Large-angle Convergent-beam Electron Diffraction Research Articles

Analysis of grain boundary dislocations by large angle convergent beam electron diffraction

Large angle convergent beam electron diffraction (LACBED) is used to analyse secondary dislocations in Σ3 and Σ9 grain boundaries in silicon. By selecting reflections from crystal planes common to the adjoining grans, LACBED images are insensitive to the boundaries except where dislocations are present. The dislocation images are closely similar to those for dislocations in single crystals and can be analysed by standard Cherns-Preston rules. It is shown that, for both boundaries, sufficient common reflections can be selected for a complete analysis, and that dislocations can be analysed assuming integer values of g · b , implying that the Burgers vectors are Displacement Shift Complete (DSC) lattice vectors. For both Σ3 and Σ9 boundaries, DSC dislocations are identified which are specific to these boundaries. The experimental conditions for the analysis of grain boundaries are explained, and the extension of the method to other coincidence boundaries is discussed.

Characterization of crystal defects in quartz by large-angle convergent-beam electron diffraction

Abstract It is shown that large-angle convergent-beam electron diffraction can be used successfully to characterize crystal defects in a radiation-sensitive material such as quartz. The cases of perfect 1/3(21 10) dislocations, partial 1/6(21 13) dislocations and Dauphina twin boundaries are considered successively. The identification of 1/6(21 13) dislocations represents the first analysis of partial dislocations in quartz.

Observation of crystal distortions in SiGeSi superlattice using a new application of large-angle convergent-beam electron diffraction

Cross-sectional specimens of Si0.67Ge0.33Si(001) strained-layer superlattice (SLS) have been employed to detect crystal distortions originated by misfit stresses in strained layers. A large-angle convergent-beam electron diffraction (LACBED) technique has been applied to (110) cross-sectional samples of the superlattice using a small spot size (nanoprobe, size 5) in a Philips EM430 transmission electron microscope at 250 kV. The technique examines displacements in the diffraction contour g = 333 in the dark-field LACBED disc on crossing the interfaces as a function of specimen tilt about the [111] axis. The displacements have been related to the rotation of (111) planes in the superlattice due to the misfit stress, the relative rotation between (111) planes in the Si and SiGe layers being measured as δθ = (1.05 ± 0.03) × 10−2 rad in agreement with a calculated rotation of 1.02 × 10−2 rad.

Models for termination of crystal boundaries in the theory of transmission electron diffraction and comparison with experimental data

Calculations of electron diffraction intensities in transmission electron microscopy commonly assume a model representing surfaces and interfaces in crystals as flat boundaries (flat-boundary model, FBM). It is shown that the independent-atom model (IAM) representing the crystal potential as a superposition of spherical atomic potentials leads to improved boundary conditions. Intensities calculated from the two models at large deviation from the Bragg peak in weak reflections (e.g. 200 in InGaAs) differ significantly. Results from both types of calculation are compared with an experimental diffraction pattern recorded using energy-filtered largeangle convergent-beam electron diffraction from an In 0.53 Ga 0.47 /InP bicrystal. It is shown that calculations using the IAM give a better agreement with experiment

Thin film relaxation in cross-sectional transmission electron microscopy specimens of GexSi1−x/Si strained-layer superlattices

A large-angle convergent-beam electron diffraction (LACBED) pattern with fine diffraction lines from a cross-sectional specimen of GexSi1−x/Si strained-layer superlattices (SLS) can give much information on local strain and misfit stress relaxation. The shift of the diffraction lines in the GeSi layers from those in the Si layers can be used to determine the strain relaxation. A profile of the thin film relaxation versus the specimen thickness is presented.

Analytical electron microscopy of Si1−xGex/Si heterostructures and local isolation structures

AbstractThe convergent beam electron diffraction (CBED) technique has been applied to determine the lattice strain in Si1−xGex/Si heterostructures and in local isolation structures. Both plan and cross-sections have been investigated by transmission electron microscopy. In the heterostructures, the strain value obtained by CBED along the growth direction ɛCRED is affected by a relaxation induced by the thinning process in a direction normal to the cross-section plane, being generally smaller than the bulk tetragonal value ɛT This effect can be overcome using the large angle CBED technique on plan sections. In addition, in the heterostructures the Ge concentration has been determined by energy dispersive X-ray spectrometry, allowing the pseudomorphicity of the samples to be evaluated. All the values of strain and Ge concentration thus obtained are in good agreement with those deduced from Rutherford backscattering spectrometry. In isolation structures, the CBED technique has been applied to determine the d...

