Large-angle Convergent-beam Electron Diffraction Research Articles

LACBED characterization of dislocation loops

The characterization of the amplitude and sign of the Burgers vector of perfect or partial dislocations from large-angle convergent-beam electron diffraction (LACBED) patterns is now a routine technique following the original idea proposed by Cherns and Preston [Proceedings of ICEM-11, Kyoto, Japan, pp. 721–722 (1986)]. The technique has already been applied to large dislocation loops present in semiconductors but in many specimens submitted to irradiation, implantation or thermal treatments, the size of the dislocation loops that are encountered are too small to be identified from normal LACBED experimental conditions. The aim of this paper is to propose solutions to enable the analysis of small dislocation loops, with diameter less than 100 nm. Examples of perfect and partial dislocation loops present in austenitic steels, Al–Cu–Mg alloys and in doped silicon are given, in which the vacancy or the interstitial type of the loops is inferred. The minimum loop size that can be studied with the present technique is about 30 nm. The present technique is similar in its capabilities to the range of methods based on the ‘inside--outside’ contrast observed on weak-beam images but is has some main operational advantages: the experiments are easy to perform and to interpret and no specific crystal orientation is required.

Phase‐Transformation‐Induced Anti‐Phase Boundary Domains in Barium Cerate Perovskite

Anti‐phase boundary (APB) domains resulting from the orthorhombic (o1, Ibmm (No. 74)) to orthorhombic (o2, Pbnm (No. 62)) phase transformation at ∼290°C in pressureless‐sintered barium cerate (BaCeO3) ceramics have been investigated by transmission electron microscopy and large‐angle convergent beam electron diffraction (LACBED). APB exhibiting symmetric π‐fringe patterns in both bright‐field and dark‐field images, lying in {011) with the fault vector R=1/2〈111〉, were determined adopting the invisibility criteria of 2πg·R=0 or 2nπ. The curved boundaries due to symmetry change can be related to the low symmetry phase by a pure translation upon phase transition. The displacement vector, R, relating the domains is the translational symmetry element from the origin to the lattice point that was lost upon transition. The formation of such domains induced by the o1→o2 phase transition is discussed in terms of change in the Bravais lattice and loss of lattice point upon the transition. The identification has also confirmed the existence of a higher symmetry orthorhombic o1 phase along the transition sequence of R3c→Ibmm→Pbnm. The increased spatial frequency of APB domains is attributed to A‐site ordering due to vacancies created by BaO loss and/or disordering of the B‐site substitutional defects generated extrinsically when doped with either a Y3+‐acceptor or a Nb5+‐donor.

CBED and LACBED characterization of crystal defects

Convergent-beam electron diffraction (CBED) obtained with a focused incident beam is well known for the identification of the point and space groups but it can also be used for the analysis of stacking faults and antiphase boundaries. Large-angle convergent-beam electron diffraction (LACBED) is performed with a large defocused incident beam and is well adapted to the characterization of most types of crystal defects: point defects, perfect and partial dislocations, stacking faults, antiphase boundaries and grain boundaries. Among the advantages of these methods with respect to the conventional transmission electron microscopy methods, are that one or few patterns are required for a full analysis and the interpretations are easy and unambiguous. The LACBED technique is particularly useful for the analysis of dislocations present in anisotropic and beam-sensitive materials.

New developments in the characterization of dislocation loops from LACBED patterns

The characterization of the Burgers vector of dislocations from large-angle convergent-beam electron diffraction (LACBED) patterns is now a well-established method. The method has already been applied to relatively large and isolated dislocation loops in semiconductors. Nevertheless, some severe experimental difficulties are encountered with small dislocation loops. By using a 2 microm selected-area aperture and a carbon contamination point to mark the loop of interest, we were able to characterize both the plane and the Burgers vector of dislocation loops of a few tens of nanometres in size present in Al-Cu-Mg alloys.

LACBED study of extended defects in 4H-SiC

Large-angle convergent-beam electron diffraction analysis was successfully performed on pairs of partial dislocations so close that their effect on Bragg lines overlap. These pairs, dragging 3C layers, were nucleated by mechanical deformation of 4H-SiC. Splitting of Bragg lines on crossing a dislocation pair can be interpreted as resulting from a single dislocation having a Burgers vector equal to the sum of the two partial dislocation ones. Splitting rules using phase-shifted reflections () are also given depending on the phase shift produced by 3C lamellae. These results give a direction in agreement with weak-beam dark-field studies and suggest that Si core dislocations have highest mobilities for low-temperature (<700○C) plastic deformation.

