Martin Linck

Efficient diffractive phase optics for electrons

Electron diffraction gratings can be used to imprint well-defined phase structure onto an electron beam. For example, diffraction gratings have been used to prepare electron beams with unique phase dislocations, such as electron vortex beams, which hold promise for the development of new imaging and spectroscopy techniques for the study of materials. However, beam intensity loss associated with absorption, scattering, and diffraction by a binary transmission grating drastically reduces the current in the beam, and thus the possible detected signal strength it may generate. Here we describe electron-transparent phase gratings that efficiently diffract transmitted electrons. These phase gratings produce electron beams with the high current necessary to generate detectable signal upon interaction with a material. The phase grating design detailed here allows for fabrication of much more complex grating structures with extremely fine features. The diffracted beams produced by these gratings are widely separated and carry the designed phase structure with high fidelity. In this work, we outline a fabrication method for high-efficiency electron diffraction gratings and present measurements of the performance of a set of simple prototypical gratings in a transmission electron microscope. We present a model for electron diffraction gratings that can be used to optimize the performance of diffractive electron optics. We also present several new holograms that utilize manipulation of phase to produce new types of highly efficient electron beams.

Imaging modes for potential mapping in semiconductor devices by electron holography with improved lateral resolution.

Electron holography is the highest resolving tool for dopant profiling at nanometre-scale resolution. In order to measure the object areas of interest in a hologram, both a wide field of view and a sufficient lateral resolution are required. The usual path of rays for recording holograms with an electron biprism using the standard objective lens does not meet these requirements, because the field of view amounts to some 10 nm only, however, at a resolution of 0.1 nm better than needed here. Therefore, instead of the standard objective lens, the Lorentz lens is widely used for holography of semiconductors, since it provides a field of view up to 1000 nm at a sufficient lateral resolution of about 10nm. Since the size of semiconductor structures is steadily shrinking, there is now a need for better lateral resolution at an appropriate field of view. Therefore, additional paths of rays for recording holograms are studied with special emphasis on the parameters field of view and lateral resolution. The findings allow an optimized scheme with a field of view of 200 nm and a lateral resolution of 3.3 nm filling the gap between the existing set-ups. In addition, the Lorentz lens is no longer required for investigation of non-magnetic materials, since the new paths of rays are realized with the standard objective lens and diffraction lens. An example proves the applicability of this arrangement for future semiconductor technology.

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.

Off-axis electron holography: Materials analysis at atomic resolution

Abstract In high-resolution off-axis electron holography, the correction of coherent aberrations allows the quantitative interpretation of the amplitude and phase of the object wave up to the information limit of the electron microscope. Since the measured object phase is directly related to the projected atomic potential for sufficiently thin samples, off-axis electron holography is expected to allow distinguishing of different elements in the reconstructed phase image (“holographic materials analysis”). This has already been verified with the example of Ga and As. However, simulations of the atomic phase shift reveal that the interpretation of the measured phase shift in terms of atomic species is generally rather complex. The findings suggest that, in some cases, the requirements as to lateral resolution and phase detection limit will be met only by electron microscopes of the next generation.

Origins and demonstrations of electrons with orbital angular momentum

The surprising message of Allen et al. (Allen et al. 1992 Phys. Rev. A 45, 8185 (doi:10.1103/PhysRevA.45.8185)) was that photons could possess orbital angular momentum in free space, which subsequently launched advancements in optical manipulation, microscopy, quantum optics, communications, many more fields. It has recently been shown that this result also applies to quantum mechanical wave functions describing massive particles (matter waves). This article discusses how electron wave functions can be imprinted with quantized phase vortices in analogous ways to twisted light, demonstrating that charged particles with non-zero rest mass can possess orbital angular momentum in free space. With Allen et al. as a bridge, connections are made between this recent work in electron vortex wave functions and much earlier works, extending a 175 year old tradition in matter wave vortices. This article is part of the themed issue ‘Optical orbital angular momentum’.

