New approach for the dynamical simulation of CBED patterns in heavily strained specimens

A new method for the dynamical simulation of convergent beam electron diffraction (CBED) patterns is proposed. In this method, the three-dimensional stationary Schrödinger equation is replaced by a two-dimensional time-dependent equation, in which the direction of propagation of the electron beam, variable z, stands as a time. We demonstrate that this approach is particularly well-suited for the calculation of the diffracted intensities in the case of a z-dependent crystal potential. The corresponding software has been developed and implemented for simulating CBED patterns of various specimens, from perfect crystals to heavily strained cross-sectional specimens. Evidence is given for the remarkable agreement between simulated and experimental patterns.     

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.     

Refinement of the 200 structure factor for GaAs using parallel and convergent beam electron nanodiffraction data

We present a new method to measure structure factors from electron spot diffraction patterns recorded under almost parallel illumination in transmission electron microscopes. Bloch wave refinement routines have been developed to refine the crystal thickness, its orientation and structure factors by comparison of experimentally recorded and calculated intensities. Our method requires a modicum of computational effort, making it suitable for contemporary personal computers. Frozen lattice and Bloch wave simulations of GaAs diffraction patterns are used to derive optimised experimental conditions. Systematic errors are estimated from the application of the method to simulated diffraction patterns and rules for the recognition of physically reasonable initial refinement conditions are derived. The method is applied to the measurement of the 200 structure factor for GaAs. We found that the influence of inelastically scattered electrons is negligible. Additionally, we measured the 200 structure factor from zero loss filtered two-dimensional convergent beam electron diffraction patterns. The precision of both methods is found to be comparable and the results agree well with each other. A deviation of more than 20% from isolated atom scattering data is observed, whereas close agreement is found with structure factors obtained from density functional theory [A. Rosenauer, M. Schowalter, F. Glas, D. Lamoen, Phys. Rev. B 72 (2005), 085326-1], which account for the redistribution of electrons due to chemical bonding via modified atomic scattering amplitudes.     

Precise measurement of third-order spherical aberration using low-order zone-axis Ronchigrams

A method for the measurement of third-order spherical aberration coefficients (C(s)) is suggested, using low-order zone-axis Ronchigrams of a crystalline material. The validity of the method is confirmed using simulated and experimental Ronchigrams taken with various probe-forming lens configurations. The precision of the measured C(s) value is drastically improved compared with that obtained from the power spectrum-analysis method. In addition, a method for roughly estimating defocus values is presented.     

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.     

Measurement of twofold astigmatism of probe-forming lens using low-order zone-axis ronchigram

By using a low-order zone-axis ronchigram of a crystalline sample, a simple method for measuring twofold astigmatism of a probe-forming lens is proposed. This method allows precise measurement of the value of astigmatism from only one experimental ronchigram.     

Effect of sample bending on diffracted intensities observed in CBED patterns of plan view strained samples

Convergent beam electron diffraction is used to study the effect of the sample bending on diffracted intensities as observed in transmission electron microscopy (TEM). Studied samples are made of thin strained semiconductor Ga(1-)(x)In(x)As epitaxial layers grown on a GaAs substrate and observed in plan view. Strong variations of the diffracted intensities are observed depending on the thinning process used for TEM foil preparation. For chemically thinned samples, strong bending of the substrate occurs, inducing modifications of both kinematical and dynamical Bragg lines. For mechanically thinned samples, bending of the substrate is negligible. Kinematical lines are unaffected whereas dynamical lines have slightly asymmetric intensities. We analyse these effects using finite element modelling to calculate the sample strain coupled with dynamical multibeam simulations for calculating the diffracted intensities. Our results correctly reproduce the qualitative features of experimental patterns, clearly demonstrating that inhomogeneous displacement fields along the electron beam within the substrate are responsible for the observed intensity modifications.     

Site-specific fracture plane determination using the FIB/TEM

A new method for the determination of the crystallographic indices of planar fracture surfaces is described. The key innovation is the use of a focused ion beam instrument to extract two transmission electron microscopy (TEM) foils from the fracture surface. Selected area diffraction of these foils in the TEM allows the determination of the fracture plane from the cross product of two crystallographic line directions contained within the plane. This allows the indices to be determined from relatively small fracture surfaces, affording fracture plane determinations from facets on polycrystalline samples. The validation of this method using cleavage fracture in pure zinc is described.     

