Higher-order Laue Zone Research Articles

Distortion Measurement of Multi-Finger Transistor Using Split Higher-Order Laue Zone Lines Analysis

A distortion measurement in a region close to the interface between different materials in LSI is performed using a convergent beam electron diffraction (CBED) pattern. Split higher-order Laue zone (HOLZ) lines emerge in the CBED pattern so that a stressing region is observed close to the interface. The calculation method of the split HOLZ lines based on kinematical approximation with the sample's deformation model well reflects the experimental results. As a result of split HOLZ line analysis using the present method, it is found that there is distortion depending on the external form of a multi-finger transistor.

Half analytical method with application to the high order Laue zone effects in monoclinic and triclinic crystals

The simulation of the high order Laue zone (HOLZ) diffractions of monoclinic and triclinic crystals is a very complicated problem. The conventional multislice (MS) method suffers from the problem of infinity of the phase grating size. To avoid the difficulty of the infinity, Chen et al. arranged the phase grating plane along the ab plane of the crystal lattice. In this paper we introduce a new method which allows the incident and exit wavefunction planes perpendicular to the zone axis without the difficulty of infinity. We name the method half analytical method. The results calculated by half analytical method are in good agreement with those calculated by the conventional MS method.

Determination of c Lattice Parameter of LiCoO2 by Convergent-Beam Electron Diffraction

The convergent-beam electron diffraction technique of transmission electron microscopy was applied to the determination of the c lattice parameter of LiCoO2. [0001] orientation which showed a sufficient number of high-order Laue zone (HOLZ) lines was found to be suitable to the work. The ratio of the distances between {0551} HOLZ line family and the interceptions of {2641} family at [0001] orientation was able to allow the c to be determined. The accuracy of the technique was high enough to assess the homogeneity of the material and to investigate the change of the c lattice parameter with variation of lithium content in the material.

Space group analysis of Sr1−xCaxTiO3 ceramics with x = 0.20, 0.27 and 0.30 through electron diffraction

The space groups of Sr1−xCaxTiO3 inthe composition range 0.20≤x≤0.30 have been investigated using powder x-ray diffraction (XRD) and electron diffractiontechniques. Electron diffraction has been used in selected area diffraction (SAD),convergent beam electron diffraction (CBED) and micro-diffraction modes to recordzero-order Laue zone (ZOLZ) and higher-order Laue zone (HOLZ) patterns. For the0.20≤x≤0.30 composition range there is still controversy regarding the correct space group:P 21/m,Pnma,Imma or I4/mcm. By invoking Rietveld refinement, detailed analysis of CBED patterns containingA2-type GM-lines and comparison between simulated ZOLZ/FOLZ andexperimentally observed SAD patterns, we have established that forSr1−xCaxTiO3 (0.20≤x≤0.30) two types of phase coexist at room temperature. These are thePnma and P 21212 orthorhombic phases, coexisting with volume fractions of about 40% and 60%respectively.

Method for determination of the displacement field in patterned nanostructures by TEM/CBED analysis of split high‐order Laue zone line profiles

A method to extract accurate information on the displacement field distribution from split high-order Laue zones lines in a convergent-beam electron diffraction pattern of nanostructures has been developed. Starting from two-dimensional many beam dynamical simulation of HOLZ patterns, we assembled a recursive procedure to reconstruct the displacement field in the investigated regions of the sample, based on the best fit of a parametrized model. This recursive procedure minimizes the differences between simulated and experimental patterns, taken in strained regions, by comparing the corresponding rocking curves of a number of high-order Laue zone reflections. Due to its sensitivity to small displacement variations along the electron beam direction, this method is able to discriminate between different models, and can be also used to map a strain field component in the specimen. We tested this method in a series of experimental convergent-beam electron diffraction patterns, taken in a shallow trench isolation structure. The method presented here is of general validity and, in principle, it can be applied to any sample where not negligible strain gradients along the beam direction are present.

Strain analysis of arsenic-doped silicon using CBED rocking curves of low-order reflections

Local lattice strains of semiconductor devices have been so far examined using higher order Laue zone (HOLZ) line patterns of convergent-beam electron diffraction (CBED). Recently, strain analyses in highly strained regions near interfaces have been reported using split HOLZ line patterns. In the present paper, it is demonstrated for arsenic-doped silicon that the use of CBED rocking curves of low-order reflections provides a promising new tool for the determination of strain distributions of highly strained specimen areas. That is, the anomalous intensity increase in the CBED rocking curves of low-order reflections is explained using a model structure with a strain gradient in the electron beam direction, which is similar to the models used for the split HOLZ line patterns.

Analysis of Fine Stress Fields in Metal Matrix Composites Using HOLZ Patterns

Aluminium alloy composites reinforced with aluminium borate whiskers (ABw), developed recently by SHIKOKU KASEI KOUGYOU Co. Ltd., Japan, were fabricated using squeeze casting. The large mismatch in the coefficients of thermal expansion (CTE) between the reinforcement material and the matrix can generate significant stress and strain in composites during thermal cycling or during fabrication of the composites when using squeeze casting. When a transmission electron microscope is used to irradiate a very small area of a thin film of the material with a convergent electron beam of several nm in diameter, High Order Laue Zone patterns (HOLZ patterns) are obtained. These HOLZ patterns can reveal fine strain fields in the reinforcement materials that are used in composites fabricated using squeeze casting. Each (001) plane in the ABw was rotated towards the [020] direction by up to 0.5 ﾟ. With a unit of nearly 400 nm × 400 nm, each (100) plane was rotated towards the [020] direction in a corkscrew pattern. In addition the strain and the stress generated during the fabrication of the composites were estimated by using the finite element methods taking into account the anisotropies in both the CTE and the elastic modulus of the reinforcement material.