Automatic software correction of residual aberrations in reconstructed HRTEM exit waves of crystalline samples

We develop an automatic and objective method to measure and correct residual aberrations in atomic-resolution HRTEM complex exit waves for crystalline samples aligned along a low-index zone axis. Our method uses the approximate rotational point symmetry of a column of atoms or single atom to iteratively calculate a best-fit numerical phase plate for this symmetry condition, and does not require information about the sample thickness or precise structure. We apply our method to two experimental focal series reconstructions, imaging a β-Si3N4 wedge with O and N doping, and a single-layer graphene grain boundary. We use peak and lattice fitting to evaluate the precision of the corrected exit waves. We also apply our method to the exit wave of a Si wedge retrieved by off-axis electron holography. In all cases, the software correction of the residual aberration function improves the accuracy of the measured exit waves.

Aberration-Corrected STEM by Means of Diffraction Gratings

In the past 15 years, the advent of aberration correction technology in electron microscopy has enabled materials analysis on the atomic scale. This is made possible by precise arrangements of multipole electrodes and magnetic solenoids to compensate the aberrations inherent to any focusing element of an electron microscope. Here, we describe an alternative method to correct for the spherical aberration of the objective lens in scanning transmission electron microscopy (STEM) using a passive, nanofabricated diffractive optical element. This holographic device is installed in the probe forming aperture of a conventional electron microscope and can be designed to remove arbitrarily complex aberrations from the electrons wave front. In this work, we show a proof-of-principle experiment that demonstrates successful correction of the spherical aberration in STEM by means of such a grating corrector (GCOR). Our GCOR enables us to record aberration-corrected high-resolution high-angle annular dark field (HAADF-) STEM images, although yet without advancement in probe current and resolution. Improvements in this technology could provide an economical solution for aberration-corrected high-resolution STEM in certain use scenarios.

Atomic-resolution Imaging Using Cs-corrected Vortex Beams

Phase gratings have been shown to produce electron beams with orbital angular momentum as demonstrated by numerous groups, and show promise for electron magnetic circular dichroism (EMCD) at the atomic scale [1, 2]. A linear diffraction grating will produce diffracted beams with a separation determined by the pitch or spacing between grating lines. A grating with a central line that forks into j + 1 central lines will produce a set of diffracted beams each containing discrete units of orbital angular momentum m = j × n in the n th diffraction order [2]. The discontinuity in the center of the grating imparts a “vortex”-type phase on the diffracted beams. We have built such a forked grating with one discontinuity, a radius of 30 m, and a grating pitch of 80 nm using focused ion beam patterning on a 50 nm thick SiN window. Figure 1 shows a low-magnification SEM image of the grating, and the inset shows the discontinuity (fork) in the center at higher magnification. The SiN thin film was patterned as a phase grating rather than an amplitude grating, and thus the 30 nm trench depth does not extend through the full thickness of the SiN thin film. Amplitude gratings have a theoretical maximum diffraction efficiency of 10.1% into the first order, but this grating achieves ~20% efficiency due to the phase grating design. High diffraction efficiency is a critical consideration for the application of diffractive optics in STEM imaging and spectroscopy.

High-Resolution Electron Holography on Ferroelectrics

Within the continuing process of miniaturization in information technology analytical tools are required to characterize materials in terms of electric and magnetic fields on the nanometer scale. In this discipline, off-axis electron holography has proven to be a measuring talent. The holographic reconstruction offers an access to the complete complex object wave, i.e. amplitude and phase of the object-modulated electron wave with all details from largest area information up to the resolution limit of the microscope [1].

Electron Microscopy with Structured Electrons

Nanofabricated diffractive optics are new tools for coherently dividing and manipulating electron wavefunctions, similar to how spatial light modulators are used to engineer light waves in optics. For example, diffraction holograms can be used in a scanning transmission electron microscope to remove aberrations [1], implement new types of interferometric phase contrast [2,3], and produce electron probes with phase vortices and quantized angular momentum [4,5].