Observations of specimen morphology effects on near-zone-axis convergent-beam electron diffraction patterns

Convergent-beam and small-area-parallel-beam electron diffraction of icosahedral quasicrystals of a melt-quenched Al-Mn alloy

Under almost all circumstances, electron diffraction patterns contain information about the phases of structure factors, a consequence of the short wavelength of an electron and its strong Coulombic interaction with matter. However, extracting this information remains a challenge and no generic method exists. In this work, a set of simple analytical expressions is derived for the intensity distribution in convergent-beam electron diffraction (CBED) patterns recorded under three-beam conditions. It is shown that these expressions can be used to identify features in three-beam CBED patterns from which three-phase invariants can be extracted directly, without any iterative refinement processes. The octant, in which the three-phase invariant lies, can be determined simply by inspection of the indexed CBED patterns (i.e. the uncertainty of the phase measurement is ±22.5°). This approach is demonstrated with the experimental measurement of three-phase invariants in two simple test cases: centrosymmetric Si and non-centrosymmetric GaAs. This method may complement existing structure determination methods by providing direct measurements of three-phase invariants to replace 'guessed' invariants in ab initio phasing methods and hence provide more stringent constraints to the structure solution.

The convergent beam electron diffraction (CBED) patterns of twisted bilayer samples exhibit interference patterns in their CBED spots. Such interference patterns can be treated as off-axis holograms and the phase of the scattered waves, meaning the interlayer distance can be reconstructed. A detailed protocol of the reconstruction procedure is provided in this study. In addition, we derive an exact formula for reconstructing the interlayer distance from the recovered phase distribution, which takes into account the different chemical compositions of the individual monolayers. It is shown that one interference fringe in a CBED spot is sufficient to reconstruct the distance between the layers, which can be practical for imaging samples with a relatively small twist angle or when probing small sample regions. The quality of the reconstructed interlayer distance is studied as a function of the twist angle. At smaller twist angles, the reconstructed interlayer distance distribution is more precise and artefact free. At larger twist angles, artefacts due to the moiré structure appear in the reconstruction. A method for the reconstruction of the average interlayer distance is presented. As for resolution, the interlayer distance can be reconstructed by the holographic approach at an accuracy of ±0.5 Å, which is a few hundred times better than the intrinsic z-resolution of diffraction limited resolution, as expressed through the spread of the measured k-values. Moreover, we show that holographic CBED imaging can detect variations as small as 0.1 Å in the interlayer distance, though the quantitative reconstruction of such variations suffers from large errors.

Accurate values of foil thickness are required in many materials science applications, such as for measurement of defect concentrations and for x-ray microanalysis absorption corrections. Kelly et al. demonstrated that convergent beam electron diffraction (CBED) patterns can be analyzed using a simple graphical technique to give values for foil thickness with ±2% accuracy. More recently, Allen extended the treatment to make use of both maxima and minima in the CBED disks. The technique requires a knowledge of the d-spacing of the reflection, the electron wavelength, an evaluation of the deviation parameter, si, associated with the i-th fringe in the diffracted beam disk, and the assignment of a set of constants to "index" the fringes.

To accurately and easily determine the polarity of AlN using transmission electron microscopy, we compare the convergent-beam electron diffraction (CBED) patterns along the widely used <112̄0 > and <11̄00 > zone-axes. For the <112̄0 > zone-axis, the diffraction disk of g= 0002 differs from that of g= 0002̄, while for <11̄00 >, the diffraction disks of g= 0002 and 0002̄ are similar. The preferential clarity of these two disks is explained using Bloch-wave dynamical theory. To further support the explanation, we compare the results of GaN case. On the basis of our analysis, we conclude that the CBED patterns of the <112̄0 > zone-axis are more useful for accurately determining AlN polarity compared to the CBED patterns along the <11̄00 > zone-axis.

The fine structure of the first-order Laue zone (FOLZ) reflections in convergent-beam electron diffraction (CBED) patterns of Gaxln1–xAsyP1–y/InP heterostructures is investigated. The FOLZ reflection fine structure consists mainly of three bright lines; the position and intensity of these bright lines were used for a quantitative interpretation, using many-beam dynamical calculations. The main factor determining the position of the lines appears to be the composition. However, HOLZ-beam coupling, absorption and thermal vibrations of atoms have a considerable effect on the position and the intensity of the lines. Values of these parameters were estimated from the CBED patterns. A good agreement between calculation and experiment could only be obtained if small static displacements of the atoms from their ideal lattice sites were included. The calculations suggest that the static displacements in the quaternary compounds should be largest on the group-V sublattice. The quasi-periodic strain fields ...

