Electron Image Plane Off-axis Holography of Atomic Structures

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.

Probing Light Atoms at Subnanometer Resolution: Realization of Scanning Transmission Electron Microscope Holography

Atomic resolution imaging of light elements in electron-transparent materials has long been a challenge. Biomolecular materials, for example, are rapidly altered by incident electrons. We demonstrate a scanning transmission electron microscopy (STEM) technique, called STEM holography, capable of efficient structural analysis of beam-sensitive nanomaterials. STEM holography measures the absolute phase and amplitude of electrons passed through a specimen via interference with a vacuum reference wave. We use an amplitude-dividing nanofabricated grating to prepare multiple beams focused at the sample. We configure the postspecimen microscope imaging system to overlap the beams, forming an interference pattern. We record and analyze the pattern at each 2D-raster-scan-position, reconstructing the complex object wave. As a demonstration, we image gold nanoparticles on an amorphous carbon substrate at 2.4 Å resolution. STEM holography offers higher contrast of the carbon while maintaining gold atomic lattice resolution compared to high angle annular dark field STEM.

Coherent and incoherent effects on the imaging and scattering process in transmission electron microscopy and off-axis electron holography

The standard treatment for the different plane wave components of incoming electrons in transmission electron microscope imaging is an incoherent superposition. However, projectile electrons in transmission electron microscopes are localized in space, and therefore have to be described as coherent wave-packets. Moreover, recent developments towards ultrafast electron microscopy and dynamic transmission electron microscopy require a description using highly localized wave-packets. Here we will extend the standard stationary modeling of the elastic scattering processes in high-resolution microscopy to a fully time-dependent approach, by using the direct solution of the time-dependent Schrödinger equation. We will draw the connection to the detection of coherent wave-packets, giving explicit implications for the reconstructed waves in off-axis electron holography. Additionally the description of incoherent aberrations is extended to incorporate the influence of the biprism accurately, leading to a modified form of the damping of spatial frequencies.

Aberration correction past and present

Electron lenses are extremely poor: if glass lenses were as bad, we should see as well with the naked eye as with a microscope! The demonstration by Otto Scherzer in 1936 that skillful lens design could never eliminate the spherical and chromatic aberrations of rotationally symmetric electron lenses was therefore most unwelcome and the other great electron optician of those years, Walter Glaser, never ceased striving to find a loophole in Scherzer's proof. In the wartime and early post-war years, the first proposals for correcting C(s) were made and in 1947, in a second milestone paper, Scherzer listed these and other ways of correcting lenses; soon after, Dennis Gabor invented holography for the same purpose. These approaches will be briefly summarized and the work that led to the successful implementation of quadupole-octopole and sextupole correctors in the 1990 s will be analysed. In conclusion, the elegant role of image algebra in describing image formation and processing and, above all, in developing new methods will be mentioned.

Off-axis electron holography in an aberration-corrected transmission electron microscope

Electron holography allows the reconstruction of the complete electron wave, and hence offers the possibility of correcting aberrations. In fact, this was shown by means of the uncorrected CM30 Special Tübingen transmission electron microscope (TEM), revealing, after numerical aberration correction, a resolution of approximately 0.1 nm, both in amplitude and phase. However, it turned out that the results suffer from a comparably poor signal-to-noise ratio. The reason is that the limited coherent electron current, given by gun brightness, has to illuminate a width of at least four times the point-spread function given by the aberrations. As, using the hardware corrector, the point-spread function shrinks considerably, the current density increases and the signal-to-noise ratio improves correspondingly. Furthermore, the phase shift at the atomic dimensions found in the image plane also increases because the collection efficiency of the optics increases with resolution. In total, the signals of atomically fine structures are better defined for quantitative evaluation. In fact, the results achieved by electron holography in a Tecnai F20 Cs-corr TEM confirm this.

High-resolution TEM and the application of direct and indirect aberration correction

Aberration correction leads to a substantial improvement in the directly interpretable resolution of transmission electron microscopes. Correction of the aberrations has been achieved electron-optically through a hexapole-based corrector and also indirectly by computational analysis of a focal or tilt series of images. These direct and indirect methods are complementary, and a combination of the two offers further advantages. Materials characterization has benefitted from the reduced delocalization and higher resolution in the corrected images. It is now possible, for example, to locate atomic columns at surfaces to higher accuracy and reliability. This article describes the JEM-2200FS in Oxford, which is equipped with correctors for both the image-forming and probe-forming lenses. Examples of the use of this instrument in the characterization of nanocrystalline catalysts are given together with initial results combining direct and indirect methods. The double corrector configuration enables direct imaging of the corrected probe, and a potential confocal imaging mode is described. Finally, modifications to a second generation instrument are outlined.