Study of strained-silicon channel metal-oxide-semiconductor field effect transistors by large angle convergent-beam electron diffraction

Strained-silicon p-type metal-oxide-semiconductor field effect transistors (pMOSFETs) have been investigated by large angle convergent-beam electron diffraction (LACBED). Longitudinal compressive strain is induced into the channel region of a p-type strained-silicon channel metal-oxide-semiconductor field effect transistor by a low-cost Ge pre-amorphization implantation for source/drain extension flow. Anomalously large longitudinal compressive strain, up to 2.5 x 10(-2), in the nanometer scale channel region of pMOSFETs has been measured using LACBED. We propose a novel scaling effect for the giant strain enhancement. Our experimental results and model analysis together reveal that the channel strain is inversely proportional to the shrinking channel length.     

STEM nanodiffraction technique for structural analysis of CoPt nanoparticles

Studying the structure of nanoparticles as a function of their size requires a correlation between the image and the diffraction pattern of single nanoparticles. Nanobeam diffraction technique is generally used but requires long and tedious TEM investigations, particularly when nanoparticles are randomly oriented on an amorphous substrate. We bring a new development to this structural study by controlling the nanoprobe of the Bright and Dark Field STEM (BF/DF STEM) modes of the TEM. The particularity of our experiment is to make the STEM nanoprobe parallel (probe size 1 nm and convergence angle <1 mrad) using a fine tuning of the focal lengths of the microscope illumination lenses. The accurate control of the beam position offered by this technique allowed us to obtain diffraction patterns of many single nanoparticles selected in the digital STEM image. By means of this technique, we demonstrate size effects on the order-disorder transition temperature in CoPt nanoparticles when their size is smaller than 3 nm.     

A practical method to detect and correct for lens distortion in the TEM

A practical, offline method for experimental detection and correction for projector lens distortion in the transmission electron microscope (TEM) operating in high-resolution (HR) and selected area electron diffraction (SAED) modes is described. Typical TEM works show that, in the simplest case, the distortion transforms on the recording device, which would be a circle into an ellipse. The first goal of the procedure described here is to determine the elongation and orientation of the ellipse. The second goal is to correct for the distortion using an ordinary graphic program. The same experimental data set may also be used to determine the actual microscope magnification and the rotation between SAED patterns and HR images. The procedure may be helpful in several quantitative applications of electron diffraction and HR imaging, for instance while performing accurate lattice parameter determination, or while determining possible metrical deviations (cell edges and angles) from a given symmetry.     

Determination of chromium valence over the range Cr(0)–Cr(VI) by electron energy loss spectroscopy

Chromium is a redox active 3d transition metal with a wide range of valences (−2 to +6) that control the geochemistry and toxicity of the element. Therefore, techniques that measure Cr valence are important bio/geochemical tools. Until now, all established methods to determine Cr valence were bulk techniques with many specific to a single, or at best, only a few oxidation state(s). We report an electron energy loss spectroscopy (EELS) technique along with an extensive suite of affined reference spectra that together, unlike other methods, can determine Cr valence (or at least constrain the possible valences) at high-spatial resolution (tens-of-nanometer scale) across a wide valence range, Cr(0)–Cr(VI). Fine structure of Cr-L_2,3 edges was parametrized by measurement of the chemical shift of the L₃ edge and the ratio of integrated intensity under the L₃ and L₂ edges. These two parameterizations were correlated to Cr valence and also the dⁿ orbital configuration which has a large influence on L-edge fine structure. We demonstrate that it is not possible to unambiguously determine Cr valence from only one fine-structure parameterization which is the method employed to determine metal valence by nearly all previous EELS studies. Rather, multiple fine-structure parameterizations must be used together if the full range of possible Cr valences is considered. However even with two parameterizations, there are limitations. For example, distinguishing Cr(IV) from Cr(III) is problematic and it may be difficult to distinguish low-spin Cr(II) from Cr(III). Nevertheless, when Cr is known to be divalent, low- and high-spin dⁿ orbital configurations can be readily distinguished.     