Prospects of the multislice method for CBED pattern calculation

We recently showed that the Multisclice method can be used to elucidate the crystal volume contribution to a CBED pattern. Here, we demonstrate in more detail how the directions of each HOLZ line, their Laue zone order, and the specimen thickness determine the volume segment of the Bragg scattering cone of the electron beam and show that secondary rescattering from this volume must take place for deficient line formation in the (000) CBED disk. Moreover, additional prospects of the multislice method are demonstrated such as calculation of line splitting in bent crystals, hollow cone dark-field CBED, large-angle CBED, and whole diffraction patterns including Kikuchi lines.

Nanoscale strain analysis of strained-Si metal-oxide-semiconductor field effect transistors by large angle convergent-beam electron diffraction

In this letter we report the characterization of local compressive strain in p-type strained-silicon channel metal-oxide-semiconductor field effect transistors by large angle convergent-beam electron diffraction. The compressive strain was induced into the channel region of gate length of 80nm strained-Si p-type metal-oxide-semiconductor field effect transistor by Ge preamorphization implantation for source/drain extension. A method to distinguish between compressive strain and shear strain in the cross-sectional transmission electron microscopy specimens is proposed.

Convergent beam electron diffraction investigation of strain induced by Ti self-aligned silicides in shallow trench Si isolation structures

The deformation induced onto silicon by the formation of Ti self-aligned silicides (salicides) in shallow trench isolation structures has been investigated by the convergent beam electron diffraction technique (CBED) in the transmission electron microscope (TEM). The splitting of the high order Laue zone (HOLZ) lines in the CBED patterns taken in TEM cross sections close to the salicide/silicon interface has been explained assuming that the salicide grains induce a local bending of the lattice planes of the underlying matrix. This bending, which affects in opposite sense the silicon areas below adjacent grains, decreases with the distance from the interface, eventually vanishing at a depth of 300–400nm. The proposed strain field has been implemented into a fully dynamical simulation of the CBED patterns and has proved to be able to reproduce both the asymmetry of the HOLZ line splitting and the associated subsidiary fringes. This model is confirmed by the shift of a Bragg contour observed in large angle CBED patterns, taken in a cross section cut along a perpendicular direction. The whole experimental results cannot be explained by just a strain relaxation of the TEM cross section, induced by the salicide film onto the underlying silicon.

CBED study of grain misorientations in AlGaN epilayers

Large angle convergent beam electron diffraction (LACBED) has been used to examine AlGaN epilayers grown by facet-controlled epitaxial lateral overgrowth on GaN/(0 0 0 1) sapphire substrates in prototype UV laser structures. The substrates, defined by masks with seed openings along a 〈 1 0 - 1 0 〉 stripe direction, had GaN seed columns with { 1 1 - 2 2 } surfaces. Studies were carried out on cross-sectional samples cut perpendicular to the stripe axis. An LACBED analysis of the orientation of (0 0 0 2) planes, and of the ( 1 1 - 2 0 ) planes parallel to the stripe axis, revealed that the AlGaN wings were both rotated by angles of 1–2×10 −2 radians about the 〈 1 0 - 1 0 〉 stripe axis with respect to the underlying GaN, and distorted due to misfit strains. It is shown that the results are consistent with the observed structure of the AlGaN/GaN and the wing/wing boundaries, and with a new model for the generation of a-type misfit dislocations at the AlGaN/GaN interface.

A TEM investigation of the lattice defects and exfoliation in hydrogen-implanted CdTe

This study focuses on characterizing the defects associated with 400 keV hydrogen-implantation of CdTe, at a dose of 1 × 1016 H+ cm−2 to 5 × 1016 H+ cm−2, with subsequent annealing. Transmission electron microscopy (TEM) and a hybrid diffraction technique, large-angle convergent-beam electron diffraction (LACBED), were used in the characterization process. Extended defects resulting from the hydrogen-implantation and annealing process include dislocations, microcracks and bubbles. Microcrack and bubble formation occurs on the cleavage planes of CdTe. Exfoliation is achieved at the higher implantation dose. High-resolution electron microscopy was used in the microstructural analysis of the microcracks. LACBED of the implanted material containing bubbles revealed a highly strained lattice with evidence of lattice distortion in-plane and in the direction of implantation.

