Higher-order Laue Zone Research Articles

Refinement of the crystal structural parameters of La2/3Ca1/3MnO3using quantitative convergent-beam electron diffraction

Crystal structural parameters (seven positional parameters and four isotropic Debye-Waller factors) of La(2/3)Ca(1/3)MnO(3) have been refined using the quantitative convergent-beam electron diffraction (QCBED) method. Using intensity information of many higher-order Laue-zone reflections simultaneously is essential to refine structural parameters accurately. The effective global optimization algorithm was used to avoid the problems of input values and local minima. The fittings of the differential coefficients of one-dimensional experimental intensities and theoretical ones calculated by the dynamical diffraction theory were carried out with the normalized Euclidean distance criterion. Thus, all of these improve the accuracy and reliability of the analysis. The calculated results with the refined parameters agree with the experiments. The refined parameters also agree with the Rietveld refinement results of neutron diffraction.

Accurate determination of the voltage of a transmission electron microscope (TEM) by 〈0 1 2〉 CBED-HOLZ analyses using GaAs crystal

Convergent beam electron diffraction (CBED) is a powerful technique to estimate lattice distortion and lattice strain in crystals. The positions of the higher-order Laue-zone (HOLZ) lines in the transmitted disc of CBED patterns are very sensitive to the lattice parameter, and can therefore be used to estimate changes in the lattice parameter. This offers the possibility to calculate lattice misfit and lattice strain. The positions of the HOLZ lines depend not only on the lattice parameter, but also on the operating voltage of the microscope. It is essential to know the actual voltage of the microscope. In the present work, (1 0 0) GaAs crystal has been used as a standard. Cross-sectional TEM specimens were prepared by argon ion beam thinning technique using a liquid nitrogen cold stage. 〈0 1 2〉 on-zone CBED technique has been used to estimate the actual voltage of the transmission electron microscope (Philips EM430T TEM), when the voltage was set at 250 kV. CBED-HOLZ simulation and analyses have been done, using JEMS software, to correlate with the experimental data. The methodologies adopted for estimating the actual voltage of TEM are discussed in this paper. The studies have also been cross-checked using 〈0 1 2〉 and 〈2 3 3〉 zone axes using (1 0 0) silicon standard. The techniques established are found to be suitable for TEMs operating at a setting voltage of about 250 kV. For the TEM studies, a regular double-tilt specimen holder is required in order to be able to get to the desired zone axes. When the experiments were repeated using a cryogenic double-tilt holder, an improvement in the sharpness of HOLZ lines was observed. Wherever possible, the use of the cryogenic double-tilt holder is recommended. Care must, however, be taken to ensure that effects such as lattice parameter changes (due to temperature changes), phase transformations etc can be properly accounted for.

Voltage refinement by deficit HOLZ line geometry

A method of refining electron beam voltage from deficit line intersections, using a quasi-kinematic scattering approximation, is described and applied to a silicon standard. It is shown that dynamical corrections are necessary for higher-index zone axes, such as 310 and 411, where a single deficit line associated with one dominant Bloch state is visible. This leads to a substantial difference in the refined voltage compared with that obtained from a purely kinematic approximation. Neglect of this dynamical correction term effectively invokes a systematic error that may lead to high precision but poor accuracy in higher-order Laue zone measurements of beam voltage or lattice parameters. Although relatively small, differences in the dynamical correction necessary for these two zones are confirmed experimentally for 100-300 keV electrons.

Strain measurements by convergent-beam electron diffraction: The importance of stress relaxation in lamella preparations

Local convergent-beam electron diffraction (CBED) patterns have been acquired on focus ion beam prepared samples in order to determine the strain field generated by a NiSi layer in a n-MOS transistor. A broadening of the high order Laue zone lines in the transmitted disk of CBED patterns is observed when approaching the NiSi∕Si interface. We show that this broadening is mainly due to the atomic plane bending that occurs as a result of the stress relaxation during the preparation of the thin lamella. From the analysis of this relaxation, we are able to determine the initial stress state of the bulk structure. The presented CBED procedure appears to be a promising tool to measure the strain and stress in any layer or structure deposited on a crystalline substrate.

