Convergent Beam Electron Diffraction Patterns Research Articles

Convergent beam electron diffraction for strain determination at the nanoscale

The convergent beam electron diffraction (CBED) technique has been used to quantify the strain in semiconducting GaInAs/GaAs epitaxial layers. Two different systems have been explored, a 100 nm thick GaInAs layer, in the case of very low indium content, and a 10 nm thick GaInAs layer, with 20 at.% In. We show that the direct analysis of the CBED patterns can only be achieved in the first system, provided that specimen and deposited layer thickness are close to each other. In the second system, which is the more frequent in epitaxial systems, we demonstrate that reliable measurements can still be obtained through quantitative fit performed using a CBED pattern simulation software specially developed for analysing non-inhomogeneouly strained specimens.

An algorithm for refinement of lattice parameters using CBED patterns

A new algorithm for calculation of lattice parameters from convergent beam electron diffraction (CBED) patterns has been developed. Like most of the previous approaches to the problem, it is an optimization procedure matching geometric elements of high order Laue zone (HOLZ) lines in experimental patterns to corresponding elements of kinematically simulated patterns. The procedure uses an original objective function based directly on the underlying algebraic equation of the HOLZ lines. Although the new approach requires crystal orientation parameters to be fitted alongside the strain components, it is easier to implement than methods used previously. It is also straightforward to apply to strain determination from multiple patterns. Numerical tests on dynamically simulated patterns show that in the case of one or two patterns, the new procedure gives results that are more reliable than the established method based on HOLZ line intersections. As an example application, the a and c parameters of a TiAl alloy are determined.

Local Strain Characterization on Strained-Si/SiGe Heterostructures with Convergent Beam Electron Diffraction and Finite Element Simulation

We introduce a novel and reliable method to quantify local strain variation in microelectronic device structures based on convergent beam electron diffraction (CBED) and finite element (FE) calculation. The match of the finite element calculation results with the experimental data not only validated the parameters used for the finite element simulations, but also gives us insights into the origin of high order Laue zone (HOLZ) line splitting in a lattice-mismatched heterostructure. The 2D and 3D calculations showed that the residual strain measured from clean and sharp CBED patterns deviate from the initial strain. The effect of a SiO2 layer on the strain in a TEM sample was also investigated by FE simulation and we found that a SiO2 layer can suppress some of the elastic deformation making it possible to obtain clean and sharp CBED patterns. The here proposed novel method uses the elastic deformation to determine the initial strain in microelectronic devices structures by combining FE simulations and CBED patterns.

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.

Effects of surface relaxation on convergent‐beam electron diffraction analysis of stress in silicon

Convergent-beam electron diffraction on cross-sectional transmission electron microscopy specimens can map strains in the silicon substrate of microelectronics devices with high spatial resolution. However, at shallow depths below the interface, most of the diffraction lines within a convergent-beam electron diffraction pattern are split, rendering pattern interpretation impossible in the classic way. The splitting effect was systematically analysed for a variety of materials, and the same qualitative behaviour that can be explained by stress relaxation at the surfaces of the thin transmission electron microscopy specimen was observed. The effects of surface relaxation are modelled by finite elements simulations. The results predict well the experimental magnitude of the splitting for a variety of diffraction lines at different positions below the interface, but fail to simulate the intensity of the secondary lines. Possible reasons for such discrepancies are discussed and assessed.

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.

Study on Monoclinic Domain of Morphotropic High Piezoelectric Pb(Mg1/3Nb2/3)O3–PbTiO3 Single Crystals by Transmission Electron Microscopy

