Strain Analysis of Si by FEM and Energy-Filtering CBED

2002 ◽  
Vol 8 (1) ◽  
pp. 11-15 ◽  
Author(s):  
Tetsuya Okuyama ◽  
Masaru Nakayama ◽  
Yoshitsugu Tomokiyo ◽  
Omer Van der Biest
Keyword(s):  
Maximum Shear Stress ◽  
Strain Analysis ◽  
Stress Fields ◽  
Shear Stresses ◽  
Direction Parallel ◽  
Energy Filtering ◽  
Lattice Strains ◽  
Probe Size ◽  
Local Lattice ◽  
Convergent Beam

Lattice strains around a platelet oxygen precipitate in Si wafer is studied by energy filtering convergent-beam electron diffraction (CBED) and calculations based on the finite element method (FEM). Local lattice strains are measured from CBED patterns obtained with a probe size less than 2 nm in a specimen thicker than 450 nm. Strains measured are compressive along a direction normal to a plate of the precipitate and tensile along a direction parallel to the plate. Two-dimensional stress fields near the precipitate are obtained with FEM computer analyses by fitting the measured strains. It appears that shear stresses are concentrated at the end of the precipitate edge and the maximum shear stress at an interface between the precipitate and the Si-matrix is 1.9 GPa. It is demonstrated that a combination of the energy filtering CBED and FEM is very useful for the study of local strains near interfaces in semiconductor devices, in particular for the study of stress fields that are too steep for application of the conventional CBED technique.

Average and local strain fields in nanocrystals

2019 ◽  
Vol 52 (2) ◽  
pp. 262-273 ◽  
Author(s):  
Shangmin Xiong ◽  
Seung-Yub Lee ◽  
Ismail Cevdet Noyan
Keyword(s):  
Gold Nanoparticles ◽  
Strain Analysis ◽  
Local Strain ◽  
Real Space ◽  
Dynamics Modeling ◽  
Lattice Strains ◽  
Unit Cells ◽  
Local Lattice ◽  
Strain Components ◽  
Average Lattice

This article presents a rigorous and self-consistent comparison of lattice distortion and deformation fields existing in energy-optimized pseudo-spherical gold nanoparticles obtained from real-space and powder diffraction strain analysis techniques. The changes in atomic positions resulting from energy optimization (relaxation) of ideally perfect gold nanoparticles were obtained using molecular dynamics modeling. The relaxed atomic coordinates were then used to compute the displacement, rotation and strain components in all unit cells within the energy-optimized (relaxed) particles. It was seen that all of these terms were distributed heterogeneously along the radial and tangential directions within the nanospheroids. The heterogeneity was largest in the first few atomic shells adjacent to the nanoparticle surface, where the continuity of crystal lattice vectors originating from the interior layers was broken because of local lattice rotations. These layers also exhibited maximum shear and normal strains. These (real-space) strain values were then compared with the average lattice strains obtained by refining the computed diffraction patterns of such particles. The results show that (i) relying solely on full-pattern refinement techniques for lattice strain analysis might lead to erroneous conclusions about the dimensionality and symmetry of deformation within relaxed nanoparticles; (ii) the lattice strains within such relaxed particles should be considered `eigenstrains' (`inherent strains') as defined by Mura [Micromechanics of Defects in Solids, (1991), 2nd ed., Springer]; and (iii) the stress/strain state within relaxed nanoparticles cannot be analyzed rigorously using the constitutive equations of linear elasticity.

Convergent-beam electron diffraction at high spatial resolution

1992 ◽  
Vol 50 (2) ◽  
pp. 1152-1153 ◽  
Author(s):  
J W Steeds
Keyword(s):  
Electron Diffraction ◽  
High Temperature Superconductors ◽  
Bloch Wave ◽  
Convergent Beam Electron Diffraction ◽  
Beam Electron ◽  
Energy Filtering ◽  
Small Probe ◽  
Transmission Electron ◽  
Electron Microscopes ◽  
Convergent Beam

That the techniques of convergent beam electron diffraction (CBED) are now widely practised is evident, both from the way in which they feature in the sale of new transmission electron microscopes (TEMs) and from the frequency with which the results appear in the literature: new phases of high temperature superconductors is a case in point. The arrival of a new generation of TEMs operating with coherent sources at 200-300kV opens up a number of new possibilities.First, there is the possibility of quantitative work of very high accuracy. The small probe will essentially eliminate thickness or orientation averaging and this, together with efficient energy filtering by a doubly-dispersive electron energy loss spectrometer, will yield results of unsurpassed quality. The Bloch wave formulation of electron diffraction has proved itself an effective and efficient method of interpreting the data. The treatment of absorption in these calculations has recently been improved with the result that <100> HOLZ polarity determinations can now be performed on III-V and II-VI semiconductors.