The effect of the signal-to-noise ratio in CBED patterns on the accuracy of lattice parameter determination.

A method of higher-order Laue zone line position measurement in convergent-beam electron diffraction (CBED) is proposed based on Hough transformation. A thorough analysis of the errors introduced by this measurement procedure is performed and their influence on the accuracy of lattice parameter determination is estimated. A criterion is derived which enables the accuracy to be predicted before experimental measurements are made and, thus, allows the selection of the best CBED geometry for parameter measurement.

Determination of In concentration in pseudomorphic InxGa1−xN quantum wells based on convergent-beam electron diffraction

An approach based on the technique of convergent-beam electron diffraction (CBED) has been used to determine the elemental composition of a pseudomorphic GaN/InxGa1−xN/GaN quantum-well structure on the nanometer scale. Areas of triangles formed by intersecting higher order Laue-zone (HOLZ) lines are highly sensitive to lattice-parameter variations. By calculating the ratio of triangle areas, the local In concentration is estimated to within ±0.5% once lattice expansion in the growth direction has been taken into account. Moreover, shifts in the HOLZ-line positions as the CBED probe is moved along the quantum well provide a simple and rapid indication of local fluctuations in In content. The technique is applicable to other pseudomorphically strained epitaxial layers.

On the site occupancy of dopants in 4H-SiC

Silicon carbide (SiC) is a semiconductor material which is widely used for devices operating under extreme conditions. The fabrication of planar electronic devices requires a high concentration of pand ndopants. This can be archieved preferentally by ion implantation because of the small diffusion coefficients of dopants in SiC. After implantation, the implan-ted atoms predominantly occupy interstitial lattice sites [1], where they are usually not electrically active. Therefore, a thermal postimplantation annealing process is necessary to electrically activate the implanted dopants and to reduce the lattice damage, however, for the case of high foreign atom concentration, the SiC matrix remains defective always [2]. Another possibility to avoid lattice defects is to incorporate the doping element in-situ during the epitaxial growth of the crystal which can be performed by chemical vapour deposition (CVD) Concerning the site occupancy of p and n dopants a number of questions remains [3,4] from Hall mobility measurements. In this paper this question will be addressed using a combined analysis of convergent beam electron diffraction (CBED) and ALCHEMI (atomic location by channelling enhanced microanalysis) for the case of Al implanted 4H-SiC. The shift of Higher Order Laue Zone (HOLZ) lines appearing in CBED patterns can be used for detection of very small lattice parameter changes ([5,6,7]). However from this shift the origin of the strain can not be distinguished e.g. whether the foreign atoms occupy lattice or interstitial sites. By means of ALCHEMI the site occupancy of atoms within a matrix lattice can be determined [8]. This method has been applied for the case of Ge implanted in SiC already [9]. Aluminium implanted hexagonal 4H-SiC (concentrations: 5*10 cm for ion implantation at 160keV and 7*10 cm 2*10 cm for CVD implanation) have been investigated using CTEM, CBED and ALCHEMI. CBED patterns were obtained on [120 80 1] at an operating high voltage of 300kV. The EDX analysis was made on [01-10] zone axis incidence for tilts of ±1/2g to ±5/2g with g=0004. CBED patterns revealed different changes in HOLZ line shapes for different dopant concentrations, which can be attributed to different lattice distortion. Models of lattice distortion were suggested and calculated by Molecular Dynamics. Their influence on the HOLZ lines appearance was simulated by the multislice method. To determine the positions of the implanted atoms inside the unit cell, the CBED simulations have been carried out for probable locations of dopants in the SiC lattice (on lattice sites, on interstitials sites or both lattice and interstitial sites) by using the results of the ALCHEMI experiments. The comparison of ALCHEMI simulations and experiments (Fig. 1 and 2) showed that in the CVD growth case the implanted Al is mostly substituting Si in the matrix and in the ionimplanted sample Al is occupying Si-lattice positions and interstitials in equal parts. The CBED experiments (Fig. 3) show a line split of a line (1-1-22) in the CBED pattern in the ionimplanted samples and no split of that line in the CVD growth samples which can be understood from the substitution of Si by Al.