Determination of Structure Factors of Al2O3 by means of Large Angle Convergent Beam Electron Diffraction

Intensities of higher order reflections in a large angle convergent beam electron diffraction (LACBED) pattern are measured for α-Al 2 O 3 and are compared with theoretical calculations in order to examine applicability of the kinematical approximation to determination of the structure factors. Effects of specimen thickness, temperature and absorption on the intensities are investigated through the dynamical theory of electron diffraction. A static displacement of Al 3+ ions from their ideal positions in a unit cell of α-Al 2 O 3 is determined from a relative change between two neighbouring high index reflections. The displacement determined through the kinematical theory of electron diffraction agrees well with the one through the dynamical theory and the ones measured by X-ray or neutron diffraction. The result demonstrates the usefulness of LACBED and the kinematical approximation.

Strains in crystals with amorphous surface films studied by convergent beam electron diffraction and high-resolution imaging

Cross-sectional specimens from crystals which are covered with amorphous surface films such as oxide or epoxy are investigated using large-angle convergent beam electron diffraction (LACBED). Stresses at the crystalline/amorphous interface are induced by the amorphous layer and lead to a relaxation of the lattice in the interfacial region during thinning of the specimen. It is shown that lattice images of crystal regions close to a crystalline/amorphous interface may be affected considerably by relaxation effects.

Effects of elastic relaxation on large-angle convergent-beam electron diffraction from cross-sectional specimens of GexSi1−x/Si strained-layer superlattices

Abstract A large-angle convergent-beam electron diffraction pattern with fine diffraction lines from a cross-sectional specimen of Gexsi1−x/Si strained-layer superlattices can give much information on local strain and misfit stress relaxation. The diffraction lines in the GeSi layers are shifted from those in the Si layers by the misfit strain and the strain relaxation. In this paper we shall demonstrate that the effects of elastic relaxation and the residual strains can be separated.

Surface relaxation of strained heterostructures revealed by Bragg line splitting in LACBED patterns

Bragg line splitting near the shadow image of a thin strained InGaAs layer, buried in GaAs and without strain relief by misfit dislocations, was found in large angle convergent beam electron diffraction (LACBED) patterns of cross-section specimens. The surface relaxation of the built-in strain and the Bragg line intensities were calculated. A qualitative agreement between the experimental Bragg line splitting and the theoretical calculations is demonstrated Closer matching was achieved using a “line-force” model of the surface relaxation, whereas a Fourier transform solution showed significant underestimation of the Bragg line splitting. The possibility of characterising the built-in strain in thin strained layers, by measuring this Bragg line splitting in LACBED patterns, has been explored.

Benefits of energy filtering for advanced convergent beam electron diffraction patterns

Energy filtering is well known to have a dramatic effect on the appearance of standard, zone-axis convergent beam electron diffraction patterns. In this paper, the effects of energy filtering on some less-common types of CBED patterns are shown. In particular, the (002) and (402) quasi-forbidden reflections in silicon are investigated, and the effects of energy filtering demonstrated. The filtering of HOLZ excess lines in large-angle zone-axis patterns is shown, as these patterns are of interest for Debye-Waller factor determination. Filtered and unfiltered bright-field large-angle CBED (LACBED) patterns of aluminum are presented along with EELS spectra to demonstrate the partial removal of inelastically scattered electrons due to the LACBED geometry.

Convergent-beam electron diffraction studies of epitaxial Si/SiO2systems

Abstract Convergent-beam electron diffraction (CBED) techniques have been applied to the study of silicon layers grown laterally on partially oxidized silicon wafers by liquid-phase epitaxy. Energy filtering of the electrons in the microscope provides CBED patterns from cross-sectional and plan-view specimens of large thickness with improved contrast and angular resolution. Cross-sections from the interfacial regions show a splitting or a broadening of the rocking profile of lines in CBED patterns. Strains at the Si–SiO2 interfaces are deduced from the patterns and related to relaxation effects in the special geometry of the cross-sectional specimens. Inference to bulk systems reveals that the Si lattice is in a state of tetragonal distortion close to the Si/SiO2 interface. Large-angle CBED patterns from plan-view specimens reveal a bending of Si layers relative to the substrate. Examples in the study of lateral coalescence of Si layers are demonstrated, such as the reversal of bending of the layers at th...

LACBED determination of structure factors and alloy composition of GeSi/Si SLS

The Taftø and Gjønnes three-beam dynamical analysis of large-angle convergent beam electron diffraction (Ultramicroscopy 17 (1985) 329) has been generalized to include high-order Laue zone corrections and has been applied to non-centrosymmetric strained layer superlattices (SLSs). The method of intersecting Kikuchi lines has been used to measure the structure factors of the Ge x Si 1− x SLS and to determine the alloy composition.