0.68Pb(Mg1/3Nb2/3)O3–0.32PbTiO3 single crystals produced by the modified Bridgman technique were poled along the [001] orientation. We discuss the low-symmetry phase domain in the morphotropic phase boundary (MPB) from a fine structural viewpoint based on the investigation by transmission electron microscopy (TEM). By using the convergent beam electron diffraction (CBED) method, we observed the crystal symmetry in each of the three orientations – [001], [101], and [111] – and determined the point and space groups. We identified the point group as m since the mirror symmetry in the [100] and [101] orientations was observed in CBED patterns obtained at the [001] and [101] incidences and no symmetry was observed in those obtained at the [111] incidence. The classification based on the kinematical extinction rule could not be applied because of the difference in the fundamental lattice between lattice systems P and C. Therefore, we compared the symmetry observed in the CBED pattern with the theoretical prediction and identified the lattice system as P. In addition, we examined the presence or absence of the glide plane and screw axis and identified the space group as Pm. We showed that the spontaneous polarization (Ps) of the monoclinic (space group Pm) domain is in the (010) plane and lies on the Mc line connecting point T that expresses a tetragonal system directed toward the [001] orientation and point O that expresses an orthorhombic system directed toward the [101] orientation. We also revealed that four Ps vectors exist equivalently with respect to the poling direction. The angle formed by any two of these vectors was almost orthogonal when observed from the [110] orientation.

Quantitative analysis of HOLZ line splitting in CBED patterns of epitaxially strained layers

A SiGe layer epitaxially grown on a silicon substrate is experimentally studied by convergent beam electron diffraction (CBED) experiments and used as a test sample to analyse the higher-order Laue zones (HOLZ) line splitting. The influence of surface strain relaxation on the broadening of HOLZ lines is confirmed. The quantitative fit of the observed HOLZ line profiles is successfully achieved using a formalism particularly well-adapted to the case of a z -dependent crystal potential ( z being the zone axis). This formalism, based on a time-dependent perturbation theory approach, proves to be much more efficient than a classical Howie–Whelan approach, to reproduce the complex HOLZ lines profile in this heavily strained test sample.

Analysis of Nanoscale Stress in Strained Silicon Materials and Microelectronics Devices by Energy-Filtered Convergent Beam Electron Diffraction

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.

Probing Nanoscale Local Lattice Strains in Advanced Si CMOS Devices by CBED: A Tutorial with Recent Results

The experimental methodology to characterize the nanoscale local lattice strain in advanced Si CMOS devices by using Focused Ion Beam (FIB) system and Convergent Beam Electron Diffraction (CBED) is discussed. Through both high spatial resolution of Transmission Electron Microscopy (TEM) and high strain sensitivity of the CBED technique, compressive lattice strains in the order of 0.001 from the nanoscale Si PMOS channel region are detected. The one-dimensional quantitative strain-mapping is performed by obtaining and simulating high quality CBED patterns with different zone axes such as <230> and <340>.

Characteristic analysis of electroless Ni plating layer for electronic packaging

AbstractThe crystallization behavior of electroless Ni–P film was investigated using X‐ray diffractometry (XRD), transmission electron microscopy (TEM) and differential scanning calorimetry (DSC). XRD analyses revealed that the amorphous state of the as‐plated Ni–P film was crystallized by heat treatment at 573 K for 1 h. Two peaks were observed simultaneously, indicating Ni and Ni3P compounds. Convergent beam electron diffraction (CBED) pattern analyses confirmed a size of the Ni3P in the crystallized Ni–P layer of 50–70 nm. The contact resistance decreased with a heat treatment, which is mainly due to the crystallized Ni–P layer and the grain growth. The activation energy calculated from DSC analyses using the Kissinger equation was 195.2 kJ/mol. Copyright © 2006 John Wiley &amp; Sons, Ltd.

Evaluation of Microstructure on SiC&lt;sub&gt;p&lt;/sub&gt;/AZ91 Magnesium Composite Fabricated by Rotation-Cylinder Method

Eco-friendly development and on-going research strategy of Rotation-Cylinder Method (RCM) is given for SiCp/AZ91 Mg composites, identifying some of the key factors that need to be controlled and indicating subsequent casting processes. RCM produces U-shaped laminar melt surface with a Rankine vortex even at high rotation speed in an ambient atmosphere, which allows quick and efficient incorporation and homogeneous distribution of SiC particulates into molten Mg alloys. Therefore, sound SiCp/AZ91 Mg composites can be manufactured in conjunction with subsequent casting processes, such as investment casting and thixocasting. A transmission electron microscopy study showed that the interfacial reaction products consist of Mg2Si, MgO, Mg17Al12 and Al6Mn, which were analyzed using primitive cell volume and zero order Laue zone pattern and single convergent beam electron diffraction pattern containing higher order Laue zone ring from a nanosized region.