Fast and reliable evaluation of lattice distortions from convergent-beam electron diffraction patterns

A manual method for higher order Laue zone (HOLZ) line detection with an improved effective high-voltage correction for fast and reliable evaluation of local lattice distortions from convergent-beam electron diffraction (CBED) is presented. It is compared with a high-precision Hough transform method with a dynamic correction for each individual HOLZ line used by Krämer and Mayer. Both methods are applied to unfiltered and filtered experimental CBED patterns. As an example, the local lattice distortions in the γ − γ′ raft-like structure of a creep-deformed single-crystal nickel-based superalloy (CMSX-6) were measured. The lattice distortions obtained from both methods were analysed and showed good agreement. As a by-product, it was noted that specimen cooling enhanced the contrast of CBED patterns to the extent that the quality of CBED patterns taken at low temperatures without energy filtering was found to be qualitatively similar to that of CBED patterns taken at room temperature with energy filtering.

Transmission electron microscopy study on ferromagnetic (Ga,Mn)N epitaxial films

We report on the crystal structure of epitaxial (Ga,Mn)N films with Mn=0.2% grown by plasma-enhanced molecular beam epitaxy, exhibiting n-type conductivity and room temperature ferromagnetism (Ms=0.76 emu/cm3, Hc=90 Oe). The additional diffraction spots are found in the zone axis of B=[11̄00] for the (Ga,Mn)N epilayer due to a single twin orientation in the closed packed hexagonal matrix. High-order Laue zone measurements reveal the expansion of lattice parameter a (3.1851–3.1865 Å) by doping Mn, demonstrating that Mn ions substitute for Ga ions in the (Ga,Mn)N.

TEM study of the interface in ceramic-reinforced aluminum-based composites

The microstructure and interfaces of aluminum matrix composites were studied using conventional and high-resolution transmission electron microscopy (HREM). Also convergent-beam electron diffraction (CBED) was used. Two kinds of Al-based ceramic-reinforced composites (Al–TiC and Al–TiB2) were studied. Transmission electron microscopy (TEM) revealed the presence of a relatively high dislocation density in the matrix of both kinds of investigated composites. The dislocation density is higher near the interface region than inside the matrix. The local strength of the matrix was determined near the reinforcing particles, using TEM at CBED. Analysis of the higher-order Laue zone (HOLZ) lines allowed a determination of the changes in the lattice constant versus the distance from the interface.

Dynamical simulations of zone axis electron channelling patterns of cubic silicon carbide

We have observed and simulated energy-dependent intensity distributions in electron channelling patterns (ECP) of cubic silicon carbide (3C SiC) which were recorded close to the (1 1 1) zone axis. The kinetic energies used were in the range from 4 to 8 keV , covering the low-energy region of the ECP technique. We explain the observed patterns by dynamical many beam simulations using a bloch wave approach for the diffraction of the incoming beam and the forward–backward-approximation for the backscattering of the electrons. The dynamical simulations reproduce the experimental patterns very well. It is found that higher-order Laue zone reflections are responsible for the strong energy sensitivity of the intensity distributions.

Identification of the Structure of a New Al—U—Fe Phase by Electron Microdiffraction Technique.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Simulation of electron channelling patterns for in situ polytype analysis of silicon carbide films

For the controlled growth of hexagonal or cubic silicon carbide (SiC) polytypes, an in situ surface analysis technique is needed which is sensitive to the crystal structure of thin films whose thicknesses are in the range of a few nanometers. Diffraction effects of electrons having kinetic energies of a few keV serve this purpose very well. X-ray photoelectron diffraction patterns and electron channelling patterns (ECP) have been proven to be useful techniques for polytype differentiation. We show that the polytype specific effects in zone axis ECP of SiC polytypes can be simulated using a Bloch wave approach. Dynamical diffraction leads to characteristic patterns which show a variety of energy dependent structures. The specific zone axis patterns are caused by many-beam effects of higher order Laue zone reflections which are strongly energy dependent. We show results for 3C, 4H and 6H SiC.