A systematic method to identify the space group from PED and CBED patterns part I - theory

Convergent beam electron diffraction (CBED) at vertical grain boundaries (parallel to the electron beam) can be applied to determine the symmetry of bicrystals. It can also be used to investigate the structure of the boundary region itself when subnanometre probe sizes are employed. In this paper it is shown that (sub)nanometre-probe CBED patterns are largely influenced by the electron-beam geometry. In particular, simulations of coherent CBED patterns based on the multislice algorithm show that the CBED pattern of an edge-on interface depends on the defocus distance between the probe position and the specimen midplane, the probe size and the beam-convergence angle. The pattern symmetry may be lower than the theoretically predicted symmetry in case of large spherical aberration. This effect increases with smaller accelerating voltages. An increase in the beam-convergence angle also increases the possibility of a non-optimum symmetry due to spherical aberration of a coherent probe. Thus, for the determination of an interface structure using subnanometre (coherent) probes, the imaging conditions play an important role.

Position averaged convergent beam electron diffraction: Theory and applications

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

The rare earth hexaborides are known for their tendency towards very high crystal perfection. They can be grown into large single crystals of very high purity by inert gas arc floating zone refinement. The authors have found that single-crystal cerium hexaboride grown in this manner contains a significant number of inclusions of an impurity phase that interrupts the otherwise single crystallinity of this prominent cathode material. An iterative approach is used to unequivocally determine the space group and the lattice parameters of the impurity phase based on geometries of convergent-beam electron diffraction (CBED) patterns and the symmetry elements that they possess in their intensity distributions. It is found that the impurity phase has a tetragonal unit cell with space group P4/mbm and lattice parameters a = b = 7.23±0.03 and c = 4.09±0.02 Å. These agree very well with those of a known material, CeB4. Confirmation that this is indeed the identity of the impurity phase is provided by quantitative CBED (QCBED) where the very close match between experimental and calculated CBED patterns has confirmed the atomic structure. Further confirmation is provided by a density functional theory calculation and also by high-angle annular dark-field scanning transmission electron microscopy.

The semiconductor industry has decreased silicon-based device feature sizes dramatically over the last two decades for improved performance. However, current technology has approached the limit of achievable enhancement via this method. Therefore, other techniques, including introducing stress into the silicon structure, are being used to further advance device performance. While these methods produce successful results, there is not a proven reliable method for stress and strain measurements on the nanometer scale characteristic of these devices. The ability to correlate local strain values with processing parameters and device performance would allow for more rapid improvements and better process control. In this research, x-ray diffraction and convergent beam electron diffraction have been utilized to quantify the strain behavior of simple and complex strained silicon-based systems. While the stress relaxation caused by thinning of the strained structures to electron transparency complicates these measurements, it has been quantified and shows reasonable agreement with expected values. The relaxation values have been incorporated into the strain determination from relative shifts in the higher order Laue zone lines visible in convergent beam electron diffraction patterns. The local strain values determined using three incident electron beam directions with different degrees of tilt relative to the device structure have been compared and exhibit excellent agreement.

Convergent beam electron diffraction (CBED) on cross-sectional transmission electron microscopy (TEM) specimens can map stress in the Si substrate of microelectronics devices with high spatial resolution. However, at shallow depths below the interface the diffraction lines within a CBED pattern are split, rendering pattern interpretation impossible in the classical way. This effect is believed to derive from a bending of the diffracting planes through the sample thickness. In this work, a variety of specimens, ranging from polycrystalline to epitaxial and amorphous materials, have been systematically analyzed. A similar qualitative distribution of the splitting effects is present in each case, but quantitative differences are observed which can be related to the stress induced by the different materials. Capping layers can partially avoid the splitting but seem to modify the strain distribution. The surface relaxation in the thin TEM specimen foil is modelled by finite elements simulations as well as with an epitaxial-layer model. The results predict well the experimental magnitude of the splitting but fail to simulate the intensity of the secondary lines. Possible explanations for such discrepancies are discussed and critically assessed.

The convergent beam electron diffraction (CBED) technique of transmission electron microscopy (TEM) has excellent capabilities for strain detection at high spatial resolution. Here we report strain measurements in a bulk s-Si/SiGe/Si wafer and in a strained 35nm PMOS device in which SiGe acts as the source and drain. CBED measurements of the composition of the relaxed SiGe buffer are in quantitative agreement with Raman spectroscopy. For the PMOS device, CBED measured a uniaxial compressive stress of 1.12GPa in the channel. However, it was found that even in the cross-sectional TEM samples with thicknesses greater than 300nm, the intrinsic surface strain relaxation was often so severe that no recognizable high-order Laue zone lines in the CBED patterns could be collected. The amorphorization of both free surfaces of the TEM sample to a range of about 80nm is proposed to minimize the impact of surface strain relaxation for future study.

Sakhaite specimens from an endogenous borate deposit in Hunan Province, China have been studied in detail by means of transmission electron microscopy (TEM). The selected area electron diffraction (SAED) patterns obtained with different crystal zone axes show that the crystal system is cubic, with a = 1.463 nm. The convergent beam electron diffraction (CBED) patterns indicate that the point group and space group of sakhaite is m3m and Fd3m, respectively. The space group of synthetic sakhaite determined by Chichagov (1974) is F4 1 32. The possible reasons why the space groups of the natural and the synthetic sakhaites are different are discussed.