Hydrogenation of Ti–12Mg blending powder during mechanical milling in liquid media containing hydrogen

The authors manufactured the metal hydrides (Ti0·88Mg0·12)H2 and (Ti0·88Mg0·12)H0·7 by a very easy and cheap way using the mechanical milling of Ti–12Mg blending powder in liquid milling media such as isopropyl alcohol, hexane and heptane as hydrogen sources. The powder was analysed by X-ray diffraction (XRD) and convergent beam electron diffraction (CBED) patterns parallel with the chemical analysis by EDX and ion coupled plasma (ICP) measurements. The hydriding reaction began when the mechanically milled particle achieved nanometre size. (Ti0·88Mg0·12)H2 was manufactured in isopropyl alcohol and hexane media, and (Ti0·88Mg0·12)H0·7 in heptane, while the Ti–12Mg blending powder milled in argon atmosphere formed the solid solution of hexagonal close packed (hcp) structure.

Crystal orientation distribution in highly oriented diamond films investigated by SEM and TEM

Orientation imaging techniques based on electron backscattering diffraction (EBSD) and convergent beam electron diffraction (CBED) pattern acquisition carried out respectively in the scanning electron microscope (SEM) and in the transmission electron microscope (TEM) were used to characterise the orientation of crystals in two highly oriented diamond (HOD) films with different thicknesses. The substrate surface modification has been also investigated by EBSD. The films were synthesised on Si(100) in a microwave plasma chemical vapor deposition (MPCVD) reactor where nucleation is initiated via an in situ pretreatment consisting in a carburization step followed by a bias enhanced nucleation (BEN). For the thin film EBSD allowed to highlight the presence of alpha-SiC on the silicon substrate as well as to evaluate their epitaxial relationship. The TEM-based system allowed to obtain more accurate misorientation data of the fine grained diamond structure corresponding to the first stages of growth. For the thicker film, EBSD was used to determine the mosaicity at the surface.

Structure of the quaternary alloy Zn0.6Mn0.4In2S4from synchrotron powder diffraction and electron transmission microscopy

The aim of the present work was to determine the structure of the quaternary alloy Zn0.6Mn0.4In2S4and to locate the Mn2+. This was accomplished by means of powder synchrotron X-ray diffraction, high-resolution microscopy and convergent-beam electron diffraction (CBED). The powder X-ray diffraction pattern was indexed in a rhombohedral cell, with cell constantsa= 3.875 (2),c= 37.208 (4) Å, and possible space groupsR\bar{3}morR3m. Rietveld refinements using different cationic arrangements in these space groups were performed. A model in space groupR3m, in which the tetrahedral and octahedral sites were occupied by different proportions of Zn, Mn and In atoms, gave the best result. The Rietveld refinement of this model led to figures of meritRwp= 9.8%,Rp= 9.1% and χ2= 11.1. Selected-area electron diffraction patterns and high-resolution transmission electron micrographs along [001] reveal the rhombohedral configuration. CBED patterns perpendicular to [001], showing the distinctive 3msymmetry, confirmed space groupR3mand the breaking of the centrosymmetry of the parent compound, ZnIn2S4.

Measurement of Crystal Symmetry using HARECXS

Convergent Beam Electron Diffraction (CBED) has long been used to measure the symmetry of crystalline materials because of its sensitivity to changes in structure. By quantitative comparison of calculated CBED patterns with experimental data it is possible to determine crystal symmetry and atomic site occupation. In a similar manner, electron channeling induced x-ray emission can be used to study crystal site occupancy. In this work we have used high angular resolution of electron channeling x-ray spectroscopy (HARECXS) in a zone axis orientation to demonstrate that crystal symmetry can be directly observed as a compliment to the CBED technique.