The software tool for lattice parameters determination from nanoareas using CBED patterns

The higher-order Laue zone lines often visible in the central discs of convergent-beam electron diffraction patterns are sensitive to small changes in the lattice parameters in nanoareas. A computer program for the determination of the lattice parameters in the regions of the deformed lattice, especially near to an interface, is presented.

Displacement fields around 1/2[111] screw dislocations in bcc metals and their defocus convergent-beam electron diffraction patterns

Displacement fields have been calculated around 1/2[111] screw dislocations with various types of core structures in bcc metals. Three types of cores are studied: two types of polarized cores with large and small extensions of the displacement fields and an isotropic core. The difference in the displacement along the [111] direction ∆uz from that for the elastic solution has been evaluated for each type of dislocation. In the outside of the core region, the Duz values are close to zero along the six directions and the regions with ∆uz > 0 and ∆uz <o are alternately arranged, lying between those directions. Appreciable difference in ∆uz has been detected between the polarized cores and the isotropic core up to large distance from the core region. The defocus convergent-beam electron diffraction patterns have been calculated for the dislocations with the incident beam parallel to the dislocation line. Winding and spiral features have been shown in the higher-order Laue zone (HOLZ) lines for the dislocated structures, which have been confirmed by a preliminary experiment. In addition, small shifts of the HOLZ lines have been shown by the calculation between the polarized cores and the isotropic one.

初学者のための電子回折解折プログラム

A computer program to assist interpretation of electron diffraction patterns is described, especially for TEM beginners. The program contains drawing of diffraction patterns including high-order Laue zones and the extinction rule, and calculation of crystal orientation from observed diffraction patterns. Furthermore, combination with a slow-scan CCD camera that takes diffraction patterns in a computer realizes real-time determination of minerals and their orientations during TEM observation.

Refinement of crystal structural parameters and charge density using convergent-beam electron diffraction--the rhombohedral phase of LaCrO3.

Atom positions and anisotropic Debye-Waller factors of the rhombohedral phase of LaCrO(3) have been refined simultaneously with the low-order structure factors, using a structure-analysis method of convergent-beam electron diffraction (CBED) proposed by Tsuda & Tanaka [Acta Cryst. (1999), A55, 939-954]. The method is based on the least-squares fitting between full dynamical calculations and energy-filtered intensities of two-dimensional higher-order Laue-zone (HOLZ) and zeroth-order Laue-zone (ZOLZ) CBED patterns. The positions of the oxygen atoms have been determined with a high precision. Clear anisotropy of the thermal vibrations of the oxygen atoms has been successfully determined by the CBED method for the first time. The charge transfer from the La and Cr atoms to the O atoms has been found from the deformation charge-density map.

Identification of the structure of a new Al–U–Fe phase by electron microdiffraction technique

The particles of an unknown intermetallic phase with the approximate composition Al 10Fe 2U were observed in a ternary Al–Fe–U alloy. The structure of this phase was investigated in a transmission electron microscope using a microdiffraction technique based on analysis of the symmetry and relative positions of reflections in the zero-order and high-order Laue zones. The phase has an orthorhombic C-centered unit cell with lattice parameters a=8.900, b=10.190 and c=8.993 Å; its crystal symmetry can be described by the Cmcm space group.

Study of the influence of higher-order Laue zones on the exit wavefunction

Based on an analytical expression of electron dynamical diffraction derived recently, the exit wavefunctions of nonperiodic samples have been calculated. The results have shown that the amplitude and phase obtained by the analytical expression were in good agreement with those obtained using the multi-slice method. Besides, the influence of the higher-order Laue zone on the wavefunction for different sample thickness was studied in detail and the results showed that the exit wavefunction is dominated by the zero-order Laue zone. When the sample is very thin, the influence of the higher-order Laue zone should be considered.

Refinement of Crystal Structural Parameters using Convergent-Beam Electron Diffraction

A procedure for refining structural parameters and charge densities using convergent-beam electron diffraction (CBED) is described. The procedure is based on the nonlinear least-squares fitting between full dynamical calculations and energy-filtered intensities of two-dimensional higher-order Laue-zone (HOLZ) and zeroth-order Laue-zone (ZOLZ) CBED patterns.