Reasonably good images of dislocations in LACBED patterns and effects of dislocation strain fields on the Bragg lines

An improved large-angle convergent beam electron diffraction (LACBED) experiment method using a Philips CM12 electron microscope is discussed. Dislocations in silicon parallel to the Bragg lines have been studied by this improved LACBED technique. Images of dislocations of reasonably good spatial resolution superimposed on LACBED patterns have been obtained. It has been found that only when the image of the dislocation is parallel and close to the low-order contour with g · b ≠ 0 can it be formed with reasonably good contrast in the LACBED patterns. Both the image of the dislocation and the changes of the contours can be visible in a single LACBED pattern, making it a convenient technique for studying the strain field of a dislocation.

Burgers vector determination of decorated dislocations in γ-TiAl by diffraction contrast and large-angle convergent-beam electron diffraction

Abstract Decorated and undecorated dislocations in γ-TiAl have been studied by conventional transmission electron microscopy using diffraction contrast and by large-angle convergent-beam electron diffraction (LACBED). The results of the Burgers vector determination for undecorated and decorated dislocations using the different techniques have been compared. For the decorated dislocations the contrast from the decorating particles and the underlying dislocation have been separated and the misfit introduced by the precipitates has been determined. Computer simulations of the contrast from decorated dislocations in LACBED patterns have been performed. The rules governing the dislocation contrast in LACBED patterns have been discussed and extended to the case of decorated dislocations. A new fringe-counting rule to determine the Burgers vectors of dislocations decorated by misfitting precipitates has been proposed. Remarkably good agreement of the computer-simulated LACBED contrast with experimental observations has been achieved.

Analysis of partial and stair-rod dislocations by large angle convergent beam electron diffraction

It is shown how large angle convergent beam electron diffraction (LACBED) can be used to analyse the Burgers vectors of partial dislocations in Si, GaAs and CdTe. By selecting reflections in which adjoining stacking faults are out of contrast, it is demonstrated that the LACBED technique can be used to analyse Shockley and Frank partial dislocations, and stair-rod dislocations of 1 6 〈110〉 type present at stacking fault intersections. The potential of the technique for studying grain boundary and dissociated dislocations in general is discussed.

Effects of dislocation strain fields on Bragg lines in an Al70Co15Ni15 decagonal quasicrystal studied by an improved LACBED technique

Effects of dislocation strain fields on Bragg lines in an Al70Co15Ni15 decagonal quasicrystal have been studied by using an improved large-angle convergent-beam electron diffraction technique. It is found that the effects are the same as that in conventional crystals.

Characterization of grain boundary misorientations in a alumina by large angle convergent beam electron diffraction

Large Angle Convergent Beam Electron Diffraction (LACBED) is used in order to characterize accurately the misorientation between grains situated on each side of grain boundaries in α alumina. It is shown that this method leads to an improved accuracy for the determination of misorientation between crystals at interfaces, when compared with the traditional diffraction and Kikuchi line techniques

Structure of a metastable Al-Ge phase determined from large angle CBED patterns

Abstract The structure of a new metastable Al-Ge phase recrystallized at 300°C from amorphous films with equiatomic composition deposited on to NaCl substrates cooled with liquid nitrogen was determined by convergent beam electron diffraction (CBED). The micron-sized crystals were tetragonal with space group 14/mcm, lattice parameters a = 6.13 Å and c = 4.92 Å, and composition Al0·9 Ge0·9. The structure was the C16 type with nominal AB 2 composition, although there was no evidence for preferential location of Ge on either A or B sites. The A atoms occupied 4(a) sites, and the B atoms were located on 8(h) sites with x = 0·158. Conditional Patterson transforms parallel to the c axis were calculated from kinematic intensities measured in focused large-angle CBED patterns. The contour maps showed clear peaks from A-B and B-B interatomic vectors. Dynamical perturbations reduced peak visibility but did not affect peak positions. The x parameter for B atoms was refined from the quasi-kinematic intensities of first-order Laue zone reflections diffracted from Bloch states localized on B atom strings in conventional CBED patterns.

Application of convergent-beam illumination methods to the study of lattice distortion across the interface

Convergent beam illumination methods were applied to the study of the lattice parameter change in the GaAs layers grown by molecular beam epitaxy (MBE) at 195°C (called LT-GaAs layers) with 1.5% of As excess. This excess of As leads to the lattice parameter change. Tetragonal distortion with a change of the lattice parameter along the growth direction was observed in four independently measured samples. The strain accumulated in the layer would explain the formation of pyramidal defects in these layers at a specific layer thickness related to the As concentration. An artifact due to the surface relaxation of the TEM thin foil is also considered. Surface relaxation was found to be present in the sample and the model was presented for the explanation of Kikuchi line shifts in the large-angle convergent-beam electron diffraction (LACBED) pattern and convergent-beam imaging methods (CBIM) pattern. The lowering the symmetry of CBED patterns from tetragonal to orthorombic observed in this study is most possible influenced by surface relaxation as well, however, the fact that similar results were obtained on four independent samples leaves this question still open for the future study.