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.

Statistical estimation of atomic positions from exit wave reconstruction with a precision in the picometer range

The local structure of Bi4W2/3Mn1/3O8Cl is determined using quantitative transmission electron microscopy. The electron exit wave, which is closely related to the projected crystal potential, is reconstructed and used as a starting point for statistical parameter estimation. This method allows us to refine all atomic positions on a local scale, including those of the light atoms, with a precision in the picometer range. Using this method one is no longer restricted to the information limit of the electron microscope. Our results are in good agreement with x-ray powder diffraction data demonstrating the reliability of the method. Moreover, it will be shown that local effects can be interpreted using this approach.

Determining the radial pair-distribution function within intergranular amorphous films by numerical nanodiffraction

We report on an alternative method to electron nanodiffraction and fluctuation microscopy for the determination of the reduced density function G(r) of amorphous areas with small cross-sections. This method is based on the numerical extraction of diffraction data from the complex-valued exit-face wave function as obtained by HRTEM focal series reconstruction or electron holography. Since it is thus possible to obtain "diffraction data" from rectangular areas of any aspect ratio, this method is particularly suited for intergranular glassy films of only 1-2 nm width, but lengths of several 100 nm. A critical comparison of this method with the already established nanodiffraction and fluctuation microscopy will be made.

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.

Off-axis electron holography with a dual-lens imaging system and its usefulness in 2-D potential mapping of semiconductor devices

A variable magnification electron holography, applicable for two-dimensional (2-D) potential mapping of semiconductor devices, employing a dual-lens imaging system is described. Imaging operation consists of a virtual image formed by the objective lens (OL) and a real image formed in a fixed imaging plane by the objective minilens. Wide variations in field of view (100-900 nm) and fringe spacing (0.7-6 nm) were obtained using a fixed biprism voltage by varying the total magnification of the dual OL system. The dual-lens system allows fringe width and spacing relative to the object to be varied roughly independently from the fringe contrast, resulting in enhanced resolution and sensitivity. The achievable fringe width and spacing cover the targets needed for devices in the semiconductor technology road map from the 350 to 45 nm node. Two-D potential maps for CMOS devices with 220 and 70 nm gate lengths were obtained.

"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.

Mean free paths for inelastic electron scattering in silicon and poly(styrene) nanospheres

The mean free paths for inelastic electron scattering, lambda(in), in silicon [Si] and poly(styrene) [PS] have been measured using off-axis electron holography in a field-emission transmission electron microscope (FEG TEM). The holographic imaging method determines both quantitative wave phase information as well as elastic energy-filtered wave amplitude information. Using the energy-filtered amplitude data, two-dimensional t/lambda(in) images are reconstructed. The present work uses spherical nanoparticles as samples, so the sample thickness at any point in a two-dimensional image can be calculated knowing the center and radius of the projected nanosphere. The thickness contribution to t/lambda(in) is removed to obtain quantitative lambda(in) values. This work finds values of lambda(i)Si = 53.8 +/- 5.5 and 88.6 +/- 6.9 nm, and lambda(PS) = 78.1 +/- 3.4 and 113.0 +/- 5.9 nm for 120 and 200 keV incident electron energies, respectively.

Ferroelectric electron holography

Ferroelectrics are increasingly important as materials in semiconductor technology, e.g. for building non-volatile memory chips. For optimisation of the properties of such devices, there is an urgent need for methods, which analyse the ferroelectric properties at nanometer scale. Furthermore, the basic understanding of the interaction of ferroelectrics with electrons in the transmission electron microscopy is still incomplete. It is shown that electron holography offers a promising way to understand and investigate ferroelectrics in the electron microscope.

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.

Does a monochromator improve the precision in quantitative HRTEM?

This paper addresses the question as to what extent the incorporation of a monochromator in an electron microscope can enhance the performance of high resolution transmission electron microscopy (HRTEM). The monochromator will reduce the chromatic aberration, and hence the information limit, at the expense of beam current, leading to a decrease in signal intensity and a corresponding decrease in signal-to-noise ratio (SNR). Both aspects, information limit and SNR, have been included in a quantitative evaluation based on the statistical precision with which the position of an atom column can be estimated. It is shown that the effect of a monochromator on the attainable precision depends on the microscope and monochromator parameters, as well as on the characteristics of the object.