Atomic Scale Strain and Composition Evaluation from High-Resolution Transmission Electron Microscopy Images

The Peak Pairs algorithm for strain mapping from HRTEM images

Strain mapping is defined as a numerical image-processing technique that measures the local shifts of image details around a crystal defect with respect to the ideal, defect-free, positions in the bulk. Algorithms to map elastic strains from high-resolution transmission electron microscopy (HRTEM) images may be classified into two categories: those based on the detection of peaks of intensity in real space and the Geometric Phase approach, calculated in Fourier space. In this paper, we discuss both categories and propose an alternative real space algorithm (Peak Pairs) based on the detection of pairs of intensity maxima in an affine transformed space dependent on the reference area. In spite of the fact that it is a real space approach, the Peak Pairs algorithm exhibits good behaviour at heavily distorted defect cores, e.g. interfaces and dislocations. Quantitative results are reported from experiments to determine local strain in different types of semiconductor heterostructures.

On the accuracy of lattice-distortion analysis directly from high-resolution transmission electron micrographs

Lattice-distortion analysis from high-resolution transmission electron micrographs offers a convenient and fast tool for direct measurement of strains in materials over a large area. In the present work, we have evaluated the accuracy of the strain measurement when the effects of the realistic experimental variables are explicitly taken into account by the use of image simulation techniques. These variables are focal setting and variation, local thickness and orientation of the sample, as well as misalignments of the sample and the incident beam. The evaluation reveals that consistency of image features and contrast within the micrographs is desired for the analysis to eliminate effects of the variations of local focus value and specimen thickness. After proper orientation of a crystalline specimen, the mis-orientation of the object will not notably influence the strain measurement even though a local bending may exist within the sample. However, the incident beam of the microscope needs to be aligned carefully as the beam misalignment may introduce a notable artefact around the interface region.

Dark field transmission electron microscope images of III–V quantum dot structures

Multi-layer quantum dot structures are becoming increasingly common in order to improve the efficiency of quantum dot lasers. Each layer of dots may be influenced by the preceding dot layer, and the dot density can vary from layer to layer. Characterization of such structures relies on the reliable determination of the shape, size and density of dots in each layer. Dark field transmission electron microscopy (TEM) images using the 002 diffraction condition are frequently used, viewing the layers edge-on in a cross-section sample. A simple model is used to describe the contrast as a function of dot size and shape, specimen thickness, and the composition of the dot and surrounding materials. Good agreement with experimental results is obtained. It is found that the dot size is not accurately related to the bright region seen in such images. While 002 images can be used to determine the size and shape of dots, a density per unit area cannot be calculated in the cross section geometry without either measuring--or assuming--the specimen thickness. In multilayer structures, plan-view TEM images show the layers as overlapping, losing the information from individual layers. By tilting a cross-section specimen to allow imaging with the dark field 113 diffraction condition, the density in individual layers can be measured. Additional information, such as wetting layer thickness variations and alignment of dots due to surface roughness or substrate offcut, can also be obtained.

Compositional analysis based on electron holography and a chemically sensitive reflection

A method for compositional analysis of low-dimensional heterostructures is presented. The suggested procedure is based on electron holography and the exploitation of the chemically sensitive (0 0 2) reflection. We apply an off-axis imaging condition with the (0 0 2) beam strongly excited and centered on the optic axis. The first side band of the hologram is centered using an "empty" reference hologram obtained for a hole of the specimen. From the centered side band we use the phase of the central (0 0 0) and the amplitude of the (0 0 2) reflections to evaluate the local composition and the local specimen thickness in an iterative and self-consistent way. Delocalization effects that lead to a shift of the spatial information of (0 0 0) and (0 0 2) reflections are taken into account. The application of the procedure is demonstrated with an AlAs/GaAs(0 0 1) superlattice with a period of 5 nm. The concentration profiles obtained are discussed in relation to segregation. The measured segregation efficiency is R = 0.51 +/- 0.02.