Limits to the spatial, energy and momentum resolution of electron energy-loss spectroscopy

We discuss various factors that determine the performance of electron energy-loss spectroscopy (EELS) and energy-filtered (EFTEM) imaging in a transmission electron microscope. Some of these factors are instrumental and have undergone substantial improvement in recent years, including the development of electron monochromators and aberration correctors. Others, such as radiation damage, delocalization of inelastic scattering and beam broadening in the specimen, derive from basic physics and are likely to remain as limitations. To aid the experimentalist, analytical expressions are given for beam broadening, delocalization length, energy broadening due to core-hole and excited-electron lifetimes, and for the momentum resolution in angle-resolved EELS.     

Bandgap measurement of thin dielectric films using monochromated STEM-EELS

High-resolution electron energy-loss spectroscopy (HR-EELS), achieved by attaching electron monochromators to transmission electron microscopes (TEM), has proved to be a powerful tool for measuring bandgaps. However, the method itself is still uncertain, due to Cerenkov loss and surface effects that can potentially influence the quality of EELS data. In the present study, we achieved an energy resolution of about 0.13 eV at 0.1 s, with a spatial resolution of a few nanometers, using a monochromated STEM-EELS technique. We also assessed various methods of bandgap measurement for a-SiNx and SiO₂ thin dielectric films. It was found that the linear fit method was more reliable than the onset reading method in avoiding the effects of Cerenkov loss and specimen thickness. The bandgap of the SiO₂ was estimated to be 8.95 eV, and those of a-SiNx with N/Si ratios of 1.46, 1.20 and 0.92 were measured as 5.3, 4.1 and 2.9 eV, respectively. These bandgap-measurement results using monochromated STEM-EELS were compared with those using Auger electron spectroscopy (AES)-reflective EELS (REELS).     

Experimental and theoretical improvements on understanding of the O K-edge of TeO2

Using an electron monochromator attached to an electron microscope, high energy-resolution electron energy-loss spectra collected from TeO2 have revealed new features in the Oxygen K-edge. Using density-functional theory in the local density and the generalized gradient approximation, we find that core-hole strength of 1.3 gives an excellent fit to our high-resolution experimental data. This indicates that screening is not weak in this oxide, as normally assumed, and that neither the ground state nor a full core-hole model is adequate in quantitative reproduction of the O K-edge in the TeO2 system.     

Composition analysis of semiconductor quantum wells by energy filtered convergent-beam electron diffraction

We show how energy-filtered convergent-beam electron diffraction (EFCBED) patterns can be used to determine the chemical composition of buried semiconductor strained quantum wells. Our method is based on a quantitative analysis of the intensities of high-order Bragg lines in the transmitted disc of EFCBED patterns taken from plan-view samples. This analysis makes it possible to determine the displacement vector R introduced between the top and bottom parts of the matrix by the deformation of the quantum well and consequently to determine its composition. This is illustrated in the case of an In(x)Ga(1-)(x)As quantum well buried in a GaAs matrix. A detailed analysis of the effect of experimental parameters on Bragg lines intensity is performed. In particular, the importance of the choice of the diffraction vector is pointed out. The relative uncertainty on the measurement of the indium content x is found to be lower than 5% and a possible occurrence of slight compositional fluctuations in the (001) growth plane is pointed out.     

A study in the computation time required for the inclusion of strain field effects in Bloch-wave simulations of TEM diffraction contrast images

As transmission electron microscopy (TEM) imaging techniques continue to become more quantitative, interpretation of the experimental images demands that accurate image simulations be computed incorporating all important aspects of the image including: compositional, crystallographic and microscope effects, as well as contrast due to strain fields arising from stresses created by lattice misfit or defects. Incorporation of the effects of strain fields in the simulation of diffraction-contrast TEM images in the Bloch-wave formalism requires the integration of a system of first-order differential equations in order to modify the excitation amplitudes and produce contrast in the image. This integration is computationally demanding with the time for integration scaling as the cube of the number of beams included in the calculation. In order to investigate the computational requirements of the integration, a variety of numerical integration packages were evaluated with respect to timing and accuracy in the simulation of quantum dot, spherical inclusion and screw dislocation images. It was determined that a class of Adams-multistep methods can provide a decrease in computation time ranging from 2 to 4 as compared to the standard Runge-Kutta 4(5) approach depending on the simulation conditions.     

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.