictions.     

The continuum normalization method for quantification of X-ray spectra in biological microanalysis. 1. Generalized bremsstrahlung production cross-sections and analysis using standards

The thin self-supporting biological specimens used for quantitative X-ray microanalysis are problematical because the sections are most unlikely to be uniform in thickness or density, so the intensities of the characteristic lines alone are not a good measure of composition. The method developed to overcome these problems was introduced by T. A. Hall in 1971 and uses the bremsstrahlung or continuum intensity recorded in the X-ray spectrum to normalize each characteristic line, and hence is frequently referred to as the continuum normalization (CN) procedure.
  Reformulating the CN method of quantification in terms of generalized cross-sections and calculating more accurate values of bremsstrahlung production using a formula allows us a better understanding of the options open to the analyst of biological thin sections by which the errors in the measurement may be reduced. If one chooses to use the original Hall (1971 ) method using Kramers cross-sections, the window measuring the continuum for normalization should be set in the 4–7 keV region for typical scanning electron microscope and microprobe beam energies, 20–40 kV, and above 10 keV for transmission electron microscope energies of 80 kV and above. Although it is clear that peak counts must not contribute to the white count, the window should be as wide as possible to reduce statistical errors.