A TEM investigation of the lattice defects and exfoliation in hydrogen-implanted CdTe

This study focuses on characterizing the defects associated with 400 keV hydrogen-implantation of CdTe, at a dose of 1 × 10 16 H + cm −2 to 5 × 10 16 H + cm −2, with subsequent annealing. Transmission electron microscopy (TEM) and a hybrid diffraction technique, large-angle convergent-beam electron diffraction (LACBED), were used in the characterization process. Extended defects resulting from the hydrogen-implantation and annealing process include dislocations, microcracks and bubbles. Microcrack and bubble formation occurs on the cleavage planes of CdTe. Exfoliation is achieved at the higher implantation dose. High-resolution electron microscopy was used in the microstructural analysis of the microcracks. LACBED of the implanted material containing bubbles revealed a highly strained lattice with evidence of lattice distortion in-plane and in the direction of implantation.

Effect of anisotropic temperature factors on convergent-beam electron diffraction intensities and measurement of the local change in the oxygen concentration of YBa2Cu3O y

The local oxygen concentration of the high-T c superconductor YBa2Cu3O y was measured from large-angle convergent-beam electron diffraction patterns using a transmission electron microscope equipped with a field emission gun with an in-column-type energy filter. The anisotropic effect of thermal vibrations of atoms was considered in the analysis of the oxygen concentration, based on the many-beam dynamic theory. The observed fluctuation in the oxygen concentration can explain the peak effect in the J c–H curve, the critical current density J c plotted as a function of applied magnetic field H.

TEM observation of nanopipes in heteroepitaxial GaN

Heteroepitaxial GaN layers grown on sapphire by metal organic vapour phase epitaxy (MOVPE) have been characterised by conventional transmission electron microscopy (TEM) on planar and cross-sectional samples, Large Angle Convergent Beam Electron Diffraction (LACBED) and by high-resolution transmission electron microscopy (HRTEM). Hollow tubes termed nanopipes were resolved on planar view and cross-sections of heteroepitaxial GaN. For advanced studies of the nature of nanopipes the LACBED method was employed. The recognition between perfect structure and screw distortion around nanopipes was performed with high accuracy using Zone Axis LACBED images.

LACBED characterization of dislocations in Cu-Al-Ni shape memory alloys processed by powder metallurgy

Powder metallurgy Cu-Al-Ni shape memory alloys show excellent thermomechanical properties, being the fracture behavior close to the one observed in single crystals. However, the microstructural mechanisms responsible of such behavior are still under study. In this paper we present the characterization of the dislocations present in these alloys by Large Angle Convergent Beam Electron Diffraction (LACBED) in two different stages of the elaboration process: after HIP compaction and after hot rolling.

Antiphase boundaries in Ni3Al ordered intermetallic—application of the CBED method

The antiphase domain structure in Ni3Al ordered intermetallics with perfect L12 superstructure has been examined. Transmission electron microscopy (TEM) investigations were performed using Jeol JEM 3010 and Philips CM30 microscopes. Conventional TEM studies, convergent-beam electron diffraction (CBED) and high-resolution electron microscopy (HRTEM) were used to elucidate the structure of the alloys. For advanced studies of the nature of antiphase boundaries, the large-angle convergent-beam electron diffraction (LACBED) method was employed. The recognition between symmetry-related and displacive domains can be performed with high accuracy using LACBED and dark-field images, even for nanosized domains.

Plastic deformation of wadsleyite: I. High-pressure deformation in compression

We have studied the plastic deformation of Mg2SiO4 wadsleyite polycrystals. Wadsleyite was synthesized from a forsterite powder in a multianvil apparatus. It was then recovered and placed in a second multianvil assembly designed to induce plastic deformation by compression between two hard alumina pistons. After the deformation experiment, the microstructures are characterized by transmission electron microscopy (TEM) and large-angle convergent beam electron diffraction (LACBED). Deformation experiments have been carried out at 15–19 GPa and at temperatures ranging from room temperature to 1800–2000 °C. Five different dislocation types have been identified by LACBED: [100], 1/2〈111〉, [010], 〈101〉 and [001]. The [001] dislocations result from dislocation reactions and not from activation of a slip system. The [010] dislocations are activated under high stresses at the beginning of the experiments and further relax by decomposition into 1/2〈111〉 dislocations or by dissociation into four 1/4[010] partial dislocations. The following slip systems have been identified: 1/2〈111〉{101}, [100](010), [100](001), [100]{011}, [100]{021}, [010](001), [010]{101} and 〈101〉(010).

