Interferometry using convergent electron diffracted beams plus an electron biprism (CBED + EBI)

Diffracted beam interferometry - Differential phase contrast image of an amorphous thin film material

Differential phase contrast based on diffracted beam interferometry is used to explain the good phase contrast found of an amorphous thin film material deposited on the surface of a gold (Au) crystal substrate. An electron biprism is used to interfere two symmetrically diffracted beams generated by the Au crystal substrate that carried the phase of the amorphous material specimen. Bragg diffraction from the Au crystal substrate is used to explain why the phase of the amorphous thin film material is so well phase imaged. The phase of the amorphous material that was deposited on the specimen's upper surface of the Au crystal substrate is canceled and thus not revealed in the phase image whereas the phase due to the amorphous material deposited on the bottom surface of the Au crystal substrate does not cancel due to having a lateral phase shift in the amorphous material specimen plane proportional to the substrate thickness and Bragg angle of the diffracted beams. The lateral phase shift enabled differential phase contrast of the amorphous material specimen.

Phase imaging dislocations using diffracted beam interferometry

A phase imaging method that measures the phase shift existing at a dislocation's core is described. The method uses the interference of two symmetrically diffracted beams on the optic axis by means of an electron biprism. Each diffracted beam carries half the phase of the dislocation core. When combined, the entire phase shift of the dislocation core is obtained.

Self-interference of split HOLZ line (SIS-HOLZ) for z-dependent atomic displacement measurement: Theoretical discussion

A characteristic of the majority of semiconductors is the presence of lattice strain varying with the nanometer scale. Strain originates from the lattice mismatch between layers of different composition deposited during epitaxial growth. Strain can increase the mobility of the charge carriers by the band gap reduction. So, measuring atomic displacement inside crystals is an important field of interest in semiconductor industry. Among all available transmission electron microscopy techniques offering nano-scale resolution measurements, convergent beam electron diffraction (CBED) patterns show the highest sensitivity to the atomic displacement. Higher Order Laue Zone (HOLZ) lines split by small non-uniform variations of lattice constant allowing to measure the atomic displacement through the crystal. However, it could only reveal the atomic displacement in two dimensions, i.e., within the x-y plane of the thin film of TEM specimen. The z-axis atomic displacement which is along the path of the electron beam has been missing. This information can be obtained by recovering the phase information across the split HOLZ line using the self-interference of the split HOLZ line (SIS-HOLZ). In this work, we report the analytical approach used to attain the phase profile across the split HOLZ line. The phase profile is studied for three different atomic displacement fields in the Si substrate at 80nm away from its interface with Si/Si_0.8Ge_0.2 superlattices.

A nanofabricated, monolithic, path-separated electron interferometer

Progress in nanofabrication technology has enabled the development of numerous electron optic elements for enhancing image contrast and manipulating electron wave functions. Here, we describe a modular, self-aligned, amplitude-division electron interferometer in a conventional transmission electron microscope. The interferometer consists of two 45-nm-thick silicon layers separated by 20 μm. This interferometer is fabricated from a single-crystal silicon cantilever on a transmission electron microscope grid by gallium focused-ion-beam milling. Using this interferometer, we obtain interference fringes in a Mach-Zehnder geometry in an unmodified 200 kV transmission electron microscope. The fringes have a period of 0.32 nm, which corresponds to the [1̄1̄1] lattice planes of silicon, and a maximum contrast of 15%. We use convergent-beam electron diffraction to quantify grating alignment and coherence. This design can potentially be scaled to millimeter-scale, and used in electron holography. It could also be applied to perform fundamental physics experiments, such as interaction-free measurement with electrons.

Electron holography for fields in solids: problems and progress

Electron holography initially was invented by Dennis Gabor for solving the problems raised by the aberrations of electron lenses in Transmission Electron Microscopy. Nowadays, after hardware correction of aberrations allows true atomic resolution of the structure, for comprehensive understanding of solids, determination of electric and magnetic nanofields is the most challenging task. Since fields are phase objects in the TEM, electron holography is the unrivaled method of choice. After more than 40 years of experimental realization and steady improvement, holography is increasingly contributing to these highly sophisticated and essential questions in materials science, as well to the understanding of electron waves and their interaction with matter.

Measurement of spatial coherence of electron beams by using a small selected-area aperture

A new method for measuring the spatial coherence of an electron beam in a transmission electron microscope is proposed. In this method, an Airy pattern produced by a circular selected-area (SA) aperture with an effective diameter of several nanometers is analyzed to obtain the degree of coherence as a function of separation in the specimen plane. Using typical TEM illumination conditions, demonstrative measurements were carried out to determine the spatial coherence length, angular size of the electron source and shape of the coherence function. Based on the results, it was shown that the ratio of the spatial coherence length to the beam radius is about 5% for a condenser aperture with a diameter of 100 μm. This means that perfectly coherent illumination exists within the small SA aperture for beam diameters larger than 560 nm. As an example application of these results, the advantage of SA diffraction over nano-beam diffraction in electron diffractive imaging is discussed. The proposed method is unaffected by temporal coherence or geometric aberrations of the lenses. The possibility of carrying out future measurements using SA apertures with conventional sizes is also discussed.

Electron beam coherence measurements using diffracted beam interferometry/holography

The intensity and coherence of elastically and inelastically scattered electrons have been studied by the interference of electron-diffracted beams using a method of diffracted beam interferometry/holography (DBI/H). In the interferograms produced, fringes were found to exist from low to high scattering angles. The intensity and coherence of the fringes are useful for understanding the contrast mismatch between experimental and simulated images found in atomic resolution images of crystals produced by transmission electron microscopy (TEM) and annular dark-field (ADF) scanning transmission electron microscopy (STEM). The fringes disappear when the interfering beams are separated from an exact overlay position, which produces a measurement of the beam's lateral coherence and holds promise for measuring the coherence of the respective quasi-particles associated with the energy loss electrons.

Fringe contrast in inelastic LACBED holography

We discuss diffraction holography in a scattering geometry reported by Herring [Ultramicroscopy 104 (2005) 261, Ultramicroscopy 106 (2006) 960] and interpreted in terms of the density matrix of the fast electrons. Whereas the previous description used an approximation replacing the LACBED by a CBED geometry and consequently left some doubts about the conclusions (namely the non-detectability of the MDFF) we now fully include the Fresnel propagator and the biprism operator in order to calculate the density matrix of the inelastically scattered electrons in LACBED geometry. We show that a defocus on the biprism with respect to the sample does not cause a significant effect on the fringe patterns that are formed when the discs are exactly overlapping. An important difference to the CBED geometry is however that the fringe contrast decreases when the shear deviates from a reciprocal lattice vector. This should enable to measure the spatial coherence for smaller shears than is possible in image holography.

Energy-filtered electron-diffracted beam holography

A method of energy-filtered electron holography is described where any two electron-diffracted beams can be interfered using an electron biprism. A Gatan image filter is used to select the energy loss of the electrons produced in the holograms. Gallium arsenide is used as the TEM specimen. This method of microscopy confirms that fringes extending beyond a limiting aperture were due to inelastically scattered electrons and specifically electrons scattered from the bulk plasmon. The degree of coherence of the zero-loss and energy-loss electrons were high and measured to be approximately 0.3, which was maintained even for the high energy-loss electrons up to 100 eV. Future systematic studies using this method should help understand the Stobbs factor and contribute to the development of quantitative high-resolution electron microscopy.