Electron Holography of Long-Range Electrostatic Fields

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.

Mapping the electrical properties of semiconductor junctions--the electron holographic approach

The need to determine the electrical properties of semiconductor junctions with high spatial resolution is as pressing now as ever. One technique that offers the possibility of quantitative high-resolution mapping of two- and three-dimensional electrostatic potential distributions is off-axis electron holography. In this study, we review some of the issues associated with interpreting phase shifts measured using off-axis electron holography, and we describe how a quantitative determination of the dopant-related electrostatic potential can be achieved for device structures. Issues that include the presence of surface "dead" layers, external electrostatic fringing fields, variations in specimen thickness and dynamical diffraction are discussed, and their impact on the quantification of results obtained using off-axis electron holography is examined.

Electron optical phase-shifts by Fourier methods: Analytical versus numerical calculations

The theoretical framework for the computation of electromagnetic fields and electron optical phase-shifts in Fourier space has been recently applied to objects with long-range fringing fields, such as reverse-biased p-n junctions and magnetic stripe domains near a specimen edge. In addition to new analytical results, in this work, we present a critical comparison between numerical and analytical computations. The influence of explicit and implicit boundary conditions on the phase shifts and phase-contrast images is also investigated in detail.

Conventional and back-side focused ion beam milling for off-axis electron holography of electrostatic potentials in transistors

Off-axis electron holography is used to characterize a linear array of transistors, which was prepared for examination in cross-sectional geometry in the transmission electron microscope (TEM) using focused ion beam (FIB) milling from the substrate side of the semiconductor device. The measured electrostatic potential is compared with results obtained from TEM specimens prepared using the more conventional 'trench' FIB geometry. The use of carbon coating to remove specimen charging effects, which result in electrostatic fringing fields outside 'trench' specimens, is demonstrated. Such fringing fields are not observed after milling from the substrate side of the device. Analysis of the measured holographic phase images suggests that the electrically inactive layer on the surface of each FIB-milled specimen typically has a thickness of 100 nm.

A Fourier approach to fields and electron optical phase-shifts calculations

The Fourier method is applied to calculate fields and electron optical phase shifts in specimens having long-range electromagnetic fields, like reverse biased p-n junctions or stripe magnetic domains. It is shown that this approach not only allows to take into account rather easily the effect of the fringing fields protruding in the space around the specimen, but also to obtain solutions to interesting models in analytical form.

An introduction to off-axis electron holography

The technique of off-axis electron holography is introduced and reviewed. The history of the topic is discussed briefly looking at the origin of electron holography and the reasons for its growth in recent years around the world. The formation and numerical reconstruction of the hologram is discussed in detail on a theoretical and practical level. The spread of holography is illustrated through a number of applications ranging from ultra high resolution studies of crystal structures, the imaging of magnetic and electric fields, the determination of sample composition and morphology and the use of holography for imaging biological specimens.