Characterization of contacting boundaries between nanoparticles with LACBED.

The boundary parameters between contacting spherical bcc-Fe particles have been characterized with the Large Angle Convergent Beam Electron Diffraction (LACBED) technique. The average accuracy of measurements can reach 0.07 degrees. The rotation parameters are interpreted using matrix algebra and evaluated according to the CSL model. The deviation between the experimental results and the reference misorientations given in the CSL model is determined. It is possible to reveal preferential misorientations between irregularly shaped particles with a size less than 100 nm. The method can be applied to nanoparticles and nanocrystalline materials with a wide range of grain orientations, and it is possible to modify it into an automatic method for TEM measurements.

CBED and LACBED: characterization of antiphase boundaries

Convergent-beam electron diffraction (CBED) and large-angle convergent-beam electron diffraction (LACBED) techniques are well adapted to the characterization of several types of crystal defects. In fact, dislocations, grain boundaries and stacking faults have already been successfully characterized with these methods. In the present paper, we describe the CBED and LACBED characterization of another type of crystal defect showing a special interest in materials science: antiphase boundaries (APBs). The first part of the paper is devoted to the determination of the effects of antiphase boundaries on CBED and LACBED patterns that could be expected from a theoretical point of view. It indicates that the superlattice excess lines present on these patterns are split into two lines with equal intensity when the incident beam is located on an APB. In the second part, we experimentally test these theoretical predictions on a specimen showing two different known types of antiphase boundaries. In a third part we indicate how these methods could be used to identify unknown APBs in a specimen. Finally, the advantages and disadvantages of both methods for the characterization of antiphase boundaries are discussed.

A useful expansion of the exponential of the sum of two non-commuting matrices, one of which is diagonal

The matrix exponential plays an important role in solving systems of linear differential equations. We will give a general expansion of the matrix exponential S = exp[?(A + B)] as Sn,m = e?bn?n,m + ?q = 1? ?l1 = 0N ? ?lq?1 = 0Nan,l1 ? alq?1,mC(q)n,l1,...,lq?1,m(B, ?) with C(q)n,l1,...,lq?1,m(B, ?) being an analytical expression in bn, bl1, bl2, ... blq?1, bm, and the scalar coefficient ?. A is a general N ? N matrix with elements an,m and B a diagonal matrix with elements bn,m = bn?n,m along its diagonal. The convergence of this expansion is shown to be superior to the Taylor expansion in terms of (?[A + B]), especially if elements of B are larger than the elements of A. The convergence and possibility of solving the phase problem through multiple scattering is demonstrated by using this expansion for the computation of large-angle convergent beam electron diffraction pattern intensities.

Analysis of dislocation loops by means of large-angle convergent beam electrondiffraction

Diffusion-induced dislocation loops in GaP and GaAs were analysed by means oflarge-angle convergent beam electron diffraction (LACBED) and conventionalcontrast methods of transmission electron microscopy. It is demonstrated thatLACBED is perfectly suited for use in analysing dislocation loops. The methodcombines analyses of the dislocation-induced splitting of Bragg lines in aLACBED pattern for the determination of the Burgers vector with analyses of theloop contrast behaviour in transmission electron microscopy bright-field imagesduring tilt experiments, from which the habit plane of the dislocation loop isdetermined. Perfect dislocation loops formed by condensation of interstitial atomsor vacancies were found, depending on the diffusion conditions. The loops possess{110}-habit planes and Burgers vectors parallel to ⟨110⟩. TheLACBED method findings are compared with results of contrast analyses basedon the so-called ‘inside–outside’ contrast of dislocation loops. Advantages of theLACBED method consist in the possibility of determining the complete Burgersvector of the dislocation loops and of an unambiguous and fast loop type analysis.