On the Splitting of High Order Laue Zone Lines in CBED Analysis of Stress in Silicon

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.

Sensitive detection of mirror symmetry by CBED applied to LaAlO3 and GdAlO3

Convergent-beam electron diffraction (CBED) patterns tilted away from major zone axes have been used to re-examine the space groups of LaAlO3 and GdAlO3 perovskites. The higher-order Laue zones (HOLZ) in CBED patterns at such tilted orientations have been found to have high sensitivity to the presence of mirror symmetry. This sensitivity has enabled the space group of LaAlO3, previously claimed to be cubic (Fm3c), to be confirmed as rhombohedral R3c by CBED. It is clear that patterns of sufficient tilt will be more sensitive for distinguishing between screw axes and glide planes than the observation of HOLZ deficit lines in zero-order Laue zone reflections. No symmetry degrading effects due to the influence of tilted crystal surfaces could be observed.

Contribution of electron precession to the identification of the space group from microdiffraction patterns

In a previous study, it was reported that the possible space groups of a crystal can be identified at a microscopic or nanoscopic scale, thanks to microdiffraction patterns obtained with a nearly parallel electron incident beam focused on a very small area of the specimen. A systematic method was proposed, which consists of the observation of a few microdiffraction patterns displaying at least two Laue zones. These microdiffraction patterns can also be obtained by using an electron precession equipment. In this case, the patterns display a very large number of reflections in the Laue zones whose intensity is the integrated intensity. These original features greatly facilitate the space group identification method and are particularly useful when the high-order Laue zones (HOLZ) are not visible on microdiffraction patterns or when very thin specimens are not available.

Many-beam dynamical simulation of electron backscatter diffraction patterns

We present an approach for the simulation of complete electron backscatter diffraction (EBSD) patterns where the relative intensity distributions in the patterns are accurately reproduced. The Bloch wave theory is applied to describe the electron diffraction process. For the simulation of experimental patterns with a large field of view, a large number of reflecting planes has to be taken into account. This is made possible by the Bethe perturbation of weak reflections. Very good agreement is obtained for simulated and experimental patterns of gallium nitride GaN { 0 0 0 1 } at 20 kV electron energy. Experimental features like zone-axis fine structure and higher-order Laue zone rings are accurately reproduced. We discuss the influence of the diffraction of the incident beam in our experiment.

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.

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.

Local Strain Measurement on Strained Si/SiGe Heterostructures Using Convergent Beam Electron Diffraction Analysis

Local strain variations in microelectronic device structures have been investigated with convergent beam electron diffraction (CBED). The analysis has been improved with a series of tasks: high order Laue zone (HOLZ) line detection by the Hough transform, HOLZ line position simulation with the kinematic theory, lattice parameter refinement by the examination of least square fitting, and theoretical strain state calculation with finite element (FE) modeling. The goal of this paper is to demonstrate the procedure of this strain measurement analysis. The actual strain variation in a TEM foil of a CMOS device structure was shown, followed by the FE in a strain Si/SiGe heterostructure. The strain data will not be included in this paper, but will be added later.

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.

Internal Stress Field in Ultrafine Grained Aluminium Fabricated by Accumulative Roll-Bonding

Internal stress field in a severely deformed aluminium with ultrafine grained microstructure has been studied by convergent-beam electron diffraction (CBED) technique in transmission electron microscopy (TEM). A commercial purity aluminium (99.1%Al) sheet was highly strained by the accumulative roll-bonding (ARB) process to evolve an ultrafine grained structure. Higher-order Laue zone (HOLZ) lines in the incidence disk of the ] 12 1 [ zone axis have been observed at various positions within an identical ultrafine grain. The key finding is that the HOLZ line pattern taken from the vicinity (~50nm) of the grain boundary (lamellar boundary) looses ) 1 1 0 ( mirror symmetry, whereas the pattern from the grain centre has the symmetry. The former and the latter represent the existence of a large non-hydrostatic stress field and a small internal stress field, respectively. The magnitude of the internal stress becomes larger with approaching to a grain boundary.

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.

Evaluation of Microstructure on SiC<sub>p</sub>/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.

Reliable Local Strain Characterization on Si/SiGe Structures in Biaxial Tension

ABSTRACTThe strain in the strained Si layer on a blanket strained Si/SiGe structure could not be determined with only convergent beam electron diffraction to high order Laue zone (HOLZ) line splitting. Combined with CBED and finite element calculations, we quantified the deformation field from HOLZ line splitting and demonstrated a procedure to determine the initial strain in the strained Si layer. Our results also gave us insights in strain relaxation in a TEM sample. The CBED technique combined with FE modeling has the potential for initial strain measurements on new generation short channel CMOS technology nodes.