Strain measurement in In0.2Ga0.8As/GaAs quantum wires by convergent beam electron diffraction

1995 ◽  
Vol 53 ◽  
pp. 444-445
Author(s):  
S. Hillyard ◽  
Y.-P. Chen ◽  
J.D. Reed ◽  
W.J. Schaff ◽  
L.F. Eastman ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Semiconductor Lasers ◽  
Quantum Wire ◽  
Quantum Wires ◽  
Convergent Beam Electron Diffraction ◽  
Zero Order ◽  
Beam Electron ◽  
Local Lattice ◽  
Device Applications ◽  
Convergent Beam

The positions of high-order Laue zone (HOLZ) lines in the zero order disc of convergent beam electron diffraction (CBED) patterns are extremely sensitive to local lattice parameters. With proper care, these can be measured to a level of one part in 104 in nanometer sized areas. Recent upgrades to the Cornell UHV STEM have made energy filtered CBED possible with a slow scan CCD, and this technique has been applied to the measurement of strain in In0.2Ga0.8 As wires.Semiconductor quantum wire structures have attracted much interest for potential device applications. For example, semiconductor lasers with quantum wires should exhibit an improvement in performance over quantum well counterparts. Strained quantum wires are expected to have even better performance. However, not much is known about the true behavior of strain in actual structures, a parameter critical to their performance.

Atomic Mechanisms of Grain Boundary Motion

2005 ◽  
Vol 502 ◽  
pp. 157-162 ◽  
Author(s):  
A. Suzuki ◽  
Yuri M. Mishin
Keyword(s):  
Molecular Dynamics ◽  
Grain Boundary ◽  
Geometric Model ◽  
Lattice Rotation ◽  
Shear Stresses ◽  
Translation Rate ◽  
Embedded Atom ◽  
Local Lattice ◽  
Symmetrical Tilt ◽  
Grain Boundary Motion

We present results of atomistic computer simulations of spontaneous and stress-induced grain boundary (GB) migration in copper. Several symmetrical tilt GBs have been studied using the embedded-atom method and molecular dynamics. The GBs are observed to spontaneously migrate in a random manner. This spontaneous GB motion is always accompanied by relative translations of the grains parallel to the GB plane. Furthermore, external shear stresses applied parallel to the GB and normal to the tilt axis induce GB migration. Strong coupling is observed between the normal GB velocity vn and the grain translation rate v||. The mechanism of GB motion is established to be local lattice rotation within the GB core that does not involve any GB diffusion or sliding. The coupling constant between vn and v|| predicted within a simple geometric model accurately matches the molecular dynamics observations.

A critical look at the Wallace-Bott hypothesis in fault-slip analysis

2013 ◽  
Vol 184 (4-5) ◽  
pp. 299-306 ◽  
Author(s):  
Richard J. Lisle
Keyword(s):  
Shear Stress ◽  
Maximum Shear Stress ◽  
Fault Slip ◽  
Shear Stresses ◽  
Homogeneous State ◽  
Slip Direction ◽  
Fault Surface ◽  
State Of Stress ◽  
Simultaneous Movement

AbstractThe assumption is widely made that slip on faults occurs in the direction of maximum resolved shear stress, an assumption known as the Wallace-Bott hypothesis. This assumption is used to theoretically predict slip directions from known in situ stresses, and also as the basis of palaeostress inversion from fault-slip data. This paper examines different situations in relation to the appropriateness of this assumption. Firstly, it is shown that the magnitude of the shear stress resolved within a plane is a function with a poorly defined maximum direction, so that shear stress values greater than 90% of the maximum occur within a wide angular range (± 26°) degrees. The situation of simultaneous movement on pairs of faults requires slip on each fault to be parallel to their mutual line of intersection. However, the resolved shear stresses arising from a homogeneous state of stress do not accord with such a slip arrangement except in the case of pairs of perpendicular faults. Where fault surfaces are non-planar, the directions of resolved shear stress in general give, according to the Wallace-Bott hypothesis, a set of slip directions of rigid fault blocks, which is generally kinematically incompatible. Finally, a simple model of a corrugated fault suggests that any anisotropy of the shear strength of the fault such as that arising from fault surface topography, can lead to a significant angular difference between the directions of maximum shear stress and the slip direction.These findings have relevance to the design of procedures used to estimate palaeostresses and the amount of data required for this type of analysis.

Advanced Evaluation Methods of Residual Stress in Bioceramics Wear Surfaces

2010 ◽  
Vol 64 ◽  
pp. 43-48
Author(s):  
Giuseppe Pezzotti
Keyword(s):  
Residual Stress ◽  
Surface Stress ◽  
Electron Probe ◽  
Stress Fields ◽  
Fluorescence Probes ◽  
Surface Residual Stress ◽  
Hip Joints ◽  
Polycrystalline Alumina ◽  
Probe Size ◽  
F Center

Photo- and electro-stimulated probes have been employed for quantitatively evaluating highly graded residual stress fields generated at the surface of alumina hip joints. Optical calibrations revealed large differences in probe size, which strongly affected the detected magnitude of residual stress. A comparison between the responses of Raman and fluorescence probes in polycrystalline alumina showed that the depth of those probes spread to an extent in the order of the tens of microns even with using a confocal probe configuration. On the other hand, the electro-stimulated luminescence emitted by oxygen vacancy sites (F+ center) in the alumina lattice represented a suitable choice for confining to a shallow volume the stress probe. The electron probe enabled confining the measurement depth to the order of the tens of nanometers. Maps of surface residual stress were collected on both main-wear and non-wear zones of an alumina femoral head. A comparison among stress maps taken at exactly the same location, but employing different probes, clarified the averaging probe effects on surface stress magnitude.

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