(001) silicon surfacial grain boundaries obtained by direct wafer bonding process: accurate control of the structure before bonding

Ultra-thin (001) silicon films bonded onto (001) silicon wafers, which form ‘surfacial grain boundaries’, are analysed by transmission electron microscopy and X-ray diffraction. The aim of this study is to find a way of controlling precisely, before direct wafer bonding, the structure of the Si/Si (001) interface. Two kinds of dislocation networks are found at the bonded interface. A square array of screw dislocations accommodates the twist between the two crystals, whereas a linear network of mixed dislocations accommodates the tilt resulting from the residual vicinality of the initial surfaces. A theoretical study shows that knowing and choosing before bonding the characteristics of these interfacial dislocations depend on the control of the ‘twist’ angle during the hydrophobic molecular bonding process. Recently, a new bonding method allows us to obtain an accuracy of ± 0.005° for the ‘twist’ angle from patterned grooves without any crystallographic measurement. The precision of this technique is compared with three different measurement of the disorientation between the two grains taken after bonding. The first one is deduced from the periodicity of the dislocation networks located at the interface. The second one is calculated from large angle convergent beam electron diffraction patterns. The last one is obtained by synchrotron X-ray diffraction. The possibility of choosing precisely the characteristics of the Si (001) ‘surfacial grain boundaries’ before direct wafer bonding process is then discussed in light of an experimental study.

Residual Strain Parameters Determinable from a CBED Pattern

Residual strain determination by convergent beam electron diffraction (CBED) is characterized by good spatial resolution. It is based on fitting experimental diffraction patterns to simulated patterns. However, the methodleads to ambiguous results. In this note, the CBED method is analyzed to identify the strain parameters which are not determinable. This is done by checking the sensitivity of goodness of fit to parameter changes. The indeterminable parameters are best specified in the Cartesian system having one of its axes, say axis '3', parallel to the beam direction. They are the '13' and '23' components of the strain tensor given in that system and a combination of its diagonal components. The methods of eliminating the ambiguity by using multiple diffraction patterns are also discussed. It is shown that two patterns may be insufficient for removing the ambiguity.

Formal conditions for unambiguous residual strain determination by CBED

The method of residual strain determination using convergent beam electron diffraction (CBED) is attractive because of its good spatial resolution. However, attempts to obtain all six independent strain components from a CBED pattern lead to ambiguous results. This paper contains analysis of the ambiguities based on the complete algorithm for matching experimental and strain-dependent simulated CBED patterns. The strain parameters which are not determinable by the CBED method are identified by examination of the most common goodness-of-fit functions. The indeterminable parameters are confirmed to be the ‘13’ and ‘23’ components and a combination of the diagonal components of the tensor given in the Cartesian systems having the ‘3’ axis parallel to the beam direction. The ambiguity can be eliminated based on multiple diffraction patterns. It is shown that two different patterns may be insufficient to get a unique strain tensor. The ambiguity can be removed only if certain characteristics of the two patterns are different, or if more than two patterns are used.

Strain analysis in silicon substrates under uniaxial and biaxial stress by convergent beam electron diffraction

A detailed description of the application of the convergent beam electron diffraction (CBED) technique for studying strain propagation in the Si1−xGex∕Si blanket wafers as well as silicon-based metal–oxide–semiconductor field-effect transistors is presented. Specifically, a simple and robust experimental procedure and analysis for silicon lattice strain measurement using the CBED technique is detailed in this article. The use of focused ion beam milling allows for better control of the thickness and site-specific analysis, especially for nanoscaled devices. A pictorial representation of the analytical conditions for the higher order Laue zone lines in CBED patterns is also reported in this work. Based on the Si lattice strain measurement results, we determined that a thin buffer layer of SiOxNy incorporated below the Si3N4 overlay film could render the uniaxial channel strain less compressive. Stress studied on Si1−xGex∕Si blanket wafers reveals that a steeper SiGe compositional gradient would induce larger biaxial strain in the underlying Si substrate and hence a smaller amount of misfit dislocations.